traderbam said:
Dear traderbam:
In order to solve your enquiry, it is necessary to make some additional assumptions and to check the consistency of desired conditions.
If you have an open loop performace yielding –40 dB level distortion, and want to achieve –90 dB performance, then you must – to a good approximation – insert 50 dB of extra gain (not introducing additional distortion of course !!) and apply negative feedback so as to adjust closed loop gain back to the desired 30 dB. The way of doing this I outlined in a previous post .
You also want to have a 3dB corner frequency of 50 KHz. This implies in a first approximation, assuming the open loop response has a 6dB/octave rolloff for unconditional stability (dominant pole), that the open loop corner frequency must be equal to 50 KHz divided by the ratio of extra gain (50 dB) to rolloff slope. If this sounds confusing, lets work through it. At 25 KHz, OL gain should be 36 dB, at 12.5 KHz it should be 42 dB, and 48 dB at 6.25 KHz, we are almost done.
Note that under these conditions, the 90 DB performance can be guaranteed only up to about the OL corner frequency of 6 KHz, deteriorating upwards, so the assumptions made do not fit the desired objective of correction in the full audio band.
One way of doing this is specifying the closed loop corner frequency to be higher, for example now working in the reverse order, if we specify an open loop corner frequency of 20 KHz and assume again a 6 dB / octave rolloff, then the closed loop corner frequency (with 50 dB correction margin) goes to 160 KHz.
Alternatively, instead of assuming a single dominant pole OL response, a more complex design can attain equal performance with lower OL bandwidth at the cost of careful compensation techniques to ensure stability. In large part the art of Control Systems Theory is concerned with these type of constraints.
Hope this helps.
Rodolfo
OOps, sorry I blundered with the numbers, the correct sequence is:
30 dB at 50 KHz corner
36 dB at 25 KHz
........
84 dB at 100 Hz
So full correction is available only up to a little over 100 Hz, or conversely the OL BW must be 20 KHz and the CL BW goes up to 6.3 MHz for a dominant pole situation.
Sorry for the confussion.
The challenge
OK, here goes a try. Only one cup of coffee under my belt, however.
If the OL distortion is -40 dB and you want -90 dB CL distortion out to 20 kHz, you need about 50 dB of NFB at 20 kHz. This would put a simple single pole rolloff design at a gain crossover of about 6 MHz, a bit too high. So we put in some T compensation to get an extra 6 dB/octave rolloff for a decade, between, say, 30 kHz and 300 kHz. That gets us a FB gain crossover at about 600 kHz.
We now have an amplifier that may meet the distortion spec, and can be made stable, but it has a CL BW of about 600 kHz. We can cheat and put a 50 kHz filter in front of it. Or, we can put an HPF capacitor across the FB resistor with a corner at 50 KHz, then break that corner at some higher frequency. If we do this, we must adjust the forward path T compensation accordingly to take into account the larger HF CL loop gain (at frequencies above 50 kHz).
Bear in mind that the requirement for a 50 kHz CL BW is not only causing us extra work, but it is giving us an HF frequency response droop of nearly a dB at 20 kHz. Why would anyone want that?
In regard to transistor speed, are you referring to the output transistors? I can make a 20 kHz bandwidth power amp with 1 MHz ft devices, but it will probably sound awful. Lots of dynamic crossover distortion at the very least.
Bob
traderbam said:Good morning Bob. Get that pot of coffee on!
No tricks. No "right" answer is sought. Make up your own assumptions. Put a stake in the ground and show the thought process.
+30dB closed loop gain...with corner at 50kHz.
distortion -90dB or better at all audible frequencies.
My question is in response to a query about how fast transistors really need to be to make a 20kHz bandwidth amp.
OK, here goes a try. Only one cup of coffee under my belt, however.
If the OL distortion is -40 dB and you want -90 dB CL distortion out to 20 kHz, you need about 50 dB of NFB at 20 kHz. This would put a simple single pole rolloff design at a gain crossover of about 6 MHz, a bit too high. So we put in some T compensation to get an extra 6 dB/octave rolloff for a decade, between, say, 30 kHz and 300 kHz. That gets us a FB gain crossover at about 600 kHz.
We now have an amplifier that may meet the distortion spec, and can be made stable, but it has a CL BW of about 600 kHz. We can cheat and put a 50 kHz filter in front of it. Or, we can put an HPF capacitor across the FB resistor with a corner at 50 KHz, then break that corner at some higher frequency. If we do this, we must adjust the forward path T compensation accordingly to take into account the larger HF CL loop gain (at frequencies above 50 kHz).
Bear in mind that the requirement for a 50 kHz CL BW is not only causing us extra work, but it is giving us an HF frequency response droop of nearly a dB at 20 kHz. Why would anyone want that?
In regard to transistor speed, are you referring to the output transistors? I can make a 20 kHz bandwidth power amp with 1 MHz ft devices, but it will probably sound awful. Lots of dynamic crossover distortion at the very least.
Bob
traderbam said:
The relevant consideration is the stability margin, and it results both form the amplitude and phase response shape. A general discussion on this topics is certainly beyond the scope of this forum.
There is no single answer to this issue, since the starting amplifier (the one with 30 dB gain and -40 dB distortion) most probably does not have a simple 6dB/octave response to begin with, so the correct approach must take into account the whole system.
Rodolfo
Since you folks appear to 'second guess' me, even when I am not contributing to this thread, let me make my opinions more clear:
First, I don't see anything that Bob Cordell wants to do in making a power amp, necessarily wrong. In fact, the last two major designs that I have made for Parasound, the JC-1 power amp and the JC-2 preamp, have lots of negative feedback, and good, but not great, open loop bandwidth. It is just too difficult for me to make good specs that are important because of Tom Holman's THX specifications, (which I could disagree with at another time), and the relative indifference of our contractors to go the extra length to match and adjust my designs. Also, the increased distortion would prevent a THX certification, which is important to us.
When it comes to PIM distortion, I stand by what Barrie Gilbert wrote in his technical article, as it seems fairly 'bullet proof' to me. He is the person who said that PIM could not be reduced with negative feedback, but that could be interpreted as saying that negative feedback does not create PIM, but unfortunately, if you have high open loop gain, you almost always have a relatively low open loop bandwidth, unless you go through special efforts, like Matti Otala did, in his first low TIM power amp that was designed at Phillips Research Labs with Jan Lostrow. (sp?)
Any special efforts, such as 12dB/octave rolloff for a certain frequency range, can be successful, I have done it myself, based on a Japanese paper (Sansui?) back in the 70's. This will certainly lower PIM and TIM and high frequency harmonic distortion as well. But what of any other more subtle effects? I don't know for sure, that might be for listening tests to find out first, just like TIM and PIM were developed from.
First, I don't see anything that Bob Cordell wants to do in making a power amp, necessarily wrong. In fact, the last two major designs that I have made for Parasound, the JC-1 power amp and the JC-2 preamp, have lots of negative feedback, and good, but not great, open loop bandwidth. It is just too difficult for me to make good specs that are important because of Tom Holman's THX specifications, (which I could disagree with at another time), and the relative indifference of our contractors to go the extra length to match and adjust my designs. Also, the increased distortion would prevent a THX certification, which is important to us.
When it comes to PIM distortion, I stand by what Barrie Gilbert wrote in his technical article, as it seems fairly 'bullet proof' to me. He is the person who said that PIM could not be reduced with negative feedback, but that could be interpreted as saying that negative feedback does not create PIM, but unfortunately, if you have high open loop gain, you almost always have a relatively low open loop bandwidth, unless you go through special efforts, like Matti Otala did, in his first low TIM power amp that was designed at Phillips Research Labs with Jan Lostrow. (sp?)
Any special efforts, such as 12dB/octave rolloff for a certain frequency range, can be successful, I have done it myself, based on a Japanese paper (Sansui?) back in the 70's. This will certainly lower PIM and TIM and high frequency harmonic distortion as well. But what of any other more subtle effects? I don't know for sure, that might be for listening tests to find out first, just like TIM and PIM were developed from.
Hi John,
Good to "see" you sir.
Since you are an accomplished designer, you will be quoted (mis-quoted), paraphrased and second guessed by some whenever your back is turned. Nature of the human animal.
Your point on mass produced products and lack of matching is understood by myself and more than a few others I'd guess. An advantage of DIY or build to order. Also a worthwhile addition to the invoice.
Your thoughts do help settle a few questions in the back of my mind though, and thanks for that.
-Chris
Edit: spelling
Good to "see" you sir.
Since you are an accomplished designer, you will be quoted (mis-quoted), paraphrased and second guessed by some whenever your back is turned. Nature of the human animal.
Your point on mass produced products and lack of matching is understood by myself and more than a few others I'd guess. An advantage of DIY or build to order. Also a worthwhile addition to the invoice.
Your thoughts do help settle a few questions in the back of my mind though, and thanks for that.
-Chris
Edit: spelling
Bogus Acronym.
Time to ditch the TIM acronym.
Discuss.
http://www.diyaudio.com/forums/showthread.php?s=&postid=420044&highlight=#post420044
Time to ditch the TIM acronym.
Discuss.
http://www.diyaudio.com/forums/showthread.php?s=&postid=420044&highlight=#post420044
traderbam said:
Well, I'm not Mike, but I am intimately familiar with Gilbert's paper on this. I would say that the statement above is putting words into Gilbert's mouth. One could consider at least two types of PIM (which I'll call AM-to-PM).
1) Conversion of the AM-to-AM tanh() open-loop distortion characteristic of an undegenerated input diff amp ahead of an integrator into a combination of AM-to-AM and AM-to-PM distortion in the closed-loop amplifier. What people seem to forget is that in doing this, the closed-loop distortion is greatly reduced by feedback relative to the open-loop distortion.
2) "Intrinsic" PIM in the open-loop amplifier, such as from a common-emitter VAS in which the nonlinear collector-base capacitance is modulated by the signal voltage. That such distortion is reduced by negative feedback is easily verified by simulation. Just take an otherwise distortionless amp with ideal controlled sources, and in the open-loop amplifier, derive the output from a buffered reverse-biased diode driven by some series resistance. The feedback doesn't care whether the open-loop distortion is AM-to-AM, AM-to-PM, or a combination. It will still reduce the distortion.
The Gilbert paper doesn't even get into case (2) above. And even in case (1), the overall distortion is reduced by feedback. It's just that in the case considered by Gilbert, the closed-loop residual contains both AM-to-AM and AM-to-PM components, while the open-loop distortion consists of only AM-to-AM.
PIM
John,
It's nice to see you here.
What were you referring to in regard to people second-guessing you? Is there something about that amplifier question posed that related to one of your designs? If so, I'm unaware of it.
I seem to recall something about the Barrie Gilbert piece awhile back. Can you point me to it and I'll give it a look?
Keep in mind what I've said in my PIM paper located on my web site: PIM in amplifiers has several origins, some of which have nothing to do with negative feedback. While it is undeniably true that the application of negative feedback to an amplifier that had no other PIM would create some PIM, in reality that is only a small part of the picture.
I built the PIM analyzer so that I could check these kinds of effects. What I found was that in the amplifiers I tested, the application of negative feedback reduced total PIM. Moreover, given that you have negative feedback, reducing the amount of negative feedback and/or increasing the open-loop bandwidth will not necessarily tend to reduce PIM. PIM results from the gain crossover frequency moving back and forth. If the gain crossover frequency still moves back and forth with low NFB and wide open-loop bandwidth (it will, in most cases), then you will still get a similar amount of feedback-generated PIM.
PIM is not hard to measure - you just need the required purpose-built test equipment. Amplifiers I measured for the PIM paper had PIM less than about 10 ns (with feedback, more without) and they were definitely not anything special as far as specimens of great design. My MOSFET power amplifier (which had 40 dB of NFB at 20 kHz and an open-loop bandwidth probably less than 1kHz, had PIM of less than 100 picoseconds. Those numbers would seem to be pretty small. The point being that lots of NFB and a low open-loop bandwidth does not in any way exacerbate PIM.
I'd actually like to measure PIM on some more amplifiers, maybe even some without any negative feedback, maybe even some tube amps.
If you can point me to that Barrie Gilbert paper I'll take a look at it.
Bob
John,
It's nice to see you here.
What were you referring to in regard to people second-guessing you? Is there something about that amplifier question posed that related to one of your designs? If so, I'm unaware of it.
I seem to recall something about the Barrie Gilbert piece awhile back. Can you point me to it and I'll give it a look?
Keep in mind what I've said in my PIM paper located on my web site: PIM in amplifiers has several origins, some of which have nothing to do with negative feedback. While it is undeniably true that the application of negative feedback to an amplifier that had no other PIM would create some PIM, in reality that is only a small part of the picture.
I built the PIM analyzer so that I could check these kinds of effects. What I found was that in the amplifiers I tested, the application of negative feedback reduced total PIM. Moreover, given that you have negative feedback, reducing the amount of negative feedback and/or increasing the open-loop bandwidth will not necessarily tend to reduce PIM. PIM results from the gain crossover frequency moving back and forth. If the gain crossover frequency still moves back and forth with low NFB and wide open-loop bandwidth (it will, in most cases), then you will still get a similar amount of feedback-generated PIM.
PIM is not hard to measure - you just need the required purpose-built test equipment. Amplifiers I measured for the PIM paper had PIM less than about 10 ns (with feedback, more without) and they were definitely not anything special as far as specimens of great design. My MOSFET power amplifier (which had 40 dB of NFB at 20 kHz and an open-loop bandwidth probably less than 1kHz, had PIM of less than 100 picoseconds. Those numbers would seem to be pretty small. The point being that lots of NFB and a low open-loop bandwidth does not in any way exacerbate PIM.
I'd actually like to measure PIM on some more amplifiers, maybe even some without any negative feedback, maybe even some tube amps.
If you can point me to that Barrie Gilbert paper I'll take a look at it.
Bob
Gilbert
Some time ago we found it on internat archives.
http://www.diyaudio.com/forums/showthread.php?postid=943808#post943808
http://www.diyaudio.com/forums/showthread.php?postid=943879#post943879
The second link worked better.
Adam
Some time ago we found it on internat archives.
http://www.diyaudio.com/forums/showthread.php?postid=943808#post943808
http://www.diyaudio.com/forums/showthread.php?postid=943879#post943879
The second link worked better.
Adam
The Gilbert article is here The typesetting is quite a mess, making it a bit more difficult to work through the equations without doing some guessing as to what the intent was. The process he goes through is roughly as follows:
1) Assume a non-inverting closed-loop op-amp with an undegenerated bipolar diff amp input stage, with all other parts of the amp distortionless. Open-loop response is assumed to be an integrator.
2) Assume an undistorted sinusoidal output voltage
3) Compute the sinusoidal output current of the diff amp
4) Using only the linear and cubic terms of the Taylor series for the inverse tanh(), compute the diff amp's differential input voltage.
5) Do the KVL equation around the input loop, essentially reflecting the distortion back to the input, like Cherry's "anti-distortion" concept.
6) Observe that the output phase varies with the input signal amplitude and gain-bandwidth product.
1) Assume a non-inverting closed-loop op-amp with an undegenerated bipolar diff amp input stage, with all other parts of the amp distortionless. Open-loop response is assumed to be an integrator.
2) Assume an undistorted sinusoidal output voltage
3) Compute the sinusoidal output current of the diff amp
4) Using only the linear and cubic terms of the Taylor series for the inverse tanh(), compute the diff amp's differential input voltage.
5) Do the KVL equation around the input loop, essentially reflecting the distortion back to the input, like Cherry's "anti-distortion" concept.
6) Observe that the output phase varies with the input signal amplitude and gain-bandwidth product.
Re: PIM
Bob et al.
regarding your post #332 I got thinking while the PIM may have very low measureable time differences at only nS's and even pS's I wonder now may it be so that the distortion pattern change due to the signal changes throughout between the rails voltages is of such an order it still will create hearable differences between "low PIM" and "high PIM" amplifiers?
PIM of only 10 nS might just look like a very small time and cheat our minds makings us thinking it can't make much for what happens inside the audio pass band while still relying on ears we still seem to be able to perceive the difference between 2 amplifiers... just a thought.
Cheers Michael
Bob et al.
regarding your post #332 I got thinking while the PIM may have very low measureable time differences at only nS's and even pS's I wonder now may it be so that the distortion pattern change due to the signal changes throughout between the rails voltages is of such an order it still will create hearable differences between "low PIM" and "high PIM" amplifiers?
PIM of only 10 nS might just look like a very small time and cheat our minds makings us thinking it can't make much for what happens inside the audio pass band while still relying on ears we still seem to be able to perceive the difference between 2 amplifiers... just a thought.
Cheers Michael
Barrie Gilbert article
John,
I read Barrie Gilbert's article this evening. His basic message is that if you use a 741 op amp in your preamp at a gain of 10X, and operate it at 10 kHz at 2V rms, you may get some PIM. No dung!!
Seriously, all of Barrie's calculations and arguments are fine, as usual, and nothing he covers contradicts anything I have said about PIM. BTW, he never mentions the word PIM.
He is discussing rather severe op amp input stage nonlinearity, in a case with an un-degenerated input differential pair with an op amp GBW of only 1 MHz operating within a stone's throw of slewing. He points out that if you apply 10 kHz to this amplifier at higher voltage levels, the input-output phase delay will be greater than at very small signal levels. No surprize. Under his conditions this amplifier is already producing tenths of a percent distortion and is on the verge of slewing. This amplifier would have been thrown out of Best Buy long before they got to the PIM measurement.
What Barrie described was just an extreme case of the "PIM" that we all agree is indeed induced by the application of negative feedback to an amplifier that has a forward path amplitude nonlinearity and no PIM to begin with. He does not discuss the many other sources of PIM in an amplifier that can overshadow this in the real world, and which ARE reduced in many cases by NFB. Note that nowhere does he subscribe to the view that more NFB or smaller open-loop bandwidth exacerbates PIM.
His analysis does remind me that there is more than one way to measure PIM. The way I did it with my PIM analyzer was, I think, inspired by Otala himself; I believe he suggested the use of a SMPTE-IM (60 Hz, 6000 Hz, 4:1) test signal for PIM measurement, although I don't recall him implementing the test that way. The other way to do it would be to amplitude-modulate a 6 kHz test signal at, say 60 Hz; this would be more reflective of what Barrie did in his analysis.
Bottom line is that I think you read a little too much into what Barrie said, and that his article definitely does not support your position. As always, I'm sure we'll agree to disgree in good spirit. I wish I could have made it to the AES to have a beer with you. Thought you'd be at RMAF.
Bob
john curl said:
John,
I read Barrie Gilbert's article this evening. His basic message is that if you use a 741 op amp in your preamp at a gain of 10X, and operate it at 10 kHz at 2V rms, you may get some PIM. No dung!!
Seriously, all of Barrie's calculations and arguments are fine, as usual, and nothing he covers contradicts anything I have said about PIM. BTW, he never mentions the word PIM.
He is discussing rather severe op amp input stage nonlinearity, in a case with an un-degenerated input differential pair with an op amp GBW of only 1 MHz operating within a stone's throw of slewing. He points out that if you apply 10 kHz to this amplifier at higher voltage levels, the input-output phase delay will be greater than at very small signal levels. No surprize. Under his conditions this amplifier is already producing tenths of a percent distortion and is on the verge of slewing. This amplifier would have been thrown out of Best Buy long before they got to the PIM measurement.
What Barrie described was just an extreme case of the "PIM" that we all agree is indeed induced by the application of negative feedback to an amplifier that has a forward path amplitude nonlinearity and no PIM to begin with. He does not discuss the many other sources of PIM in an amplifier that can overshadow this in the real world, and which ARE reduced in many cases by NFB. Note that nowhere does he subscribe to the view that more NFB or smaller open-loop bandwidth exacerbates PIM.
His analysis does remind me that there is more than one way to measure PIM. The way I did it with my PIM analyzer was, I think, inspired by Otala himself; I believe he suggested the use of a SMPTE-IM (60 Hz, 6000 Hz, 4:1) test signal for PIM measurement, although I don't recall him implementing the test that way. The other way to do it would be to amplitude-modulate a 6 kHz test signal at, say 60 Hz; this would be more reflective of what Barrie did in his analysis.
Bottom line is that I think you read a little too much into what Barrie said, and that his article definitely does not support your position. As always, I'm sure we'll agree to disgree in good spirit. I wish I could have made it to the AES to have a beer with you. Thought you'd be at RMAF.
Bob