diff --git "a/1b4-R6NjZOA.txt" "b/1b4-R6NjZOA.txt"
new file mode 100644--- /dev/null
+++ "b/1b4-R6NjZOA.txt"
@@ -0,0 +1,10231 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi in the last
+
+ align:start position:0%
+hi in the last
+ 
+
+ align:start position:0%
+hi in the last
+session we looked at the possibility of
+
+ align:start position:0%
+session we looked at the possibility of
+ 
+
+ align:start position:0%
+session we looked at the possibility of
+comp compensating a feedback system by
+
+ align:start position:0%
+comp compensating a feedback system by
+ 
+
+ align:start position:0%
+comp compensating a feedback system by
+using minor Loop compensation where we
+
+ align:start position:0%
+using minor Loop compensation where we
+ 
+
+ align:start position:0%
+using minor Loop compensation where we
+construct a system that has two Loops by
+
+ align:start position:0%
+construct a system that has two Loops by
+ 
+
+ align:start position:0%
+construct a system that has two Loops by
+adjusting the feedback element or
+
+ align:start position:0%
+adjusting the feedback element or
+ 
+
+ align:start position:0%
+adjusting the feedback element or
+properly select collecting the feedback
+
+ align:start position:0%
+properly select collecting the feedback
+ 
+
+ align:start position:0%
+properly select collecting the feedback
+element in an inner or minor loop we're
+
+ align:start position:0%
+element in an inner or minor loop we're
+ 
+
+ align:start position:0%
+element in an inner or minor loop we're
+able to compensate the
+
+ align:start position:0%
+able to compensate the
+ 
+
+ align:start position:0%
+able to compensate the
+system in today's session and the
+
+ align:start position:0%
+system in today's session and the
+ 
+
+ align:start position:0%
+system in today's session and the
+following one I'd like to look at how we
+
+ align:start position:0%
+following one I'd like to look at how we
+ 
+
+ align:start position:0%
+following one I'd like to look at how we
+do this with an actual existing
+
+ align:start position:0%
+do this with an actual existing
+ 
+
+ align:start position:0%
+do this with an actual existing
+operational amplifier and how we choose
+
+ align:start position:0%
+operational amplifier and how we choose
+ 
+
+ align:start position:0%
+operational amplifier and how we choose
+compensation in particular minor Loop
+
+ align:start position:0%
+compensation in particular minor Loop
+ 
+
+ align:start position:0%
+compensation in particular minor Loop
+compensation to tailor that operational
+
+ align:start position:0%
+compensation to tailor that operational
+ 
+
+ align:start position:0%
+compensation to tailor that operational
+amplifier to a variety of
+
+ align:start position:0%
+amplifier to a variety of
+ 
+
+ align:start position:0%
+amplifier to a variety of
+applications the amplifier that we're
+
+ align:start position:0%
+applications the amplifier that we're
+ 
+
+ align:start position:0%
+applications the amplifier that we're
+going to use is one that's been in
+
+ align:start position:0%
+going to use is one that's been in
+ 
+
+ align:start position:0%
+going to use is one that's been in
+existence for 10 or 15 years
+
+ align:start position:0%
+existence for 10 or 15 years
+ 
+
+ align:start position:0%
+existence for 10 or 15 years
+it's the type 101a or equivalently the
+
+ align:start position:0%
+it's the type 101a or equivalently the
+ 
+
+ align:start position:0%
+it's the type 101a or equivalently the
+301a the difference between those two
+
+ align:start position:0%
+301a the difference between those two
+ 
+
+ align:start position:0%
+301a the difference between those two
+designations simply reflects the
+
+ align:start position:0%
+designations simply reflects the
+ 
+
+ align:start position:0%
+designations simply reflects the
+temperature range over which
+
+ align:start position:0%
+temperature range over which
+ 
+
+ align:start position:0%
+temperature range over which
+specifications are guaranteed and a
+
+ align:start position:0%
+specifications are guaranteed and a
+ 
+
+ align:start position:0%
+specifications are guaranteed and a
+minor grade out on certain parameters so
+
+ align:start position:0%
+minor grade out on certain parameters so
+ 
+
+ align:start position:0%
+minor grade out on certain parameters so
+we'll use this readily available and
+
+ align:start position:0%
+we'll use this readily available and
+ 
+
+ align:start position:0%
+we'll use this readily available and
+quite inexpensive operational
+
+ align:start position:0%
+quite inexpensive operational
+ 
+
+ align:start position:0%
+quite inexpensive operational
+amplifier and there are several
+
+ align:start position:0%
+amplifier and there are several
+ 
+
+ align:start position:0%
+amplifier and there are several
+considerations that we have to factor
+
+ align:start position:0%
+considerations that we have to factor
+ 
+
+ align:start position:0%
+considerations that we have to factor
+into our thinking that reflect the
+
+ align:start position:0%
+into our thinking that reflect the
+ 
+
+ align:start position:0%
+into our thinking that reflect the
+reality of that amplifier
+
+ align:start position:0%
+reality of that amplifier
+ 
+
+ align:start position:0%
+reality of that amplifier
+first of all the amplifier is
+
+ align:start position:0%
+first of all the amplifier is
+ 
+
+ align:start position:0%
+first of all the amplifier is
+constructed using a commonly used
+
+ align:start position:0%
+constructed using a commonly used
+ 
+
+ align:start position:0%
+constructed using a commonly used
+integrated circuit process one of the
+
+ align:start position:0%
+integrated circuit process one of the
+ 
+
+ align:start position:0%
+integrated circuit process one of the
+limitations of that process has to do
+
+ align:start position:0%
+limitations of that process has to do
+ 
+
+ align:start position:0%
+limitations of that process has to do
+with fabrication of PNP transistors and
+
+ align:start position:0%
+with fabrication of PNP transistors and
+ 
+
+ align:start position:0%
+with fabrication of PNP transistors and
+a consequence of of that limitation is
+
+ align:start position:0%
+a consequence of of that limitation is
+ 
+
+ align:start position:0%
+a consequence of of that limitation is
+that if we form a feedback loop using
+
+ align:start position:0%
+that if we form a feedback loop using
+ 
+
+ align:start position:0%
+that if we form a feedback loop using
+the 101a type operational amplifier it's
+
+ align:start position:0%
+the 101a type operational amplifier it's
+ 
+
+ align:start position:0%
+the 101a type operational amplifier it's
+impossible to get crossover frequencies
+
+ align:start position:0%
+impossible to get crossover frequencies
+ 
+
+ align:start position:0%
+impossible to get crossover frequencies
+in the overall feedback loop much above
+
+ align:start position:0%
+in the overall feedback loop much above
+ 
+
+ align:start position:0%
+in the overall feedback loop much above
+a megahertz without the overall Loop
+
+ align:start position:0%
+a megahertz without the overall Loop
+ 
+
+ align:start position:0%
+a megahertz without the overall Loop
+becoming unstable and the reason for
+
+ align:start position:0%
+becoming unstable and the reason for
+ 
+
+ align:start position:0%
+becoming unstable and the reason for
+that as I say has to do with poor
+
+ align:start position:0%
+that as I say has to do with poor
+ 
+
+ align:start position:0%
+that as I say has to do with poor
+Dynamic performance associated with the
+
+ align:start position:0%
+Dynamic performance associated with the
+ 
+
+ align:start position:0%
+Dynamic performance associated with the
+lateral pnps in particular above about a
+
+ align:start position:0%
+lateral pnps in particular above about a
+ 
+
+ align:start position:0%
+lateral pnps in particular above about a
+megahertz they look very much like time
+
+ align:start position:0%
+megahertz they look very much like time
+ 
+
+ align:start position:0%
+megahertz they look very much like time
+delays and we're not able to compensate
+
+ align:start position:0%
+delays and we're not able to compensate
+ 
+
+ align:start position:0%
+delays and we're not able to compensate
+as we recall for the phase shift
+
+ align:start position:0%
+as we recall for the phase shift
+ 
+
+ align:start position:0%
+as we recall for the phase shift
+associated with a pure time delay so we
+
+ align:start position:0%
+associated with a pure time delay so we
+ 
+
+ align:start position:0%
+associated with a pure time delay so we
+have to bear in mind when we're doing
+
+ align:start position:0%
+have to bear in mind when we're doing
+ 
+
+ align:start position:0%
+have to bear in mind when we're doing
+our compensation that any Loop that
+
+ align:start position:0%
+our compensation that any Loop that
+ 
+
+ align:start position:0%
+our compensation that any Loop that
+includes this kind of an amplifier the
+
+ align:start position:0%
+includes this kind of an amplifier the
+ 
+
+ align:start position:0%
+includes this kind of an amplifier the
+major Loop crossover is constrained to
+
+ align:start position:0%
+major Loop crossover is constrained to
+ 
+
+ align:start position:0%
+major Loop crossover is constrained to
+somewhere on the order of megahertz
+
+ align:start position:0%
+somewhere on the order of megahertz
+ 
+
+ align:start position:0%
+somewhere on the order of megahertz
+actually that's been getting a little
+
+ align:start position:0%
+actually that's been getting a little
+ 
+
+ align:start position:0%
+actually that's been getting a little
+bit better with time reflecting process
+
+ align:start position:0%
+bit better with time reflecting process
+ 
+
+ align:start position:0%
+bit better with time reflecting process
+improvements we'll see in the amplifier
+
+ align:start position:0%
+improvements we'll see in the amplifier
+ 
+
+ align:start position:0%
+improvements we'll see in the amplifier
+we we're using now uh we can get about 2
+
+ align:start position:0%
+we we're using now uh we can get about 2
+ 
+
+ align:start position:0%
+we we're using now uh we can get about 2
+megahertz crossovers without too much
+
+ align:start position:0%
+megahertz crossovers without too much
+ 
+
+ align:start position:0%
+megahertz crossovers without too much
+trouble the quantity G subm over two
+
+ align:start position:0%
+trouble the quantity G subm over two
+ 
+
+ align:start position:0%
+trouble the quantity G subm over two
+which we mentioned last time enters into
+
+ align:start position:0%
+which we mentioned last time enters into
+ 
+
+ align:start position:0%
+which we mentioned last time enters into
+the approximation for the open loop
+
+ align:start position:0%
+the approximation for the open loop
+ 
+
+ align:start position:0%
+the approximation for the open loop
+transfer function of the amplifier is
+
+ align:start position:0%
+transfer function of the amplifier is
+ 
+
+ align:start position:0%
+transfer function of the amplifier is
+about 2 * 10us 4 Mo for this
+
+ align:start position:0%
+about 2 * 10us 4 Mo for this
+ 
+
+ align:start position:0%
+about 2 * 10us 4 Mo for this
+amplifier uh that reflects the fact that
+
+ align:start position:0%
+amplifier uh that reflects the fact that
+ 
+
+ align:start position:0%
+amplifier uh that reflects the fact that
+the input transistors are running at 10
+
+ align:start position:0%
+the input transistors are running at 10
+ 
+
+ align:start position:0%
+the input transistors are running at 10
+microamp consequently the corresponding
+
+ align:start position:0%
+microamp consequently the corresponding
+ 
+
+ align:start position:0%
+microamp consequently the corresponding
+transconductance is about four time 10us
+
+ align:start position:0%
+transconductance is about four time 10us
+ 
+
+ align:start position:0%
+transconductance is about four time 10us
+4th modes there's again a manufacturing
+
+ align:start position:0%
+4th modes there's again a manufacturing
+ 
+
+ align:start position:0%
+4th modes there's again a manufacturing
+variation on that but a a nominal value
+
+ align:start position:0%
+variation on that but a a nominal value
+ 
+
+ align:start position:0%
+variation on that but a a nominal value
+for the trans conductance or the
+
+ align:start position:0%
+for the trans conductance or the
+ 
+
+ align:start position:0%
+for the trans conductance or the
+quantity G sub m/2 is about 2 * 10us 4 m
+
+ align:start position:0%
+quantity G sub m/2 is about 2 * 10us 4 m
+ 
+
+ align:start position:0%
+quantity G sub m/2 is about 2 * 10us 4 m
+a final thing that we didn't mention
+
+ align:start position:0%
+a final thing that we didn't mention
+ 
+
+ align:start position:0%
+a final thing that we didn't mention
+last time but will become important
+
+ align:start position:0%
+last time but will become important
+ 
+
+ align:start position:0%
+last time but will become important
+actually in the session that follows
+
+ align:start position:0%
+actually in the session that follows
+ 
+
+ align:start position:0%
+actually in the session that follows
+this one is that certain kinds of of
+
+ align:start position:0%
+this one is that certain kinds of of
+ 
+
+ align:start position:0%
+this one is that certain kinds of of
+monor loop compensation result in
+
+ align:start position:0%
+monor loop compensation result in
+ 
+
+ align:start position:0%
+monor loop compensation result in
+stability of problems associated with a
+
+ align:start position:0%
+stability of problems associated with a
+ 
+
+ align:start position:0%
+stability of problems associated with a
+minor Loop itself and so we have to be
+
+ align:start position:0%
+minor Loop itself and so we have to be
+ 
+
+ align:start position:0%
+minor Loop itself and so we have to be
+careful when we do the compensation in
+
+ align:start position:0%
+careful when we do the compensation in
+ 
+
+ align:start position:0%
+careful when we do the compensation in
+this system or in any other system that
+
+ align:start position:0%
+this system or in any other system that
+ 
+
+ align:start position:0%
+this system or in any other system that
+uses minor Loop compensation to make
+
+ align:start position:0%
+uses minor Loop compensation to make
+ 
+
+ align:start position:0%
+uses minor Loop compensation to make
+sure that the minor Loop remains
+
+ align:start position:0%
+sure that the minor Loop remains
+ 
+
+ align:start position:0%
+sure that the minor Loop remains
+acceptably
+
+ align:start position:0%
+acceptably
+ 
+
+ align:start position:0%
+acceptably
+stable one kind of compensation that we
+
+ align:start position:0%
+stable one kind of compensation that we
+ 
+
+ align:start position:0%
+stable one kind of compensation that we
+can Implement very easily in monor Loop
+
+ align:start position:0%
+can Implement very easily in monor Loop
+ 
+
+ align:start position:0%
+can Implement very easily in monor Loop
+form is so-called single pole
+
+ align:start position:0%
+form is so-called single pole
+ 
+
+ align:start position:0%
+form is so-called single pole
+compensation what we do there is use a
+
+ align:start position:0%
+compensation what we do there is use a
+ 
+
+ align:start position:0%
+compensation what we do there is use a
+single capacitor as the compensating
+
+ align:start position:0%
+single capacitor as the compensating
+ 
+
+ align:start position:0%
+single capacitor as the compensating
+element that's sort of a degenerate case
+
+ align:start position:0%
+element that's sort of a degenerate case
+ 
+
+ align:start position:0%
+element that's sort of a degenerate case
+of a two-port and if we go through the
+
+ align:start position:0%
+of a two-port and if we go through the
+ 
+
+ align:start position:0%
+of a two-port and if we go through the
+numbers we find out that the transfer
+
+ align:start position:0%
+numbers we find out that the transfer
+ 
+
+ align:start position:0%
+numbers we find out that the transfer
+admittance for a capacitor a single
+
+ align:start position:0%
+admittance for a capacitor a single
+ 
+
+ align:start position:0%
+admittance for a capacitor a single
+capacitor is simply equal to the value
+
+ align:start position:0%
+capacitor is simply equal to the value
+ 
+
+ align:start position:0%
+capacitor is simply equal to the value
+of the capacitance let's call it C subc
+
+ align:start position:0%
+of the capacitance let's call it C subc
+ 
+
+ align:start position:0%
+of the capacitance let's call it C subc
+Time s consequently when we evaluated
+
+ align:start position:0%
+Time s consequently when we evaluated
+ 
+
+ align:start position:0%
+Time s consequently when we evaluated
+our approximation to the open loop
+
+ align:start position:0%
+our approximation to the open loop
+ 
+
+ align:start position:0%
+our approximation to the open loop
+transfer function of the amplifier it
+
+ align:start position:0%
+transfer function of the amplifier it
+ 
+
+ align:start position:0%
+transfer function of the amplifier it
+would be G subm over 2 * C sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can look at what we're trying to
+
+ align:start position:0%
+we can look at what we're trying to
+ 
+
+ align:start position:0%
+we can look at what we're trying to
+accomplish with this sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compensation from remember from last
+
+ align:start position:0%
+compensation from remember from last
+ 
+
+ align:start position:0%
+compensation from remember from last
+time we mentioned that the way we
+
+ align:start position:0%
+time we mentioned that the way we
+ 
+
+ align:start position:0%
+time we mentioned that the way we
+determine the
+
+ align:start position:0%
+determine the
+ 
+
+ align:start position:0%
+determine the
+actual open loop transfer function of
+
+ align:start position:0%
+actual open loop transfer function of
+ 
+
+ align:start position:0%
+actual open loop transfer function of
+the amplifier with
+
+ align:start position:0%
+the amplifier with
+ 
+
+ align:start position:0%
+the amplifier with
+compensation is to First
+
+ align:start position:0%
+compensation is to First
+ 
+
+ align:start position:0%
+compensation is to First
+draw the uncompensated transfer function
+
+ align:start position:0%
+draw the uncompensated transfer function
+ 
+
+ align:start position:0%
+draw the uncompensated transfer function
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+amplifier here I've assumed that our
+
+ align:start position:0%
+amplifier here I've assumed that our
+ 
+
+ align:start position:0%
+amplifier here I've assumed that our
+amplifier is actually three pole here's
+
+ align:start position:0%
+amplifier is actually three pole here's
+ 
+
+ align:start position:0%
+amplifier is actually three pole here's
+one pole Two Poles three poles but the
+
+ align:start position:0%
+one pole Two Poles three poles but the
+ 
+
+ align:start position:0%
+one pole Two Poles three poles but the
+details of this aren't important the
+
+ align:start position:0%
+details of this aren't important the
+ 
+
+ align:start position:0%
+details of this aren't important the
+point is we do have the uncompensated
+
+ align:start position:0%
+point is we do have the uncompensated
+ 
+
+ align:start position:0%
+point is we do have the uncompensated
+open loop transfer function of the
+
+ align:start position:0%
+open loop transfer function of the
+ 
+
+ align:start position:0%
+open loop transfer function of the
+amplifier that which would result if we
+
+ align:start position:0%
+amplifier that which would result if we
+ 
+
+ align:start position:0%
+amplifier that which would result if we
+disabled the compensating network but
+
+ align:start position:0%
+disabled the compensating network but
+ 
+
+ align:start position:0%
+disabled the compensating network but
+included its loading so that's this
+
+ align:start position:0%
+included its loading so that's this
+ 
+
+ align:start position:0%
+included its loading so that's this
+curve then we draw the
+
+ align:start position:0%
+curve then we draw the
+ 
+
+ align:start position:0%
+curve then we draw the
+approximation and in the case where we
+
+ align:start position:0%
+approximation and in the case where we
+ 
+
+ align:start position:0%
+approximation and in the case where we
+use a single capacitor we of course get
+
+ align:start position:0%
+use a single capacitor we of course get
+ 
+
+ align:start position:0%
+use a single capacitor we of course get
+a one pole approximation inversely
+
+ align:start position:0%
+a one pole approximation inversely
+ 
+
+ align:start position:0%
+a one pole approximation inversely
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+so here's the
+
+ align:start position:0%
+so here's the
+ 
+
+ align:start position:0%
+so here's the
+approximation then to a good degree of
+
+ align:start position:0%
+approximation then to a good degree of
+ 
+
+ align:start position:0%
+approximation then to a good degree of
+approximation why our overall
+
+ align:start position:0%
+approximation why our overall
+ 
+
+ align:start position:0%
+approximation why our overall
+compensated open loop transfer function
+
+ align:start position:0%
+compensated open loop transfer function
+ 
+
+ align:start position:0%
+compensated open loop transfer function
+for the amplifier is simply the lower of
+
+ align:start position:0%
+for the amplifier is simply the lower of
+ 
+
+ align:start position:0%
+for the amplifier is simply the lower of
+these two curves at all
+
+ align:start position:0%
+these two curves at all
+ 
+
+ align:start position:0%
+these two curves at all
+frequencies we've showed some dotted
+
+ align:start position:0%
+frequencies we've showed some dotted
+ 
+
+ align:start position:0%
+frequencies we've showed some dotted
+lines here over a range of frequencies
+
+ align:start position:0%
+lines here over a range of frequencies
+ 
+
+ align:start position:0%
+lines here over a range of frequencies
+where the open loop transfer function of
+
+ align:start position:0%
+where the open loop transfer function of
+ 
+
+ align:start position:0%
+where the open loop transfer function of
+the operational amplifier is in fact
+
+ align:start position:0%
+the operational amplifier is in fact
+ 
+
+ align:start position:0%
+the operational amplifier is in fact
+controlled by minor Loop feedback
+
+ align:start position:0%
+controlled by minor Loop feedback
+ 
+
+ align:start position:0%
+controlled by minor Loop feedback
+remember the inequalities between the
+
+ align:start position:0%
+remember the inequalities between the
+ 
+
+ align:start position:0%
+remember the inequalities between the
+uncompensated transfer function and the
+
+ align:start position:0%
+uncompensated transfer function and the
+ 
+
+ align:start position:0%
+uncompensated transfer function and the
+approximation involving the transfer
+
+ align:start position:0%
+approximation involving the transfer
+ 
+
+ align:start position:0%
+approximation involving the transfer
+admittance of the compensating element
+
+ align:start position:0%
+admittance of the compensating element
+ 
+
+ align:start position:0%
+admittance of the compensating element
+are such that in this region the
+
+ align:start position:0%
+are such that in this region the
+ 
+
+ align:start position:0%
+are such that in this region the
+amplifier open loop performance is very
+
+ align:start position:0%
+amplifier open loop performance is very
+ 
+
+ align:start position:0%
+amplifier open loop performance is very
+directly controlled by minor Loop
+
+ align:start position:0%
+directly controlled by minor Loop
+ 
+
+ align:start position:0%
+directly controlled by minor Loop
+compensation and so over this range of
+
+ align:start position:0%
+compensation and so over this range of
+ 
+
+ align:start position:0%
+compensation and so over this range of
+frequencies we can estimate the open
+
+ align:start position:0%
+frequencies we can estimate the open
+ 
+
+ align:start position:0%
+frequencies we can estimate the open
+loop transfer function of the amplifier
+
+ align:start position:0%
+loop transfer function of the amplifier
+ 
+
+ align:start position:0%
+loop transfer function of the amplifier
+based only on a knowledge of its of the
+
+ align:start position:0%
+based only on a knowledge of its of the
+ 
+
+ align:start position:0%
+based only on a knowledge of its of the
+transconductance of its first stage Ag
+
+ align:start position:0%
+transconductance of its first stage Ag
+ 
+
+ align:start position:0%
+transconductance of its first stage Ag
+and the compensating element that we're
+
+ align:start position:0%
+and the compensating element that we're
+ 
+
+ align:start position:0%
+and the compensating element that we're
+using in this case a
+
+ align:start position:0%
+using in this case a
+ 
+
+ align:start position:0%
+using in this case a
+capacitor the effect on the angle
+
+ align:start position:0%
+capacitor the effect on the angle
+ 
+
+ align:start position:0%
+capacitor the effect on the angle
+associated with the open loop transfer
+
+ align:start position:0%
+associated with the open loop transfer
+ 
+
+ align:start position:0%
+associated with the open loop transfer
+function is shown below uh here we have
+
+ align:start position:0%
+function is shown below uh here we have
+ 
+
+ align:start position:0%
+function is shown below uh here we have
+the original uncompensated for transfer
+
+ align:start position:0%
+the original uncompensated for transfer
+ 
+
+ align:start position:0%
+the original uncompensated for transfer
+function assumed to be three pole but
+
+ align:start position:0%
+function assumed to be three pole but
+ 
+
+ align:start position:0%
+function assumed to be three pole but
+again that's that's not horribly
+
+ align:start position:0%
+again that's that's not horribly
+ 
+
+ align:start position:0%
+again that's that's not horribly
+important the effect of adding the
+
+ align:start position:0%
+important the effect of adding the
+ 
+
+ align:start position:0%
+important the effect of adding the
+compensation the single pole
+
+ align:start position:0%
+compensation the single pole
+ 
+
+ align:start position:0%
+compensation the single pole
+compensation is to force a single pole
+
+ align:start position:0%
+compensation is to force a single pole
+ 
+
+ align:start position:0%
+compensation is to force a single pole
+rollof between this frequency and some
+
+ align:start position:0%
+rollof between this frequency and some
+ 
+
+ align:start position:0%
+rollof between this frequency and some
+much higher frequency and so we have a
+
+ align:start position:0%
+much higher frequency and so we have a
+ 
+
+ align:start position:0%
+much higher frequency and so we have a
+long range of frequencies here where the
+
+ align:start position:0%
+long range of frequencies here where the
+ 
+
+ align:start position:0%
+long range of frequencies here where the
+amplifier open loop transfer function is
+
+ align:start position:0%
+amplifier open loop transfer function is
+ 
+
+ align:start position:0%
+amplifier open loop transfer function is
+in fact following a single pole roll off
+
+ align:start position:0%
+in fact following a single pole roll off
+ 
+
+ align:start position:0%
+in fact following a single pole roll off
+we get approximately 90° of phase shift
+
+ align:start position:0%
+we get approximately 90° of phase shift
+ 
+
+ align:start position:0%
+we get approximately 90° of phase shift
+so here we have a situation where the
+
+ align:start position:0%
+so here we have a situation where the
+ 
+
+ align:start position:0%
+so here we have a situation where the
+use of a single capacitor and in fact
+
+ align:start position:0%
+use of a single capacitor and in fact
+ 
+
+ align:start position:0%
+use of a single capacitor and in fact
+quite a small one as we see controls the
+
+ align:start position:0%
+quite a small one as we see controls the
+ 
+
+ align:start position:0%
+quite a small one as we see controls the
+transfer function over a very wide range
+
+ align:start position:0%
+transfer function over a very wide range
+ 
+
+ align:start position:0%
+transfer function over a very wide range
+of frequencies and in fact gives us an
+
+ align:start position:0%
+of frequencies and in fact gives us an
+ 
+
+ align:start position:0%
+of frequencies and in fact gives us an
+approximately single pole rolloff over a
+
+ align:start position:0%
+approximately single pole rolloff over a
+ 
+
+ align:start position:0%
+approximately single pole rolloff over a
+very wide range of
+
+ align:start position:0%
+very wide range of
+ 
+
+ align:start position:0%
+very wide range of
+frequencies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a frequently used value when we design
+
+ align:start position:0%
+a frequently used value when we design
+ 
+
+ align:start position:0%
+a frequently used value when we design
+an amplifier that includes internal
+
+ align:start position:0%
+an amplifier that includes internal
+ 
+
+ align:start position:0%
+an amplifier that includes internal
+compensation rather than one where we
+
+ align:start position:0%
+compensation rather than one where we
+ 
+
+ align:start position:0%
+compensation rather than one where we
+can add the compensation ourselves an
+
+ align:start position:0%
+can add the compensation ourselves an
+ 
+
+ align:start position:0%
+can add the compensation ourselves an
+amplifier such as a 741 as I mentioned
+
+ align:start position:0%
+amplifier such as a 741 as I mentioned
+ 
+
+ align:start position:0%
+amplifier such as a 741 as I mentioned
+last time is one that uses this General
+
+ align:start position:0%
+last time is one that uses this General
+ 
+
+ align:start position:0%
+last time is one that uses this General
+topology the general two-stage topology
+
+ align:start position:0%
+topology the general two-stage topology
+ 
+
+ align:start position:0%
+topology the general two-stage topology
+but it has an internal capacitor and the
+
+ align:start position:0%
+but it has an internal capacitor and the
+ 
+
+ align:start position:0%
+but it has an internal capacitor and the
+value of that capacitor is typically 30
+
+ align:start position:0%
+value of that capacitor is typically 30
+ 
+
+ align:start position:0%
+value of that capacitor is typically 30
+paaf
+
+ align:start position:0%
+paaf
+ 
+
+ align:start position:0%
+paaf
+farads the transconductance of 74 41
+
+ align:start position:0%
+farads the transconductance of 74 41
+ 
+
+ align:start position:0%
+farads the transconductance of 74 41
+input transistor is the same as for for
+
+ align:start position:0%
+input transistor is the same as for for
+ 
+
+ align:start position:0%
+input transistor is the same as for for
+the 101a and consequently the quantity G
+
+ align:start position:0%
+the 101a and consequently the quantity G
+ 
+
+ align:start position:0%
+the 101a and consequently the quantity G
+subm / 2 * C sub CS is equal to G subm /
+
+ align:start position:0%
+subm / 2 * C sub CS is equal to G subm /
+ 
+
+ align:start position:0%
+subm / 2 * C sub CS is equal to G subm /
+2 or 2 * 10- 4 Moses divided 3 * 10-
+
+ align:start position:0%
+2 or 2 * 10- 4 Moses divided 3 * 10-
+ 
+
+ align:start position:0%
+2 or 2 * 10- 4 Moses divided 3 * 10-
+11th farads in the case of a 30 paa
+
+ align:start position:0%
+11th farads in the case of a 30 paa
+ 
+
+ align:start position:0%
+11th farads in the case of a 30 paa
+farad capacitor and then thus our
+
+ align:start position:0%
+farad capacitor and then thus our
+ 
+
+ align:start position:0%
+farad capacitor and then thus our
+approximation to the open loop transfer
+
+ align:start position:0%
+approximation to the open loop transfer
+ 
+
+ align:start position:0%
+approximation to the open loop transfer
+function is about 6.7 * 10 6/
+
+ align:start position:0%
+function is about 6.7 * 10 6/
+ 
+
+ align:start position:0%
+function is about 6.7 * 10 6/
+s that transfer function actually holds
+
+ align:start position:0%
+s that transfer function actually holds
+ 
+
+ align:start position:0%
+s that transfer function actually holds
+over a range of frequencies that
+
+ align:start position:0%
+over a range of frequencies that
+ 
+
+ align:start position:0%
+over a range of frequencies that
+typically extends from about 10 Hertz to
+
+ align:start position:0%
+typically extends from about 10 Hertz to
+ 
+
+ align:start position:0%
+typically extends from about 10 Hertz to
+roughly a megahertz so here a 30 paa
+
+ align:start position:0%
+roughly a megahertz so here a 30 paa
+ 
+
+ align:start position:0%
+roughly a megahertz so here a 30 paa
+farad capacitor compensates the
+
+ align:start position:0%
+farad capacitor compensates the
+ 
+
+ align:start position:0%
+farad capacitor compensates the
+amplifier dominates its performance over
+
+ align:start position:0%
+amplifier dominates its performance over
+ 
+
+ align:start position:0%
+amplifier dominates its performance over
+about a factor of 10 5th to one in
+
+ align:start position:0%
+about a factor of 10 5th to one in
+ 
+
+ align:start position:0%
+about a factor of 10 5th to one in
+frequency that's very significant
+
+ align:start position:0%
+frequency that's very significant
+ 
+
+ align:start position:0%
+frequency that's very significant
+actually for the fabrication of
+
+ align:start position:0%
+actually for the fabrication of
+ 
+
+ align:start position:0%
+actually for the fabrication of
+integrated circuits because using this
+
+ align:start position:0%
+integrated circuits because using this
+ 
+
+ align:start position:0%
+integrated circuits because using this
+minor Loop technique in the topology
+
+ align:start position:0%
+minor Loop technique in the topology
+ 
+
+ align:start position:0%
+minor Loop technique in the topology
+we've discussed we're able to compensate
+
+ align:start position:0%
+we've discussed we're able to compensate
+ 
+
+ align:start position:0%
+we've discussed we're able to compensate
+the amplifier with a size capacitor that
+
+ align:start position:0%
+the amplifier with a size capacitor that
+ 
+
+ align:start position:0%
+the amplifier with a size capacitor that
+can be fitted onto the onto the chip it
+
+ align:start position:0%
+can be fitted onto the onto the chip it
+ 
+
+ align:start position:0%
+can be fitted onto the onto the chip it
+doesn't consume excessive chip area and
+
+ align:start position:0%
+doesn't consume excessive chip area and
+ 
+
+ align:start position:0%
+doesn't consume excessive chip area and
+so one of the things that made internal
+
+ align:start position:0%
+so one of the things that made internal
+ 
+
+ align:start position:0%
+so one of the things that made internal
+compensation of operational amplifiers
+
+ align:start position:0%
+compensation of operational amplifiers
+ 
+
+ align:start position:0%
+compensation of operational amplifiers
+possible was exploitation of this sort
+
+ align:start position:0%
+possible was exploitation of this sort
+ 
+
+ align:start position:0%
+possible was exploitation of this sort
+of minor Loop
+
+ align:start position:0%
+of minor Loop
+ 
+
+ align:start position:0%
+of minor Loop
+topology the reason for the choice of a
+
+ align:start position:0%
+topology the reason for the choice of a
+ 
+
+ align:start position:0%
+topology the reason for the choice of a
+30 peared capacitor and fixed
+
+ align:start position:0%
+30 peared capacitor and fixed
+ 
+
+ align:start position:0%
+30 peared capacitor and fixed
+compensation amplifiers is that that
+
+ align:start position:0%
+compensation amplifiers is that that
+ 
+
+ align:start position:0%
+compensation amplifiers is that that
+forces crossover in other words we we go
+
+ align:start position:0%
+forces crossover in other words we we go
+ 
+
+ align:start position:0%
+forces crossover in other words we we go
+through Unity gain in the amplifier for
+
+ align:start position:0%
+through Unity gain in the amplifier for
+ 
+
+ align:start position:0%
+through Unity gain in the amplifier for
+the amplifier open loop transfer
+
+ align:start position:0%
+the amplifier open loop transfer
+ 
+
+ align:start position:0%
+the amplifier open loop transfer
+function at a frequency of course of 6.7
+
+ align:start position:0%
+function at a frequency of course of 6.7
+ 
+
+ align:start position:0%
+function at a frequency of course of 6.7
+time 10 6 radians per second or about a
+
+ align:start position:0%
+time 10 6 radians per second or about a
+ 
+
+ align:start position:0%
+time 10 6 radians per second or about a
+megahertz and uh we mentioned that the
+
+ align:start position:0%
+megahertz and uh we mentioned that the
+ 
+
+ align:start position:0%
+megahertz and uh we mentioned that the
+phase shift problems associated with the
+
+ align:start position:0%
+phase shift problems associated with the
+ 
+
+ align:start position:0%
+phase shift problems associated with the
+Dynamics of the PNP transistors that are
+
+ align:start position:0%
+Dynamics of the PNP transistors that are
+ 
+
+ align:start position:0%
+Dynamics of the PNP transistors that are
+typically used in this topology are such
+
+ align:start position:0%
+typically used in this topology are such
+ 
+
+ align:start position:0%
+typically used in this topology are such
+that we have to constrain crossover to
+
+ align:start position:0%
+that we have to constrain crossover to
+ 
+
+ align:start position:0%
+that we have to constrain crossover to
+about a megahertz or else we'll get
+
+ align:start position:0%
+about a megahertz or else we'll get
+ 
+
+ align:start position:0%
+about a megahertz or else we'll get
+stability problems so this amplifier one
+
+ align:start position:0%
+stability problems so this amplifier one
+ 
+
+ align:start position:0%
+stability problems so this amplifier one
+that uses a 30 peaka farad capacitor is
+
+ align:start position:0%
+that uses a 30 peaka farad capacitor is
+ 
+
+ align:start position:0%
+that uses a 30 peaka farad capacitor is
+an example of one that will be Unity
+
+ align:start position:0%
+an example of one that will be Unity
+ 
+
+ align:start position:0%
+an example of one that will be Unity
+gain stable in other words if we form a
+
+ align:start position:0%
+gain stable in other words if we form a
+ 
+
+ align:start position:0%
+gain stable in other words if we form a
+feedback loop with f equal to 1 by
+
+ align:start position:0%
+feedback loop with f equal to 1 by
+ 
+
+ align:start position:0%
+feedback loop with f equal to 1 by
+connecting the output of the amplifier
+
+ align:start position:0%
+connecting the output of the amplifier
+ 
+
+ align:start position:0%
+connecting the output of the amplifier
+directly back to its input the resultant
+
+ align:start position:0%
+directly back to its input the resultant
+ 
+
+ align:start position:0%
+directly back to its input the resultant
+configuration should be stable since the
+
+ align:start position:0%
+configuration should be stable since the
+ 
+
+ align:start position:0%
+configuration should be stable since the
+major Loop thus formed crosses over at
+
+ align:start position:0%
+major Loop thus formed crosses over at
+ 
+
+ align:start position:0%
+major Loop thus formed crosses over at
+about a
+
+ align:start position:0%
+about a
+ 
+
+ align:start position:0%
+about a
+megahertz the problem is that that sort
+
+ align:start position:0%
+megahertz the problem is that that sort
+ 
+
+ align:start position:0%
+megahertz the problem is that that sort
+of compensation is overly conservative
+
+ align:start position:0%
+of compensation is overly conservative
+ 
+
+ align:start position:0%
+of compensation is overly conservative
+in many applications it's fine if we
+
+ align:start position:0%
+in many applications it's fine if we
+ 
+
+ align:start position:0%
+in many applications it's fine if we
+have direct feedback from the output to
+
+ align:start position:0%
+have direct feedback from the output to
+ 
+
+ align:start position:0%
+have direct feedback from the output to
+the input but it really deteriorates the
+
+ align:start position:0%
+the input but it really deteriorates the
+ 
+
+ align:start position:0%
+the input but it really deteriorates the
+dynamic performance in many many other
+
+ align:start position:0%
+dynamic performance in many many other
+ 
+
+ align:start position:0%
+dynamic performance in many many other
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+configurations let's consider the
+
+ align:start position:0%
+configurations let's consider the
+ 
+
+ align:start position:0%
+configurations let's consider the
+following here we have an operational
+
+ align:start position:0%
+following here we have an operational
+ 
+
+ align:start position:0%
+following here we have an operational
+amplifier
+
+ align:start position:0%
+amplifier
+ 
+
+ align:start position:0%
+amplifier
+connected as a non-inverting amplifier
+
+ align:start position:0%
+connected as a non-inverting amplifier
+ 
+
+ align:start position:0%
+connected as a non-inverting amplifier
+of course we've seen this configuration
+
+ align:start position:0%
+of course we've seen this configuration
+ 
+
+ align:start position:0%
+of course we've seen this configuration
+before we have attenuation from the
+
+ align:start position:0%
+before we have attenuation from the
+ 
+
+ align:start position:0%
+before we have attenuation from the
+output back to the inverting input via
+
+ align:start position:0%
+output back to the inverting input via
+ 
+
+ align:start position:0%
+output back to the inverting input via
+the R1 R2 network uh we have a single
+
+ align:start position:0%
+the R1 R2 network uh we have a single
+ 
+
+ align:start position:0%
+the R1 R2 network uh we have a single
+capacitor that's used for compensation
+
+ align:start position:0%
+capacitor that's used for compensation
+ 
+
+ align:start position:0%
+capacitor that's used for compensation
+and I'd like to investigate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configuration the block diagram assuming
+
+ align:start position:0%
+configuration the block diagram assuming
+ 
+
+ align:start position:0%
+configuration the block diagram assuming
+that we can represent the amplifier by
+
+ align:start position:0%
+that we can represent the amplifier by
+ 
+
+ align:start position:0%
+that we can represent the amplifier by
+our approximation has a forward path
+
+ align:start position:0%
+our approximation has a forward path
+ 
+
+ align:start position:0%
+our approximation has a forward path
+that will be simply the approximation G
+
+ align:start position:0%
+that will be simply the approximation G
+ 
+
+ align:start position:0%
+that will be simply the approximation G
+subm over 2 time C sub
+
+ align:start position:0%
+subm over 2 time C sub
+ 
+
+ align:start position:0%
+subm over 2 time C sub
+CS the feedback path reflects the
+
+ align:start position:0%
+CS the feedback path reflects the
+ 
+
+ align:start position:0%
+CS the feedback path reflects the
+attenuation provided by the R1 R1 plus
+
+ align:start position:0%
+attenuation provided by the R1 R1 plus
+ 
+
+ align:start position:0%
+attenuation provided by the R1 R1 plus
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+network if we estimate the closed loop
+
+ align:start position:0%
+network if we estimate the closed loop
+ 
+
+ align:start position:0%
+network if we estimate the closed loop
+gain based on this expression for the
+
+ align:start position:0%
+gain based on this expression for the
+ 
+
+ align:start position:0%
+gain based on this expression for the
+forward path gain we get the expression
+
+ align:start position:0%
+forward path gain we get the expression
+ 
+
+ align:start position:0%
+forward path gain we get the expression
+shown G subm / 2 C sub CS 1 + G subm / 2
+
+ align:start position:0%
+shown G subm / 2 C sub CS 1 + G subm / 2
+ 
+
+ align:start position:0%
+shown G subm / 2 C sub CS 1 + G subm / 2
+CCS * f 1 minus the loop transmission
+
+ align:start position:0%
+CCS * f 1 minus the loop transmission
+ 
+
+ align:start position:0%
+CCS * f 1 minus the loop transmission
+assuming that the uh loop transmission
+
+ align:start position:0%
+assuming that the uh loop transmission
+ 
+
+ align:start position:0%
+assuming that the uh loop transmission
+can use this estimate for the forward
+
+ align:start position:0%
+can use this estimate for the forward
+ 
+
+ align:start position:0%
+can use this estimate for the forward
+path gain and if we rearrange terms
+
+ align:start position:0%
+path gain and if we rearrange terms
+ 
+
+ align:start position:0%
+path gain and if we rearrange terms
+basically multiply numerator and
+
+ align:start position:0%
+basically multiply numerator and
+ 
+
+ align:start position:0%
+basically multiply numerator and
+denominator by the reciprocal of the
+
+ align:start position:0%
+denominator by the reciprocal of the
+ 
+
+ align:start position:0%
+denominator by the reciprocal of the
+second term in the denominator we find
+
+ align:start position:0%
+second term in the denominator we find
+ 
+
+ align:start position:0%
+second term in the denominator we find
+out that the closed loop gain is single
+
+ align:start position:0%
+out that the closed loop gain is single
+ 
+
+ align:start position:0%
+out that the closed loop gain is single
+pole has a value 1/ F the ideal closed
+
+ align:start position:0%
+pole has a value 1/ F the ideal closed
+ 
+
+ align:start position:0%
+pole has a value 1/ F the ideal closed
+loop gain which results at low
+
+ align:start position:0%
+loop gain which results at low
+ 
+
+ align:start position:0%
+loop gain which results at low
+frequencies uh and then a single pole
+
+ align:start position:0%
+frequencies uh and then a single pole
+ 
+
+ align:start position:0%
+frequencies uh and then a single pole
+rollof where the time constant
+
+ align:start position:0%
+rollof where the time constant
+ 
+
+ align:start position:0%
+rollof where the time constant
+associated with that roll off is related
+
+ align:start position:0%
+associated with that roll off is related
+ 
+
+ align:start position:0%
+associated with that roll off is related
+to the ratio of c subc and and
+
+ align:start position:0%
+to the ratio of c subc and and
+ 
+
+ align:start position:0%
+to the ratio of c subc and and
+F now the problem is that as we go to
+
+ align:start position:0%
+F now the problem is that as we go to
+ 
+
+ align:start position:0%
+F now the problem is that as we go to
+larger and larger closed loop gains in
+
+ align:start position:0%
+larger and larger closed loop gains in
+ 
+
+ align:start position:0%
+larger and larger closed loop gains in
+other words if we go back to our
+
+ align:start position:0%
+other words if we go back to our
+ 
+
+ align:start position:0%
+other words if we go back to our
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+amplifier and in order to get higher
+
+ align:start position:0%
+amplifier and in order to get higher
+ 
+
+ align:start position:0%
+amplifier and in order to get higher
+close close loop gains of course we'd
+
+ align:start position:0%
+close close loop gains of course we'd
+ 
+
+ align:start position:0%
+close close loop gains of course we'd
+make R1 smaller relative to R2 thereby
+
+ align:start position:0%
+make R1 smaller relative to R2 thereby
+ 
+
+ align:start position:0%
+make R1 smaller relative to R2 thereby
+lowering F and since the ideal Clos Loop
+
+ align:start position:0%
+lowering F and since the ideal Clos Loop
+ 
+
+ align:start position:0%
+lowering F and since the ideal Clos Loop
+gain for this non-inverting
+
+ align:start position:0%
+gain for this non-inverting
+ 
+
+ align:start position:0%
+gain for this non-inverting
+configuration is of course simply 1 over
+
+ align:start position:0%
+configuration is of course simply 1 over
+ 
+
+ align:start position:0%
+configuration is of course simply 1 over
+F why as we lower that ratio we make F
+
+ align:start position:0%
+F why as we lower that ratio we make F
+ 
+
+ align:start position:0%
+F why as we lower that ratio we make F
+smaller we get progressively higher
+
+ align:start position:0%
+smaller we get progressively higher
+ 
+
+ align:start position:0%
+smaller we get progressively higher
+closed loop gains the problem is that
+
+ align:start position:0%
+closed loop gains the problem is that
+ 
+
+ align:start position:0%
+closed loop gains the problem is that
+for a fixed value of compensating
+
+ align:start position:0%
+for a fixed value of compensating
+ 
+
+ align:start position:0%
+for a fixed value of compensating
+capacitor if C subc is fixed why
+
+ align:start position:0%
+capacitor if C subc is fixed why
+ 
+
+ align:start position:0%
+capacitor if C subc is fixed why
+the as we lower F the time con
+
+ align:start position:0%
+the as we lower F the time con
+ 
+
+ align:start position:0%
+the as we lower F the time con
+associated with the closed loop pole
+
+ align:start position:0%
+associated with the closed loop pole
+ 
+
+ align:start position:0%
+associated with the closed loop pole
+gets progressively larger in other words
+
+ align:start position:0%
+gets progressively larger in other words
+ 
+
+ align:start position:0%
+gets progressively larger in other words
+the amplifier gets slower as we go to
+
+ align:start position:0%
+the amplifier gets slower as we go to
+ 
+
+ align:start position:0%
+the amplifier gets slower as we go to
+larger and larger closed loop gains
+
+ align:start position:0%
+larger and larger closed loop gains
+ 
+
+ align:start position:0%
+larger and larger closed loop gains
+however consider what happens if as we
+
+ align:start position:0%
+however consider what happens if as we
+ 
+
+ align:start position:0%
+however consider what happens if as we
+change F we modify C subc we change C
+
+ align:start position:0%
+change F we modify C subc we change C
+ 
+
+ align:start position:0%
+change F we modify C subc we change C
+subc in about a proportionate way and if
+
+ align:start position:0%
+subc in about a proportionate way and if
+ 
+
+ align:start position:0%
+subc in about a proportionate way and if
+we do that why we can keep the Dynamics
+
+ align:start position:0%
+we do that why we can keep the Dynamics
+ 
+
+ align:start position:0%
+we do that why we can keep the Dynamics
+the closed loop Dynamics fairly constant
+
+ align:start position:0%
+the closed loop Dynamics fairly constant
+ 
+
+ align:start position:0%
+the closed loop Dynamics fairly constant
+we can again look at the effect of that
+
+ align:start position:0%
+we can again look at the effect of that
+ 
+
+ align:start position:0%
+we can again look at the effect of that
+on one of our earlier view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs this is the curve that is g subm
+
+ align:start position:0%
+graphs this is the curve that is g subm
+ 
+
+ align:start position:0%
+graphs this is the curve that is g subm
+over 2 * c subc s as we change the value
+
+ align:start position:0%
+over 2 * c subc s as we change the value
+ 
+
+ align:start position:0%
+over 2 * c subc s as we change the value
+of C subc to larger values the curve
+
+ align:start position:0%
+of C subc to larger values the curve
+ 
+
+ align:start position:0%
+of C subc to larger values the curve
+moves down as we decrease the value of C
+
+ align:start position:0%
+moves down as we decrease the value of C
+ 
+
+ align:start position:0%
+moves down as we decrease the value of C
+subc the curve moves up implying wider
+
+ align:start position:0%
+subc the curve moves up implying wider
+ 
+
+ align:start position:0%
+subc the curve moves up implying wider
+bandwidth out of the amplifier itself
+
+ align:start position:0%
+bandwidth out of the amplifier itself
+ 
+
+ align:start position:0%
+bandwidth out of the amplifier itself
+now as we decrease C subc the unity gain
+
+ align:start position:0%
+now as we decrease C subc the unity gain
+ 
+
+ align:start position:0%
+now as we decrease C subc the unity gain
+frequency of the amplifier
+
+ align:start position:0%
+frequency of the amplifier
+ 
+
+ align:start position:0%
+frequency of the amplifier
+itself will increase and in fact may
+
+ align:start position:0%
+itself will increase and in fact may
+ 
+
+ align:start position:0%
+itself will increase and in fact may
+very easily become a go above a
+
+ align:start position:0%
+very easily become a go above a
+ 
+
+ align:start position:0%
+very easily become a go above a
+megahertz for certain values of c subc
+
+ align:start position:0%
+megahertz for certain values of c subc
+ 
+
+ align:start position:0%
+megahertz for certain values of c subc
+in fact if C subc is less than about 30
+
+ align:start position:0%
+in fact if C subc is less than about 30
+ 
+
+ align:start position:0%
+in fact if C subc is less than about 30
+picarats the unity gain frequency of the
+
+ align:start position:0%
+picarats the unity gain frequency of the
+ 
+
+ align:start position:0%
+picarats the unity gain frequency of the
+amplifier
+
+ align:start position:0%
+amplifier
+ 
+
+ align:start position:0%
+amplifier
+itself extends Beyond a megahertz that's
+
+ align:start position:0%
+itself extends Beyond a megahertz that's
+ 
+
+ align:start position:0%
+itself extends Beyond a megahertz that's
+no problem though if F gets
+
+ align:start position:0%
+no problem though if F gets
+ 
+
+ align:start position:0%
+no problem though if F gets
+correspondingly smaller since the
+
+ align:start position:0%
+correspondingly smaller since the
+ 
+
+ align:start position:0%
+correspondingly smaller since the
+crossover frequency of the major Loop is
+
+ align:start position:0%
+crossover frequency of the major Loop is
+ 
+
+ align:start position:0%
+crossover frequency of the major Loop is
+the one one we have to worry about in in
+
+ align:start position:0%
+the one one we have to worry about in in
+ 
+
+ align:start position:0%
+the one one we have to worry about in in
+terms of of loop stability problem so
+
+ align:start position:0%
+terms of of loop stability problem so
+ 
+
+ align:start position:0%
+terms of of loop stability problem so
+here as we lower F we can make
+
+ align:start position:0%
+here as we lower F we can make
+ 
+
+ align:start position:0%
+here as we lower F we can make
+corresponding changes in C subc the
+
+ align:start position:0%
+corresponding changes in C subc the
+ 
+
+ align:start position:0%
+corresponding changes in C subc the
+overall major Loop still crosses over at
+
+ align:start position:0%
+overall major Loop still crosses over at
+ 
+
+ align:start position:0%
+overall major Loop still crosses over at
+frequencies of of about a megahertz or
+
+ align:start position:0%
+frequencies of of about a megahertz or
+ 
+
+ align:start position:0%
+frequencies of of about a megahertz or
+so and so we don't get into stability
+
+ align:start position:0%
+so and so we don't get into stability
+ 
+
+ align:start position:0%
+so and so we don't get into stability
+problems because of the lateral PNP
+
+ align:start position:0%
+problems because of the lateral PNP
+ 
+
+ align:start position:0%
+problems because of the lateral PNP
+transistors let's see how this works in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice here we have a a board that
+
+ align:start position:0%
+practice here we have a a board that
+ 
+
+ align:start position:0%
+practice here we have a a board that
+includes an amplifier where we can
+
+ align:start position:0%
+includes an amplifier where we can
+ 
+
+ align:start position:0%
+includes an amplifier where we can
+change the compensating element and the
+
+ align:start position:0%
+change the compensating element and the
+ 
+
+ align:start position:0%
+change the compensating element and the
+rest of the equipment then includes a
+
+ align:start position:0%
+rest of the equipment then includes a
+ 
+
+ align:start position:0%
+rest of the equipment then includes a
+power supply which simply Powers the
+
+ align:start position:0%
+power supply which simply Powers the
+ 
+
+ align:start position:0%
+power supply which simply Powers the
+amplifier in question a signal generator
+
+ align:start position:0%
+amplifier in question a signal generator
+ 
+
+ align:start position:0%
+amplifier in question a signal generator
+that allows us to put steps or other
+
+ align:start position:0%
+that allows us to put steps or other
+ 
+
+ align:start position:0%
+that allows us to put steps or other
+test signals into the amplifier and an
+
+ align:start position:0%
+test signals into the amplifier and an
+ 
+
+ align:start position:0%
+test signals into the amplifier and an
+oscilloscope to look at the resultant
+
+ align:start position:0%
+oscilloscope to look at the resultant
+ 
+
+ align:start position:0%
+oscilloscope to look at the resultant
+responses if we examine this board in
+
+ align:start position:0%
+responses if we examine this board in
+ 
+
+ align:start position:0%
+responses if we examine this board in
+detail it has more than we're actually
+
+ align:start position:0%
+detail it has more than we're actually
+ 
+
+ align:start position:0%
+detail it has more than we're actually
+actually going to use in this
+
+ align:start position:0%
+actually going to use in this
+ 
+
+ align:start position:0%
+actually going to use in this
+demonstration we're actually just using
+
+ align:start position:0%
+demonstration we're actually just using
+ 
+
+ align:start position:0%
+demonstration we're actually just using
+this little corner of it here is a 301a
+
+ align:start position:0%
+this little corner of it here is a 301a
+ 
+
+ align:start position:0%
+this little corner of it here is a 301a
+type operation amplifier right here
+
+ align:start position:0%
+type operation amplifier right here
+ 
+
+ align:start position:0%
+type operation amplifier right here
+there are two terminals uh on that
+
+ align:start position:0%
+there are two terminals uh on that
+ 
+
+ align:start position:0%
+there are two terminals uh on that
+amplifier here and here that are
+
+ align:start position:0%
+amplifier here and here that are
+ 
+
+ align:start position:0%
+amplifier here and here that are
+connected to the compensating or that
+
+ align:start position:0%
+connected to the compensating or that
+ 
+
+ align:start position:0%
+connected to the compensating or that
+allow us to connect the compensating
+
+ align:start position:0%
+allow us to connect the compensating
+ 
+
+ align:start position:0%
+allow us to connect the compensating
+element to the amplifier we're presently
+
+ align:start position:0%
+element to the amplifier we're presently
+ 
+
+ align:start position:0%
+element to the amplifier we're presently
+using a single capacitor for
+
+ align:start position:0%
+using a single capacitor for
+ 
+
+ align:start position:0%
+using a single capacitor for
+compensation as I mentioned single pole
+
+ align:start position:0%
+compensation as I mentioned single pole
+ 
+
+ align:start position:0%
+compensation as I mentioned single pole
+compensation here is that compensating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor in this particular amplifier
+
+ align:start position:0%
+capacitor in this particular amplifier
+ 
+
+ align:start position:0%
+capacitor in this particular amplifier
+or with this particular amplifier we
+
+ align:start position:0%
+or with this particular amplifier we
+ 
+
+ align:start position:0%
+or with this particular amplifier we
+found that we get very nice stable
+
+ align:start position:0%
+found that we get very nice stable
+ 
+
+ align:start position:0%
+found that we get very nice stable
+responses with just a small amount of
+
+ align:start position:0%
+responses with just a small amount of
+ 
+
+ align:start position:0%
+responses with just a small amount of
+overshoot as presently shown on the
+
+ align:start position:0%
+overshoot as presently shown on the
+ 
+
+ align:start position:0%
+overshoot as presently shown on the
+oscilloscope in unity feedback
+
+ align:start position:0%
+oscilloscope in unity feedback
+ 
+
+ align:start position:0%
+oscilloscope in unity feedback
+configurations when we use actually a
+
+ align:start position:0%
+configurations when we use actually a
+ 
+
+ align:start position:0%
+configurations when we use actually a
+20pa farad capacitor also if we look at
+
+ align:start position:0%
+20pa farad capacitor also if we look at
+ 
+
+ align:start position:0%
+20pa farad capacitor also if we look at
+the transconductance of this amplifier
+
+ align:start position:0%
+the transconductance of this amplifier
+ 
+
+ align:start position:0%
+the transconductance of this amplifier
+we find it's a little bit higher than
+
+ align:start position:0%
+we find it's a little bit higher than
+ 
+
+ align:start position:0%
+we find it's a little bit higher than
+the nominal value cross over with a 20pa
+
+ align:start position:0%
+the nominal value cross over with a 20pa
+ 
+
+ align:start position:0%
+the nominal value cross over with a 20pa
+farad capacitor or the unity gain
+
+ align:start position:0%
+farad capacitor or the unity gain
+ 
+
+ align:start position:0%
+farad capacitor or the unity gain
+frequency with a 20 peaf farad capacitor
+
+ align:start position:0%
+frequency with a 20 peaf farad capacitor
+ 
+
+ align:start position:0%
+frequency with a 20 peaf farad capacitor
+is actually about 2 megahertz in this
+
+ align:start position:0%
+is actually about 2 megahertz in this
+ 
+
+ align:start position:0%
+is actually about 2 megahertz in this
+particular amplifier the switches on the
+
+ align:start position:0%
+particular amplifier the switches on the
+ 
+
+ align:start position:0%
+particular amplifier the switches on the
+front of the Box in particular these two
+
+ align:start position:0%
+front of the Box in particular these two
+ 
+
+ align:start position:0%
+front of the Box in particular these two
+switches uh allow us to change F thereby
+
+ align:start position:0%
+switches uh allow us to change F thereby
+ 
+
+ align:start position:0%
+switches uh allow us to change F thereby
+establishing different values for the
+
+ align:start position:0%
+establishing different values for the
+ 
+
+ align:start position:0%
+establishing different values for the
+ideal closed loop gain right now we're
+
+ align:start position:0%
+ideal closed loop gain right now we're
+ 
+
+ align:start position:0%
+ideal closed loop gain right now we're
+set up for a closed loop gain of one
+
+ align:start position:0%
+set up for a closed loop gain of one
+ 
+
+ align:start position:0%
+set up for a closed loop gain of one
+with f equals 1 as I mentioned earlier
+
+ align:start position:0%
+with f equals 1 as I mentioned earlier
+ 
+
+ align:start position:0%
+with f equals 1 as I mentioned earlier
+we have the 20 peaka farad
+
+ align:start position:0%
+we have the 20 peaka farad
+ 
+
+ align:start position:0%
+we have the 20 peaka farad
+capacitor and we're looking at the
+
+ align:start position:0%
+capacitor and we're looking at the
+ 
+
+ align:start position:0%
+capacitor and we're looking at the
+resultant step response the horizontal
+
+ align:start position:0%
+resultant step response the horizontal
+ 
+
+ align:start position:0%
+resultant step response the horizontal
+scale is 100 nond per Division and one
+
+ align:start position:0%
+scale is 100 nond per Division and one
+ 
+
+ align:start position:0%
+scale is 100 nond per Division and one
+very good measure of speed of response
+
+ align:start position:0%
+very good measure of speed of response
+ 
+
+ align:start position:0%
+very good measure of speed of response
+of course which is easily interpreted in
+
+ align:start position:0%
+of course which is easily interpreted in
+ 
+
+ align:start position:0%
+of course which is easily interpreted in
+terms of bandwidth is the 10 to 90% rise
+
+ align:start position:0%
+terms of bandwidth is the 10 to 90% rise
+ 
+
+ align:start position:0%
+terms of bandwidth is the 10 to 90% rise
+time for the system uh so let's see here
+
+ align:start position:0%
+time for the system uh so let's see here
+ 
+
+ align:start position:0%
+time for the system uh so let's see here
+is the 10% point up here is the 90%
+
+ align:start position:0%
+is the 10% point up here is the 90%
+ 
+
+ align:start position:0%
+is the 10% point up here is the 90%
+Point uh we have just about one and a
+
+ align:start position:0%
+Point uh we have just about one and a
+ 
+
+ align:start position:0%
+Point uh we have just about one and a
+half divisions horizontally between
+
+ align:start position:0%
+half divisions horizontally between
+ 
+
+ align:start position:0%
+half divisions horizontally between
+those two points we're at 100 NCS per
+
+ align:start position:0%
+those two points we're at 100 NCS per
+ 
+
+ align:start position:0%
+those two points we're at 100 NCS per
+Division and so we have a rise time of
+
+ align:start position:0%
+Division and so we have a rise time of
+ 
+
+ align:start position:0%
+Division and so we have a rise time of
+about 150 Nan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds so let's tabulate values here
+
+ align:start position:0%
+seconds so let's tabulate values here
+ 
+
+ align:start position:0%
+seconds so let's tabulate values here
+we're running at an ideal Clos Loop gain
+
+ align:start position:0%
+we're running at an ideal Clos Loop gain
+ 
+
+ align:start position:0%
+we're running at an ideal Clos Loop gain
+or a low frequency gain a KN which is
+
+ align:start position:0%
+or a low frequency gain a KN which is
+ 
+
+ align:start position:0%
+or a low frequency gain a KN which is
+equal to 1 over F we're running uh at a
+
+ align:start position:0%
+equal to 1 over F we're running uh at a
+ 
+
+ align:start position:0%
+equal to 1 over F we're running uh at a
+Clos Loop gain of one for this
+
+ align:start position:0%
+Clos Loop gain of one for this
+ 
+
+ align:start position:0%
+Clos Loop gain of one for this
+particular part of the demonstration and
+
+ align:start position:0%
+particular part of the demonstration and
+ 
+
+ align:start position:0%
+particular part of the demonstration and
+the rise time that we measure is about
+
+ align:start position:0%
+the rise time that we measure is about
+ 
+
+ align:start position:0%
+the rise time that we measure is about
+150 NCS we're using a 20 pea farad
+
+ align:start position:0%
+150 NCS we're using a 20 pea farad
+ 
+
+ align:start position:0%
+150 NCS we're using a 20 pea farad
+capacitor when we make that
+
+ align:start position:0%
+capacitor when we make that
+ 
+
+ align:start position:0%
+capacitor when we make that
+measurement for Unity feedback for an of
+
+ align:start position:0%
+measurement for Unity feedback for an of
+ 
+
+ align:start position:0%
+measurement for Unity feedback for an of
+one the optimum value of the capacitor
+
+ align:start position:0%
+one the optimum value of the capacitor
+ 
+
+ align:start position:0%
+one the optimum value of the capacitor
+is close to the 20 paa farad value going
+
+ align:start position:0%
+is close to the 20 paa farad value going
+ 
+
+ align:start position:0%
+is close to the 20 paa farad value going
+to smaller values of capacitor in in
+
+ align:start position:0%
+to smaller values of capacitor in in
+ 
+
+ align:start position:0%
+to smaller values of capacitor in in
+this with this value of f would result
+
+ align:start position:0%
+this with this value of f would result
+ 
+
+ align:start position:0%
+this with this value of f would result
+in progressively more overshoot
+
+ align:start position:0%
+in progressively more overshoot
+ 
+
+ align:start position:0%
+in progressively more overshoot
+progressively poorer stability uh
+
+ align:start position:0%
+progressively poorer stability uh
+ 
+
+ align:start position:0%
+progressively poorer stability uh
+because we'd be pushing the crossover of
+
+ align:start position:0%
+because we'd be pushing the crossover of
+ 
+
+ align:start position:0%
+because we'd be pushing the crossover of
+the major Loop out toward higher
+
+ align:start position:0%
+the major Loop out toward higher
+ 
+
+ align:start position:0%
+the major Loop out toward higher
+frequencies if we wish to we could slow
+
+ align:start position:0%
+frequencies if we wish to we could slow
+ 
+
+ align:start position:0%
+frequencies if we wish to we could slow
+the overall system we can certainly use
+
+ align:start position:0%
+the overall system we can certainly use
+ 
+
+ align:start position:0%
+the overall system we can certainly use
+larger than 20 pea farad capacitors uh
+
+ align:start position:0%
+larger than 20 pea farad capacitors uh
+ 
+
+ align:start position:0%
+larger than 20 pea farad capacitors uh
+that would result in in somewh improved
+
+ align:start position:0%
+that would result in in somewh improved
+ 
+
+ align:start position:0%
+that would result in in somewh improved
+stability although the stability of this
+
+ align:start position:0%
+stability although the stability of this
+ 
+
+ align:start position:0%
+stability although the stability of this
+one certainly looks good for many
+
+ align:start position:0%
+one certainly looks good for many
+ 
+
+ align:start position:0%
+one certainly looks good for many
+applications but would also generally
+
+ align:start position:0%
+applications but would also generally
+ 
+
+ align:start position:0%
+applications but would also generally
+slow the system and in fact the
+
+ align:start position:0%
+slow the system and in fact the
+ 
+
+ align:start position:0%
+slow the system and in fact the
+crossover of the major Loop would drop
+
+ align:start position:0%
+crossover of the major Loop would drop
+ 
+
+ align:start position:0%
+crossover of the major Loop would drop
+just about in proportion to that
+
+ align:start position:0%
+just about in proportion to that
+ 
+
+ align:start position:0%
+just about in proportion to that
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+size now let's change the gain of the
+
+ align:start position:0%
+size now let's change the gain of the
+ 
+
+ align:start position:0%
+size now let's change the gain of the
+amplifier so that it's running at a at a
+
+ align:start position:0%
+amplifier so that it's running at a at a
+ 
+
+ align:start position:0%
+amplifier so that it's running at a at a
+closed loop gain of 10 rather than one
+
+ align:start position:0%
+closed loop gain of 10 rather than one
+ 
+
+ align:start position:0%
+closed loop gain of 10 rather than one
+in other words we'll change F by means
+
+ align:start position:0%
+in other words we'll change F by means
+ 
+
+ align:start position:0%
+in other words we'll change F by means
+of this switch to a tenth and when we do
+
+ align:start position:0%
+of this switch to a tenth and when we do
+ 
+
+ align:start position:0%
+of this switch to a tenth and when we do
+that we'll notice that the scope Trace
+
+ align:start position:0%
+that we'll notice that the scope Trace
+ 
+
+ align:start position:0%
+that we'll notice that the scope Trace
+gets considerably larger reflecting the
+
+ align:start position:0%
+gets considerably larger reflecting the
+ 
+
+ align:start position:0%
+gets considerably larger reflecting the
+factor of 10 increase in gain let me
+
+ align:start position:0%
+factor of 10 increase in gain let me
+ 
+
+ align:start position:0%
+factor of 10 increase in gain let me
+change the scale the vertical scale on
+
+ align:start position:0%
+change the scale the vertical scale on
+ 
+
+ align:start position:0%
+change the scale the vertical scale on
+the oscilloscope by again a factor of
+
+ align:start position:0%
+the oscilloscope by again a factor of
+ 
+
+ align:start position:0%
+the oscilloscope by again a factor of
+10 the important thing though for our
+
+ align:start position:0%
+10 the important thing though for our
+ 
+
+ align:start position:0%
+10 the important thing though for our
+purposes is that the step response has
+
+ align:start position:0%
+purposes is that the step response has
+ 
+
+ align:start position:0%
+purposes is that the step response has
+gotten much slower let's change the time
+
+ align:start position:0%
+gotten much slower let's change the time
+ 
+
+ align:start position:0%
+gotten much slower let's change the time
+scale and in fact here we are at one 1
+
+ align:start position:0%
+scale and in fact here we are at one 1
+ 
+
+ align:start position:0%
+scale and in fact here we are at one 1
+microsc per division
+
+ align:start position:0%
+microsc per division
+ 
+
+ align:start position:0%
+microsc per division
+horizontally and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can now measure the 10 to 90%
+
+ align:start position:0%
+and we can now measure the 10 to 90%
+ 
+
+ align:start position:0%
+and we can now measure the 10 to 90%
+rise
+
+ align:start position:0%
+rise
+ 
+
+ align:start position:0%
+rise
+time now between here and here we notice
+
+ align:start position:0%
+time now between here and here we notice
+ 
+
+ align:start position:0%
+time now between here and here we notice
+again it's very close to one and a half
+
+ align:start position:0%
+again it's very close to one and a half
+ 
+
+ align:start position:0%
+again it's very close to one and a half
+divisions uh this time we're at 1
+
+ align:start position:0%
+divisions uh this time we're at 1
+ 
+
+ align:start position:0%
+divisions uh this time we're at 1
+microsc per division so we have a rise
+
+ align:start position:0%
+microsc per division so we have a rise
+ 
+
+ align:start position:0%
+microsc per division so we have a rise
+time with a 20 pea farad capacitor of 1
+
+ align:start position:0%
+time with a 20 pea farad capacitor of 1
+ 
+
+ align:start position:0%
+time with a 20 pea farad capacitor of 1
+a half micros seconds when we have f a
+
+ align:start position:0%
+a half micros seconds when we have f a
+ 
+
+ align:start position:0%
+a half micros seconds when we have f a
+10th or 1 over F equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice that the ratio is 10:1 which is
+
+ align:start position:0%
+notice that the ratio is 10:1 which is
+ 
+
+ align:start position:0%
+notice that the ratio is 10:1 which is
+exactly what we'd expect we found out
+
+ align:start position:0%
+exactly what we'd expect we found out
+ 
+
+ align:start position:0%
+exactly what we'd expect we found out
+that the time constant associated with
+
+ align:start position:0%
+that the time constant associated with
+ 
+
+ align:start position:0%
+that the time constant associated with
+the closed loop gain uh was proportional
+
+ align:start position:0%
+the closed loop gain uh was proportional
+ 
+
+ align:start position:0%
+the closed loop gain uh was proportional
+to the ratio C subc over F here we've
+
+ align:start position:0%
+to the ratio C subc over F here we've
+ 
+
+ align:start position:0%
+to the ratio C subc over F here we've
+kept C subc fixed we've changed F by a
+
+ align:start position:0%
+kept C subc fixed we've changed F by a
+ 
+
+ align:start position:0%
+kept C subc fixed we've changed F by a
+factor of a tenth we'd anticipate that
+
+ align:start position:0%
+factor of a tenth we'd anticipate that
+ 
+
+ align:start position:0%
+factor of a tenth we'd anticipate that
+the closed loop response would slow by
+
+ align:start position:0%
+the closed loop response would slow by
+ 
+
+ align:start position:0%
+the closed loop response would slow by
+just about that factor of 10 and in fact
+
+ align:start position:0%
+just about that factor of 10 and in fact
+ 
+
+ align:start position:0%
+just about that factor of 10 and in fact
+it does we also notice a little change
+
+ align:start position:0%
+it does we also notice a little change
+ 
+
+ align:start position:0%
+it does we also notice a little change
+in the character of the response uh the
+
+ align:start position:0%
+in the character of the response uh the
+ 
+
+ align:start position:0%
+in the character of the response uh the
+original response this one had just a
+
+ align:start position:0%
+original response this one had just a
+ 
+
+ align:start position:0%
+original response this one had just a
+little bit of
+
+ align:start position:0%
+little bit of
+ 
+
+ align:start position:0%
+little bit of
+overshoot once we uh are observing this
+
+ align:start position:0%
+overshoot once we uh are observing this
+ 
+
+ align:start position:0%
+overshoot once we uh are observing this
+response we noticed it looked very very
+
+ align:start position:0%
+response we noticed it looked very very
+ 
+
+ align:start position:0%
+response we noticed it looked very very
+much first
+
+ align:start position:0%
+much first
+ 
+
+ align:start position:0%
+much first
+order however we have lost the factor of
+
+ align:start position:0%
+order however we have lost the factor of
+ 
+
+ align:start position:0%
+order however we have lost the factor of
+10 in band in in response time or in
+
+ align:start position:0%
+10 in band in in response time or in
+ 
+
+ align:start position:0%
+10 in band in in response time or in
+bandwidth and we can buy that back by
+
+ align:start position:0%
+bandwidth and we can buy that back by
+ 
+
+ align:start position:0%
+bandwidth and we can buy that back by
+lowering the size of the capacitor by
+
+ align:start position:0%
+lowering the size of the capacitor by
+ 
+
+ align:start position:0%
+lowering the size of the capacitor by
+about a factor of 10 there's a a little
+
+ align:start position:0%
+about a factor of 10 there's a a little
+ 
+
+ align:start position:0%
+about a factor of 10 there's a a little
+bit of departure from the ideal case
+
+ align:start position:0%
+bit of departure from the ideal case
+ 
+
+ align:start position:0%
+bit of departure from the ideal case
+here there are a couple of uh effects in
+
+ align:start position:0%
+here there are a couple of uh effects in
+ 
+
+ align:start position:0%
+here there are a couple of uh effects in
+the amplifier that actually Force us to
+
+ align:start position:0%
+the amplifier that actually Force us to
+ 
+
+ align:start position:0%
+the amplifier that actually Force us to
+use a a capacitor that's somewhat larger
+
+ align:start position:0%
+use a a capacitor that's somewhat larger
+ 
+
+ align:start position:0%
+use a a capacitor that's somewhat larger
+than than on10th of of the previous
+
+ align:start position:0%
+than than on10th of of the previous
+ 
+
+ align:start position:0%
+than than on10th of of the previous
+value but we've made up a capacitor in
+
+ align:start position:0%
+value but we've made up a capacitor in
+ 
+
+ align:start position:0%
+value but we've made up a capacitor in
+that range uh made up a capacitor of
+
+ align:start position:0%
+that range uh made up a capacitor of
+ 
+
+ align:start position:0%
+that range uh made up a capacitor of
+about three Peak farads or
+
+ align:start position:0%
+about three Peak farads or
+ 
+
+ align:start position:0%
+about three Peak farads or
+thereabouts and we'll replace the
+
+ align:start position:0%
+thereabouts and we'll replace the
+ 
+
+ align:start position:0%
+thereabouts and we'll replace the
+compensating
+
+ align:start position:0%
+compensating
+ 
+
+ align:start position:0%
+compensating
+element with this lower value
+
+ align:start position:0%
+element with this lower value
+ 
+
+ align:start position:0%
+element with this lower value
+compensating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor and we find find out that we
+
+ align:start position:0%
+capacitor and we find find out that we
+ 
+
+ align:start position:0%
+capacitor and we find find out that we
+get a response that's very similar to
+
+ align:start position:0%
+get a response that's very similar to
+ 
+
+ align:start position:0%
+get a response that's very similar to
+the original one here we have just a a
+
+ align:start position:0%
+the original one here we have just a a
+ 
+
+ align:start position:0%
+the original one here we have just a a
+little bit of overshoot so we're back to
+
+ align:start position:0%
+little bit of overshoot so we're back to
+ 
+
+ align:start position:0%
+little bit of overshoot so we're back to
+corresponding to stability actually
+
+ align:start position:0%
+corresponding to stability actually
+ 
+
+ align:start position:0%
+corresponding to stability actually
+probably a little bit better than the
+
+ align:start position:0%
+probably a little bit better than the
+ 
+
+ align:start position:0%
+probably a little bit better than the
+original one this this capacitor might
+
+ align:start position:0%
+original one this this capacitor might
+ 
+
+ align:start position:0%
+original one this this capacitor might
+be a little larger uh than the one that
+
+ align:start position:0%
+be a little larger uh than the one that
+ 
+
+ align:start position:0%
+be a little larger uh than the one that
+would give us exactly the same amount of
+
+ align:start position:0%
+would give us exactly the same amount of
+ 
+
+ align:start position:0%
+would give us exactly the same amount of
+of overshoot as we got in the first
+
+ align:start position:0%
+of overshoot as we got in the first
+ 
+
+ align:start position:0%
+of overshoot as we got in the first
+experiment we can measure the 10 to 90%
+
+ align:start position:0%
+experiment we can measure the 10 to 90%
+ 
+
+ align:start position:0%
+experiment we can measure the 10 to 90%
+rise time in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case uh and and let's see let me go back
+
+ align:start position:0%
+case uh and and let's see let me go back
+ 
+
+ align:start position:0%
+case uh and and let's see let me go back
+to 100 nond per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+division uh here's 10% 90% Let's see we
+
+ align:start position:0%
+division uh here's 10% 90% Let's see we
+ 
+
+ align:start position:0%
+division uh here's 10% 90% Let's see we
+have one two about two and a half
+
+ align:start position:0%
+have one two about two and a half
+ 
+
+ align:start position:0%
+have one two about two and a half
+divisions and
+
+ align:start position:0%
+divisions and
+ 
+
+ align:start position:0%
+divisions and
+so we're able to by choosing an
+
+ align:start position:0%
+so we're able to by choosing an
+ 
+
+ align:start position:0%
+so we're able to by choosing an
+appropriate capacitor reduce the rise
+
+ align:start position:0%
+appropriate capacitor reduce the rise
+ 
+
+ align:start position:0%
+appropriate capacitor reduce the rise
+time not quite to its original value but
+
+ align:start position:0%
+time not quite to its original value but
+ 
+
+ align:start position:0%
+time not quite to its original value but
+we get about
+
+ align:start position:0%
+we get about
+ 
+
+ align:start position:0%
+we get about
+250 Nan so rather than losing a factor
+
+ align:start position:0%
+250 Nan so rather than losing a factor
+ 
+
+ align:start position:0%
+250 Nan so rather than losing a factor
+of 10:1 in bandwidth or rise time we've
+
+ align:start position:0%
+of 10:1 in bandwidth or rise time we've
+ 
+
+ align:start position:0%
+of 10:1 in bandwidth or rise time we've
+lost a factor of of maybe
+
+ align:start position:0%
+lost a factor of of maybe
+ 
+
+ align:start position:0%
+lost a factor of of maybe
+6:1 well let's
+
+ align:start position:0%
+6:1 well let's
+ 
+
+ align:start position:0%
+6:1 well let's
+continue let's first of all go back to
+
+ align:start position:0%
+continue let's first of all go back to
+ 
+
+ align:start position:0%
+continue let's first of all go back to
+the original 20 paa
+
+ align:start position:0%
+the original 20 paa
+ 
+
+ align:start position:0%
+the original 20 paa
+farad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor and now up the gain by another
+
+ align:start position:0%
+capacitor and now up the gain by another
+ 
+
+ align:start position:0%
+capacitor and now up the gain by another
+factor of 10 if I throw this switch down
+
+ align:start position:0%
+factor of 10 if I throw this switch down
+ 
+
+ align:start position:0%
+factor of 10 if I throw this switch down
+we get a a closed loop gain of 100 we
+
+ align:start position:0%
+we get a a closed loop gain of 100 we
+ 
+
+ align:start position:0%
+we get a a closed loop gain of 100 we
+make f
+
+ align:start position:0%
+make f
+ 
+
+ align:start position:0%
+make f
+1/100th let me do that and again I have
+
+ align:start position:0%
+1/100th let me do that and again I have
+ 
+
+ align:start position:0%
+1/100th let me do that and again I have
+to change the vertical scale on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscilloscope we find out now the the
+
+ align:start position:0%
+oscilloscope we find out now the the
+ 
+
+ align:start position:0%
+oscilloscope we find out now the the
+bandwidth is so deteriorated with the
+
+ align:start position:0%
+bandwidth is so deteriorated with the
+ 
+
+ align:start position:0%
+bandwidth is so deteriorated with the
+original value for the capacitor that we
+
+ align:start position:0%
+original value for the capacitor that we
+ 
+
+ align:start position:0%
+original value for the capacitor that we
+have to slow the signal generator so let
+
+ align:start position:0%
+have to slow the signal generator so let
+ 
+
+ align:start position:0%
+have to slow the signal generator so let
+me do that so that we reach final
+
+ align:start position:0%
+me do that so that we reach final
+ 
+
+ align:start position:0%
+me do that so that we reach final
+value all right and here is the step
+
+ align:start position:0%
+value all right and here is the step
+ 
+
+ align:start position:0%
+value all right and here is the step
+response that corresponds to a 20 peaka
+
+ align:start position:0%
+response that corresponds to a 20 peaka
+ 
+
+ align:start position:0%
+response that corresponds to a 20 peaka
+farad capacitor and a closed loop gain
+
+ align:start position:0%
+farad capacitor and a closed loop gain
+ 
+
+ align:start position:0%
+farad capacitor and a closed loop gain
+of 100
+
+ align:start position:0%
+of 100
+ 
+
+ align:start position:0%
+of 100
+uh the amplitude is down just a little
+
+ align:start position:0%
+uh the amplitude is down just a little
+ 
+
+ align:start position:0%
+uh the amplitude is down just a little
+bit let me increase that so that we can
+
+ align:start position:0%
+bit let me increase that so that we can
+ 
+
+ align:start position:0%
+bit let me increase that so that we can
+easily measure the 10 to 90% rise
+
+ align:start position:0%
+easily measure the 10 to 90% rise
+ 
+
+ align:start position:0%
+easily measure the 10 to 90% rise
+time we notice the response is very much
+
+ align:start position:0%
+time we notice the response is very much
+ 
+
+ align:start position:0%
+time we notice the response is very much
+first order uh here we're at five
+
+ align:start position:0%
+first order uh here we're at five
+ 
+
+ align:start position:0%
+first order uh here we're at five
+microsc per division uh one two just a
+
+ align:start position:0%
+microsc per division uh one two just a
+ 
+
+ align:start position:0%
+microsc per division uh one two just a
+little bit more than three divisions so
+
+ align:start position:0%
+little bit more than three divisions so
+ 
+
+ align:start position:0%
+little bit more than three divisions so
+we have a 10 to 90% rise time of just
+
+ align:start position:0%
+we have a 10 to 90% rise time of just
+ 
+
+ align:start position:0%
+we have a 10 to 90% rise time of just
+about 15 micros seconds again we're
+
+ align:start position:0%
+about 15 micros seconds again we're
+ 
+
+ align:start position:0%
+about 15 micros seconds again we're
+since we're
+
+ align:start position:0%
+since we're
+ 
+
+ align:start position:0%
+since we're
+comparing in this column uh the response
+
+ align:start position:0%
+comparing in this column uh the response
+ 
+
+ align:start position:0%
+comparing in this column uh the response
+that we get with an equal value for C
+
+ align:start position:0%
+that we get with an equal value for C
+ 
+
+ align:start position:0%
+that we get with an equal value for C
+subc but progressively smaller values of
+
+ align:start position:0%
+subc but progressively smaller values of
+ 
+
+ align:start position:0%
+subc but progressively smaller values of
+f we'd anticipate that this value would
+
+ align:start position:0%
+f we'd anticipate that this value would
+ 
+
+ align:start position:0%
+f we'd anticipate that this value would
+simply go as 1 over F and we see that
+
+ align:start position:0%
+simply go as 1 over F and we see that
+ 
+
+ align:start position:0%
+simply go as 1 over F and we see that
+that's that's what
+
+ align:start position:0%
+that's that's what
+ 
+
+ align:start position:0%
+that's that's what
+happens again we can get close to our
+
+ align:start position:0%
+happens again we can get close to our
+ 
+
+ align:start position:0%
+happens again we can get close to our
+original speed of response by removing
+
+ align:start position:0%
+original speed of response by removing
+ 
+
+ align:start position:0%
+original speed of response by removing
+the 20 pea farad
+
+ align:start position:0%
+the 20 pea farad
+ 
+
+ align:start position:0%
+the 20 pea farad
+capacitor and replacing it with one
+
+ align:start position:0%
+capacitor and replacing it with one
+ 
+
+ align:start position:0%
+capacitor and replacing it with one
+that has been chosen to say it's not
+
+ align:start position:0%
+that has been chosen to say it's not
+ 
+
+ align:start position:0%
+that has been chosen to say it's not
+quite 1/ 100th of the original value but
+
+ align:start position:0%
+quite 1/ 100th of the original value but
+ 
+
+ align:start position:0%
+quite 1/ 100th of the original value but
+one that's been
+
+ align:start position:0%
+one that's been
+ 
+
+ align:start position:0%
+one that's been
+chosen to yield very close to the
+
+ align:start position:0%
+chosen to yield very close to the
+ 
+
+ align:start position:0%
+chosen to yield very close to the
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+Dynamics and we get that sort of a
+
+ align:start position:0%
+Dynamics and we get that sort of a
+ 
+
+ align:start position:0%
+Dynamics and we get that sort of a
+response much faster notice very nearly
+
+ align:start position:0%
+response much faster notice very nearly
+ 
+
+ align:start position:0%
+response much faster notice very nearly
+vertical rise on this kind of a time
+
+ align:start position:0%
+vertical rise on this kind of a time
+ 
+
+ align:start position:0%
+vertical rise on this kind of a time
+scale uh we can now speed up the
+
+ align:start position:0%
+scale uh we can now speed up the
+ 
+
+ align:start position:0%
+scale uh we can now speed up the
+generator once
+
+ align:start position:0%
+generator once
+ 
+
+ align:start position:0%
+generator once
+again look at the response in
+
+ align:start position:0%
+again look at the response in
+ 
+
+ align:start position:0%
+again look at the response in
+detail and again our 10 to 90 % rise
+
+ align:start position:0%
+detail and again our 10 to 90 % rise
+ 
+
+ align:start position:0%
+detail and again our 10 to 90 % rise
+time we're now back to a time scale of
+
+ align:start position:0%
+time we're now back to a time scale of
+ 
+
+ align:start position:0%
+time we're now back to a time scale of
+200 nond per division uh the 10 to 90%
+
+ align:start position:0%
+200 nond per division uh the 10 to 90%
+ 
+
+ align:start position:0%
+200 nond per division uh the 10 to 90%
+rise time is back to about 500
+
+ align:start position:0%
+rise time is back to about 500
+ 
+
+ align:start position:0%
+rise time is back to about 500
+NCS one two two and a half divisions uh
+
+ align:start position:0%
+NCS one two two and a half divisions uh
+ 
+
+ align:start position:0%
+NCS one two two and a half divisions uh
+at 200 nond per
+
+ align:start position:0%
+at 200 nond per
+ 
+
+ align:start position:0%
+at 200 nond per
+division so again we haven't quite
+
+ align:start position:0%
+division so again we haven't quite
+ 
+
+ align:start position:0%
+division so again we haven't quite
+gotten back to the original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case but we're roughly a factor of 30
+
+ align:start position:0%
+case but we're roughly a factor of 30
+ 
+
+ align:start position:0%
+case but we're roughly a factor of 30
+faster than uh the case that that
+
+ align:start position:0%
+faster than uh the case that that
+ 
+
+ align:start position:0%
+faster than uh the case that that
+resulted when we use the capacitor that
+
+ align:start position:0%
+resulted when we use the capacitor that
+ 
+
+ align:start position:0%
+resulted when we use the capacitor that
+was selected for Unity gain stability or
+
+ align:start position:0%
+was selected for Unity gain stability or
+ 
+
+ align:start position:0%
+was selected for Unity gain stability or
+for Unity feedback so we've made a very
+
+ align:start position:0%
+for Unity feedback so we've made a very
+ 
+
+ align:start position:0%
+for Unity feedback so we've made a very
+very dramatic Improvement in the
+
+ align:start position:0%
+very dramatic Improvement in the
+ 
+
+ align:start position:0%
+very dramatic Improvement in the
+bandwidth of the amplifier by simply
+
+ align:start position:0%
+bandwidth of the amplifier by simply
+ 
+
+ align:start position:0%
+bandwidth of the amplifier by simply
+choosing the compensating capacitor as a
+
+ align:start position:0%
+choosing the compensating capacitor as a
+ 
+
+ align:start position:0%
+choosing the compensating capacitor as a
+function of the closed loop
+
+ align:start position:0%
+function of the closed loop
+ 
+
+ align:start position:0%
+function of the closed loop
+gain finally let me go back to the
+
+ align:start position:0%
+gain finally let me go back to the
+ 
+
+ align:start position:0%
+gain finally let me go back to the
+original value the 20 paaf farad
+
+ align:start position:0%
+original value the 20 paaf farad
+ 
+
+ align:start position:0%
+original value the 20 paaf farad
+compensating capacitor one last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and now let's increase the closed
+
+ align:start position:0%
+time and now let's increase the closed
+ 
+
+ align:start position:0%
+time and now let's increase the closed
+loop gain to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th000 uh we clearly are going very very
+
+ align:start position:0%
+th000 uh we clearly are going very very
+ 
+
+ align:start position:0%
+th000 uh we clearly are going very very
+slowly let's slow down the generator uh
+
+ align:start position:0%
+slowly let's slow down the generator uh
+ 
+
+ align:start position:0%
+slowly let's slow down the generator uh
+things saturate we've got to put in a
+
+ align:start position:0%
+things saturate we've got to put in a
+ 
+
+ align:start position:0%
+things saturate we've got to put in a
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+signal uh we still haven't reached final
+
+ align:start position:0%
+signal uh we still haven't reached final
+ 
+
+ align:start position:0%
+signal uh we still haven't reached final
+value all
+
+ align:start position:0%
+value all
+ 
+
+ align:start position:0%
+value all
+right now we finally have things
+
+ align:start position:0%
+right now we finally have things
+ 
+
+ align:start position:0%
+right now we finally have things
+adjusted so that we can see the rise
+
+ align:start position:0%
+adjusted so that we can see the rise
+ 
+
+ align:start position:0%
+adjusted so that we can see the rise
+time with the 20 peaka farad capacitor
+
+ align:start position:0%
+time with the 20 peaka farad capacitor
+ 
+
+ align:start position:0%
+time with the 20 peaka farad capacitor
+at a closed loop gain of a
+
+ align:start position:0%
+at a closed loop gain of a
+ 
+
+ align:start position:0%
+at a closed loop gain of a
+th000 and if we make the rise time
+
+ align:start position:0%
+th000 and if we make the rise time
+ 
+
+ align:start position:0%
+th000 and if we make the rise time
+measurement this time let's see we're at
+
+ align:start position:0%
+measurement this time let's see we're at
+ 
+
+ align:start position:0%
+measurement this time let's see we're at
+50 micros seconds per division uh so we
+
+ align:start position:0%
+50 micros seconds per division uh so we
+ 
+
+ align:start position:0%
+50 micros seconds per division uh so we
+have one two again just about three
+
+ align:start position:0%
+have one two again just about three
+ 
+
+ align:start position:0%
+have one two again just about three
+divisions for the rise time uh so we
+
+ align:start position:0%
+divisions for the rise time uh so we
+ 
+
+ align:start position:0%
+divisions for the rise time uh so we
+have a rise time of about 150 micros
+
+ align:start position:0%
+have a rise time of about 150 micros
+ 
+
+ align:start position:0%
+have a rise time of about 150 micros
+seconds our amplifier as we anticipated
+
+ align:start position:0%
+seconds our amplifier as we anticipated
+ 
+
+ align:start position:0%
+seconds our amplifier as we anticipated
+has gotten a
+
+ align:start position:0%
+has gotten a
+ 
+
+ align:start position:0%
+has gotten a
+factor of a thousand slower than the
+
+ align:start position:0%
+factor of a thousand slower than the
+ 
+
+ align:start position:0%
+factor of a thousand slower than the
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+case if we interpret this in in
+
+ align:start position:0%
+case if we interpret this in in
+ 
+
+ align:start position:0%
+case if we interpret this in in
+bandwidth in terms of bandwidth rather
+
+ align:start position:0%
+bandwidth in terms of bandwidth rather
+ 
+
+ align:start position:0%
+bandwidth in terms of bandwidth rather
+than rise time here we had a bandwidth
+
+ align:start position:0%
+than rise time here we had a bandwidth
+ 
+
+ align:start position:0%
+than rise time here we had a bandwidth
+of very nearly 2 MHz or actually a
+
+ align:start position:0%
+of very nearly 2 MHz or actually a
+ 
+
+ align:start position:0%
+of very nearly 2 MHz or actually a
+little bit more remember the product of
+
+ align:start position:0%
+little bit more remember the product of
+ 
+
+ align:start position:0%
+little bit more remember the product of
+Rise time times bandwidth in hertz is
+
+ align:start position:0%
+Rise time times bandwidth in hertz is
+ 
+
+ align:start position:0%
+Rise time times bandwidth in hertz is
+about. 35 so this corresponds to
+
+ align:start position:0%
+about. 35 so this corresponds to
+ 
+
+ align:start position:0%
+about. 35 so this corresponds to
+something like 2.3 megahertz of closed
+
+ align:start position:0%
+something like 2.3 megahertz of closed
+ 
+
+ align:start position:0%
+something like 2.3 megahertz of closed
+loop
+
+ align:start position:0%
+loop
+ 
+
+ align:start position:0%
+loop
+bandwidth this corresponds to a factor
+
+ align:start position:0%
+bandwidth this corresponds to a factor
+ 
+
+ align:start position:0%
+bandwidth this corresponds to a factor
+of a th000 smaller than that
+
+ align:start position:0%
+of a th000 smaller than that
+ 
+
+ align:start position:0%
+of a th000 smaller than that
+approximately 2 khz so here at a closed
+
+ align:start position:0%
+approximately 2 khz so here at a closed
+ 
+
+ align:start position:0%
+approximately 2 khz so here at a closed
+loop gain of a th000 we're not even able
+
+ align:start position:0%
+loop gain of a th000 we're not even able
+ 
+
+ align:start position:0%
+loop gain of a th000 we're not even able
+to accomplish
+
+ align:start position:0%
+to accomplish
+ 
+
+ align:start position:0%
+to accomplish
+to to get significantly through the
+
+ align:start position:0%
+to to get significantly through the
+ 
+
+ align:start position:0%
+to to get significantly through the
+audio band The bandwidth of the
+
+ align:start position:0%
+audio band The bandwidth of the
+ 
+
+ align:start position:0%
+audio band The bandwidth of the
+amplifier is about 2 khz if we had used
+
+ align:start position:0%
+amplifier is about 2 khz if we had used
+ 
+
+ align:start position:0%
+amplifier is about 2 khz if we had used
+a 741 which uses fixed compensation for
+
+ align:start position:0%
+a 741 which uses fixed compensation for
+ 
+
+ align:start position:0%
+a 741 which uses fixed compensation for
+all of these experiments uh its numbers
+
+ align:start position:0%
+all of these experiments uh its numbers
+ 
+
+ align:start position:0%
+all of these experiments uh its numbers
+are such that we'd actually have about a
+
+ align:start position:0%
+are such that we'd actually have about a
+ 
+
+ align:start position:0%
+are such that we'd actually have about a
+kilohertz of bandwidth under these
+
+ align:start position:0%
+kilohertz of bandwidth under these
+ 
+
+ align:start position:0%
+kilohertz of bandwidth under these
+conditions well let's see what we can do
+
+ align:start position:0%
+conditions well let's see what we can do
+ 
+
+ align:start position:0%
+conditions well let's see what we can do
+if we compensate the amplifier properly
+
+ align:start position:0%
+if we compensate the amplifier properly
+ 
+
+ align:start position:0%
+if we compensate the amplifier properly
+instead of using the fixed
+
+ align:start position:0%
+instead of using the fixed
+ 
+
+ align:start position:0%
+instead of using the fixed
+compensation uh let me remove the
+
+ align:start position:0%
+compensation uh let me remove the
+ 
+
+ align:start position:0%
+compensation uh let me remove the
+compensation entirely when we do that
+
+ align:start position:0%
+compensation entirely when we do that
+ 
+
+ align:start position:0%
+compensation entirely when we do that
+our approximation begins to break break
+
+ align:start position:0%
+our approximation begins to break break
+ 
+
+ align:start position:0%
+our approximation begins to break break
+down a little bit but we find out that
+
+ align:start position:0%
+down a little bit but we find out that
+ 
+
+ align:start position:0%
+down a little bit but we find out that
+even we can now speed up things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh even with this large a value of f in
+
+ align:start position:0%
+uh even with this large a value of f in
+ 
+
+ align:start position:0%
+uh even with this large a value of f in
+the feedback path or the small a value
+
+ align:start position:0%
+the feedback path or the small a value
+ 
+
+ align:start position:0%
+the feedback path or the small a value
+of F this much attenuation in the
+
+ align:start position:0%
+of F this much attenuation in the
+ 
+
+ align:start position:0%
+of F this much attenuation in the
+feedback path the amplifier is actually
+
+ align:start position:0%
+feedback path the amplifier is actually
+ 
+
+ align:start position:0%
+feedback path the amplifier is actually
+still underdamped we notice considerable
+
+ align:start position:0%
+still underdamped we notice considerable
+ 
+
+ align:start position:0%
+still underdamped we notice considerable
+overshoot to the step response with no
+
+ align:start position:0%
+overshoot to the step response with no
+ 
+
+ align:start position:0%
+overshoot to the step response with no
+comp compens ation we we see there might
+
+ align:start position:0%
+comp compens ation we we see there might
+ 
+
+ align:start position:0%
+comp compens ation we we see there might
+be something like 30% overshoot or 40%
+
+ align:start position:0%
+be something like 30% overshoot or 40%
+ 
+
+ align:start position:0%
+be something like 30% overshoot or 40%
+overshoot uh reasonably high frequency
+
+ align:start position:0%
+overshoot uh reasonably high frequency
+ 
+
+ align:start position:0%
+overshoot uh reasonably high frequency
+ring ringing at at about 300 kohtz we
+
+ align:start position:0%
+ring ringing at at about 300 kohtz we
+ 
+
+ align:start position:0%
+ring ringing at at about 300 kohtz we
+have one microsc per division
+
+ align:start position:0%
+have one microsc per division
+ 
+
+ align:start position:0%
+have one microsc per division
+horizontally now so let's see if we can
+
+ align:start position:0%
+horizontally now so let's see if we can
+ 
+
+ align:start position:0%
+horizontally now so let's see if we can
+compensate that if we uh really believed
+
+ align:start position:0%
+compensate that if we uh really believed
+ 
+
+ align:start position:0%
+compensate that if we uh really believed
+our numbers we'd conclude that we needed
+
+ align:start position:0%
+our numbers we'd conclude that we needed
+ 
+
+ align:start position:0%
+our numbers we'd conclude that we needed
+20 paa farads divided by a th000 and
+
+ align:start position:0%
+20 paa farads divided by a th000 and
+ 
+
+ align:start position:0%
+20 paa farads divided by a th000 and
+that seems somewhat unrealistic actually
+
+ align:start position:0%
+that seems somewhat unrealistic actually
+ 
+
+ align:start position:0%
+that seems somewhat unrealistic actually
+we need a capacitor a little bit larger
+
+ align:start position:0%
+we need a capacitor a little bit larger
+ 
+
+ align:start position:0%
+we need a capacitor a little bit larger
+than that but let's get our capacitor
+
+ align:start position:0%
+than that but let's get our capacitor
+ 
+
+ align:start position:0%
+than that but let's get our capacitor
+this way I simply have two pieces of
+
+ align:start position:0%
+this way I simply have two pieces of
+ 
+
+ align:start position:0%
+this way I simply have two pieces of
+wire that I'll put into the compensating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Terminals and we now have a very
+
+ align:start position:0%
+Terminals and we now have a very
+ 
+
+ align:start position:0%
+Terminals and we now have a very
+convenient method for adjusting
+
+ align:start position:0%
+convenient method for adjusting
+ 
+
+ align:start position:0%
+convenient method for adjusting
+capacitance at very small values uh if
+
+ align:start position:0%
+capacitance at very small values uh if
+ 
+
+ align:start position:0%
+capacitance at very small values uh if
+we get these
+
+ align:start position:0%
+we get these
+ 
+
+ align:start position:0%
+we get these
+apart we have the undercompensated case
+
+ align:start position:0%
+apart we have the undercompensated case
+ 
+
+ align:start position:0%
+apart we have the undercompensated case
+with a reasonable amount of overshoot as
+
+ align:start position:0%
+with a reasonable amount of overshoot as
+ 
+
+ align:start position:0%
+with a reasonable amount of overshoot as
+we move the two wires
+
+ align:start position:0%
+we move the two wires
+ 
+
+ align:start position:0%
+we move the two wires
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+we're able to get progressively better
+
+ align:start position:0%
+we're able to get progressively better
+ 
+
+ align:start position:0%
+we're able to get progressively better
+damping here's a critically damp case no
+
+ align:start position:0%
+damping here's a critically damp case no
+ 
+
+ align:start position:0%
+damping here's a critically damp case no
+overshoot the closed loop holes are
+
+ align:start position:0%
+overshoot the closed loop holes are
+ 
+
+ align:start position:0%
+overshoot the closed loop holes are
+appear to all be on the real axis and
+
+ align:start position:0%
+appear to all be on the real axis and
+ 
+
+ align:start position:0%
+appear to all be on the real axis and
+let's see if we can get back to pretty
+
+ align:start position:0%
+let's see if we can get back to pretty
+ 
+
+ align:start position:0%
+let's see if we can get back to pretty
+close to the original
+
+ align:start position:0%
+close to the original
+ 
+
+ align:start position:0%
+close to the original
+situation something like that so in this
+
+ align:start position:0%
+situation something like that so in this
+ 
+
+ align:start position:0%
+situation something like that so in this
+way by adjusting the capacitance we're
+
+ align:start position:0%
+way by adjusting the capacitance we're
+ 
+
+ align:start position:0%
+way by adjusting the capacitance we're
+able to very well control the Dynamics
+
+ align:start position:0%
+able to very well control the Dynamics
+ 
+
+ align:start position:0%
+able to very well control the Dynamics
+the transient response also we get back
+
+ align:start position:0%
+the transient response also we get back
+ 
+
+ align:start position:0%
+the transient response also we get back
+to a very
+
+ align:start position:0%
+to a very
+ 
+
+ align:start position:0%
+to a very
+respectable value for Rise time here
+
+ align:start position:0%
+respectable value for Rise time here
+ 
+
+ align:start position:0%
+respectable value for Rise time here
+we're at 500 NCS per
+
+ align:start position:0%
+we're at 500 NCS per
+ 
+
+ align:start position:0%
+we're at 500 NCS per
+division uh if we measure the 10 to 90%
+
+ align:start position:0%
+division uh if we measure the 10 to 90%
+ 
+
+ align:start position:0%
+division uh if we measure the 10 to 90%
+rise time we find out it's just about
+
+ align:start position:0%
+rise time we find out it's just about
+ 
+
+ align:start position:0%
+rise time we find out it's just about
+two divisions on that time scale from
+
+ align:start position:0%
+two divisions on that time scale from
+ 
+
+ align:start position:0%
+two divisions on that time scale from
+here to
+
+ align:start position:0%
+here to
+ 
+
+ align:start position:0%
+here to
+here so uh we get about a one micr
+
+ align:start position:0%
+here so uh we get about a one micr
+ 
+
+ align:start position:0%
+here so uh we get about a one micr
+second Rise time roughly a factor of 150
+
+ align:start position:0%
+second Rise time roughly a factor of 150
+ 
+
+ align:start position:0%
+second Rise time roughly a factor of 150
+to one Improvement in rise time and
+
+ align:start position:0%
+to one Improvement in rise time and
+ 
+
+ align:start position:0%
+to one Improvement in rise time and
+correspondingly bandwidth when we
+
+ align:start position:0%
+correspondingly bandwidth when we
+ 
+
+ align:start position:0%
+correspondingly bandwidth when we
+compensate with this small value of
+
+ align:start position:0%
+compensate with this small value of
+ 
+
+ align:start position:0%
+compensate with this small value of
+capacitor we still have something like a
+
+ align:start position:0%
+capacitor we still have something like a
+ 
+
+ align:start position:0%
+capacitor we still have something like a
+350 khz closed loop bandwidth at a gain
+
+ align:start position:0%
+350 khz closed loop bandwidth at a gain
+ 
+
+ align:start position:0%
+350 khz closed loop bandwidth at a gain
+of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th000 we might question the practicality
+
+ align:start position:0%
+th000 we might question the practicality
+ 
+
+ align:start position:0%
+th000 we might question the practicality
+of all of this when in fact in order to
+
+ align:start position:0%
+of all of this when in fact in order to
+ 
+
+ align:start position:0%
+of all of this when in fact in order to
+compensate we have to do something like
+
+ align:start position:0%
+compensate we have to do something like
+ 
+
+ align:start position:0%
+compensate we have to do something like
+this and wave two two components two
+
+ align:start position:0%
+this and wave two two components two
+ 
+
+ align:start position:0%
+this and wave two two components two
+wands at each other but in reality we
+
+ align:start position:0%
+wands at each other but in reality we
+ 
+
+ align:start position:0%
+wands at each other but in reality we
+find out we can do that fairly well if
+
+ align:start position:0%
+find out we can do that fairly well if
+ 
+
+ align:start position:0%
+find out we can do that fairly well if
+we back off just a little bit from sort
+
+ align:start position:0%
+we back off just a little bit from sort
+ 
+
+ align:start position:0%
+we back off just a little bit from sort
+of the optimum situation and and
+
+ align:start position:0%
+of the optimum situation and and
+ 
+
+ align:start position:0%
+of the optimum situation and and
+conclude that we're going to
+
+ align:start position:0%
+conclude that we're going to
+ 
+
+ align:start position:0%
+conclude that we're going to
+overcompensate a little bit maybe only
+
+ align:start position:0%
+overcompensate a little bit maybe only
+ 
+
+ align:start position:0%
+overcompensate a little bit maybe only
+get 100 or or 150 khz of bandwidth
+
+ align:start position:0%
+get 100 or or 150 khz of bandwidth
+ 
+
+ align:start position:0%
+get 100 or or 150 khz of bandwidth
+instead of trying to stretch things out
+
+ align:start position:0%
+instead of trying to stretch things out
+ 
+
+ align:start position:0%
+instead of trying to stretch things out
+and get 350 khz we can do that quite
+
+ align:start position:0%
+and get 350 khz we can do that quite
+ 
+
+ align:start position:0%
+and get 350 khz we can do that quite
+repeatedly furthermore there are
+
+ align:start position:0%
+repeatedly furthermore there are
+ 
+
+ align:start position:0%
+repeatedly furthermore there are
+techniques which certainly have been
+
+ align:start position:0%
+techniques which certainly have been
+ 
+
+ align:start position:0%
+techniques which certainly have been
+used uh for example you can lay out a
+
+ align:start position:0%
+used uh for example you can lay out a
+ 
+
+ align:start position:0%
+used uh for example you can lay out a
+printed circuit board and and peel back
+
+ align:start position:0%
+printed circuit board and and peel back
+ 
+
+ align:start position:0%
+printed circuit board and and peel back
+foil or something to make the adjustment
+
+ align:start position:0%
+foil or something to make the adjustment
+ 
+
+ align:start position:0%
+foil or something to make the adjustment
+to tailor particular circuit values to a
+
+ align:start position:0%
+to tailor particular circuit values to a
+ 
+
+ align:start position:0%
+to tailor particular circuit values to a
+specific operational amplifier but it's
+
+ align:start position:0%
+specific operational amplifier but it's
+ 
+
+ align:start position:0%
+specific operational amplifier but it's
+say if you're a little bit concerned
+
+ align:start position:0%
+say if you're a little bit concerned
+ 
+
+ align:start position:0%
+say if you're a little bit concerned
+about that why you can certainly get
+
+ align:start position:0%
+about that why you can certainly get
+ 
+
+ align:start position:0%
+about that why you can certainly get
+most of the benefits be a little bit
+
+ align:start position:0%
+most of the benefits be a little bit
+ 
+
+ align:start position:0%
+most of the benefits be a little bit
+more conservative by by simply
+
+ align:start position:0%
+more conservative by by simply
+ 
+
+ align:start position:0%
+more conservative by by simply
+overcompensating a little bit and ending
+
+ align:start position:0%
+overcompensating a little bit and ending
+ 
+
+ align:start position:0%
+overcompensating a little bit and ending
+up with still far far better Dynamics
+
+ align:start position:0%
+up with still far far better Dynamics
+ 
+
+ align:start position:0%
+up with still far far better Dynamics
+than those that result if you use a
+
+ align:start position:0%
+than those that result if you use a
+ 
+
+ align:start position:0%
+than those that result if you use a
+fixed compensating
+
+ align:start position:0%
+fixed compensating
+ 
+
+ align:start position:0%
+fixed compensating
+element well single pole compensation is
+
+ align:start position:0%
+element well single pole compensation is
+ 
+
+ align:start position:0%
+element well single pole compensation is
+a very good general purpose kind of
+
+ align:start position:0%
+a very good general purpose kind of
+ 
+
+ align:start position:0%
+a very good general purpose kind of
+compensation uh it's the one that's
+
+ align:start position:0%
+compensation uh it's the one that's
+ 
+
+ align:start position:0%
+compensation uh it's the one that's
+normally used when when fixed comp
+
+ align:start position:0%
+normally used when when fixed comp
+ 
+
+ align:start position:0%
+normally used when when fixed comp
+compensation amplifiers are sold it say
+
+ align:start position:0%
+compensation amplifiers are sold it say
+ 
+
+ align:start position:0%
+compensation amplifiers are sold it say
+it it can be certainly designed so that
+
+ align:start position:0%
+it it can be certainly designed so that
+ 
+
+ align:start position:0%
+it it can be certainly designed so that
+the amplifier is stable in a variety of
+
+ align:start position:0%
+the amplifier is stable in a variety of
+ 
+
+ align:start position:0%
+the amplifier is stable in a variety of
+feedback connections it's only or one of
+
+ align:start position:0%
+feedback connections it's only or one of
+ 
+
+ align:start position:0%
+feedback connections it's only or one of
+its problems is simply that it's overly
+
+ align:start position:0%
+its problems is simply that it's overly
+ 
+
+ align:start position:0%
+its problems is simply that it's overly
+conservative in many applications as
+
+ align:start position:0%
+conservative in many applications as
+ 
+
+ align:start position:0%
+conservative in many applications as
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+seen another
+
+ align:start position:0%
+seen another
+ 
+
+ align:start position:0%
+seen another
+possibility uh is to consider the
+
+ align:start position:0%
+possibility uh is to consider the
+ 
+
+ align:start position:0%
+possibility uh is to consider the
+following let's
+
+ align:start position:0%
+following let's
+ 
+
+ align:start position:0%
+following let's
+suppose that
+
+ align:start position:0%
+suppose that
+ 
+
+ align:start position:0%
+suppose that
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+the open loop transfer function of the
+
+ align:start position:0%
+the open loop transfer function of the
+ 
+
+ align:start position:0%
+the open loop transfer function of the
+amplifier without compensation when we
+
+ align:start position:0%
+amplifier without compensation when we
+ 
+
+ align:start position:0%
+amplifier without compensation when we
+consider the effects of loading by the
+
+ align:start position:0%
+consider the effects of loading by the
+ 
+
+ align:start position:0%
+consider the effects of loading by the
+compensating Network in in general why
+
+ align:start position:0%
+compensating Network in in general why
+ 
+
+ align:start position:0%
+compensating Network in in general why
+the the compensating network doesn't the
+
+ align:start position:0%
+the the compensating network doesn't the
+ 
+
+ align:start position:0%
+the the compensating network doesn't the
+loading of the compensating Network
+
+ align:start position:0%
+loading of the compensating Network
+ 
+
+ align:start position:0%
+loading of the compensating Network
+usually doesn't change that curve much
+
+ align:start position:0%
+usually doesn't change that curve much
+ 
+
+ align:start position:0%
+usually doesn't change that curve much
+so let's suppose somehow we know that
+
+ align:start position:0%
+so let's suppose somehow we know that
+ 
+
+ align:start position:0%
+so let's suppose somehow we know that
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+the uncompensated open loop transfer
+
+ align:start position:0%
+the uncompensated open loop transfer
+ 
+
+ align:start position:0%
+the uncompensated open loop transfer
+function for the amplifier if we use
+
+ align:start position:0%
+function for the amplifier if we use
+ 
+
+ align:start position:0%
+function for the amplifier if we use
+single pole compensation and possibly
+
+ align:start position:0%
+single pole compensation and possibly
+ 
+
+ align:start position:0%
+single pole compensation and possibly
+adjust it for Unity gain at a megahertz
+
+ align:start position:0%
+adjust it for Unity gain at a megahertz
+ 
+
+ align:start position:0%
+adjust it for Unity gain at a megahertz
+or something like that why this is the
+
+ align:start position:0%
+or something like that why this is the
+ 
+
+ align:start position:0%
+or something like that why this is the
+approximating function our
+
+ align:start position:0%
+approximating function our
+ 
+
+ align:start position:0%
+approximating function our
+approximation tells us that at least
+
+ align:start position:0%
+approximation tells us that at least
+ 
+
+ align:start position:0%
+approximation tells us that at least
+over from here to this frequency and and
+
+ align:start position:0%
+over from here to this frequency and and
+ 
+
+ align:start position:0%
+over from here to this frequency and and
+possibly Beyond we'll have basically a
+
+ align:start position:0%
+possibly Beyond we'll have basically a
+ 
+
+ align:start position:0%
+possibly Beyond we'll have basically a
+single pole rollof associated with the
+
+ align:start position:0%
+single pole rollof associated with the
+ 
+
+ align:start position:0%
+single pole rollof associated with the
+open loop transfer function of the
+
+ align:start position:0%
+open loop transfer function of the
+ 
+
+ align:start position:0%
+open loop transfer function of the
+amplifier uh we might wonder though
+
+ align:start position:0%
+amplifier uh we might wonder though
+ 
+
+ align:start position:0%
+amplifier uh we might wonder though
+we're throwing away a good bit of
+
+ align:start position:0%
+we're throwing away a good bit of
+ 
+
+ align:start position:0%
+we're throwing away a good bit of
+amplifier capability this area here
+
+ align:start position:0%
+amplifier capability this area here
+ 
+
+ align:start position:0%
+amplifier capability this area here
+represents a region where the amplifier
+
+ align:start position:0%
+represents a region where the amplifier
+ 
+
+ align:start position:0%
+represents a region where the amplifier
+has considerably more open loop gain
+
+ align:start position:0%
+has considerably more open loop gain
+ 
+
+ align:start position:0%
+has considerably more open loop gain
+potential than we're actually using
+
+ align:start position:0%
+potential than we're actually using
+ 
+
+ align:start position:0%
+potential than we're actually using
+we've had a squeeze sze down the open
+
+ align:start position:0%
+we've had a squeeze sze down the open
+ 
+
+ align:start position:0%
+we've had a squeeze sze down the open
+loop gain over a very wide range of
+
+ align:start position:0%
+loop gain over a very wide range of
+ 
+
+ align:start position:0%
+loop gain over a very wide range of
+frequencies in order to make the
+
+ align:start position:0%
+frequencies in order to make the
+ 
+
+ align:start position:0%
+frequencies in order to make the
+amplifier
+
+ align:start position:0%
+amplifier
+ 
+
+ align:start position:0%
+amplifier
+stable well what would happen if we used
+
+ align:start position:0%
+stable well what would happen if we used
+ 
+
+ align:start position:0%
+stable well what would happen if we used
+a somewhat different kind of roll off a
+
+ align:start position:0%
+a somewhat different kind of roll off a
+ 
+
+ align:start position:0%
+a somewhat different kind of roll off a
+somewhat more heroic roll off if you
+
+ align:start position:0%
+somewhat more heroic roll off if you
+ 
+
+ align:start position:0%
+somewhat more heroic roll off if you
+will uh let's keep a single pole roll
+
+ align:start position:0%
+will uh let's keep a single pole roll
+ 
+
+ align:start position:0%
+will uh let's keep a single pole roll
+off in the vicinity of crossover let's
+
+ align:start position:0%
+off in the vicinity of crossover let's
+ 
+
+ align:start position:0%
+off in the vicinity of crossover let's
+assume this is a plot of the AF product
+
+ align:start position:0%
+assume this is a plot of the AF product
+ 
+
+ align:start position:0%
+assume this is a plot of the AF product
+so it includes F let's keep a single
+
+ align:start position:0%
+so it includes F let's keep a single
+ 
+
+ align:start position:0%
+so it includes F let's keep a single
+pole roll off in the vicinity of
+
+ align:start position:0%
+pole roll off in the vicinity of
+ 
+
+ align:start position:0%
+pole roll off in the vicinity of
+crossover but let's roll off as 1 / s
+
+ align:start position:0%
+crossover but let's roll off as 1 / s
+ 
+
+ align:start position:0%
+crossover but let's roll off as 1 / s
+squ at lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequencies maybe something like so our
+
+ align:start position:0%
+frequencies maybe something like so our
+ 
+
+ align:start position:0%
+frequencies maybe something like so our
+approximation now becomes one/ s squ or
+
+ align:start position:0%
+approximation now becomes one/ s squ or
+ 
+
+ align:start position:0%
+approximation now becomes one/ s squ or
+some constant over s s and then a single
+
+ align:start position:0%
+some constant over s s and then a single
+ 
+
+ align:start position:0%
+some constant over s s and then a single
+pole roll off uh the actual open loop
+
+ align:start position:0%
+pole roll off uh the actual open loop
+ 
+
+ align:start position:0%
+pole roll off uh the actual open loop
+transfer function of the amplifier again
+
+ align:start position:0%
+transfer function of the amplifier again
+ 
+
+ align:start position:0%
+transfer function of the amplifier again
+would be the lower of these two curves
+
+ align:start position:0%
+would be the lower of these two curves
+ 
+
+ align:start position:0%
+would be the lower of these two curves
+at all frequencies so it might look
+
+ align:start position:0%
+at all frequencies so it might look
+ 
+
+ align:start position:0%
+at all frequencies so it might look
+something like that but the important
+
+ align:start position:0%
+something like that but the important
+ 
+
+ align:start position:0%
+something like that but the important
+point is that we've picked up a good bit
+
+ align:start position:0%
+point is that we've picked up a good bit
+ 
+
+ align:start position:0%
+point is that we've picked up a good bit
+of area in here we've increased
+
+ align:start position:0%
+of area in here we've increased
+ 
+
+ align:start position:0%
+of area in here we've increased
+desensitivity over a very wide range of
+
+ align:start position:0%
+desensitivity over a very wide range of
+ 
+
+ align:start position:0%
+desensitivity over a very wide range of
+frequencies by using two- pole
+
+ align:start position:0%
+frequencies by using two- pole
+ 
+
+ align:start position:0%
+frequencies by using two- pole
+compensation as opposed to one pole
+
+ align:start position:0%
+compensation as opposed to one pole
+ 
+
+ align:start position:0%
+compensation as opposed to one pole
+compensation in order to implement two-
+
+ align:start position:0%
+compensation in order to implement two-
+ 
+
+ align:start position:0%
+compensation in order to implement two-
+pole compensation we want to make the
+
+ align:start position:0%
+pole compensation we want to make the
+ 
+
+ align:start position:0%
+pole compensation we want to make the
+ratio G subm over 2 y Sub C of s have
+
+ align:start position:0%
+ratio G subm over 2 y Sub C of s have
+ 
+
+ align:start position:0%
+ratio G subm over 2 y Sub C of s have
+the general form K to S + 1/ s^ 2 the k/
+
+ align:start position:0%
+the general form K to S + 1/ s^ 2 the k/
+ 
+
+ align:start position:0%
+the general form K to S + 1/ s^ 2 the k/
+s^2 would give us the 1/ s^2 roll off at
+
+ align:start position:0%
+s^2 would give us the 1/ s^2 roll off at
+ 
+
+ align:start position:0%
+s^2 would give us the 1/ s^2 roll off at
+low frequencies we then put in a zero
+
+ align:start position:0%
+low frequencies we then put in a zero
+ 
+
+ align:start position:0%
+low frequencies we then put in a zero
+which causes our Loop transmission to go
+
+ align:start position:0%
+which causes our Loop transmission to go
+ 
+
+ align:start position:0%
+which causes our Loop transmission to go
+as 1/ s in the vicinity of crossover uh
+
+ align:start position:0%
+as 1/ s in the vicinity of crossover uh
+ 
+
+ align:start position:0%
+as 1/ s in the vicinity of crossover uh
+hopefully getting enough phase margin
+
+ align:start position:0%
+hopefully getting enough phase margin
+ 
+
+ align:start position:0%
+hopefully getting enough phase margin
+for acceptably stable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+performance in this case we really have
+
+ align:start position:0%
+performance in this case we really have
+ 
+
+ align:start position:0%
+performance in this case we really have
+to use a two-port network in order to
+
+ align:start position:0%
+to use a two-port network in order to
+ 
+
+ align:start position:0%
+to use a two-port network in order to
+achieve our desired short circuit
+
+ align:start position:0%
+achieve our desired short circuit
+ 
+
+ align:start position:0%
+achieve our desired short circuit
+transfer admittance we want to get a
+
+ align:start position:0%
+transfer admittance we want to get a
+ 
+
+ align:start position:0%
+transfer admittance we want to get a
+short circuit transfer admittance of the
+
+ align:start position:0%
+short circuit transfer admittance of the
+ 
+
+ align:start position:0%
+short circuit transfer admittance of the
+form some constant time s^2 over to s+
+
+ align:start position:0%
+form some constant time s^2 over to s+
+ 
+
+ align:start position:0%
+form some constant time s^2 over to s+
+one we can't do that as a with a single
+
+ align:start position:0%
+one we can't do that as a with a single
+ 
+
+ align:start position:0%
+one we can't do that as a with a single
+element as we did in the case of one
+
+ align:start position:0%
+element as we did in the case of one
+ 
+
+ align:start position:0%
+element as we did in the case of one
+pole compensation
+
+ align:start position:0%
+pole compensation
+ 
+
+ align:start position:0%
+pole compensation
+where we wanted a short circuit transfer
+
+ align:start position:0%
+where we wanted a short circuit transfer
+ 
+
+ align:start position:0%
+where we wanted a short circuit transfer
+ad admittance just proportional to
+
+ align:start position:0%
+ad admittance just proportional to
+ 
+
+ align:start position:0%
+ad admittance just proportional to
+S we can
+
+ align:start position:0%
+S we can
+ 
+
+ align:start position:0%
+S we can
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+get the desired form for the short
+
+ align:start position:0%
+get the desired form for the short
+ 
+
+ align:start position:0%
+get the desired form for the short
+circuit transfer admittance out of a t
+
+ align:start position:0%
+circuit transfer admittance out of a t
+ 
+
+ align:start position:0%
+circuit transfer admittance out of a t
+Network as shown here we have two
+
+ align:start position:0%
+Network as shown here we have two
+ 
+
+ align:start position:0%
+Network as shown here we have two
+capacitors a single resistor uh if we
+
+ align:start position:0%
+capacitors a single resistor uh if we
+ 
+
+ align:start position:0%
+capacitors a single resistor uh if we
+measure the ratio of I subn to V subn we
+
+ align:start position:0%
+measure the ratio of I subn to V subn we
+ 
+
+ align:start position:0%
+measure the ratio of I subn to V subn we
+find out it has a desired form some
+
+ align:start position:0%
+find out it has a desired form some
+ 
+
+ align:start position:0%
+find out it has a desired form some
+constant times s s over another constant
+
+ align:start position:0%
+constant times s s over another constant
+ 
+
+ align:start position:0%
+constant times s s over another constant
+Time s + one and by appropriately
+
+ align:start position:0%
+Time s + one and by appropriately
+ 
+
+ align:start position:0%
+Time s + one and by appropriately
+choosing C1 C2 and R we can adjust the
+
+ align:start position:0%
+choosing C1 C2 and R we can adjust the
+ 
+
+ align:start position:0%
+choosing C1 C2 and R we can adjust the
+constants so this kind of a t network uh
+
+ align:start position:0%
+constants so this kind of a t network uh
+ 
+
+ align:start position:0%
+constants so this kind of a t network uh
+will in fact give us the sort of
+
+ align:start position:0%
+will in fact give us the sort of
+ 
+
+ align:start position:0%
+will in fact give us the sort of
+two-pole rolloff that we'd like to have
+
+ align:start position:0%
+two-pole rolloff that we'd like to have
+ 
+
+ align:start position:0%
+two-pole rolloff that we'd like to have
+if we use that kind of a network for
+
+ align:start position:0%
+if we use that kind of a network for
+ 
+
+ align:start position:0%
+if we use that kind of a network for
+compensation the
+
+ align:start position:0%
+compensation the
+ 
+
+ align:start position:0%
+compensation the
+effect on the amplifier transfer
+
+ align:start position:0%
+effect on the amplifier transfer
+ 
+
+ align:start position:0%
+effect on the amplifier transfer
+function again uh assuming an
+
+ align:start position:0%
+function again uh assuming an
+ 
+
+ align:start position:0%
+function again uh assuming an
+uncompensated transfer function
+
+ align:start position:0%
+uncompensated transfer function
+ 
+
+ align:start position:0%
+uncompensated transfer function
+including loading that's sort of three
+
+ align:start position:0%
+including loading that's sort of three
+ 
+
+ align:start position:0%
+including loading that's sort of three
+pole here's the 1 / s s 1/ s
+
+ align:start position:0%
+pole here's the 1 / s s 1/ s
+ 
+
+ align:start position:0%
+pole here's the 1 / s s 1/ s
+approximation and again we use the we
+
+ align:start position:0%
+approximation and again we use the we
+ 
+
+ align:start position:0%
+approximation and again we use the we
+get the lower of those two curves at all
+
+ align:start position:0%
+get the lower of those two curves at all
+ 
+
+ align:start position:0%
+get the lower of those two curves at all
+frequencies uh here we might argue that
+
+ align:start position:0%
+frequencies uh here we might argue that
+ 
+
+ align:start position:0%
+frequencies uh here we might argue that
+between about this
+
+ align:start position:0%
+between about this
+ 
+
+ align:start position:0%
+between about this
+frequency and this one the approximation
+
+ align:start position:0%
+frequency and this one the approximation
+ 
+
+ align:start position:0%
+frequency and this one the approximation
+the 1 / S2 and then a zero kind of
+
+ align:start position:0%
+the 1 / S2 and then a zero kind of
+ 
+
+ align:start position:0%
+the 1 / S2 and then a zero kind of
+approximation very accurately predict
+
+ align:start position:0%
+approximation very accurately predict
+ 
+
+ align:start position:0%
+approximation very accurately predict
+the behavior of the amplifier so the
+
+ align:start position:0%
+the behavior of the amplifier so the
+ 
+
+ align:start position:0%
+the behavior of the amplifier so the
+hope is that we'd have the crossover in
+
+ align:start position:0%
+hope is that we'd have the crossover in
+ 
+
+ align:start position:0%
+hope is that we'd have the crossover in
+our major Loop would occur somewhere in
+
+ align:start position:0%
+our major Loop would occur somewhere in
+ 
+
+ align:start position:0%
+our major Loop would occur somewhere in
+this region we could use the
+
+ align:start position:0%
+this region we could use the
+ 
+
+ align:start position:0%
+this region we could use the
+approximation to predict Behavior if we
+
+ align:start position:0%
+approximation to predict Behavior if we
+ 
+
+ align:start position:0%
+approximation to predict Behavior if we
+look at the angle we see a pattern
+
+ align:start position:0%
+look at the angle we see a pattern
+ 
+
+ align:start position:0%
+look at the angle we see a pattern
+that's very much like that which results
+
+ align:start position:0%
+that's very much like that which results
+ 
+
+ align:start position:0%
+that's very much like that which results
+with lag
+
+ align:start position:0%
+with lag
+ 
+
+ align:start position:0%
+with lag
+compensation uh the compensated angle
+
+ align:start position:0%
+compensation uh the compensated angle
+ 
+
+ align:start position:0%
+compensation uh the compensated angle
+dips down close to minus 180° possibly
+
+ align:start position:0%
+dips down close to minus 180° possibly
+ 
+
+ align:start position:0%
+dips down close to minus 180° possibly
+if this range of frequencies is
+
+ align:start position:0%
+if this range of frequencies is
+ 
+
+ align:start position:0%
+if this range of frequencies is
+large uh comes back back up in the
+
+ align:start position:0%
+large uh comes back back up in the
+ 
+
+ align:start position:0%
+large uh comes back back up in the
+vicinity of crossover crossover is
+
+ align:start position:0%
+vicinity of crossover crossover is
+ 
+
+ align:start position:0%
+vicinity of crossover crossover is
+assumed to occur crossover in the major
+
+ align:start position:0%
+assumed to occur crossover in the major
+ 
+
+ align:start position:0%
+assumed to occur crossover in the major
+Loop is assumed to occur in here
+
+ align:start position:0%
+Loop is assumed to occur in here
+ 
+
+ align:start position:0%
+Loop is assumed to occur in here
+somewhere comes back up so that we get
+
+ align:start position:0%
+somewhere comes back up so that we get
+ 
+
+ align:start position:0%
+somewhere comes back up so that we get
+adequate phase margin at crossover and
+
+ align:start position:0%
+adequate phase margin at crossover and
+ 
+
+ align:start position:0%
+adequate phase margin at crossover and
+then eventually Trails off this is the
+
+ align:start position:0%
+then eventually Trails off this is the
+ 
+
+ align:start position:0%
+then eventually Trails off this is the
+kind of a pattern that we very
+
+ align:start position:0%
+kind of a pattern that we very
+ 
+
+ align:start position:0%
+kind of a pattern that we very
+frequently get with lag compensation so
+
+ align:start position:0%
+frequently get with lag compensation so
+ 
+
+ align:start position:0%
+frequently get with lag compensation so
+the 1/ S squ sort of minor Loop
+
+ align:start position:0%
+the 1/ S squ sort of minor Loop
+ 
+
+ align:start position:0%
+the 1/ S squ sort of minor Loop
+compensation or the kind of minor Loop
+
+ align:start position:0%
+compensation or the kind of minor Loop
+ 
+
+ align:start position:0%
+compensation or the kind of minor Loop
+compensation that forces a 1/ s squ
+
+ align:start position:0%
+compensation that forces a 1/ s squ
+ 
+
+ align:start position:0%
+compensation that forces a 1/ s squ
+rolloff over a wide range of frequencies
+
+ align:start position:0%
+rolloff over a wide range of frequencies
+ 
+
+ align:start position:0%
+rolloff over a wide range of frequencies
+is sort of the parallel to lag
+
+ align:start position:0%
+is sort of the parallel to lag
+ 
+
+ align:start position:0%
+is sort of the parallel to lag
+compensation in the series compensated
+
+ align:start position:0%
+compensation in the series compensated
+ 
+
+ align:start position:0%
+compensation in the series compensated
+case again I'd like to look at the
+
+ align:start position:0%
+case again I'd like to look at the
+ 
+
+ align:start position:0%
+case again I'd like to look at the
+effects of of using or the results of
+
+ align:start position:0%
+effects of of using or the results of
+ 
+
+ align:start position:0%
+effects of of using or the results of
+using 1/ S2
+
+ align:start position:0%
+using 1/ S2
+ 
+
+ align:start position:0%
+using 1/ S2
+compensation uh here we have
+
+ align:start position:0%
+compensation uh here we have
+ 
+
+ align:start position:0%
+compensation uh here we have
+another part in our in our system
+
+ align:start position:0%
+another part in our in our system
+ 
+
+ align:start position:0%
+another part in our in our system
+another portion where we have the
+
+ align:start position:0%
+another portion where we have the
+ 
+
+ align:start position:0%
+another portion where we have the
+amplifier uh that allows us to you look
+
+ align:start position:0%
+amplifier uh that allows us to you look
+ 
+
+ align:start position:0%
+amplifier uh that allows us to you look
+at 1/s squared compensation uh we we use
+
+ align:start position:0%
+at 1/s squared compensation uh we we use
+ 
+
+ align:start position:0%
+at 1/s squared compensation uh we we use
+a a somewhat different configuration
+
+ align:start position:0%
+a a somewhat different configuration
+ 
+
+ align:start position:0%
+a a somewhat different configuration
+here actually uh we use the amplifier
+
+ align:start position:0%
+here actually uh we use the amplifier
+ 
+
+ align:start position:0%
+here actually uh we use the amplifier
+connected as a Unity gain inverter and
+
+ align:start position:0%
+connected as a Unity gain inverter and
+ 
+
+ align:start position:0%
+connected as a Unity gain inverter and
+the reason for that is that we're able
+
+ align:start position:0%
+the reason for that is that we're able
+ 
+
+ align:start position:0%
+the reason for that is that we're able
+to very easily look at the error signal
+
+ align:start position:0%
+to very easily look at the error signal
+ 
+
+ align:start position:0%
+to very easily look at the error signal
+we connect the the amplifier as a Unity
+
+ align:start position:0%
+we connect the the amplifier as a Unity
+ 
+
+ align:start position:0%
+we connect the the amplifier as a Unity
+gain inverter and let me if I can look
+
+ align:start position:0%
+gain inverter and let me if I can look
+ 
+
+ align:start position:0%
+gain inverter and let me if I can look
+at at a view graph that shows that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topology uh here's the configuration we
+
+ align:start position:0%
+topology uh here's the configuration we
+ 
+
+ align:start position:0%
+topology uh here's the configuration we
+simply have an equal valued input and
+
+ align:start position:0%
+simply have an equal valued input and
+ 
+
+ align:start position:0%
+simply have an equal valued input and
+feedback resistor we have the T Network
+
+ align:start position:0%
+feedback resistor we have the T Network
+ 
+
+ align:start position:0%
+feedback resistor we have the T Network
+that does compensation in this case we
+
+ align:start position:0%
+that does compensation in this case we
+ 
+
+ align:start position:0%
+that does compensation in this case we
+chose elements in the t uh so that Unity
+
+ align:start position:0%
+chose elements in the t uh so that Unity
+ 
+
+ align:start position:0%
+chose elements in the t uh so that Unity
+gain frequency in the amplifier uh is
+
+ align:start position:0%
+gain frequency in the amplifier uh is
+ 
+
+ align:start position:0%
+gain frequency in the amplifier uh is
+about 1 and a 12 megahertz the 2:1
+
+ align:start position:0%
+about 1 and a 12 megahertz the 2:1
+ 
+
+ align:start position:0%
+about 1 and a 12 megahertz the 2:1
+attenuation provided by the feedback
+
+ align:start position:0%
+attenuation provided by the feedback
+ 
+
+ align:start position:0%
+attenuation provided by the feedback
+Network forces overall crossover uh at
+
+ align:start position:0%
+Network forces overall crossover uh at
+ 
+
+ align:start position:0%
+Network forces overall crossover uh at
+about uh uh 1 MHz or or something like
+
+ align:start position:0%
+about uh uh 1 MHz or or something like
+ 
+
+ align:start position:0%
+about uh uh 1 MHz or or something like
+that uh the zero uh comes in at at about
+
+ align:start position:0%
+that uh the zero uh comes in at at about
+ 
+
+ align:start position:0%
+that uh the zero uh comes in at at about
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+kilohertz uh so
+
+ align:start position:0%
+kilohertz uh so
+ 
+
+ align:start position:0%
+kilohertz uh so
+this combination of values as we say
+
+ align:start position:0%
+this combination of values as we say
+ 
+
+ align:start position:0%
+this combination of values as we say
+gives us the 1/ s^ squ rolloff breaks
+
+ align:start position:0%
+gives us the 1/ s^ squ rolloff breaks
+ 
+
+ align:start position:0%
+gives us the 1/ s^ squ rolloff breaks
+back to 1 / s in the vicinity of
+
+ align:start position:0%
+back to 1 / s in the vicinity of
+ 
+
+ align:start position:0%
+back to 1 / s in the vicinity of
+crossover and the advantage of the
+
+ align:start position:0%
+crossover and the advantage of the
+ 
+
+ align:start position:0%
+crossover and the advantage of the
+inverter topology as opposed to the
+
+ align:start position:0%
+inverter topology as opposed to the
+ 
+
+ align:start position:0%
+inverter topology as opposed to the
+non-inverting configuration we used
+
+ align:start position:0%
+non-inverting configuration we used
+ 
+
+ align:start position:0%
+non-inverting configuration we used
+earlier is that the signal at this point
+
+ align:start position:0%
+earlier is that the signal at this point
+ 
+
+ align:start position:0%
+earlier is that the signal at this point
+is a direct measure of the error in the
+
+ align:start position:0%
+is a direct measure of the error in the
+ 
+
+ align:start position:0%
+is a direct measure of the error in the
+system we can look at this point with an
+
+ align:start position:0%
+system we can look at this point with an
+ 
+
+ align:start position:0%
+system we can look at this point with an
+oscilloscope and ideally this voltage
+
+ align:start position:0%
+oscilloscope and ideally this voltage
+ 
+
+ align:start position:0%
+oscilloscope and ideally this voltage
+should be zero uh the output should
+
+ align:start position:0%
+should be zero uh the output should
+ 
+
+ align:start position:0%
+should be zero uh the output should
+ideally be the negative of the input uh
+
+ align:start position:0%
+ideally be the negative of the input uh
+ 
+
+ align:start position:0%
+ideally be the negative of the input uh
+assuming no loading by the amplifier
+
+ align:start position:0%
+assuming no loading by the amplifier
+ 
+
+ align:start position:0%
+assuming no loading by the amplifier
+this point uh should reflect error
+
+ align:start position:0%
+this point uh should reflect error
+ 
+
+ align:start position:0%
+this point uh should reflect error
+directly if the I output were exactly
+
+ align:start position:0%
+directly if the I output were exactly
+ 
+
+ align:start position:0%
+directly if the I output were exactly
+the negative of the input this point
+
+ align:start position:0%
+the negative of the input this point
+ 
+
+ align:start position:0%
+the negative of the input this point
+would be at zero to the extent that it's
+
+ align:start position:0%
+would be at zero to the extent that it's
+ 
+
+ align:start position:0%
+would be at zero to the extent that it's
+not we get a direct measure of error and
+
+ align:start position:0%
+not we get a direct measure of error and
+ 
+
+ align:start position:0%
+not we get a direct measure of error and
+so this configuration allows us to
+
+ align:start position:0%
+so this configuration allows us to
+ 
+
+ align:start position:0%
+so this configuration allows us to
+readly look at the error of the system
+
+ align:start position:0%
+readly look at the error of the system
+ 
+
+ align:start position:0%
+readly look at the error of the system
+and that's the reason that we use it in
+
+ align:start position:0%
+and that's the reason that we use it in
+ 
+
+ align:start position:0%
+and that's the reason that we use it in
+preference to the non-inverting
+
+ align:start position:0%
+preference to the non-inverting
+ 
+
+ align:start position:0%
+preference to the non-inverting
+configuration so as I say we have that
+
+ align:start position:0%
+configuration so as I say we have that
+ 
+
+ align:start position:0%
+configuration so as I say we have that
+amplifier here we have a buffer
+
+ align:start position:0%
+amplifier here we have a buffer
+ 
+
+ align:start position:0%
+amplifier here we have a buffer
+amplifier wi that allows us to look at
+
+ align:start position:0%
+amplifier wi that allows us to look at
+ 
+
+ align:start position:0%
+amplifier wi that allows us to look at
+the error signal and present that signal
+
+ align:start position:0%
+the error signal and present that signal
+ 
+
+ align:start position:0%
+the error signal and present that signal
+on an oscilloscope when we wish
+
+ align:start position:0%
+on an oscilloscope when we wish
+ 
+
+ align:start position:0%
+on an oscilloscope when we wish
+to and we're able to very quickly change
+
+ align:start position:0%
+to and we're able to very quickly change
+ 
+
+ align:start position:0%
+to and we're able to very quickly change
+from 1 /s to 1/ s^ squ compensation
+
+ align:start position:0%
+from 1 /s to 1/ s^ squ compensation
+ 
+
+ align:start position:0%
+from 1 /s to 1/ s^ squ compensation
+maintaining crossover frequency by
+
+ align:start position:0%
+maintaining crossover frequency by
+ 
+
+ align:start position:0%
+maintaining crossover frequency by
+simply lifting the resistor in the
+
+ align:start position:0%
+simply lifting the resistor in the
+ 
+
+ align:start position:0%
+simply lifting the resistor in the
+middle leg of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T we're first going to look at the small
+
+ align:start position:0%
+T we're first going to look at the small
+ 
+
+ align:start position:0%
+T we're first going to look at the small
+signal response of the amplifier uh and
+
+ align:start position:0%
+signal response of the amplifier uh and
+ 
+
+ align:start position:0%
+signal response of the amplifier uh and
+let's look first at what happens with
+
+ align:start position:0%
+let's look first at what happens with
+ 
+
+ align:start position:0%
+let's look first at what happens with
+1/s
+
+ align:start position:0%
+1/s
+ 
+
+ align:start position:0%
+1/s
+compensation uh here we have removed the
+
+ align:start position:0%
+compensation uh here we have removed the
+ 
+
+ align:start position:0%
+compensation uh here we have removed the
+resistor in the T network uh simply
+
+ align:start position:0%
+resistor in the T network uh simply
+ 
+
+ align:start position:0%
+resistor in the T network uh simply
+switched it out open circuited the
+
+ align:start position:0%
+switched it out open circuited the
+ 
+
+ align:start position:0%
+switched it out open circuited the
+resistor and we get the rise time that
+
+ align:start position:0%
+resistor and we get the rise time that
+ 
+
+ align:start position:0%
+resistor and we get the rise time that
+we we
+
+ align:start position:0%
+we we
+ 
+
+ align:start position:0%
+we we
+show uh let me see if I can make things
+
+ align:start position:0%
+show uh let me see if I can make things
+ 
+
+ align:start position:0%
+show uh let me see if I can make things
+go just a little bit faster
+
+ align:start position:0%
+go just a little bit faster
+ 
+
+ align:start position:0%
+go just a little bit faster
+here uh we get a rise time in this case
+
+ align:start position:0%
+here uh we get a rise time in this case
+ 
+
+ align:start position:0%
+here uh we get a rise time in this case
+of of a couple of 100 nond 300 nond
+
+ align:start position:0%
+of of a couple of 100 nond 300 nond
+ 
+
+ align:start position:0%
+of of a couple of 100 nond 300 nond
+something like that reflecting roughly a
+
+ align:start position:0%
+something like that reflecting roughly a
+ 
+
+ align:start position:0%
+something like that reflecting roughly a
+megahertz crossover reasonably well
+
+ align:start position:0%
+megahertz crossover reasonably well
+ 
+
+ align:start position:0%
+megahertz crossover reasonably well
+damped response uh if we switch to 1 s^
+
+ align:start position:0%
+damped response uh if we switch to 1 s^
+ 
+
+ align:start position:0%
+damped response uh if we switch to 1 s^
+s compensation the zero is back I think
+
+ align:start position:0%
+s compensation the zero is back I think
+ 
+
+ align:start position:0%
+s compensation the zero is back I think
+actually if we go through the numbers
+
+ align:start position:0%
+actually if we go through the numbers
+ 
+
+ align:start position:0%
+actually if we go through the numbers
+for this network the zero is back about
+
+ align:start position:0%
+for this network the zero is back about
+ 
+
+ align:start position:0%
+for this network the zero is back about
+a factor of five or six or seven from
+
+ align:start position:0%
+a factor of five or six or seven from
+ 
+
+ align:start position:0%
+a factor of five or six or seven from
+crossover we notice very little change
+
+ align:start position:0%
+crossover we notice very little change
+ 
+
+ align:start position:0%
+crossover we notice very little change
+as I go from 1 / s to 1 / s^2
+
+ align:start position:0%
+as I go from 1 / s to 1 / s^2
+ 
+
+ align:start position:0%
+as I go from 1 / s to 1 / s^2
+compensation very little change in the
+
+ align:start position:0%
+compensation very little change in the
+ 
+
+ align:start position:0%
+compensation very little change in the
+relative stability the phase margin of
+
+ align:start position:0%
+relative stability the phase margin of
+ 
+
+ align:start position:0%
+relative stability the phase margin of
+the two systems is is very nearly
+
+ align:start position:0%
+the two systems is is very nearly
+ 
+
+ align:start position:0%
+the two systems is is very nearly
+comparable the zero is located well
+
+ align:start position:0%
+comparable the zero is located well
+ 
+
+ align:start position:0%
+comparable the zero is located well
+enough below crossover the equivalent to
+
+ align:start position:0%
+enough below crossover the equivalent to
+ 
+
+ align:start position:0%
+enough below crossover the equivalent to
+locating the zero of a lag Network far
+
+ align:start position:0%
+locating the zero of a lag Network far
+ 
+
+ align:start position:0%
+locating the zero of a lag Network far
+enough below crossover uh so that the
+
+ align:start position:0%
+enough below crossover uh so that the
+ 
+
+ align:start position:0%
+enough below crossover uh so that the
+stability is comparable uh there is one
+
+ align:start position:0%
+stability is comparable uh there is one
+ 
+
+ align:start position:0%
+stability is comparable uh there is one
+effect that I'll point out and we'll
+
+ align:start position:0%
+effect that I'll point out and we'll
+ 
+
+ align:start position:0%
+effect that I'll point out and we'll
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+later notice that when we use 1/s
+
+ align:start position:0%
+later notice that when we use 1/s
+ 
+
+ align:start position:0%
+later notice that when we use 1/s
+compensation the response goes up to
+
+ align:start position:0%
+compensation the response goes up to
+ 
+
+ align:start position:0%
+compensation the response goes up to
+final value pretty much settles there uh
+
+ align:start position:0%
+final value pretty much settles there uh
+ 
+
+ align:start position:0%
+final value pretty much settles there uh
+and the speed of the response is is
+
+ align:start position:0%
+and the speed of the response is is
+ 
+
+ align:start position:0%
+and the speed of the response is is
+compatible with the 1 mahz crossover
+
+ align:start position:0%
+compatible with the 1 mahz crossover
+ 
+
+ align:start position:0%
+compatible with the 1 mahz crossover
+frequency if I use 1/ s^2 compensation
+
+ align:start position:0%
+frequency if I use 1/ s^2 compensation
+ 
+
+ align:start position:0%
+frequency if I use 1/ s^2 compensation
+the basic response is very much the same
+
+ align:start position:0%
+the basic response is very much the same
+ 
+
+ align:start position:0%
+the basic response is very much the same
+the relative stability is very much the
+
+ align:start position:0%
+the relative stability is very much the
+ 
+
+ align:start position:0%
+the relative stability is very much the
+same but we notice a a sort of long
+
+ align:start position:0%
+same but we notice a a sort of long
+ 
+
+ align:start position:0%
+same but we notice a a sort of long
+tail uh we can see that let me up the
+
+ align:start position:0%
+tail uh we can see that let me up the
+ 
+
+ align:start position:0%
+tail uh we can see that let me up the
+amplitude just a little
+
+ align:start position:0%
+amplitude just a little
+ 
+
+ align:start position:0%
+amplitude just a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+and look at
+
+ align:start position:0%
+and look at
+ 
+
+ align:start position:0%
+and look at
+the final part of the response we notice
+
+ align:start position:0%
+the final part of the response we notice
+ 
+
+ align:start position:0%
+the final part of the response we notice
+a fairly prolonged tail uh the time
+
+ align:start position:0%
+a fairly prolonged tail uh the time
+ 
+
+ align:start position:0%
+a fairly prolonged tail uh the time
+constant associated with that taale is
+
+ align:start position:0%
+constant associated with that taale is
+ 
+
+ align:start position:0%
+constant associated with that taale is
+somewhere on the order of a microsc
+
+ align:start position:0%
+somewhere on the order of a microsc
+ 
+
+ align:start position:0%
+somewhere on the order of a microsc
+we're at a a 500 NCS per Division and
+
+ align:start position:0%
+we're at a a 500 NCS per Division and
+ 
+
+ align:start position:0%
+we're at a a 500 NCS per Division and
+from here to here the tail May shrink by
+
+ align:start position:0%
+from here to here the tail May shrink by
+ 
+
+ align:start position:0%
+from here to here the tail May shrink by
+to one minus one over e of final value
+
+ align:start position:0%
+to one minus one over e of final value
+ 
+
+ align:start position:0%
+to one minus one over e of final value
+so uh we have a time constant of roughly
+
+ align:start position:0%
+so uh we have a time constant of roughly
+ 
+
+ align:start position:0%
+so uh we have a time constant of roughly
+a microsc we'll have more to say about
+
+ align:start position:0%
+a microsc we'll have more to say about
+ 
+
+ align:start position:0%
+a microsc we'll have more to say about
+that in a little while but that's the
+
+ align:start position:0%
+that in a little while but that's the
+ 
+
+ align:start position:0%
+that in a little while but that's the
+only really noticeable difference that
+
+ align:start position:0%
+only really noticeable difference that
+ 
+
+ align:start position:0%
+only really noticeable difference that
+we see in the small signal input to
+
+ align:start position:0%
+we see in the small signal input to
+ 
+
+ align:start position:0%
+we see in the small signal input to
+Output step responses of the
+
+ align:start position:0%
+Output step responses of the
+ 
+
+ align:start position:0%
+Output step responses of the
+system now let's look at at errors for
+
+ align:start position:0%
+system now let's look at at errors for
+ 
+
+ align:start position:0%
+system now let's look at at errors for
+certain kinds of inputs or for one input
+
+ align:start position:0%
+certain kinds of inputs or for one input
+ 
+
+ align:start position:0%
+certain kinds of inputs or for one input
+in particular what I'd like to do is
+
+ align:start position:0%
+in particular what I'd like to do is
+ 
+
+ align:start position:0%
+in particular what I'd like to do is
+drive the system with a triangle wave
+
+ align:start position:0%
+drive the system with a triangle wave
+ 
+
+ align:start position:0%
+drive the system with a triangle wave
+Drive our amplifier with a triangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wave and let's put in a a much larger
+
+ align:start position:0%
+wave and let's put in a a much larger
+ 
+
+ align:start position:0%
+wave and let's put in a a much larger
+one than we now have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's begin to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up uh in fact this amplifier has an
+
+ align:start position:0%
+up uh in fact this amplifier has an
+ 
+
+ align:start position:0%
+up uh in fact this amplifier has an
+output dynamic range of about plus or
+
+ align:start position:0%
+output dynamic range of about plus or
+ 
+
+ align:start position:0%
+output dynamic range of about plus or
+minus 10 volts and let's drive very
+
+ align:start position:0%
+minus 10 volts and let's drive very
+ 
+
+ align:start position:0%
+minus 10 volts and let's drive very
+close to that here we are at 5 volts per
+
+ align:start position:0%
+close to that here we are at 5 volts per
+ 
+
+ align:start position:0%
+close to that here we are at 5 volts per
+division let me run the input amplitude
+
+ align:start position:0%
+division let me run the input amplitude
+ 
+
+ align:start position:0%
+division let me run the input amplitude
+up to the point where we're getting an
+
+ align:start position:0%
+up to the point where we're getting an
+ 
+
+ align:start position:0%
+up to the point where we're getting an
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+amplitude of about 20 volts Peak to Peak
+
+ align:start position:0%
+amplitude of about 20 volts Peak to Peak
+ 
+
+ align:start position:0%
+amplitude of about 20 volts Peak to Peak
+plus or minus 10 volts so let's move
+
+ align:start position:0%
+plus or minus 10 volts so let's move
+ 
+
+ align:start position:0%
+plus or minus 10 volts so let's move
+that up in there so that's the the input
+
+ align:start position:0%
+that up in there so that's the the input
+ 
+
+ align:start position:0%
+that up in there so that's the the input
+signal and the output signal really to
+
+ align:start position:0%
+signal and the output signal really to
+ 
+
+ align:start position:0%
+signal and the output signal really to
+the amplifier to a good degree of
+
+ align:start position:0%
+the amplifier to a good degree of
+ 
+
+ align:start position:0%
+the amplifier to a good degree of
+approximation the output signal which is
+
+ align:start position:0%
+approximation the output signal which is
+ 
+
+ align:start position:0%
+approximation the output signal which is
+the one we're actually looking at is
+
+ align:start position:0%
+the one we're actually looking at is
+ 
+
+ align:start position:0%
+the one we're actually looking at is
+simply the negative of the input signal
+
+ align:start position:0%
+simply the negative of the input signal
+ 
+
+ align:start position:0%
+simply the negative of the input signal
+so there's our triangle uh we're running
+
+ align:start position:0%
+so there's our triangle uh we're running
+ 
+
+ align:start position:0%
+so there's our triangle uh we're running
+now at about uh 5 kohtz were 50 microc
+
+ align:start position:0%
+now at about uh 5 kohtz were 50 microc
+ 
+
+ align:start position:0%
+now at about uh 5 kohtz were 50 microc
+per division uh the period of this
+
+ align:start position:0%
+per division uh the period of this
+ 
+
+ align:start position:0%
+per division uh the period of this
+waveform is about four divisions or 200
+
+ align:start position:0%
+waveform is about four divisions or 200
+ 
+
+ align:start position:0%
+waveform is about four divisions or 200
+micros seconds so we get the uh we're
+
+ align:start position:0%
+micros seconds so we get the uh we're
+ 
+
+ align:start position:0%
+micros seconds so we get the uh we're
+running at about 5 khz let's first look
+
+ align:start position:0%
+running at about 5 khz let's first look
+ 
+
+ align:start position:0%
+running at about 5 khz let's first look
+at the error signal when we have 1/s
+
+ align:start position:0%
+at the error signal when we have 1/s
+ 
+
+ align:start position:0%
+at the error signal when we have 1/s
+compensation uh we have the error signal
+
+ align:start position:0%
+compensation uh we have the error signal
+ 
+
+ align:start position:0%
+compensation uh we have the error signal
+on the second Channel and let me put
+
+ align:start position:0%
+on the second Channel and let me put
+ 
+
+ align:start position:0%
+on the second Channel and let me put
+that on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simultaneously uh we need
+
+ align:start position:0%
+simultaneously uh we need
+ 
+
+ align:start position:0%
+simultaneously uh we need
+a much
+
+ align:start position:0%
+a much
+ 
+
+ align:start position:0%
+a much
+larger look at much smaller signals here
+
+ align:start position:0%
+larger look at much smaller signals here
+ 
+
+ align:start position:0%
+larger look at much smaller signals here
+a much higher scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factor and what we see is an error
+
+ align:start position:0%
+factor and what we see is an error
+ 
+
+ align:start position:0%
+factor and what we see is an error
+signal let's get a zero line for that
+
+ align:start position:0%
+signal let's get a zero line for that
+ 
+
+ align:start position:0%
+signal let's get a zero line for that
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there what we see is an error signal
+
+ align:start position:0%
+there what we see is an error signal
+ 
+
+ align:start position:0%
+there what we see is an error signal
+that's very very nearly a square wave it
+
+ align:start position:0%
+that's very very nearly a square wave it
+ 
+
+ align:start position:0%
+that's very very nearly a square wave it
+goes let's say we're at 10 molts per
+
+ align:start position:0%
+goes let's say we're at 10 molts per
+ 
+
+ align:start position:0%
+goes let's say we're at 10 molts per
+division uh and so it goes somewhere on
+
+ align:start position:0%
+division uh and so it goes somewhere on
+ 
+
+ align:start position:0%
+division uh and so it goes somewhere on
+the order of plus 15 molts and minus5
+
+ align:start position:0%
+the order of plus 15 molts and minus5
+ 
+
+ align:start position:0%
+the order of plus 15 molts and minus5
+molts is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable well let's see we said that
+
+ align:start position:0%
+reasonable well let's see we said that
+ 
+
+ align:start position:0%
+reasonable well let's see we said that
+when we use single pole
+
+ align:start position:0%
+when we use single pole
+ 
+
+ align:start position:0%
+when we use single pole
+compensation the open loop transfer
+
+ align:start position:0%
+compensation the open loop transfer
+ 
+
+ align:start position:0%
+compensation the open loop transfer
+function of the operational amplifier
+
+ align:start position:0%
+function of the operational amplifier
+ 
+
+ align:start position:0%
+function of the operational amplifier
+over a wide range of frequencies is
+
+ align:start position:0%
+over a wide range of frequencies is
+ 
+
+ align:start position:0%
+over a wide range of frequencies is
+proportional to 1 / s that's what we
+
+ align:start position:0%
+proportional to 1 / s that's what we
+ 
+
+ align:start position:0%
+proportional to 1 / s that's what we
+mean by having a single pole roll off
+
+ align:start position:0%
+mean by having a single pole roll off
+ 
+
+ align:start position:0%
+mean by having a single pole roll off
+the amplifier looks sort of like an an
+
+ align:start position:0%
+the amplifier looks sort of like an an
+ 
+
+ align:start position:0%
+the amplifier looks sort of like an an
+integrator from its input terminals its
+
+ align:start position:0%
+integrator from its input terminals its
+ 
+
+ align:start position:0%
+integrator from its input terminals its
+differential input terminals to its
+
+ align:start position:0%
+differential input terminals to its
+ 
+
+ align:start position:0%
+differential input terminals to its
+output or alternatively the output
+
+ align:start position:0%
+output or alternatively the output
+ 
+
+ align:start position:0%
+output or alternatively the output
+voltage of the amplifier is the integral
+
+ align:start position:0%
+voltage of the amplifier is the integral
+ 
+
+ align:start position:0%
+voltage of the amplifier is the integral
+of the voltage applied at its input at
+
+ align:start position:0%
+of the voltage applied at its input at
+ 
+
+ align:start position:0%
+of the voltage applied at its input at
+the very input terminals in the
+
+ align:start position:0%
+the very input terminals in the
+ 
+
+ align:start position:0%
+the very input terminals in the
+amplifier not the input of the overall
+
+ align:start position:0%
+amplifier not the input of the overall
+ 
+
+ align:start position:0%
+amplifier not the input of the overall
+feedback loop fine if we have a triangle
+
+ align:start position:0%
+feedback loop fine if we have a triangle
+ 
+
+ align:start position:0%
+feedback loop fine if we have a triangle
+wave at the output and that's the
+
+ align:start position:0%
+wave at the output and that's the
+ 
+
+ align:start position:0%
+wave at the output and that's the
+integral of the input the input of
+
+ align:start position:0%
+integral of the input the input of
+ 
+
+ align:start position:0%
+integral of the input the input of
+course is the derivative with some scale
+
+ align:start position:0%
+course is the derivative with some scale
+ 
+
+ align:start position:0%
+course is the derivative with some scale
+factor of that output signal we have a
+
+ align:start position:0%
+factor of that output signal we have a
+ 
+
+ align:start position:0%
+factor of that output signal we have a
+triangle wave at the output we have a
+
+ align:start position:0%
+triangle wave at the output we have a
+ 
+
+ align:start position:0%
+triangle wave at the output we have a
+square wave at the input so this is
+
+ align:start position:0%
+square wave at the input so this is
+ 
+
+ align:start position:0%
+square wave at the input so this is
+perfectly reason able this is the sort
+
+ align:start position:0%
+perfectly reason able this is the sort
+ 
+
+ align:start position:0%
+perfectly reason able this is the sort
+of of response we'd
+
+ align:start position:0%
+of of response we'd
+ 
+
+ align:start position:0%
+of of response we'd
+anticipate if we uh got a triangle wave
+
+ align:start position:0%
+anticipate if we uh got a triangle wave
+ 
+
+ align:start position:0%
+anticipate if we uh got a triangle wave
+or have force a triangle wave at the
+
+ align:start position:0%
+or have force a triangle wave at the
+ 
+
+ align:start position:0%
+or have force a triangle wave at the
+output uh and have an amplifier whose
+
+ align:start position:0%
+output uh and have an amplifier whose
+ 
+
+ align:start position:0%
+output uh and have an amplifier whose
+open loop transfer function rolls off as
+
+ align:start position:0%
+open loop transfer function rolls off as
+ 
+
+ align:start position:0%
+open loop transfer function rolls off as
+1/
+
+ align:start position:0%
+1/
+ 
+
+ align:start position:0%
+1/
+s now let's see what happens when we
+
+ align:start position:0%
+s now let's see what happens when we
+ 
+
+ align:start position:0%
+s now let's see what happens when we
+switch to 1 / s^2 compensation so to do
+
+ align:start position:0%
+switch to 1 / s^2 compensation so to do
+ 
+
+ align:start position:0%
+switch to 1 / s^2 compensation so to do
+that I will simply throw this
+
+ align:start position:0%
+that I will simply throw this
+ 
+
+ align:start position:0%
+that I will simply throw this
+switch and notice that
+
+ align:start position:0%
+switch and notice that
+ 
+
+ align:start position:0%
+switch and notice that
+the error most of the time gets much
+
+ align:start position:0%
+the error most of the time gets much
+ 
+
+ align:start position:0%
+the error most of the time gets much
+smaller there are a series of of really
+
+ align:start position:0%
+smaller there are a series of of really
+ 
+
+ align:start position:0%
+smaller there are a series of of really
+what amount to impulses that we can't
+
+ align:start position:0%
+what amount to impulses that we can't
+ 
+
+ align:start position:0%
+what amount to impulses that we can't
+see very well let's see if we can
+
+ align:start position:0%
+see very well let's see if we can
+ 
+
+ align:start position:0%
+see very well let's see if we can
+brighten them up uh there's a series of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impulses here here here here
+
+ align:start position:0%
+impulses here here here here
+ 
+
+ align:start position:0%
+impulses here here here here
+here and the rest of the time the error
+
+ align:start position:0%
+here and the rest of the time the error
+ 
+
+ align:start position:0%
+here and the rest of the time the error
+is very very nearly zero to within our
+
+ align:start position:0%
+is very very nearly zero to within our
+ 
+
+ align:start position:0%
+is very very nearly zero to within our
+our ability to measure it this line is
+
+ align:start position:0%
+our ability to measure it this line is
+ 
+
+ align:start position:0%
+our ability to measure it this line is
+zero does do that make
+
+ align:start position:0%
+zero does do that make
+ 
+
+ align:start position:0%
+zero does do that make
+sense well here we we have changed the
+
+ align:start position:0%
+sense well here we we have changed the
+ 
+
+ align:start position:0%
+sense well here we we have changed the
+amplifier so that over a wide range of
+
+ align:start position:0%
+amplifier so that over a wide range of
+ 
+
+ align:start position:0%
+amplifier so that over a wide range of
+frequencies its open loop transfer
+
+ align:start position:0%
+frequencies its open loop transfer
+ 
+
+ align:start position:0%
+frequencies its open loop transfer
+function falls off as 1 / S2 in other
+
+ align:start position:0%
+function falls off as 1 / S2 in other
+ 
+
+ align:start position:0%
+function falls off as 1 / S2 in other
+words over a wide range of frequencies
+
+ align:start position:0%
+words over a wide range of frequencies
+ 
+
+ align:start position:0%
+words over a wide range of frequencies
+the output is the second integral of the
+
+ align:start position:0%
+the output is the second integral of the
+ 
+
+ align:start position:0%
+the output is the second integral of the
+error signal or correspondingly the
+
+ align:start position:0%
+error signal or correspondingly the
+ 
+
+ align:start position:0%
+error signal or correspondingly the
+error signal is the second derivative of
+
+ align:start position:0%
+error signal is the second derivative of
+ 
+
+ align:start position:0%
+error signal is the second derivative of
+the output signal we have a series of
+
+ align:start position:0%
+the output signal we have a series of
+ 
+
+ align:start position:0%
+the output signal we have a series of
+ramps at the output a triangle wave at
+
+ align:start position:0%
+ramps at the output a triangle wave at
+ 
+
+ align:start position:0%
+ramps at the output a triangle wave at
+the output why we'd anticipate that that
+
+ align:start position:0%
+the output why we'd anticipate that that
+ 
+
+ align:start position:0%
+the output why we'd anticipate that that
+the input signal would be the second
+
+ align:start position:0%
+the input signal would be the second
+ 
+
+ align:start position:0%
+the input signal would be the second
+derivative of the triangle wave or a
+
+ align:start position:0%
+derivative of the triangle wave or a
+ 
+
+ align:start position:0%
+derivative of the triangle wave or a
+series of impulses of course they're not
+
+ align:start position:0%
+series of impulses of course they're not
+ 
+
+ align:start position:0%
+series of impulses of course they're not
+perfect impulses they don't go to
+
+ align:start position:0%
+perfect impulses they don't go to
+ 
+
+ align:start position:0%
+perfect impulses they don't go to
+infinity and all that uh reflecting the
+
+ align:start position:0%
+infinity and all that uh reflecting the
+ 
+
+ align:start position:0%
+infinity and all that uh reflecting the
+the fact that we don't have a 1 / s^ s
+
+ align:start position:0%
+the fact that we don't have a 1 / s^ s
+ 
+
+ align:start position:0%
+the fact that we don't have a 1 / s^ s
+transfer function at all frequencies but
+
+ align:start position:0%
+transfer function at all frequencies but
+ 
+
+ align:start position:0%
+transfer function at all frequencies but
+we get a series of of small
+
+ align:start position:0%
+we get a series of of small
+ 
+
+ align:start position:0%
+we get a series of of small
+impulses and the important point is that
+
+ align:start position:0%
+impulses and the important point is that
+ 
+
+ align:start position:0%
+impulses and the important point is that
+most of the time the error is much much
+
+ align:start position:0%
+most of the time the error is much much
+ 
+
+ align:start position:0%
+most of the time the error is much much
+lower for one over s^2 compensation than
+
+ align:start position:0%
+lower for one over s^2 compensation than
+ 
+
+ align:start position:0%
+lower for one over s^2 compensation than
+it is for 1 / s compensation that simply
+
+ align:start position:0%
+it is for 1 / s compensation that simply
+ 
+
+ align:start position:0%
+it is for 1 / s compensation that simply
+reflects the fact that the open loop
+
+ align:start position:0%
+reflects the fact that the open loop
+ 
+
+ align:start position:0%
+reflects the fact that the open loop
+transfer function with 1 / s^2
+
+ align:start position:0%
+transfer function with 1 / s^2
+ 
+
+ align:start position:0%
+transfer function with 1 / s^2
+compensation is much much larger at many
+
+ align:start position:0%
+compensation is much much larger at many
+ 
+
+ align:start position:0%
+compensation is much much larger at many
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+frequencies uh recall that the
+
+ align:start position:0%
+frequencies uh recall that the
+ 
+
+ align:start position:0%
+frequencies uh recall that the
+comparison between the two was as shown
+
+ align:start position:0%
+comparison between the two was as shown
+ 
+
+ align:start position:0%
+comparison between the two was as shown
+here we have
+
+ align:start position:0%
+here we have
+ 
+
+ align:start position:0%
+here we have
+the orange curve showing the 1 / s s
+
+ align:start position:0%
+the orange curve showing the 1 / s s
+ 
+
+ align:start position:0%
+the orange curve showing the 1 / s s
+compensation the yellow curve showing
+
+ align:start position:0%
+compensation the yellow curve showing
+ 
+
+ align:start position:0%
+compensation the yellow curve showing
+the single pole
+
+ align:start position:0%
+the single pole
+ 
+
+ align:start position:0%
+the single pole
+compensation and over all of these
+
+ align:start position:0%
+compensation and over all of these
+ 
+
+ align:start position:0%
+compensation and over all of these
+frequencies we have have considerably
+
+ align:start position:0%
+frequencies we have have considerably
+ 
+
+ align:start position:0%
+frequencies we have have considerably
+higher open loop gain from the two-pole
+
+ align:start position:0%
+higher open loop gain from the two-pole
+ 
+
+ align:start position:0%
+higher open loop gain from the two-pole
+compensated amplifier we'd anticipate
+
+ align:start position:0%
+compensated amplifier we'd anticipate
+ 
+
+ align:start position:0%
+compensated amplifier we'd anticipate
+and prove the sensitivity for any signal
+
+ align:start position:0%
+and prove the sensitivity for any signal
+ 
+
+ align:start position:0%
+and prove the sensitivity for any signal
+where the majority of the signal
+
+ align:start position:0%
+where the majority of the signal
+ 
+
+ align:start position:0%
+where the majority of the signal
+frequency components lay in this region
+
+ align:start position:0%
+frequency components lay in this region
+ 
+
+ align:start position:0%
+frequency components lay in this region
+where most of the signal energy was
+
+ align:start position:0%
+where most of the signal energy was
+ 
+
+ align:start position:0%
+where most of the signal energy was
+concentrated in this region uh the
+
+ align:start position:0%
+concentrated in this region uh the
+ 
+
+ align:start position:0%
+concentrated in this region uh the
+triangle wave that we've chosen happens
+
+ align:start position:0%
+triangle wave that we've chosen happens
+ 
+
+ align:start position:0%
+triangle wave that we've chosen happens
+to be one like that where the 5 KZ
+
+ align:start position:0%
+to be one like that where the 5 KZ
+ 
+
+ align:start position:0%
+to be one like that where the 5 KZ
+fundamental and the appropriate
+
+ align:start position:0%
+fundamental and the appropriate
+ 
+
+ align:start position:0%
+fundamental and the appropriate
+harmonics lie in this region or most of
+
+ align:start position:0%
+harmonics lie in this region or most of
+ 
+
+ align:start position:0%
+harmonics lie in this region or most of
+them lie in this region we get greatly
+
+ align:start position:0%
+them lie in this region we get greatly
+ 
+
+ align:start position:0%
+them lie in this region we get greatly
+improved desensitivity a much small
+
+ align:start position:0%
+improved desensitivity a much small
+ 
+
+ align:start position:0%
+improved desensitivity a much small
+smaller error signal in the system in
+
+ align:start position:0%
+smaller error signal in the system in
+ 
+
+ align:start position:0%
+smaller error signal in the system in
+fact we haven't particularly cheated by
+
+ align:start position:0%
+fact we haven't particularly cheated by
+ 
+
+ align:start position:0%
+fact we haven't particularly cheated by
+by picking a particularly fortunate test
+
+ align:start position:0%
+by picking a particularly fortunate test
+ 
+
+ align:start position:0%
+by picking a particularly fortunate test
+signal if we uh uh use the sonoid
+
+ align:start position:0%
+signal if we uh uh use the sonoid
+ 
+
+ align:start position:0%
+signal if we uh uh use the sonoid
+anywhere from this frequency to this
+
+ align:start position:0%
+anywhere from this frequency to this
+ 
+
+ align:start position:0%
+anywhere from this frequency to this
+frequency the numbers here are are
+
+ align:start position:0%
+frequency the numbers here are are
+ 
+
+ align:start position:0%
+frequency the numbers here are are
+something like 10 Hertz and 100 or 150
+
+ align:start position:0%
+something like 10 Hertz and 100 or 150
+ 
+
+ align:start position:0%
+something like 10 Hertz and 100 or 150
+ktz any signal in that region uh
+
+ align:start position:0%
+ktz any signal in that region uh
+ 
+
+ align:start position:0%
+ktz any signal in that region uh
+would or any signal whose dominant
+
+ align:start position:0%
+would or any signal whose dominant
+ 
+
+ align:start position:0%
+would or any signal whose dominant
+spectral components lay in that region
+
+ align:start position:0%
+spectral components lay in that region
+ 
+
+ align:start position:0%
+spectral components lay in that region
+would get a considerably smaller error
+
+ align:start position:0%
+would get a considerably smaller error
+ 
+
+ align:start position:0%
+would get a considerably smaller error
+signal with 1 / s squ compensation than
+
+ align:start position:0%
+signal with 1 / s squ compensation than
+ 
+
+ align:start position:0%
+signal with 1 / s squ compensation than
+with one /s
+
+ align:start position:0%
+with one /s
+ 
+
+ align:start position:0%
+with one /s
+compensation
+
+ align:start position:0%
+compensation
+ 
+
+ align:start position:0%
+compensation
+well why don't we always use 1/ s^ squ
+
+ align:start position:0%
+well why don't we always use 1/ s^ squ
+ 
+
+ align:start position:0%
+well why don't we always use 1/ s^ squ
+compensation one of the problems is it's
+
+ align:start position:0%
+compensation one of the problems is it's
+ 
+
+ align:start position:0%
+compensation one of the problems is it's
+nowhere near as general purpose the 1/ S
+
+ align:start position:0%
+nowhere near as general purpose the 1/ S
+ 
+
+ align:start position:0%
+nowhere near as general purpose the 1/ S
+squ compensation really has to be very
+
+ align:start position:0%
+squ compensation really has to be very
+ 
+
+ align:start position:0%
+squ compensation really has to be very
+carefully tailored to the particular
+
+ align:start position:0%
+carefully tailored to the particular
+ 
+
+ align:start position:0%
+carefully tailored to the particular
+application we have to cross over in the
+
+ align:start position:0%
+application we have to cross over in the
+ 
+
+ align:start position:0%
+application we have to cross over in the
+region where the open loop transfer
+
+ align:start position:0%
+region where the open loop transfer
+ 
+
+ align:start position:0%
+region where the open loop transfer
+function is dropping off as 1 / s if we
+
+ align:start position:0%
+function is dropping off as 1 / s if we
+ 
+
+ align:start position:0%
+function is dropping off as 1 / s if we
+cross over at lower free frequencies we
+
+ align:start position:0%
+cross over at lower free frequencies we
+ 
+
+ align:start position:0%
+cross over at lower free frequencies we
+run into a stability problem because of
+
+ align:start position:0%
+run into a stability problem because of
+ 
+
+ align:start position:0%
+run into a stability problem because of
+limited phase margin uh in the case of
+
+ align:start position:0%
+limited phase margin uh in the case of
+ 
+
+ align:start position:0%
+limited phase margin uh in the case of
+single pole compensation why we're able
+
+ align:start position:0%
+single pole compensation why we're able
+ 
+
+ align:start position:0%
+single pole compensation why we're able
+to if if we lower crossover frequency we
+
+ align:start position:0%
+to if if we lower crossover frequency we
+ 
+
+ align:start position:0%
+to if if we lower crossover frequency we
+the system becomes slower but stability
+
+ align:start position:0%
+the system becomes slower but stability
+ 
+
+ align:start position:0%
+the system becomes slower but stability
+isn't compromised however that's not the
+
+ align:start position:0%
+isn't compromised however that's not the
+ 
+
+ align:start position:0%
+isn't compromised however that's not the
+case with 1/ s squ so we have to be a
+
+ align:start position:0%
+case with 1/ s squ so we have to be a
+ 
+
+ align:start position:0%
+case with 1/ s squ so we have to be a
+little bit more careful in our choice we
+
+ align:start position:0%
+little bit more careful in our choice we
+ 
+
+ align:start position:0%
+little bit more careful in our choice we
+have to know the application somewhat
+
+ align:start position:0%
+have to know the application somewhat
+ 
+
+ align:start position:0%
+have to know the application somewhat
+better um another consideration is what
+
+ align:start position:0%
+better um another consideration is what
+ 
+
+ align:start position:0%
+better um another consideration is what
+happens if we somehow Force another pole
+
+ align:start position:0%
+happens if we somehow Force another pole
+ 
+
+ align:start position:0%
+happens if we somehow Force another pole
+in the loop suppose we could pass L load
+
+ align:start position:0%
+in the loop suppose we could pass L load
+ 
+
+ align:start position:0%
+in the loop suppose we could pass L load
+the amplifier which has the effect of
+
+ align:start position:0%
+the amplifier which has the effect of
+ 
+
+ align:start position:0%
+the amplifier which has the effect of
+forcing another pole if we do that why
+
+ align:start position:0%
+forcing another pole if we do that why
+ 
+
+ align:start position:0%
+forcing another pole if we do that why
+we find out that that with one over s
+
+ align:start position:0%
+we find out that that with one over s
+ 
+
+ align:start position:0%
+we find out that that with one over s
+squ compensation stability or
+
+ align:start position:0%
+squ compensation stability or
+ 
+
+ align:start position:0%
+squ compensation stability or
+instability is a very real possibility
+
+ align:start position:0%
+instability is a very real possibility
+ 
+
+ align:start position:0%
+instability is a very real possibility
+and because we can force crossover back
+
+ align:start position:0%
+and because we can force crossover back
+ 
+
+ align:start position:0%
+and because we can force crossover back
+to relatively lower frequencies where
+
+ align:start position:0%
+to relatively lower frequencies where
+ 
+
+ align:start position:0%
+to relatively lower frequencies where
+the amplifier even without the
+
+ align:start position:0%
+the amplifier even without the
+ 
+
+ align:start position:0%
+the amplifier even without the
+additional load has limited phase margin
+
+ align:start position:0%
+additional load has limited phase margin
+ 
+
+ align:start position:0%
+additional load has limited phase margin
+we then add the additional Pole from the
+
+ align:start position:0%
+we then add the additional Pole from the
+ 
+
+ align:start position:0%
+we then add the additional Pole from the
+load capacitor and instability is a very
+
+ align:start position:0%
+load capacitor and instability is a very
+ 
+
+ align:start position:0%
+load capacitor and instability is a very
+real possibility so there are those
+
+ align:start position:0%
+real possibility so there are those
+ 
+
+ align:start position:0%
+real possibility so there are those
+kinds of disadvantages but again if it's
+
+ align:start position:0%
+kinds of disadvantages but again if it's
+ 
+
+ align:start position:0%
+kinds of disadvantages but again if it's
+carefully chosen if we know the
+
+ align:start position:0%
+carefully chosen if we know the
+ 
+
+ align:start position:0%
+carefully chosen if we know the
+application we know what loads to
+
+ align:start position:0%
+application we know what loads to
+ 
+
+ align:start position:0%
+application we know what loads to
+anticipate we know the capacitors aren't
+
+ align:start position:0%
+anticipate we know the capacitors aren't
+ 
+
+ align:start position:0%
+anticipate we know the capacitors aren't
+included uh it it gives us very
+
+ align:start position:0%
+included uh it it gives us very
+ 
+
+ align:start position:0%
+included uh it it gives us very
+dramatically improved desensitivity as
+
+ align:start position:0%
+dramatically improved desensitivity as
+ 
+
+ align:start position:0%
+dramatically improved desensitivity as
+we've seen from the demonstration
+
+ align:start position:0%
+we've seen from the demonstration
+ 
+
+ align:start position:0%
+we've seen from the demonstration
+there's one final effect associated with
+
+ align:start position:0%
+there's one final effect associated with
+ 
+
+ align:start position:0%
+there's one final effect associated with
+either the two-pole compensation or the
+
+ align:start position:0%
+either the two-pole compensation or the
+ 
+
+ align:start position:0%
+either the two-pole compensation or the
+same sort of thing happens with lag
+
+ align:start position:0%
+same sort of thing happens with lag
+ 
+
+ align:start position:0%
+same sort of thing happens with lag
+compensation recall the sort of
+
+ align:start position:0%
+compensation recall the sort of
+ 
+
+ align:start position:0%
+compensation recall the sort of
+prolonged settling transient we saw when
+
+ align:start position:0%
+prolonged settling transient we saw when
+ 
+
+ align:start position:0%
+prolonged settling transient we saw when
+we applied small steps to the system we
+
+ align:start position:0%
+we applied small steps to the system we
+ 
+
+ align:start position:0%
+we applied small steps to the system we
+we can explain that as follows here's a
+
+ align:start position:0%
+we can explain that as follows here's a
+ 
+
+ align:start position:0%
+we can explain that as follows here's a
+root Locus diagram uh here we have
+
+ align:start position:0%
+root Locus diagram uh here we have
+ 
+
+ align:start position:0%
+root Locus diagram uh here we have
+assumed two low frequency poles uh
+
+ align:start position:0%
+assumed two low frequency poles uh
+ 
+
+ align:start position:0%
+assumed two low frequency poles uh
+they're not actually coincident as I've
+
+ align:start position:0%
+they're not actually coincident as I've
+ 
+
+ align:start position:0%
+they're not actually coincident as I've
+shown them but this models the uh
+
+ align:start position:0%
+shown them but this models the uh
+ 
+
+ align:start position:0%
+shown them but this models the uh
+two-pole rolloff that starts at low
+
+ align:start position:0%
+two-pole rolloff that starts at low
+ 
+
+ align:start position:0%
+two-pole rolloff that starts at low
+frequencies we have a zero which
+
+ align:start position:0%
+frequencies we have a zero which
+ 
+
+ align:start position:0%
+frequencies we have a zero which
+flattens out the curve to a 1/s roll off
+
+ align:start position:0%
+flattens out the curve to a 1/s roll off
+ 
+
+ align:start position:0%
+flattens out the curve to a 1/s roll off
+in the vicinity of
+
+ align:start position:0%
+in the vicinity of
+ 
+
+ align:start position:0%
+in the vicinity of
+crossover and then I've assumed some
+
+ align:start position:0%
+crossover and then I've assumed some
+ 
+
+ align:start position:0%
+crossover and then I've assumed some
+additional high frequency poles
+
+ align:start position:0%
+additional high frequency poles
+ 
+
+ align:start position:0%
+additional high frequency poles
+associated with the amplifier we've seen
+
+ align:start position:0%
+associated with the amplifier we've seen
+ 
+
+ align:start position:0%
+associated with the amplifier we've seen
+this kind of pattern before or we get a
+
+ align:start position:0%
+this kind of pattern before or we get a
+ 
+
+ align:start position:0%
+this kind of pattern before or we get a
+a root Locus picture that depending on
+
+ align:start position:0%
+a root Locus picture that depending on
+ 
+
+ align:start position:0%
+a root Locus picture that depending on
+the relative spacing of the poles in
+
+ align:start position:0%
+the relative spacing of the poles in
+ 
+
+ align:start position:0%
+the relative spacing of the poles in
+zero either circles around comes
+
+ align:start position:0%
+zero either circles around comes
+ 
+
+ align:start position:0%
+zero either circles around comes
+back one branch coming back to the zero
+
+ align:start position:0%
+back one branch coming back to the zero
+ 
+
+ align:start position:0%
+back one branch coming back to the zero
+another one going out here meeting an
+
+ align:start position:0%
+another one going out here meeting an
+ 
+
+ align:start position:0%
+another one going out here meeting an
+incoming branch and then finally
+
+ align:start position:0%
+incoming branch and then finally
+ 
+
+ align:start position:0%
+incoming branch and then finally
+breaking off like so or again for a
+
+ align:start position:0%
+breaking off like so or again for a
+ 
+
+ align:start position:0%
+breaking off like so or again for a
+different arrangement of the zero and
+
+ align:start position:0%
+different arrangement of the zero and
+ 
+
+ align:start position:0%
+different arrangement of the zero and
+poles uh does
+
+ align:start position:0%
+poles uh does
+ 
+
+ align:start position:0%
+poles uh does
+something like this we looked at this
+
+ align:start position:0%
+something like this we looked at this
+ 
+
+ align:start position:0%
+something like this we looked at this
+case in detail when we were when we
+
+ align:start position:0%
+case in detail when we were when we
+ 
+
+ align:start position:0%
+case in detail when we were when we
+first introduced the idea of root Locus
+
+ align:start position:0%
+first introduced the idea of root Locus
+ 
+
+ align:start position:0%
+first introduced the idea of root Locus
+in any case we normally operate this
+
+ align:start position:0%
+in any case we normally operate this
+ 
+
+ align:start position:0%
+in any case we normally operate this
+amplifier with its dominant closed loop
+
+ align:start position:0%
+amplifier with its dominant closed loop
+ 
+
+ align:start position:0%
+amplifier with its dominant closed loop
+Pooles out here somewhere and under
+
+ align:start position:0%
+Pooles out here somewhere and under
+ 
+
+ align:start position:0%
+Pooles out here somewhere and under
+those conditions the uh transient
+
+ align:start position:0%
+those conditions the uh transient
+ 
+
+ align:start position:0%
+those conditions the uh transient
+responses corresponding to the two
+
+ align:start position:0%
+responses corresponding to the two
+ 
+
+ align:start position:0%
+responses corresponding to the two
+amplifiers look pretty much the same
+
+ align:start position:0%
+amplifiers look pretty much the same
+ 
+
+ align:start position:0%
+amplifiers look pretty much the same
+because they're dominated by or the two
+
+ align:start position:0%
+because they're dominated by or the two
+ 
+
+ align:start position:0%
+because they're dominated by or the two
+possibilities look pretty much the same
+
+ align:start position:0%
+possibilities look pretty much the same
+ 
+
+ align:start position:0%
+possibilities look pretty much the same
+they're dominated by this closed loop
+
+ align:start position:0%
+they're dominated by this closed loop
+ 
+
+ align:start position:0%
+they're dominated by this closed loop
+pole pair
+
+ align:start position:0%
+pole pair
+ 
+
+ align:start position:0%
+pole pair
+however down in this region there's a
+
+ align:start position:0%
+however down in this region there's a
+ 
+
+ align:start position:0%
+however down in this region there's a
+pole zero doublet there's a zero
+
+ align:start position:0%
+pole zero doublet there's a zero
+ 
+
+ align:start position:0%
+pole zero doublet there's a zero
+associated with our
+
+ align:start position:0%
+associated with our
+ 
+
+ align:start position:0%
+associated with our
+compensation if you will the zero
+
+ align:start position:0%
+compensation if you will the zero
+ 
+
+ align:start position:0%
+compensation if you will the zero
+appears in the forward path the tal S
+
+ align:start position:0%
+appears in the forward path the tal S
+ 
+
+ align:start position:0%
+appears in the forward path the tal S
+Plus One expression in the forward path
+
+ align:start position:0%
+Plus One expression in the forward path
+ 
+
+ align:start position:0%
+Plus One expression in the forward path
+this Branch for the types of aot fots
+
+ align:start position:0%
+this Branch for the types of aot fots
+ 
+
+ align:start position:0%
+this Branch for the types of aot fots
+that we normally use has moved in quite
+
+ align:start position:0%
+that we normally use has moved in quite
+ 
+
+ align:start position:0%
+that we normally use has moved in quite
+close to the zero so we have a low
+
+ align:start position:0%
+close to the zero so we have a low
+ 
+
+ align:start position:0%
+close to the zero so we have a low
+frequency zero and at just a slightly
+
+ align:start position:0%
+frequency zero and at just a slightly
+ 
+
+ align:start position:0%
+frequency zero and at just a slightly
+higher frequency of pole they very
+
+ align:start position:0%
+higher frequency of pole they very
+ 
+
+ align:start position:0%
+higher frequency of pole they very
+nearly cancel they they're separated by
+
+ align:start position:0%
+nearly cancel they they're separated by
+ 
+
+ align:start position:0%
+nearly cancel they they're separated by
+a few percent uh the basic transient
+
+ align:start position:0%
+a few percent uh the basic transient
+ 
+
+ align:start position:0%
+a few percent uh the basic transient
+response is that associated with the
+
+ align:start position:0%
+response is that associated with the
+ 
+
+ align:start position:0%
+response is that associated with the
+complex conjugate pole pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what we do is look if you will at
+
+ align:start position:0%
+but what we do is look if you will at
+ 
+
+ align:start position:0%
+but what we do is look if you will at
+the complex conjugate pole pair through
+
+ align:start position:0%
+the complex conjugate pole pair through
+ 
+
+ align:start position:0%
+the complex conjugate pole pair through
+a filter that has the following form
+
+ align:start position:0%
+a filter that has the following form
+ 
+
+ align:start position:0%
+a filter that has the following form
+here's the closely spaced dublet
+
+ align:start position:0%
+here's the closely spaced dublet
+ 
+
+ align:start position:0%
+here's the closely spaced dublet
+epsilon's a small number uh as the
+
+ align:start position:0%
+epsilon's a small number uh as the
+ 
+
+ align:start position:0%
+epsilon's a small number uh as the
+situation was shown in the view graph we
+
+ align:start position:0%
+situation was shown in the view graph we
+ 
+
+ align:start position:0%
+situation was shown in the view graph we
+have a zero at a somewhat lower
+
+ align:start position:0%
+have a zero at a somewhat lower
+ 
+
+ align:start position:0%
+have a zero at a somewhat lower
+frequency than the pole so we can
+
+ align:start position:0%
+frequency than the pole so we can
+ 
+
+ align:start position:0%
+frequency than the pole so we can
+visualize the system as as being one
+
+ align:start position:0%
+visualize the system as as being one
+ 
+
+ align:start position:0%
+visualize the system as as being one
+that gives us the step response
+
+ align:start position:0%
+that gives us the step response
+ 
+
+ align:start position:0%
+that gives us the step response
+corresponding to the two poles the
+
+ align:start position:0%
+corresponding to the two poles the
+ 
+
+ align:start position:0%
+corresponding to the two poles the
+dominant pole pair but we view that step
+
+ align:start position:0%
+dominant pole pair but we view that step
+ 
+
+ align:start position:0%
+dominant pole pair but we view that step
+response through a filter that has this
+
+ align:start position:0%
+response through a filter that has this
+ 
+
+ align:start position:0%
+response through a filter that has this
+transfer function well the step response
+
+ align:start position:0%
+transfer function well the step response
+ 
+
+ align:start position:0%
+transfer function well the step response
+of this transfer function is of the
+
+ align:start position:0%
+of this transfer function is of the
+ 
+
+ align:start position:0%
+of this transfer function is of the
+following form uh this is basically the
+
+ align:start position:0%
+following form uh this is basically the
+ 
+
+ align:start position:0%
+following form uh this is basically the
+uncompensated or the overcompensated
+
+ align:start position:0%
+uncompensated or the overcompensated
+ 
+
+ align:start position:0%
+uncompensated or the overcompensated
+scope probe if you adjust the transient
+
+ align:start position:0%
+scope probe if you adjust the transient
+ 
+
+ align:start position:0%
+scope probe if you adjust the transient
+response of a scope probe what you're
+
+ align:start position:0%
+response of a scope probe what you're
+ 
+
+ align:start position:0%
+response of a scope probe what you're
+really doing is trying to get a pole in
+
+ align:start position:0%
+really doing is trying to get a pole in
+ 
+
+ align:start position:0%
+really doing is trying to get a pole in
+a zero doublet to cancel each other uh
+
+ align:start position:0%
+a zero doublet to cancel each other uh
+ 
+
+ align:start position:0%
+a zero doublet to cancel each other uh
+so this is the case where we haven't
+
+ align:start position:0%
+so this is the case where we haven't
+ 
+
+ align:start position:0%
+so this is the case where we haven't
+perfectly compensated the scope probe
+
+ align:start position:0%
+perfectly compensated the scope probe
+ 
+
+ align:start position:0%
+perfectly compensated the scope probe
+this is the highpass version of the
+
+ align:start position:0%
+this is the highpass version of the
+ 
+
+ align:start position:0%
+this is the highpass version of the
+thing where the zero is located at a
+
+ align:start position:0%
+thing where the zero is located at a
+ 
+
+ align:start position:0%
+thing where the zero is located at a
+slightly lower frequency or a slightly
+
+ align:start position:0%
+slightly lower frequency or a slightly
+ 
+
+ align:start position:0%
+slightly lower frequency or a slightly
+longer time constant than the pole the
+
+ align:start position:0%
+longer time constant than the pole the
+ 
+
+ align:start position:0%
+longer time constant than the pole the
+step response of that sort of system uh
+
+ align:start position:0%
+step response of that sort of system uh
+ 
+
+ align:start position:0%
+step response of that sort of system uh
+is as follows if we put in a unit step
+
+ align:start position:0%
+is as follows if we put in a unit step
+ 
+
+ align:start position:0%
+is as follows if we put in a unit step
+we get a in this case with a zero at
+
+ align:start position:0%
+we get a in this case with a zero at
+ 
+
+ align:start position:0%
+we get a in this case with a zero at
+lower frequency we get an output that
+
+ align:start position:0%
+lower frequency we get an output that
+ 
+
+ align:start position:0%
+lower frequency we get an output that
+overshoots final value by an amount
+
+ align:start position:0%
+overshoots final value by an amount
+ 
+
+ align:start position:0%
+overshoots final value by an amount
+Epsilon decays with a time constant
+
+ align:start position:0%
+Epsilon decays with a time constant
+ 
+
+ align:start position:0%
+Epsilon decays with a time constant
+corresponding to the pole location in
+
+ align:start position:0%
+corresponding to the pole location in
+ 
+
+ align:start position:0%
+corresponding to the pole location in
+our particular case the pole is located
+
+ align:start position:0%
+our particular case the pole is located
+ 
+
+ align:start position:0%
+our particular case the pole is located
+at a considerably lower frequency than
+
+ align:start position:0%
+at a considerably lower frequency than
+ 
+
+ align:start position:0%
+at a considerably lower frequency than
+the dominant response associated with
+
+ align:start position:0%
+the dominant response associated with
+ 
+
+ align:start position:0%
+the dominant response associated with
+the dominant pole pair and so what we
+
+ align:start position:0%
+the dominant pole pair and so what we
+ 
+
+ align:start position:0%
+the dominant pole pair and so what we
+see is the highfrequency
+
+ align:start position:0%
+see is the highfrequency
+ 
+
+ align:start position:0%
+see is the highfrequency
+response the overshoot if you will as
+
+ align:start position:0%
+response the overshoot if you will as
+ 
+
+ align:start position:0%
+response the overshoot if you will as
+the dominant response but there's a long
+
+ align:start position:0%
+the dominant response but there's a long
+ 
+
+ align:start position:0%
+the dominant response but there's a long
+tail that reflects the much longer time
+
+ align:start position:0%
+tail that reflects the much longer time
+ 
+
+ align:start position:0%
+tail that reflects the much longer time
+constant associated with the pole of the
+
+ align:start position:0%
+constant associated with the pole of the
+ 
+
+ align:start position:0%
+constant associated with the pole of the
+pole zero doublet and that sort of thing
+
+ align:start position:0%
+pole zero doublet and that sort of thing
+ 
+
+ align:start position:0%
+pole zero doublet and that sort of thing
+happens as I say with lag compensation
+
+ align:start position:0%
+happens as I say with lag compensation
+ 
+
+ align:start position:0%
+happens as I say with lag compensation
+as well as as with
+
+ align:start position:0%
+as well as as with
+ 
+
+ align:start position:0%
+as well as as with
+two- pole compensation when we do
+
+ align:start position:0%
+two- pole compensation when we do
+ 
+
+ align:start position:0%
+two- pole compensation when we do
+feedback compensation and so one of the
+
+ align:start position:0%
+feedback compensation and so one of the
+ 
+
+ align:start position:0%
+feedback compensation and so one of the
+disadvantages of this sort of
+
+ align:start position:0%
+disadvantages of this sort of
+ 
+
+ align:start position:0%
+disadvantages of this sort of
+compensation uh may be that if we if we
+
+ align:start position:0%
+compensation uh may be that if we if we
+ 
+
+ align:start position:0%
+compensation uh may be that if we if we
+are really concerned about settling to a
+
+ align:start position:0%
+are really concerned about settling to a
+ 
+
+ align:start position:0%
+are really concerned about settling to a
+very small fraction of final value that
+
+ align:start position:0%
+very small fraction of final value that
+ 
+
+ align:start position:0%
+very small fraction of final value that
+settling time may be
+
+ align:start position:0%
+settling time may be
+ 
+
+ align:start position:0%
+settling time may be
+compromised next time we'll look at two
+
+ align:start position:0%
+compromised next time we'll look at two
+ 
+
+ align:start position:0%
+compromised next time we'll look at two
+other ways that we can use monor Loop
+
+ align:start position:0%
+other ways that we can use monor Loop
+ 
+
+ align:start position:0%
+other ways that we can use monor Loop
+compensation for specific applications
+
+ align:start position:0%
+compensation for specific applications
+ 
+
+ align:start position:0%
+compensation for specific applications
+to improve the performance of this type
+
+ align:start position:0%
+to improve the performance of this type
+ 
+
+ align:start position:0%
+to improve the performance of this type
+of operational amplifier thank
+
+ align:start position:0%
+of operational amplifier thank
+ 
+
+ align:start position:0%
+of operational amplifier thank
+you
\ No newline at end of file