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Old 20th January 2007, 02:40 AM   #21
andy_c is offline andy_c  United States
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Way back earlier in this thread we were talking about PIM and also the Gilbert article. I had made the assertion that one could modify Gilbert's analysis to allow the second stage transimpedance to have any input-output phase shift. When that is done, the computed AM-to-PM distortion (according to Gilbert's simplified model) approaches zero as the second-stage input-output phase shift approaches zero. The case of very low phase shift would of course correspond to very wide open-loop bandwidth.

PMA then asked me to provide some formulas to show this, but at the time I hadn't written it up. I ended up writing up some preliminary stuff for a web page, but by the time I did so, the conversation had drifted to other subjects.

I just uploaded that info to my web site. It can be found here. This page is not linked anywhere from my site, so you can only get to it directly with the above URL.

As I mention on this page, Gilbert does not take into account any other source of PIM besides the input stage AM-to-AM being converted to AM-to-PM. He assumes a distortionless VAS, which is clearly not the case in practice. I also mention that according to this modification of Gilbert's simplified analysis, trying to make the phase shift of the second-stage transimpedance very small (by having a wide open-loop bandwidth) results in an increase in overall distortion - even though it would consist of only AM-to-AM components.

Clearly this does not take into account things like nonlinear VAS loading that Adam mentioned. I'd be interested to see if Adam's sim used a two-stage or three-stage EF (or some other configuration) for the output stage.

As you'll notice, the info on that page is in somewhat of a state of disarray. As I was writing, it became clear to me that doing a more thorough job would require more time than I was willing to put into it.
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Old 20th January 2007, 03:03 AM   #22
PB2 is offline PB2  United States
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Quote:
Originally posted by Bob Cordell


It has been shown that having wide open loop bandwidth does not help PIM and related nonlinearities. It all comes out in the wash. I know this may seem non-intuitive. The less-well-defined pole has movement that has less effect on the result. A pole at 100 Hz that moves around 10% will have about the same effect as a pole at 10 kHz that moves around 0.1%. Putting in a shunt resistance that moves the pole from 100 Hz to 10 kHz and at the same time reduces pole uncertainty from 10% to 0.1% has no net effect. The underlying effect causing pole shift, e.g., nonlinear capacitance, has not changed, and its effect on propogation delay through the circuit has not changed by adding shunt resistance. SPICE it, you'll see.

A simple Darlinton output stage is completely inadequate for reasons of the nonlinear resistance you cite, at the very least. With a triple, this issue pretty much goes away. I'd go with the triple, with a VAS that is not artifically loaded by a resistor. The addition of that resistor will never decrease distortion; it will only increase it.

Bob
Bob, just to make sure that I understand you. Are you saying that given the open loop case, and say for example a two tone IM test of 100 and 110 Hz that the measurement will be the same with and without the resistor, and the same output level?
I realize that this is not specifically a PIM test but it should serve the purpose. I've deliberately chosen low frequencies.

Pete B.
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Old 20th January 2007, 03:49 AM   #23
PB2 is offline PB2  United States
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Quote:
Originally posted by andy_c
.... It can be found here. This page is not linked anywhere from my site, so you can only get to it directly with the above URL.
Hi Andy,

Nice work once again. We discussed this some time ago here as I recall: http://www.diyaudio.com/forums/showt...556#post548556

I agree with your conclusion here:
"Recall that is the transimpedance amp's phase shift from input to output. If this is zero, then (25) evaluates to zero and all PIM (according to this greatly simplified model) disappears. Of course, as previously mentioned, this assumes the open-loop amplifier has no elements that themselves generate PIM - an unrealistic assumption."

Your analysis does show, as I see it, that wide open loop bandwidth in the VAS reduces this particular source of PIM and is the reason that I prefer reasonably wide open loop bandwidth.

You then state:
"Another thing should be considered. In order to reduce the input-output phase shift of the transimpedance stage, one must reduce the magnitude of its transimpedance. This in turn increases the current demands on the input stage, resulting in the magnitude of the input differential voltage vd(t) becoming larger. This ends up increasing the overall distortion - even though it consists of only an AM-to-AM component when the phase shift of the transimpedance is zero."

If I'm reading you correctly, it seems that your suggesting emitter degeneration in the VAS, and I believe what you state is true for this particular case. However, what about the comparision to using a smaller Cdom capacitor, or a VAS transistor with a higher ft, I believe that these would have lower PIM since they would not necessarily reduce the magnitude of the transimpedance.
The analysis also assumes no diff amp emitter degeneration, which we now know is not the best approach. Using it would tend to offset the higher vd(t), when required.
The problem is complex and I appreciate the work that you've done even with this simplification. Thanks again.

Pete B.
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Old 20th January 2007, 04:43 AM   #24
andy_c is offline andy_c  United States
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Quote:
Originally posted by PB2
You then state:
"Another thing should be considered. In order to reduce the input-output phase shift of the transimpedance stage, one must reduce the magnitude of its transimpedance. This in turn increases the current demands on the input stage, resulting in the magnitude of the input differential voltage vd(t) becoming larger. This ends up increasing the overall distortion - even though it consists of only an AM-to-AM component when the phase shift of the transimpedance is zero."
Aargh. As you can see, this is a work in progress :-). I just fixed that so it now says "In order to reduce the input-output phase shift of the transimpedance stage while keeping the gain-bandwidth product constant, one must reduce the magnitude of its low-frequency transimpedance. This in turn increases the current demands on the input stage at frequencies below the new open-loop pole, resulting in the magnitude of the input differential voltage vd(t) becoming larger at these frequencies. This ends up increasing the overall distortion at frequencies below the new open-loop pole - even though it consists of only an AM-to-AM component when the phase shift of the transimpedance is zero." Thanks for pointing out this error.

Quote:
If I'm reading you correctly, it seems that your suggesting emitter degeneration in the VAS, and I believe what you state is true for this particular case. However, what about the comparision to using a smaller Cdom capacitor, or a VAS transistor with a higher ft, I believe that these would have lower PIM since they would not necessarily reduce the magnitude of the transimpedance.
The analysis also assumes no diff amp emitter degeneration, which we now know is not the best approach. Using it would tend to offset the higher vd(t), when required.
The problem is complex and I appreciate the work that you've done even with this simplification. Thanks again.
Well, I'm not really advocating reducing the low-frequency transimpedance. My remarks were intended more in the context of "If one were to do so...". But if one were to attempt this with emitter degeneration in the VAS, that may not necessariily reduce the low-frequency transimpedance much, since it typically increases the output impedance of the stage. The effect would be pretty dependent on the specifics of the design though. I was thinking more in terms of the shunt resistor to ground that some people use at the VAS output. Of course, reducing the Miller cap would also accomplish this, but I'm assuming the gain-bandwidth product has already been chosen to be some fixed value - namely one that maximizes GBW while still ensuring stability. If reducing the compensation cap for a fixed input stage gm is possible without affecting stability, this says its choice was not optimal to begin with. Talking about changing open-loop bandwidth without keeping GBW constant can be a big source of confusion, so I'd like to avoid that.

Regarding the assumption of no emitter degeneration, my original intention in equation (8) was to eventually extend the analysis to allow "a" to be arbitrary rather than being fixed at the value given by equation (9). This could be used to model emitter degeneration of the input stage.

The whole analysis is in a partially completed state and will probably remain that way though. The amount of effort spent on making this into a good presentation is in my view not worth it for at least two reasons:

1) The analysis on which it is based is greatly oversimplified, yet the equations become complex.

2) It just ends up being fodder for flame wars anyway.

I will try to correct any errors or unclear statements such as what you've pointed out though. Thanks for your comments.
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Old 20th January 2007, 12:16 PM   #25
PB2 is offline PB2  United States
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Default Perspective on Open Loop Bandwidth Comparisons

I have been meaning to comment to Bob and several other people to clarify my position where I generally prefer higher open loop bandwidth.

When I hear low open loop bandwidth in OP amps and power amps I tend to think of a large Cdom cap and the old 741 OP amp. When I suggest that higher open loop bandwidth is better, I am thinking of a design with a goal for high open loop bandwidth which usually suggests no Cdom cap (so that it can be specified by the designer in the case of an OP amp) and if the OL bandwidth is raised further it implies to me (not necessarily, but likely) that a better VAS transistor is used or some RF technique (Cascoding, etc.) has been used to improve the design. I think of the 318 OP amp or the modern derivatives.

High OL bandwidth suggests (not necessarily) that the effects of non-linear junction capacitance have been moved up in frequency where they will do less harm in the audio band. While holding the GBW constant is important when making some comparisions, this is not my thinking when I state that I prefer higher OL bandwidth in casual conversation.

High OL bandwidth stated as a comparision of the 741 to 318 OP amp or a similar situation with power amps was described to me by the professor who I studied Audio Engineering with. I'm not suggesting that I accept all the conclusions of Otala or Leach, or anyone else when I state that I prefer higher open loop bandwidth. And rarely do I think of the resistor at the output of the VAS to ground in these discussions.

Let me point out one more thing, the analysis often offered by Barrie, Self and others is usually small signal, or worse mainly a small signal model applied to the large signal case. Looking at hfe or ft versus Ic it can be seen that these parameters vary greatly over the swing and load conditions of a power amp. This is a good reason IMO to sometimes trade off OL gain for an amplifier that is more consistent from small to large signals and thus more straight forward to compensate for stability. Another reason to use emitter degeneration, for example, is to produce a design that is more tolerant of component variations such as hfe.

Pete B.
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Old 20th January 2007, 12:30 PM   #26
PB2 is offline PB2  United States
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Quote:
Originally posted by andy_c


Aargh. As you can see, this is a work in progress :-). I just fixed that so it now says "In order to reduce the input-output phase shift of the transimpedance stage while keeping the gain-bandwidth product constant, one must reduce the magnitude of its low-frequency transimpedance. This in turn increases the current demands on the input stage at frequencies below the new open-loop pole, resulting in the magnitude of the input differential voltage vd(t) becoming larger at these frequencies. This ends up increasing the overall distortion at frequencies below the new open-loop pole - even though it consists of only an AM-to-AM component when the phase shift of the transimpedance is zero." Thanks for pointing out this error.



Well, I'm not really advocating reducing the low-frequency transimpedance. My remarks were intended more in the context of "If one were to do so...". But if one were to attempt this with emitter degeneration in the VAS, that may not necessariily reduce the low-frequency transimpedance much, since it typically increases the output impedance of the stage. The effect would be pretty dependent on the specifics of the design though. I was thinking more in terms of the shunt resistor to ground that some people use at the VAS output. Of course, reducing the Miller cap would also accomplish this, but I'm assuming the gain-bandwidth product has already been chosen to be some fixed value - namely one that maximizes GBW while still ensuring stability. If reducing the compensation cap for a fixed input stage gm is possible without affecting stability, this says its choice was not optimal to begin with. Talking about changing open-loop bandwidth without keeping GBW constant can be a big source of confusion, so I'd like to avoid that.

Regarding the assumption of no emitter degeneration, my original intention in equation (8) was to eventually extend the analysis to allow "a" to be arbitrary rather than being fixed at the value given by equation (9). This could be used to model emitter degeneration of the input stage.

The whole analysis is in a partially completed state and will probably remain that way though. The amount of effort spent on making this into a good presentation is in my view not worth it for at least two reasons:

1) The analysis on which it is based is greatly oversimplified, yet the equations become complex.

2) It just ends up being fodder for flame wars anyway.

I will try to correct any errors or unclear statements such as what you've pointed out though. Thanks for your comments.
Andy, I don't think your original writeup was in error, I just wanted to point out another perspective on the situation. Your analysis is top notch and I certainly understand that it is time consuming so I hope that you will continue as time permits. I am certainly not interested in any flame wars, just to consider the different ways of applying the analysis and having constructive conversation. Your pages would probably be the first place I'd point someone wanting to learn about these issues because of the clarity and accuracy of your work, same for your SPICE model analysis.

Regarding simplified models, we have to start somewhere, however they become much more useful when the complexity reaches a level where it covers the major sources of a particular point of interest. Gilbert seemed to ignore the one that you have now covered.

Pete B.
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Old 20th January 2007, 03:10 PM   #27
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Gentlemen, this interesting digression into the topic negative feedback has gotten a bit off-topic of error correction, yet it is a discussion at the heart of audio power amplifier design. I'm wondering if we should split off yet another thread that is appropriately on the subject of negative feedback.

Let me know your thoughts.

Bob
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Old 20th January 2007, 03:20 PM   #28
andy_c is offline andy_c  United States
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Default Re: Perspective on Open Loop Bandwidth Comparisons

Quote:
Originally posted by PB2
When I hear low open loop bandwidth in OP amps and power amps I tend to think of a large Cdom cap and the old 741 OP amp. When I suggest that higher open loop bandwidth is better, I am thinking of a design with a goal for high open loop bandwidth which usually suggests no Cdom cap (so that it can be specified by the designer in the case of an OP amp) and if the OL bandwidth is raised further it implies to me (not necessarily, but likely) that a better VAS transistor is used or some RF technique (Cascoding, etc.) has been used to improve the design. I think of the 318 OP amp or the modern derivatives.
Well, let me say that what I mean by "open loop bandwidth" is "the -3dB frequency of the open-loop gain" (same as Otala's definition). Let's take your example of the 318 op-amp. Looking at the graph at the top right of page 5 of the National data sheet, it appears that the open-loop bandwidth is somewhere around 70 Hz. I would refer to this as a low open-loop bandwidth. As another example, have a look at the AD825 op-amp, figure 12 on page 6. The open-loop bandwidth appears to be around 10 kHz. I'd refer to this as a high open-loop bandwidth.

In a typical op-amp design, the DC open-loop gain and the open-loop bandwidth are both difficult to control. Yet the GBW, = gm/(2*pi*Ccomp), can be controlled very easily by the combo of input stage gm and compensation cap Ccomp. The idea of associating wide open-loop bandwidth with low Ccomp, as well as your use of the 318 as an example of wide open loop bandwidth suggests to me that you're implicitly referring to GBW when you say "open loop bandwidth".
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Old 20th January 2007, 03:30 PM   #29
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Quote:
Originally posted by john curl
Who cares about more slew rate, IF you have virtually no TIM, already? THEN, other factors 'might' become more important.
Bob, you are stuck on 'TIM' and ignoring 'DIM' which Matti had already coined as early as 1976, when I worked with him.
I, too, did NOT like his ignoring slew rate as a number, and his insistence (in the late '70's) that high open loop bandwidth appeared to be necessary, but Walt Jung's and my work on op amps, both as IC's and discrete, tend to go in this direction, when listening to the results.

John, as I understand it, "TIM" was the term coined by Matti to describe the distortion itself, and perhaps its mechanism as well. The term "DIM" was coined by Matti to describe his proposed test for TIM. Indeed, he specified DIM-30 and DIM-100 as two DIM tests where 30 kHz and 100 kHz LPF's were used on the test signal, respectively. The test signal was a 3.18 kHz square wave and a 15 kHz sinusoid, mixed in a ratio of 4:1, IIRC. All of us have on occasion interchanged these terms, often using the term TIM when we should have been saying DIM when in reference to a measurement.

I have always measured TIM using the DIM test, and have certainly not ignored it. The DIM test reveals HF non-linearity in general, not just limited to TIM distortion. I showed in my paper that DIM and THD-20 were highly correlated, so that the more-available THD-20 test could also be used as a good indicator of the presence of TIM and other HF nonlinearity.

While slew rate is certainly a very important factor in the TIM mechanism and in resulting DIM measurements, it is not the only factor, and I think we agree on that. For example, "soft" TIM occurs at levels below slew rate limiting as slew rate limiting is approached. Similarly, any HF nonlinearity, such as in the VAS, will generate a measurable DIM result, just as it will generate a measurable THD-20 result, and just as it will generate a measurable CCIF IM result. Too little slew rate will certainly give you TIM, but a very high slew rate will not guarantee the absence of measurable DIM.

You are largely correct in saying "who cares about slew rate if you have virtually no TIM already?" When you say that, though, by what means are you saying you have virtually no TIM? (or DIM?). Is this based on doing the DIM-30 or DIM-100 test on your amplifier, or on something else? The reason I ask is that in practice, from a measurement point of view, it is difficult to distinguish TIM distortion from any other type of HF nonlinearity.

Cheers,
Bob
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Old 20th January 2007, 05:05 PM   #30
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Default Re: Re: Perspective on Open Loop Bandwidth Comparisons

Quote:
Originally posted by andy_c


Well, let me say that what I mean by "open loop bandwidth" is "the -3dB frequency of the open-loop gain" (same as Otala's definition).
In a typical op-amp design, the DC open-loop gain and the open-loop bandwidth are both difficult to control. Yet the GBW, = gm/(2*pi*Ccomp), can be controlled very easily by the combo of input stage gm and compensation cap Ccomp.
AD829, for example, has OLG F-3dB corner at some 10kHz, and quite high OLG of 100dB.

In my experience, the amplifiers with high OLG frequency corner and reasonable high OLG gain do sound better than those with corner at some 10Hz.
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