Thoughts Concerning Cordell, Otala, and Gilbert papers

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PB2 said:



.... Let me point out that the ringing is probably near the peak frequency certainly over 100 kHz and I doubt there is any real world audio signal with fast enough rise time to produce ringing....

While it makes perfect sense, I suggest to be taken with a grain of salt.

Depending on amplifier topology (high gain dominant pole op-amp for example, see Gilbert) it may well happen significant harmonic signals are present within the amplifier signal path (not at the output terminals) falling in the peaking zone.

That being the case, intermodulation products resulting from these components could be enhanced by underdamping, within the audio band.

I hasten to remark this is speculation on my part, but in the vein of pointing to hidden and implementation dependent sources of problems.

Rodolfo
 
PB2 said:
Anyway, they point out that this peaking causes ringing on square waves and therefore it cannot be right as far as a straight wire with gain - my interpretation.

I totally agree with you Pete.

There is no such a thing ,as square waves in music program.

Also the ringing from square waves ,from the signal generator are dependent of the signal generator rise time.

I prefer to perform the "null test" with music from a CD. And anytime that the null is more "silent" the sound subjectively gets better.

The null is so powerfully , as a tool for developing amplifiers that grounding errors, power supply errors become easily detected.

Is interesting that the usual miller capacitor in the VAS, is the stabilization method ,that gives the worst null. A capacitor to ground in the VAS stage produce a much better null. Our friend in this forum , Graham Maynard ,come to the same conclusion (although, by other reasons).
 
ingrast said:


While it makes perfect sense, I suggest to be taken with a grain of salt.

Depending on amplifier topology (high gain dominant pole op-amp for example, see Gilbert) it may well happen significant harmonic signals are present within the amplifier signal path (not at the output terminals) falling in the peaking zone.

That being the case, intermodulation products resulting from these components could be enhanced by underdamping, within the audio band.

I hasten to remark this is speculation on my part, but in the vein of pointing to hidden and implementation dependent sources of problems.

Rodolfo

Hi Rodolfo,
If what you said ever did happen those intermodulation products would not null out, they'd be there in the difference signal and therefore I think this claim is far fetched since the amp does provide an excellent null. I appreciate that you offer that your point is speculation. I would also hope that a system has some filtering to remove garbage above 50 to 100 kHz.
 
Tube_Dude said:


I totally agree with you Pete.

There is no such a thing ,as square waves in music program.

Also the ringing from square waves ,from the signal generator are dependent of the signal generator rise time.

I prefer to perform the "null test" with music from a CD. And anytime that the null is more "silent" the sound subjectively gets better.

The null is so powerfully , as a tool for developing amplifiers that grounding errors, power supply errors become easily detected.

Is interesting that the usual miller capacitor in the VAS, is the stabilization method ,that gives the worst null. A capacitor to ground in the VAS stage produce a much better null. Our friend in this forum , Graham Maynard ,come to the same conclusion (although, by other reasons).

Yes, this makes sense and it's interesting to note that the distortion in the Leach amp is .006% at 20 Hz, starts to rise from about 1 kHz and reaches .29 % at 20 kHz partly due to Cdom compensation as can be seen in Figure 4:
http://users.ece.gatech.edu/~mleach/lowtim/bckgrnd.html
Even .29% is low, and I don't get alarmed about it but the technical challenge to have low distortion even at high frequencies is interesting. It is interesting to contrast this with the Bryston amps which have very low distortion across the audio band.
 
PB2 said:


Hi Rodolfo,
If what you said ever did happen those intermodulation products would not null out, they'd be there in the difference signal and therefore I think this claim is far fetched since the amp does provide an excellent null. I appreciate that you offer that your point is speculation. I would also hope that a system has some filtering to remove garbage above 50 to 100 kHz.

If the null is consistent across the audio band and with any type of program material, then there is obviously no problem and that is why I also agree and support the null test as an ultimate objective performance assesment. Much more so if dynamically recorded and dissected. I even belive it is possible to construct from it, "signatures" pertaining to different approachs to design.

In my previous post I was thinking on the type of source like 1KHz or IM test signals. Then with some topologies there exists the possibility as speculated.

Rodolfo
 
LM3886 and high performance.

On another related line, I am doing some work with the LM3886 and find it truly remarkable in performance.
I mention this for in the "what's your reasoning .." thread, one of the last subjects touched involving jcx and Walt Jung among others, was the linearity concerns of the classic input differential stage, the comparison among BJT and FET implementations, and the consequences of emitter degeneration.

Interestingly, though the LM3886 implements a textbook topology (if we belive the published simplified schematic) the input differential PNP gain stage uses heavy emitter degeneration (1.1 K resistors). At this level, linearity improvement in this stage may well be at the root of its excellent behaviour (I've measured THD of 0.004% with an input signal measuring 0.002% for example)

Rodolfo
 
Re: LM3886 and high performance.

ingrast said:


Interestingly, though the LM3886 implements a textbook topology (if we belive the published simplified schematic) the input differential PNP gain stage uses heavy emitter degeneration (1.1 K resistors). At this level, linearity improvement in this stage may well be at the root of its excellent behaviour (I've measured THD of 0.004% with an input signal measuring 0.002% for example)

Rodolfo

Hi Rudolfo

Are you talking about THD (measured the classical way) or about null testing ?

If you do some null test measuring , in some amps , you will see that when you degenerate the emitters of the input LTP ,the null always get worst.

Please do some null tests...it's very enlightening !
 
PB2 said:
I first read about the issues with non-zero common-mode inputs in an article by Eric F. Taylor Wireless World, 1977. Edit: I mentioned the August issue in the first post here, there was a second part in the September issue. Taylor states that the varying Vcb with a common mode signal the diff amp input impedance is non-linear. I believe that this is due to the non-linear Miller capacitance.
Edit: We should note that this means the performance of the amp will depend on the driving source impedance.

Hi Pete,

Sorry to take so long to get back to you. The whole common-mode distortion thing is kind of complex, and I haven't sorted out what's really going on. Taylor's description makes a lot of sense, but there's also a couple of other scenarios with common-mode that come to mind.

In the derivation of the simplified expression

Idm = I0 * tanh(Vdm/2VT)

there's no restriction on the nature of I0. Specifically, it can be a function of time. Suppose the current source is not perfect, such that the common-mode input voltage sets up an AC component of I0. It's pretty clear you'll have multiplication in the time domain between two AC signals, so the diff amp will really be acting like a two-quadrant Gilbert cell mixer. The difference-mode input voltage will be modulated by a scaled and possibly distorted version of the common-mode input, producing additional distortion. I've seen this in the design of an RF diff amp that originally used a resistor instead of a current source (bad idea!).

Another scenario relates to the varying Vcb that Taylor mentions. In addition to the varying collector-base capacitance from this, the Early effect causes the transistor beta to be modulated with Vcb, causing the low-frequency input impedance to be somewhat Vcb-dependent as well.

As to which of these is dominant, I haven't a clue! :)

Just a quick thought about your AM-to-PM question, wouldn't it follow than any amplitude non-linearity (really transconductance non-linearity) turns into AM-to-PM in any Cdom compensated circuit since the integrator is a frequency dependent component? Edit: I think of this as an integrator where the resistor (diff amp transconductance) is amplitude, frequency, and/or time dependent.
I also notice that many such as Self assume a Cdom compensated circuit in their discussions, and I don't believe that the same conclusions are reached when Cdom is not used. I understand that it does apply, obviously, to most OP amps.

If you go through Gilbert's math, you'll see that the AM-to-PM comes from amplitude compression of the fundamental, combined with the quadrature phase relationship of the difference-mode input voltage relative to the output. Doing the KVL equations around the input loop at the fundamental frequency gives the AM-to-PM result. But suppose the nature of the nonlinearity ahead of the integrator were purely even order? Even-order nonlinearities don't produce any fundamental compression at all, just a DC distortion component in addition to the even-order harmonics. So if the nature of the distortion is even-order ahead of the integrator, there will be no closed-loop AM-to-PM contribution from that (because there is no amplitude compression of the fundamental). But for odd-order, yes I agree.

However, this jumped out at me (pg 2, 3rd paragraph): "Because the dominant source of nonlinearity is in the input cell, the distortion will be lowest in the voltage-follower mode." Shouldn't this be: unity gain inverting amplifier here, and not voltage-follower mode? Edit: Perhaps he was only considering non-inverting? Gilbert's analysis is familiar to me, it brings back memories from semiconductor classes.

He's only considering the non-inverting case. Also, the tanh() expression above that Gilbert uses is computed assuming zero collector-base capacitance, infinite Early voltage, and infinite CMRR. So while the distortion will probably be lowest in the unity-gain inverting mode in practice, the formulas Gilbert uses don't take into account any of the distortion terms from non-zero common-mode input. Within the limited scope of the errors he's considering, the statement is true, but I'll bet that in practice you're exactly correct.
 
Tube_Dude said:
Is interesting that the usual miller capacitor in the VAS, is the stabilization method ,that gives the worst null. A capacitor to ground in the VAS stage produce a much better null.

If you do some null test measuring , in some amps , you will see that when you degenerate the emitters of the input LTP ,the null always get worst.

If you want these tests to be fair, the gain-bandwidth product (which determines the margin of stability) should be held constant. Suppose you increase the emitter degeneration of a given amp such that the input stage gm is cut in half. To keep the gain-bandwidth product constant, the Miller compensation cap would also need to be cut in half, since the gain bandwidth product in rad/sec is gm/C. If you just cut gm in half, you'll be cutting the bandwidth in half, and cutting the high-frequency feedback in half. This would make the null test worse.

Regarding the case of the Miller C vs C to ground from the VAS output, if you take the Miller C, remove it and place a capacitor of the same value from the VAS output to ground, you'll increase the gain-bandwidth product dramatically. This will improve the null, assuming the amp is still stable. It was shown by Baxandall years ago that for the same gain-bandwidth product, the Miller C approach is greatly superior. To get the same gain-bandwidth product, it takes a very large capacitor to ground from the VAS output. This makes the high-frequency distortion quite large because the VAS will run out of output current trying to drive it at high frequencies. The exception to this is the case where the VAS is not a CE stage and the amp has the folded cascode topology. In that case, a Miller capacitor is not an option and the gain-bandwidth product is still gm/C. For the case where the VAS is a CE stage and the compensation cap is from the VAS output to ground, the gain-bandwidth product is much greater than gm/C but is not straightforward to compute.

My guess is that in both the cases you refer to above, you're not making the other changes that are necessary to hold the gain-bandwidth constant.
 
andy_c said:
Regarding the case of the Miller C vs C to ground from the VAS output, if you take the Miller C, remove it and place a capacitor of the same value from the VAS output to ground, you'll increase the gain-bandwidth product dramatically. This will improve the null, assuming the amp is still stable.

Hi Andy_C

Thanks for your input!.

When I talk about ,to change the compensation from Miller compensation , to capacitor from VAS to ground ,of course , that the capacitor is not of the some value or the amp will become undercompensated.

The crux , for a good null with music program is to use the more feedback possible in the audio band and for achieve this, sometimes can be useful to use two pole compensation.

For example , if you perform a null test with music program ,with a NE 5534 (that use two pole compensation) and a "non plus ultra" famous audio op amp (pick one you like) if you hear the residual null ,you will see (hear :) ) that the NE is more "silent".

The null is very interesting , because we can see in practice , how the circuits behave in real world conditions and playing real audio program.
 
andy_c said:

Sorry to take so long to get back to you. The whole common-mode distortion thing is kind of complex, and I haven't sorted out what's really going on. Taylor's description makes a lot of sense, but there's also a couple of other scenarios with common-mode that come to mind.

In the derivation of the simplified expression

Idm = I0 * tanh(Vdm/2VT)

there's no restriction on the nature of I0. Specifically, it can be a function of time. Suppose the current source is not perfect, such that the common-mode input voltage sets up an AC component of I0. It's pretty clear you'll have multiplication in the time domain between two AC signals, so the diff amp will really be acting like a two-quadrant Gilbert cell mixer. The difference-mode input voltage will be modulated by a scaled and possibly distorted version of the common-mode input, producing additional distortion. I've seen this in the design of an RF diff amp that originally used a resistor instead of a current source (bad idea!).

Another scenario relates to the varying Vcb that Taylor mentions. In addition to the varying collector-base capacitance from this, the Early effect causes the transistor beta to be modulated with Vcb, causing the low-frequency input impedance to be somewhat Vcb-dependent as well.


Yes, it is complicated and I understand your points, while the thread topic is the papers I tend to lean toward real world circuits while getting some insight from the simplified models in these papers. I like Gilbert's paper but as even he points out it is highly simplified. I'm mostly interested in power amp design but of course we can get insight into what's going on from these papers. It's been some time since I read the Taylor's papers, and I don't have plans right now to dig too deep into them. I was aware of the other distortion mechanisms that you mention. Noting the frequency dependency and nature of the distortion can help determine the source.
I brought up the common mode issue because it applied to Cordell's paper and is important for general use of OP amps especially with large signals at unity gain. But the analysis is very different for an amp with smaller input signals, degeneration in the diff amp, and non-linear parasitic device Miller capacitance rather than the more linear case where Cdom capacitance is used.
 
andy_c said:

If you go through Gilbert's math, you'll see that the AM-to-PM comes from amplitude compression of the fundamental, combined with the quadrature phase relationship of the difference-mode input voltage relative to the output. Doing the KVL equations around the input loop at the fundamental frequency gives the AM-to-PM result. But suppose the nature of the nonlinearity ahead of the integrator were purely even order? Even-order nonlinearities don't produce any fundamental compression at all, just a DC distortion component in addition to the even-order harmonics. So if the nature of the distortion is even-order ahead of the integrator, there will be no closed-loop AM-to-PM contribution from that (because there is no amplitude compression of the fundamental). But for odd-order, yes I agree.

I loosly took your AM-to-PM to be amplitude non-linearity to PM. As I see it, any transconductance non-linearity will cause the dominant pole to move in frequency and result in modulation of the phase. I wasn't concerned only with AM, but I realize that was what you stated.

andy_c said:

He's only considering the non-inverting case. Also, the tanh() expression above that Gilbert uses is computed assuming zero collector-base capacitance, infinite Early voltage, and infinite CMRR. So while the distortion will probably be lowest in the unity-gain inverting mode in practice, the formulas Gilbert uses don't take into account any of the distortion terms from non-zero common-mode input. Within the limited scope of the errors he's considering, the statement is true, but I'll bet that in practice you're exactly correct.

Thanks, this makes sense.
 
PB2 said:
I loosly took your AM-to-PM to be amplitude non-linearity to PM. As I see it, any transconductance non-linearity will cause the dominant pole to move in frequency and result in modulation of the phase. I wasn't concerned only with AM, but I realize that was what you stated.

It seems there's a subtle but important difference in our terminology. I agree completely that any transconductance nonlinearity ahead of the integrator will result in instantaneous phase modulation, with associated distortion terms. But Gilbert's analysis, and the terminology I've been using assumes we're looking at something like a table of input-ouput phase shift at the fundamental frequency vs the amplitude of a sinusoid at the input (not the instantaneous input voltage value). Setting the integrator aside for a moment, if only even-order nonlinearities are present in the transconductance, there is no compression or expansion of the fundamental at all - only even-order distortion terms, plus a DC distortion term. Now if we include the integrator, and again assume only even-order nonlinearities, a table of input-output phase shift at the fundamental vs the ampllitude of the input sinusoid will be constant with input amplitude. Of course, the instantaneous phase shift will not be constant in this case. It's just that when we resolve the output signal to a spectrum of the fundamental plus the harmonics at various fixed input amplitudes, the phase of the output fundamental doesn't vary with the amplitude of the input fundamental at all when only even-order distortion exists ahead of the integrator.
 
andy_c said:

Regarding the case of the Miller C vs C to ground from the VAS output, if you take the Miller C, remove it and place a capacitor of the same value from the VAS output to ground, you'll increase the gain-bandwidth product dramatically. This will improve the null, assuming the amp is still stable. It was shown by Baxandall years ago that for the same gain-bandwidth product, the Miller C approach is greatly superior. To get the same gain-bandwidth product, it takes a very large capacitor to ground from the VAS output. This makes the high-frequency distortion quite large because the VAS will run out of output current trying to drive it at high frequencies. The exception to this is the case where the VAS is not a CE stage and the amp has the folded cascode topology. In that case, a Miller capacitor is not an option and the gain-bandwidth product is still gm/C. For the case where the VAS is a CE stage and the compensation cap is from the VAS output to ground, the gain-bandwidth product is much greater than gm/C but is not straightforward to compute.

I understand and agree with what your saying about holding the gain bandwidth product constant for comparison. I've read some of Baxandal's work but I don't recall that one. I wonder what sort of simplifying assumptions he made and if his analysis equally applies to power amps where voltage swings are so large and load impedances low. My intuitive feeling and many commercial designs show that a mixed solution is best in a power amp.

Do you have a preferred power amp topology? I only offer the Hafler XL as an example that offers a good null but I have no strong preference for the topology.
 
PB2 said:
I've read some of Baxandal's work but I don't recall that one. I wonder what sort of simplifying assumptions he made and if his analysis equally applies to power amps where voltage swings are so large and load impedances low.

Have you read Self's book? He refers to Baxandall's article in there. I don't have the Baxandall article though. I don't agree with a lot of Self's views, but there's definitely some really good stuff in there. The idea of looking at a Miller-compensated VAS as a local feedback amplifier and the implications of that for the overall distortion of the amp were a revelation to me. All the arguments, assumptions etc are documented there.

Do you have a preferred power amp topology?

I originally started out playing around with the simulation of a current feedback design. After discovering that the simulated distortion was totally awful, I read the Self book. I realized what the problem was. Then I went on a spree of analyzing many different input stage/VAS combos, assuming an ideal unity gain VCVS for the output stage. I was looking not only for low THD, but also minimal high-order harmonics. After looking at many configurations, I found that the standard single-ended Lin topology worked best according to that criterion. You might be interested in looking at the thread "Amplifier Topology Subjective Effects". There's some interesting discussion there. That was before I realized just how good the Lin topology could be made to be.
 
andy_c said:

Have you read Self's book? He refers to Baxandall's article in there. I don't have the Baxandall article though. I don't agree with a lot of Self's views, but there's definitely some really good stuff in there. The idea of looking at a Miller-compensated VAS as a local feedback amplifier and the implications of that for the overall distortion of the amp were a revelation to me. All the arguments, assumptions etc are documented there.
I've only read Self's web site and came to the same conclusions that there's a lot of really good material but also several things I disagree with. Odd that he points out the advantages of CFP then doesn't use it.

andy_c said:

I originally started out playing around with the simulation of a current feedback design. After discovering that the simulated distortion was totally awful, I read the Self book. I realized what the problem was. Then I went on a spree of analyzing many different input stage/VAS combos, assuming an ideal unity gain VCVS for the output stage. I was looking not only for low THD, but also minimal high-order harmonics. After looking at many configurations, I found that the standard single-ended Lin topology worked best according to that criterion. You might be interested in looking at the thread "Amplifier Topology Subjective Effects". There's some interesting discussion there. That was before I realized just how good the Lin topology could be made to be.

Interesting, I did much of the same many years ago but more by reading articles than by simulation. Lost interest when the null tests proved that it was not too hard to build an excellent amp. I'm leaning now toward a blend of Self's work, the JE-990, and actually perhaps the Tiger. These are all single ended diff amp. Don't know if I'll actually find the time to build/rebuild anything. Thanks for the reference to that thread, I'll take a look.
 
PB2 said:
Forgot to ask if you've taken a look at the Bryston schematics? I'd be curious to hear your opinion about the design?

Yikes! I looked at the 3b, and it's a strange topology. I must admit I can't think of anything very kind to say about it.

In a couple of places, they're introducing a zero in the open-loop gain to compensate for a pole. For example, the capacitor in parallel with R40 in the 3b does this. I've tried this technique in the lab when I was in college in the '70s. What I found was that one could get good pole-zero cancellation experimentally with a given transistor. But then, after replacing the transistor with another of the same vendor and type, the cancellation was way off. The idea of course is to get stability by looking at the problem purely in the frequency domain. But there are a number of articles published in the 1970s where the authors discuss how attempts at pole-zero cancellation pretty much hose the settling time. Anybody who has ever played around on the bench with composite op-amps (which also use pole-zero cancellation techniques), trying to get a combination of low offset and noise, and high slew rate knows that the settling time of these configurations is really awful.

I should probably just keep quiet, as this is sounding like a rant...
 
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