Bob Cordell's Power amplifier book

[Bob Cordell]

Originally Posted by michaelkiwanuka

THANK YOU! Precisely what i have been saying all along and been told by some it didn't constitute "hard evidence".

Hi Mike,

I have verified the same thing with my own simulations, where there is a substantial peak in the total loop gain around the output stage (as seen by the output stage). This is quite interesting, but is certainly not any kind of hard evidence that TPC is somehow superior to TMC, which is what you have been arguing.

Moreover, bear in mind that this peaking behavior when seen in the total output stage loop gain with TMC, is arrived at via two feedback loops surrounding the output stage. This in my mind is a significant architectural distinction from TPC (which only has one loop around the output stage).

The important question remains, which approach, in practice is better, where better's definition remains somewhat of an issue of contention.

If we adjust each of the three techniques individually so that the output stage sees the same phase margin and at least, say 6dB gain margin, and then see which one delivers the lowest distortion, maybe that is a means of fair comparison. In such an approach, not all of the designs would have the same gain crossover frequency, either around the output stage or in the amplifier's global loop. We would essentially be saying which one gives lowest distortion for the same amount of stability as seen by the output stage.

Of course, in my view, we would first do this without any use of a lead network in the global feedback path. If we subsequently wanted to allow comparisons using a lead network, we would then allow its use in any of the three compensation approaches.

Cheers,
Bob

[megajocke]

Originally Posted by Edmond Stuart

Hi Joakim,

Referring to your post #1252, I have a few (dumb?) questions:
How did you calculate tau1 and tau2 for the TPC version? The same way as for the TMC version? Also, how do you define tau1 and tau2 for the lead compensation. Maybe the answers are obvious (and I have missed something), but I want to make absolutely sure that during the further evaluation of TPC and TMC, we are not going to talk at cross-purposes.

Cheers,
Edmond

Hi Edmond,

Initially tau1 and tau2 were just the time constants of the lead type transfer function in the equation for I3 (see my third handwritten page). From the beginning I hadn't considered what the transfer functions from the two inputs of the front end to the output actually were, but I continued by deriving the transimpedance of the TPC VAS in figure (8), a front end equivalent to the TMC version, which is

Z(s) = - D (s tau3 + 1) / (s^2), where tau3 = R (C1+C2) and D = 1 / (R C1 C2)

the output voltage of the front end then becomes

Vd = Z * I3 = D (s tau3 + 1)/(s^2) gm [Vin - Vfb/A (s tau2 + 1)/(s tau1 + 1)]

but tau1 from the I3 expression is the same as tau3 because

tau1 = k R C1 = R (C1 + C2) = tau3

which makes the front end output voltage

Vd = D gm [ (s tau1 + 1) Vin - (s tau2 + 1) Vfb/A ] / (s^2)

for the TMC and the calculated equivalent TPC+lead version.

I realized later that there is another practical way to implement a TMC equivalent TPC circuit which does not require a lead network in the feedback path, and that is to select another TPC VAS transimpedance Z' with tau3' = tau2 instead of tau1.

Then a lag network with transfer function (s tau1 + 1)/(s tau2 + 1) is inserted in the input signal path to the LTP instead of the lead network in the feedback path to give the same Vd.

Vd = Z' * I3' = D' (s tau3' + 1)/(s^2) gm [(s tau1 + 1)/(s tau2 + 1) Vin - Vfb/A]

which also becomes, because tau3' = tau2,

Vd = Z' * I3' = D' gm [ (s tau1 + 1) Vin - (s tau2 + 1) Vfb/A ]/(s^2).

But after that, you may want to consider removing the zero at tau1, which shows up in the closed loop response, by inserting a standard low-pass filter instead with transfer function 1/(s tau2 + 1). If the impedance of the source feeding the power amplifier is low or known this could just be the standard input slew rate/RF ingress limiting filter.

Cheers and happy new year everyone! (Skål och gott nytt år till er alla!)

[michaelkiwanuka]

Originally Posted by Bob Cordell

Hi Mike,

I have verified the same thing with my own simulations, where there is a substantial peak in the total loop gain around the output stage (as seen by the output stage). This is quite interesting, but is certainly not any kind of hard evidence that TPC is somehow superior to TMC, which is what you have been arguing.

No. What i have been arguing (and provided proof in simulation) is the fact that the total loop gain about the output stage (that due to the major loop and minor loop) alone with TMC is the same as the major loop gain about the whole amplifier with TPC.

i.e: TMC does not improve the total loop gain about the output stage over that provided by TPC. This is why TPC is superior to TMC because this same loop gain is available for the whole amplifier not just the output stage.

[wahab]

Originally Posted by michaelkiwanuka

No. What i have been arguing (and provided proof in simulation) is the fact that the total loop gain about the output stage (that due to the major loop and minor loop) alone with TMC is the same as the major loop gain about the whole amplifier with TPC.

i.e: TMC does not improve the total loop gain about the output stage over that provided by TPC. This is why TPC is superior to TMC because this same loop gain is available for the whole amplifier not just the output stage.

As relentlessely said , TPC load the VAS and has between
6 to 15 db less OLG to start with compared to TMC...

It seems that you didn t check this point, otherwise you wouldn t
insist in this claim, which hold more of some sort of dogmatism
that from some basical scientific approach...

[michaelkiwanuka]

Have you run the sim?

As i have already stated the loading on the second stage cannot not be appreciable because the difference in the total loop gain about the output stage would also be large.

[wahab]

Originally Posted by michaelkiwanuka

Have you run the sim?

.

yes, it s two posts above....

Originally Posted by michaelkiwanuka

As i have already stated the loading on the second stage cannot not be appreciable because the difference in the total loop gain about the output stage would also be large.

For the OLG difference to be noticable when closing the loops,
that is a different story.
As pointed many times, THD reduction seems comparable for both
compensation scheme, although TPC seems to have an advantage
in some cases that wasn t pointed yet in this thread, but i just wait
for some more elements before coming to conclusions..

The remaining debate is wether TMC ot TPC has "better" step
response/stability along with a misunderstanding about the initial
conditions, i.e, the values of network that optimize the said compensation
schemes, as using the same values for both TPC and TMC seems to me
more of an exercise of style than a clever way to find what exactly
can be extracted from the two contenders...

[Edmond Stuart]

Hi Joakim,

Thanks for the formulas. Next year (that is, very soon ), I will have a close look at it.

Skål och gott nytt år !!!
Edmond.

[jcx]

Originally Posted by WuYit

Joakim,
great work, but the "problems" lie in the time domain rather than in the frequency domain and both aspects have to be observed simultaneously. You can`t disregard the time response, however,.that is not easily evaluated.

Originally Posted by abraxalito

I think on reflection I read you over-literally, perhaps your meaning was closer to 'let's get a balance between the two domains, not focus over-much on the frequency domain'. In that I'm with you - I've noticed a tendency (not so much in this thread, more so in the digital ones) for high-res FFTs to bedazzle people into thinking they're seeing the whole picture when they're merely appreciating one side of the coin...

to stretch/extend the analogy the "coin" is infinitely thin so the reverse follows exactly the contour of the obverse - ie fourier and time domain convey exactly the same information being "duals" and it is only a question of ease of human interpretation that that one would choose between them depending on what you want to "see"



I hope everyone here has a some what more sophisticated knowledge of Signals and System but I get really really tired of people thinking they're saying something meaningful when thay try to discredit the "meter readers" for "only looking at sine waves" - or fft, or THD...

...they're all tools with strengths and weaknesses

and the formal "time domain" system theory tool is "Modern Control Theory" State Space representation - are you seriously proposing to introduce that into a diy forum? - I don't think I've ever seen a practicing engineer use state space tools for amplifier circuit design

[PB2]

Originally Posted by jcx

and the formal "time domain" system theory tool is "Modern Control Theory" State Space representation - are you seriously proposing to introduce that into a diy forum? - I don't think I've ever seen a practicing engineer use state space tools for amplifier circuit design

We had specific courses on control theory when I was in school and IIRC it was not taught out of the EE department since it had application to many fields. Ogata was the text book and I was impressed with both the text and the course:
Amazon.com: Modern Control Engineering (5th Edition) (9780136156734): Katsuhiko Ogata: Books

Do you have a preferred text?

[jcx]

the course I took was taught by the Mech E dept and used Ogata (1st ed)

I've since bought Dorsey's, Goodwin's control theory books

you need the "cultural" knowledge of State Space to read any recent control literature and many fundamental properties of control theory are expressed as proofs in advanced Linear Algebra using State Space representation - many theorems have extensions to nonlinear systems that have only been proven in the last decade or so - and at those levels my knowledge is strictly "cultural"

but I think that for problems that can be adequately represented as SISO LTI then "Classical Control Theory" growing from Bode's work is far more accessible/useful - and some advanced results including nonlinear techniques are usable in "Classical" form (Popov, Small Gain Theorem's Circle criteria)

I try not to miss any chances to recommend BJ Lurie's work - although his books are hard to understand and "buggy" - needing 2nd editions but he really shows how to use Classical Control techniques - you can still view his old site with archive.org Dr. Boris J. Lurie's Homepage: Classical Feedback Control
one thing Lurie does really well is show that the “conservation” relation for the total amount of feedback - the “Bode Integral” is exactly such a practical "good theory" - and has been the underpinning fundamental argument behind my posts in this thread

http://trs-new.jpl.nasa.gov/dspace/b.../1/98-0905.pdf

Happy New Year, and may all of your nonlinearities be Locally Lipschitz