Demonstrating that TPC and so-called "TMC" are related - diyAudio
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Old 2nd October 2013, 11:44 AM   #1
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Default Demonstrating that TPC and so-called "TMC" are related

I have previously shown that an amplifier with TPC possesses exactly the same major loop gain across the audio band as the total loop gain enjoyed by the second stage and the output stage alone with so-called "TMC" provided the same compensation elements are used in both cases.

This proves that TPC and "TMC" are, in fact, two sides of the same coin, and that "TMC" is merely TPC localised to the second stage and the output stage.

In order to characterise the major loop transmission of TPC with respect to the transmission of the minor loop about the output stage with "TMC" (in the presence of the major loop) outside the audio band, a second order model of the generic (Thompson) amplifier is used. This consists of a differential voltage controlled current source for the input (transadmittance) stage (TAS) driving a transimpedance stage (TIS) whose two uncompensated dominant poles are modeled by a parallel RC network at its input and output.

This second order model is preferred to previous demonstrations in which real transistors were used because it excludes extraneous singularities from the system, and, therefore, permits the isolation of those singularities that are intrinsic to the two compensation methods.

The attached extract from a yet-to-be-published paper of mine explains how the second order model works.

From the attached graph, it is apparent, as explicated above, that the total loop gain (in the audio band and up to 100KHz) about the second stage and the output stage with "TMC" (red trace) is exactly the same as the major loop gain with TPC (blue trace).

Secondly, it is clear that the initial double-pole roll-off with TPC reverts, as expected, to a single pole roll-off due to the introduction of a zero, and that the same zero also obtains in the "TMC" minor loop. With the latter it is also apparent that the zero is closely followed by a zero-pole doublet. These three singularities together have the net effect of causing the response of the "TMC" minor loop to appear in parallel with that due to the major loop with TPC at frequencies beyond those of their common dominant zero.

Clearly, a stable "TMC" loop can be realised by merely calculating the component values required to give a stable major loop with TPC, and then simply connecting the TPC resistor to the output to give a stable "TMC" compensator.

Caution must, of course, be exercised to ensure that the slightly greater unity loop transmission frequency of the "TMC" minor loop (compared to that of the TPC major loop) doesn't compromise stability of the loop.
Attached Images
File Type: png TPC vs TMC01.png (24.6 KB, 308 views)
File Type: png TPC vs TMC02.png (53.7 KB, 295 views)
Attached Files
File Type: asc TMCvsTPC5.asc (5.4 KB, 15 views)
File Type: pdf Miller_compensation.pdf (133.7 KB, 29 views)

Last edited by michaelkiwanuka; 12th October 2013 at 01:07 PM.
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Old 2nd October 2013, 12:22 PM   #2
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Quote:
Originally Posted by michaelkiwanuka View Post
Caution must, of course, be exercised to ensure that the slightly greater unity loop transmission frequency of the "TMC" minor loop (compared to that of the TPC major loop) doesn't compromise stability of the loop.
Doesn't your simulation show the TMC with substantially BETTER PhaseM than the TPC, despite the small increase in cross-over frequency?
1/3 radian is not trivial.

Best wishes
David
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Old 2nd October 2013, 12:32 PM   #3
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"TMC" shows some fifteen degrees better phase margin at unity minor loop gain frequency because it has two dominant zeros following the dominant coincident poles.

Note, however, that this is not necessarily an advantage as the unity minor loop gain frequency with "TMC" is nearly an octave higher than that due to the major loop with TPC.

You can establish this yourself by running the simulation; I attached the .asc file to the introductory post.
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Old 2nd October 2013, 12:49 PM   #4
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These two circuits:

Click the image to open in full size.

have identical connectivity, and identical component values. Additional trace loop appears in left hand circuit. Does simulation account for trace length, and loop area? Loops existence in simulation may change calculations due to additional node with differences in results plots >100kHz strictly due to differing number of round off errors.

All I see here is modeling error of two identical circuits.
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Old 2nd October 2013, 12:53 PM   #5
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Quote:
Originally Posted by Barleywater View Post
These two circuits have identical connectivity, and identical component values. Additional trace loop appears in left hand circuit. Does simulation account for trace length, and loop area? Loops existence in simulation may change calculations due to additional node with differences in results plots >100kHz strictly due to differing number of round off errors.

All I see here is modeling error of two identical circuits.
No. These two circuits have identical component values, but, self-evidently, NOT identical connectivity.

No. There is no "modelling error of two identical circuits".

Of course simulation does not "account for trace length and loop area". You've missed the point I fear. The purpose of simulation is to gain insight into circuit behaviour; in this case, the conduct of "TMC" with respect to TPC without consideration of extraneous third order singularities due to "trace length and loop area", and so on and so forth.

Last edited by michaelkiwanuka; 2nd October 2013 at 01:04 PM.
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Old 2nd October 2013, 02:00 PM   #6
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Yes, I see now. One more cup of coffee. Sorry for the bother.

Thanks for the demonstration.
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Old 2nd October 2013, 02:05 PM   #7
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Quote:
Originally Posted by michaelkiwanuka View Post
"TMC" shows some fifteen degrees better phase margin at unity minor loop gain frequency because it has two dominant zeros following the dominant coincident poles.

Note, however, that this is not necessarily an advantage as the unity minor loop gain frequency with "TMC" is nearly an octave higher than that due to the major loop with TPC.
Usually an increased loop crossover frequency is an issue because it impacts stability.
But in this case, despite the increase in frequency the TMC is a third of a radian better.
The resultant improvement in stability is what matters.
Well done on the post of the asc.

Best wishes
David
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Old 2nd October 2013, 02:07 PM   #8
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Quote:
Originally Posted by michaelkiwanuka View Post
...
This proves that TPC and "TMC" are, in fact, two sides of the same coin, and that "TMC" is merely TPC localised to the second stage and the output stage.
...
I think I agree, but a major difference in a real circuit would be that the TPC load the VAS significantly more than a TMC do?

"The TMC is a bootstrapped TPC."
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Old 2nd October 2013, 02:17 PM   #9
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Originally Posted by wissting View Post
I think I agree, but a major difference in a real circuit would be that the TPC load the VAS significantly more than a TMC do?
I haven't seen any evidence that this is the case.
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Old 2nd October 2013, 02:41 PM   #10
sreten is offline sreten  United Kingdom
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Quote:
Originally Posted by michaelkiwanuka View Post
I haven't seen any evidence that this is the case.
Hi,

It looks to be the case to me. 1K to ground and 1K
bootstrapped from the output looks different loading.

Unless I'm missing something the current through the
1K will be lower for the bootstrapped case than ground.

Doug Self got slew rate limiting with TPC due to the
VAS not be able to drive the resistor to ground.

rgds, sreten.
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