Bob Cordell's Power amplifier book

Congratulations on your excellent book, Bob. I got my copy a few days ago and have enjoyed it thoroughly. Its layout makes it easy to read and your methods of explanation give me a different way of thinking about how amps work. Very well done!
Cheers, Ken

Hi Ken,

I really appreciate the nice feedback. I hope you continue to enjoy the book.

Cheers,
Bob
 
Hi Pete,

I chose 500 kHz closed-loop bandwidth for all of the amplifiers in Chapter 3 as a safe and consistent value, and this resulted in the 300 pF Miller capacitance. With about 2.45 mA/transistor, it looks like the calculated closed-loop bandwidth for the citation 12 would be over 2 MHz in theory, way too dangerous.

However, note the 390 ohm base-emitter resistor on the VAS transistor, suggesting that if its Vbe is 0.7V, then the standing current for the LTP transistor driving it is really only about 1.8 mA, suggesting a nominal LTP imbalance. This would result in a 12V/us slew rate in the ideal case, still much more than the simple amplifier that I showed, but with an apparent dangerously high closed loop bandwidth. The real transistors used may make the idealized closed loop bandwidth estimates wrong, however.

You might want to simulate the Citation 12 and see what you get. I could be wrong, its still early in the morning.

Cheers,
Bob

They did change the tail resistor to 12K in later revisions of the Citation 12 which should provide better diff pair balance. It doesn't really matter if the slew rate is 10 or 20V/us as even 10 is enough to avoid slew rate limiting at 20KHz and 50W and the associated distortion. Seems I forgot to mention the diff pair overload when it slews and this would be a good illustration for a section on SID.

The Citation did not have a reputation for blowing up so it seems that there was enough stability margin at least for typical speaker loads.

The measured THD20 at 60W into 8 ohms from a test report for the Citation 12 was about .08% in one channel and .1% in the other.

My point is that these simple topologies have been used for years and have not resulted in such high levels of distortion as shown in your analysis.

Are you interested in the gain and phase margin from a SPICE simulation or more the predicted THD20 at full power? I have simulated it, but it was many years ago and I did not have the best models. I've also scratch built a copy and measured it on the bench but that was about 30 years ago when I was a young teen.

I just looked up the RCA reference design, it has an 18K tail resistor for about 2.2 mA tail current and a 47 pF Cdom cap - that works out to about 23V/uS slew rate ignorning the Miller capacitance of the VAS. It is probably not so insignificant with such a small Cdom. The VAS is a 40408 with an Ft of 100 MHz no capacitances given.
 
Last edited:
It doesn't really matter if the slew rate is 10 or 20V/us as even 10 is enough to avoid slew rate limiting at 20KHz and 50W and the associated distortion. Seems I forgot to mention the diff pair overload when it slews and this would be a good illustration for a section on SID.

I've been reading the book fairly carefully from the beginning and the part where Bob talks about slew rate was where I started to have some questions. It seems to me that slew rate is a bit of a red herring when talking about amplifier quality because THD-20 is a much better indicator of what's going down. Bruno Putzeys points this out in one of his UcD application notes on distortion. Slew rate limiting isn't an all-or-nothing thing, the figure quoted is a measure of extreme non-linearity in the IPS - so rather than knowing the hard limit (which would be gross non-linearity) its much better to know what the distortion curve looks like at higher frequency.

Its the rather more subtle increase in HF distortion caused by IPS non-linearity that's of much greater interest than the hard limit. At least, that's my take.
 
I've been reading the book fairly carefully from the beginning and the part where Bob talks about slew rate was where I started to have some questions. It seems to me that slew rate is a bit of a red herring when talking about amplifier quality because THD-20 is a much better indicator of what's going down. Bruno Putzeys points this out in one of his UcD application notes on distortion. Slew rate limiting isn't an all-or-nothing thing, the figure quoted is a measure of extreme non-linearity in the IPS - so rather than knowing the hard limit (which would be gross non-linearity) its much better to know what the distortion curve looks like at higher frequency.

Its the rather more subtle increase in HF distortion caused by IPS non-linearity that's of much greater interest than the hard limit. At least, that's my take.

Hmmm, I have to strongly disagree with you, once it slews the VAS output does not keep up with the signal, and thus the output does not keep up which leads to the input diff pair overloading - it is a mess and that is why Bob reports 4.8% THD20 at 50W and 8 ohm for his Figure 3.1 design. Take Bob's zip file, chop out the extra transistors and drop R5 to 3.8K to make it like Figure 3.1, and try it for Cdom = 100 and 300 pF at 50W 8 ohm load. The THD20 drops to .033% at 50W with an 8 ohm load with a 100p Cdom value.
 
Now my book has arrived and I have had a few hours time to read.

Chapter 3 starts with showing the need for input degeneration. When Ottala wrote his articles that was new to me and I had never seen it. Peter Gardes articles were help in understanding too.

In a another thread here there was a link ( JAES july 67 ) to Locanthis T-circuit amp. This amp has input degeneration. Does anyone know of any earlier use?

Was Daugherty and Greiners article written then?

Edit: I googled and found when it was written.

Daugherty, D. Greiner, R.
Some design objectives for audio power amplifiers
Mar 1966

/örjan
 
Last edited:
They did change the tail resistor to 12K in later revisions of the Citation 12 which should provide better diff pair balance. It doesn't really matter if the slew rate is 10 or 20V/us as even 10 is enough to avoid slew rate limiting at 20KHz and 50W and the associated distortion. Seems I forgot to mention the diff pair overload when it slews and this would be a good illustration for a section on SID.

The Citation did not have a reputation for blowing up so it seems that there was enough stability margin at least for typical speaker loads.

The measured THD20 at 60W into 8 ohms from a test report for the Citation 12 was about .08% in one channel and .1% in the other.

My point is that these simple topologies have been used for years and have not resulted in such high levels of distortion as shown in your analysis.

Are you interested in the gain and phase margin from a SPICE simulation or more the predicted THD20 at full power? I have simulated it, but it was many years ago and I did not have the best models. I've also scratch built a copy and measured it on the bench but that was about 30 years ago when I was a young teen.

I just looked up the RCA reference design, it has an 18K tail resistor for about 2.2 mA tail current and a 47 pF Cdom cap - that works out to about 23V/uS slew rate ignorning the Miller capacitance of the VAS. It is probably not so insignificant with such a small Cdom. The VAS is a 40408 with an Ft of 100 MHz no capacitances given.

Hi Pete,

If you simulate the Citation 12, I'd be most interested in knowing the gain crossover frequency you get. If it is much over 500 kHz, I'd be concerned for an amplifier of that vintage for stability. Without thinking about it real hard, it is difficult to understand how the amplifier with such a simple topology could achieve such high slew rate as you quote without having a high gain crossover frequency. The math for straight Miller compensation does not leave a lot of wiggle room.

As a start, you can probably get a ballpark idea just by simulating it with the transistors I used in the example simulation I posted, recognizing of course that those transistors are somewhat faster than the ones originally used in the Citation 12.

THD-20 at 60W of 0.1% is not that great. Note that the large numbers I show are for a case where the amplifier is in actual slew rate limiting. Once hard slew limiting is reached, the numbers go though the roof. Note also that the numbers I got for THD1 for that simple topology were quite reasonable.

For that simple amp, I probably should have shown a curve of THD-20 vs power so that the onset of SR limiting and its effect on THD-20 could be seen in perspective.

Cheers,
Bob
 
I've been reading the book fairly carefully from the beginning and the part where Bob talks about slew rate was where I started to have some questions. It seems to me that slew rate is a bit of a red herring when talking about amplifier quality because THD-20 is a much better indicator of what's going down. Bruno Putzeys points this out in one of his UcD application notes on distortion. Slew rate limiting isn't an all-or-nothing thing, the figure quoted is a measure of extreme non-linearity in the IPS - so rather than knowing the hard limit (which would be gross non-linearity) its much better to know what the distortion curve looks like at higher frequency.

Its the rather more subtle increase in HF distortion caused by IPS non-linearity that's of much greater interest than the hard limit. At least, that's my take.

Hi Abraxalito,

Slew rate certainly isn't everything, but it is not a red herring. It certainly defines the onset of what some have called hard TIM, and at that point the amplifier is long gone from good sound quality.

What you are referring to is what some have called "soft TIM", and it reflects the increasing nonlinearity of the input stage as it is subjected to larger error signals that may occur when the signal applied to the amplifier exhibits a high rate of change, but one that is smaller than the slew rate limit.

It is good to know the slew rate of an amplifier because that helps one get an idea for how much margin there is against slew rate limiting and also suggests how far away from soft TIM the amplifier may be operating on real signals. It is nice to have a slew rate margin of at least 5:1 against the maximum slew rate of a full-amplitude 20 kHz sinusoid, for example.

However, you are also correct in pointing out the value of the THD-20 measurement in assessing high-frequency nonlinearity in general, regarless of whether the cause is in the input stage or elsewhere (which may have nothing to do with the so-called TIM mechanism).

Regarding THD-20 measurements for class-D amplifiers, WATCH OUT! They are often almost totally worthless because an AES17 LPF is often used ahead of the THD analyzer to prevent the analyzer from overloading in the presence of the residual HF noise from the class D amplifier. The AES17 filter has a sharp cutoff just above 20 kHz. See the the discussion of measurements for class D amplifiers in the last chapter of my book.

In my opinion, one of the only valid HF nonlinearity measurements for class D amplifiers is the 19+20 kHz CCIF IM distortion measurement which, thankfully, John Atkinson does in his Stereophile reviews of class D amplifiers. Many class D amplifiers do quite poorly on this test.

Cheers,
Bob
 
It is good to know the slew rate of an amplifier because that helps one get an idea for how much margin there is against slew rate limiting and also suggests how far away from soft TIM the amplifier may be operating on real signals. It is nice to have a slew rate margin of at least 5:1 against the maximum slew rate of a full-amplitude 20 kHz sinusoid, for example.

To follow this avenue a little further, thinking out loud - it does seem we're agreed that the slew rate number, referring as it does to the hard limit, is only telling us how far we are from that hard limit. Nobody wants to go anywhere near that, we're all agreed that its nasty.

What the slew rate number does not tell us is where the non-linearity starts to rise (soft TIM). That's from the input stage topology and whether there's any emitter degeneration (assuming we've a bipolar IPS), is it not? This area where we're entering into soft TIM is more of interest and seems more relevant to amplifier quality.

So here's a couple of questions arising. Firstly, is it possible to design an amp that has a degenerated LTP which has the same slew rate as an otherwise topologically identical amp having a non-degen IPS? Perhaps the degen IPS only would need a reduced tail current over the non-degen version? Assuming that its possible, then would both amps go into soft TIM at the same signal level?

What I'd like to get a handle on is the ratio you've mentioned - the slew rate margin - and whether this ratio is going to be the same for all amp topologies, degen LTP and non-degen, bipolar and JFET input. If so, how is the margin arrived at?
 
Pete - the link to the zip file didn't work for me, it took me directly to post #701 on this very thread. What did I do wrong?

The ZIP file that I used was in post #576 on page 58 of this thread, odd that link works for me.

I'm finding that the simulator hangs occasionally but I've made a lot of changes so not sure if Bob's file will have the problem let us know if it does. And it might be the duplicate transistor def, could just rename Bob's dupilcate transistor model and then change it in the schematic to match.
 
Last edited: