Bob Cordell's Power amplifier book

[Bob Cordell]

Bob,

I'm trying understand the conclusions from Cherry's paper (Feedback, Sensitivity, and Stability of Audio Power Amplifiers) and square that the presentation in your book. In particular on page 128 you discuss the nonlinearity of the VAS due to change in transconductance with change in collector current. But if the conclusion of Cherry's paper is valid then the transconductance of VAS is not of significance.

What's up? Please read my post that proceeds this one for my finding and argument. The best I can surmise is that if you want current gain in the VAS and you want to do it with only one or two transistors (as contrasted with Groner's solution) then you have to use a CE stage and live with some messiness.

And, on a different topic, I preordered the second edition of your book at Amazon. I knew it was on the horizon so I open this thread occasionally to check progress. That's what brought me here recently.

Best,
Jeff

I think that the significance of the transconductance of the VAS will always be a matter of degree, depending on the details of the circuit, the frequency range we are talking about, and the details of how the amplifier is being compensated. Bear in mind that even if we are driving the VAS with a perfect current from a mirror-loaded IPS, there is still a load resistance at that input node to the VAS in the form of the effective input resistance of the VAS transistor due to finite beta (or of the pair of transistors if a 2EF VAS).

With tongue only partially in cheek, it is always instructive and useful to examine the behavior of circuits in the limit, as certain parameters go to an extreme. It is clear that the VAS would not work if its transconductance went to zero .

Thanks for your interest in the second edition!

Cheers,
Bob

 

[Bob Cordell]

I remember that in a letter to Electonics World + Wireless World (I do not have the exact reference, that may be circa 1995), Douglas Self spoke of a double regime, changing from transconductance at low frequencies to transimpedance at frequencies at which the compensation capacitor becomes effective.

In the sixth edition of his book "Audio Power Amplifier Design", page #183, he wrote :
"It is often stated that adding a resistance in the VAS emitter connection introduces local feedback. This is just not true, because the VAS accepts a current input rather than a voltage input, so the voltage developed across the emitter does not cause negative feedback."

I would argue that saying that the VAS accepts a current input rather than a voltage input is a gross over simplification and a rather gross generalization.

Cheers,
Bob

 

[svjeff]

I remember that in a letter to Electonics World + Wireless World (I do not have the exact reference, that may be circa 1995), Douglas Self spoke of a double regime, changing from transconductance at low frequencies to transimpedance at frequencies at which the compensation capacitor becomes effective.

In the sixth edition of his book "Audio Power Amplifier Design", page #183, he wrote :
"It is often stated that adding a resistance in the VAS emitter connection introduces local feedback. This is just not true, because the VAS accepts a current input rather than a voltage input, so the voltage developed across the emitter does not cause negative feedback."

The sensitivity functions that Cherry calculated were complex, as they involved impedances. The sensitivity of gm_VAS was negligible over frequency.

The Cherry paper that I keep referring to is well worth getting as it analyzes the very topology that is the focus of much of Bob's book (and Self's too I suppose although I've not seen it). AND, to make it even more germane to this thread, Dr. R. R. Cordell is thanked in the Acknowledgement. (Sadly, Bob was demoted in the follow-up paper.)

 

[svjeff]

With tongue only partially in cheek, it is always instructive and useful to examine the behavior of circuits in the limit, as certain parameters go to an extreme. It is clear that the VAS would not work if its transconductance went to zero .

Good point and a good reminder. That method, along with dimensional analysis, probably got me through school. There is an assumption made in my argument that because the sensitivity to transconductance of the VAS is negligible that the transconductance is irrelevant. But that is not what the sensitivity analysis is saying. Looking at the behavior in the limit, as you suggest, points this out quite plainly.

Thanks Bob!

 

[ostripper]

Yes , examine the behavior of a real circuit that exists in front of you.
OS

 

[poldaaudio]

I have to disagree with some of your points. First, in terms of numbers, I typically run my VAS at 10 mA, so re' is about 2.6 ohms. I usually degenerate by a factor of about 10 with a 22 ohm emitter resistor. So this is relatively less degeneration that you are describing. For a 20 mA VAS, this would correspond to a degeneration resistor of only about 10 ohms.

With the Miller compensation shunt feedback, the output impedance of the VAS at high frequencies will theoretically be on the order of 25 ohms or so when the VAS is run at 10 mA and degenerated 10:1. This is pretty low. In practice, the VAS output impedance will be a bit higher due to the attenuation of the Miller capacitor against the input capacitance of the first VAS transistor. Simulation will confirm this.

The issues being discussed here also underline the great advantage of using an output triple instead of a mere output double. If you are concerned about VAS output impedance not being low enough, it seems you should also be concerned about the input impedance of the output stage not being high enough.

The use of a push-pull VAS improves things in many ways, but is of limited relevance to the matter here of whether the VAS should be degenerated or not. The push pull VAS brings added performance to the table by largely suppressing 2H created in the VAS and by doubling the amount of signal current the VAS can deliver for a given amount of VAS bias current. The helps the VAS better drive the Miller compensation capacitor and the output stage.

Cheers,
Bob

I've seen plenty of designs with much more VAS degeneration than 22 ohms and I never said that a symmetrical VAS confers no benefit in terms of even harmonic cancellation or anything else.

You're entitled to your dismissive opinion that VAS degeneration isn't something we should bother thinking about and that "25 ohms at high frequencies" is all that matters.

Here is a quick simulation of an idealized amplifier plotting VAS collector impedance:

The VAS emitter degeneration is stepped from 1 ohm to 100 ohms in 10 ohm steps.
The 1uA AC current source facilitates measuring the impedance at the VAS collector.
The vertical scale in volts can be read directly in ohms.
The 100T inductor disables the global feedback loop for AC analysis in the frequency range of interest.

Even at 1kHz the difference in collector impedance is still very significant, spanning from 60 ohms to more than 900.

 

[AnalogJoe]

Another question Bob, when calculating the slew rate of simple Miller compensated amplifier, you divide the tail current by 2 and then divide that by the compensation capacitor, so taking one of the examples of your book: if the tail current is say 2mA, you divide that by 2 and then divided by say a 30pF cap to give 1mA/30pF = 33 V/usec. But I've seen other authors that do not divide the tail current by two, they simply divide the entire tail current by the Miller compensation cap, what am I missing?

 

[brian92fs]

I believe this is impacted by the inclusion of a current mirror on the LTP. When a current mirror is used, nearly the full tail current should be available. Someone please correct me if this is misstated.

 

[svjeff]

The recent post by poldaaudio prompted me to revisit the simple LTSpice model that I began some weeks back. I prefer to focus in as much as possible on the thing of interest so I didn't create anything more involved than I thought absolutely necessary. Having done a dc sweep to determine the base current that will result in about 25V on the collector I set the current source at the base to that value. RE was stepped over 4 decades and the impedance at the collector node plotted vs. frequency. Substitute "ohms" for "volts" on the left axis and the numbers may be read directly as impedance.

Most of the variation in impedance is seen above 100 kHz and not much is seen at 1 kHz. The last graphs shows the transresistance gain, V(collector)/I(base_node), and the voltage gain, V(collector)/V(base). So is the current source connected VAS better viewed as current or voltage driven?

 

[keantoken]

So is the current source connected VAS better viewed as current or voltage driven?

Find out how the design in front of you behaves, don't burden yourself with rule of thumb if you don't have to.

 

[Bob Cordell]

I believe this is impacted by the inclusion of a current mirror on the LTP. When a current mirror is used, nearly the full tail current should be available. Someone please correct me if this is misstated.

You are exactly right. It depends on whether or not the input differential pair is loaded by a current mirror or not.

Cheers,
Bob

 

[AnalogJoe]

You are exactly right. It depends on whether or not the input differential pair is loaded by a current mirror or not.

Cheers,
Bob

I see, so using a current mirror not only doubles the transconductance but also the Slew Rate!, whilst helping reduce distortion by keeping the collector currents balanced, it seems like that current mirror is a huge bargain.

 

[Mark Johnson]

Minimalists prefer not to put the signal through another two (!) highly nonlinear devices. They also prefer to avoid what James Solomon's educational article calls "the mirror pole" as shown in his Figure 19(a), attached below.

A link to the Solomon article appears in post #7322 of this thread, among many other places.

_

 

[jan.didden]

Mark, why is this Cm-pole significant, since the voltage across it is pretty much constant?

Jan

 

[syn08]

Mark, why is this Cm-pole significant, since the voltage across it is pretty much constant?

That's irrelevant. The "mirror pole" is draining current from the transistor collector, at a frequency of I/(2*PI*C*Vt) where Vt=kT/q and I is half of the long tail current. Assuming this is the one an only pole in the input stage, since it drains current for only half of the input stage signal, the overall frequency response has a pole-zero pair, separated by an octave. But unless this pair occurs close to the amplifier UGF, where it can significantly degrade the phase margin, it is of little importance. You can plug some values in the above pole formula and you will find that mostly micropower op amps could be potentially affected. So while the "mirror pole" can be significant in certain cases, it can safely be ignored in any discrete design.

 

[svjeff]

The expression given in the Solomon paper for the pole frequency due to Cm involves the tail current, I1. In his example I1 = 1 uA which gave a pole frequency of just under a MHz. Assuming the capacitances are otherwise the same, and a discreet implementation with a tail current 3 orders of magnitude greater, this pole would be around 100 MHz.

I agree with sSound that the current mirror load on the input diff pair seems quite a bargain and Bob notes this in his book, page 64.

Long ago (1980-ish) when I was struggling to reconcile the different PA design approaches I asked Nelson Pass about current mirror load for the input diff pair, after all, why wouldn't one use them? He replied that he didn't like the sound. To this day I don't believe I've seen him use one in any of his published designs. Go figure.

Jeff

 

[Mark Johnson]

Minimalists prefer not to put the signal through another two (!) highly nonlinear devices.

 

[syn08]

Minimalists prefer not to put the signal through another two (!) highly nonlinear devices.

Yes, those nonlinearities easily pile up . I wonder how many (!) such nonlinearities were in the signal path from the studio microphones to your speakers or headphones.

 

[jan.didden]

That's irrelevant. The "mirror pole" is draining current from the transistor collector, at a frequency of I/(2*PI*C*Vt) where Vt=kT/q and I is half of the long tail current.

I'm sorry, not looking for a fight, but sincerely don't get it.
We have a cap where (assuming an ideal supply) the voltage is absolutely constant. How can any current flow through a cap that has a non-varying voltage across it?

I'm sure you're right, I just don't get it ...

Jan

 

[syn08]

I'm sorry, not looking for a fight, but sincerely don't get it.
We have a cap where (assuming an ideal supply) the voltage is absolutely constant. How can any current flow through a cap that has a non-varying voltage across it?

I'm sure you're right, I just don't get it ...

I believe you are confusing the DC voltage (indeed approximately constant) with the AC Vbe voltage. Drawing the equivalent schematic using the bipolar small signal model will show the difference.

As usual, large signal vs. small signal models can be confusing...