Bob Cordell's Power amplifier book

Bob, Thanks for the asc, but I'm confused - I just started poking at the sim and find the fft is the flat/rising spray of harmonics that usually indicates "hard" nonlinearity, some stage is limiting (or deadband?)

the diff pair bias looked light with extreme level of degen by other audio PA schematics I'm familiar with - so I bumped the tail current ~4x, cut degen R 10x - and anticipated fixing up compensation - but the amp still works in sim with 10x gain increase?? - some bouncing esp. with added Cload but not oscillating??
I suppose it could be called conservative design - but unless the models are just inadequate for stability estimates I would ask why such excess conservatism - leaving 20 dB distortion reduction on the cutting room floor so to speak
in any event it may not be not useful to explore compenstion in a sim that won't oscillate with 10x loop gain increase and 1nF direct Cload

I would like to know if this is the expected/intended behavior and maybe my instincts are just all wrong since I mostly look at Class Headphone level circuits with the luxury of >100MHz output devices

Hi jcx,

I think that what you are seeing in the FFT are high-frequency harmonics due to crossover distortion that are at a high enough frequency where they are not reduced by negative feedback. Keep in mind that this amplifier is not one to write home about, with a single pair of output transistors driving a 4-ohm load. I have not lookede hard at this, but I think that this is what you are seeing.

I do like to run my BJT input pairs with 10:1 degeneration, which provides good linearity and good slew rate. This may seem like throwing away too much gain, but there is plenty of gain to go around, especially when the input pair is loaded with a current mirror, the VAS is a Darlinton, and the output stage is a Triple. Note also that the 10:1 degeneration does not make the noise as bad as one might think; input-referred noise of this amplifier is less than 7 nV/rt Hz. Note that this is partly helped by the low impedance of the feedback network. The low impedance of the feedback network also minimizes any excess phase contribution where the feedback hits the input stage.

The phase margin for the TMC version is indeed quite good, somewhat surprizingy so. The quiescent operating ft of the output transistors is about 6 MHz. I just arbitrarily chose a gain crossover frequency of 1 MHz, which I consider to be safe in the real world for this design. I may be on the conservative side, but sometimes excess phase is not modeled well in output stages, and also the margins will decrease with signal swings.

Cheers,
Bob
 
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[snip]I also will be happy to see what you can do with this if you put in some lead compensation. Once again, however, I remind you that the TMC amplifier needs no lead compensation to perform really well.

Cheers,
Bob

Bob,

Something about lead compensation on the feedback resistor that isn't completely clear to me.
The way I understand it is that it provides a phase lead inside the feedback loop increasing stability. But at the same time, it does increase the high-frequency feedback factor thus leading to increased peaking.
So this lead comp at the same time provides increased stability AND increased peaking.
Secondly, since it increases feedback at higher freqs it also decreases distortion at higher freqs. So in the end you get better stability, more peaking and less distortion. Correct?

jan didden
 
Bob,

Something about lead compensation on the feedback resistor that isn't completely clear to me.
The way I understand it is that it provides a phase lead inside the feedback loop increasing stability. But at the same time, it does increase the high-frequency feedback factor thus leading to increased peaking.
So this lead comp at the same time provides increased stability AND increased peaking.
Secondly, since it increases feedback at higher freqs it also decreases distortion at higher freqs. So in the end you get better stability, more peaking and less distortion. Correct?

jan didden

Hi Jan,

The phase lead inside the feedback loop is meant to compensate (to a certain extent) for the additional phase lag (and phase dip) created by the TPC network. As a result, you get less peaking and overshoot (as far as originating from TPC). The downside is that also the unity loop gain frequency is increased. As a result, less stability.

Cheers,
E.
 
AX tech editor
Joined 2002
Paid Member
Hi Jan,

The phase lead inside the feedback loop is meant to compensate (to a certain extent) for the additional phase lag (and phase dip) created by the TPC network. As a result, you get less peaking and overshoot (as far as originating from TPC). The downside is that also the unity loop gain frequency is increased. As a result, less stability.

Cheers,
E.

Hi Edmond,

Thanks, I actually messed up my query.
I was thinking about a lead-lag compensation across the feedback resistor rather than a pure lead network. (I wasn't addressing any particular comp method, rather a 'standard' feedback loop).
Let me think a bit more about it.

jan
 
Hi Edmond,

Hi Bob,

First, thank you for explanation and the files.

[snip]
So, TPC and TMC give about the same distortion result with identical components, but this is academic because each technique wants to have a different ratio for best performance. This is what I have been trying to say all along, perhaps not very well.

You said it very well. The only problem is that some people are stone-deaf to your arguments.

It is thus silly to require the use of the same set of components for an honest apples-apples comparison. It is more appropriate to compare the techniques when each is set agressively enough to yield the same distortion performance, if possible.

Of course! By nature, TPC and TMC are totally different compensation techniques. Hence the optimal components values are different too. So the alleged requirement of equal values for a fair apples-apples comparison, is 'utter nonsense'.

Notably, the TPC amplifier with equally low distortion as the TMC amplifier exhibits 67% small-signal squarewave overshoot and +3dB closed loop gain peaking. Large signal squarewave response exhibits ringing.

Cheers,
Bob

In the mean time, I've run a simulation with the same compensation components, though a simpler OPS: double EF, instead of triple EF.
I got roughly the same results, including 65% overshoot with TPC.

I also tried to get rid of the phase dip and overshoot by means of lead compensation in the feedback path. But it appears to be impossible to remove them completely, not to mention the unwanted implications of an increased unity loop gain frequency.

Cheers,
E.
 
Bob,

Something about lead compensation on the feedback resistor that isn't completely clear to me.
The way I understand it is that it provides a phase lead inside the feedback loop increasing stability. But at the same time, it does increase the high-frequency feedback factor thus leading to increased peaking.
So this lead comp at the same time provides increased stability AND increased peaking.
Secondly, since it increases feedback at higher freqs it also decreases distortion at higher freqs. So in the end you get better stability, more peaking and less distortion. Correct?

jan didden

Hi Jan,

Not quite correct. The frequency range in which feedback lead compensation provides phase lead is mainly intended to be in the vicinity of the gain crossover frequency, so as to provide better phase margin. As such, the increased loop gain that it may tend to provide will not really decrease high-frequency distortion. By improving phase margin, it should actually tend to decrease frequency response peaking. The trick is to make sure that the lead compensation provides helpful phase lead while not providing so much increased feedback loop gain that it seriously compromizes gain margin. Phase lead compensation thus must be applied gingerly.

One can also think of phase lead compensation as an attempt to cancel one pole in the feedback loop gain transfer function.

The ability of the phase lead capacitor to provide a more direct path from EMI at the speaker terminals back to the input stage is a potential disadvantage.

Cheers,
Bob
 
Hi Bob and Edmond,

A series combination of 4879 ohms and 44 pF across the 3800 ohm feedback resistor in the TPC simulation Bob posted will give the same phase lead that the TMC network itself is providing from the output directly to the VAS in the TMC version.

The loop gain around the output stage then becomes about the same for both the TPC and TMC versions with a gain crossover frequency of about 1.7 MHz. With this lead compensation network the TPC version neither has overshoot nor closed-loop frequency response peaking, just like the TMC version. See post 1200 for more details. I can post my derivation of these values if you are interested.

Regards,
Joakim
 
jcx,
[snip]
Bob,

I played a bit with the TMC network and came to the same conclusion as syn08 did earlier but by a different method: the TMC network can, as far as the forward gain and feedback gain of the frontend is concerned, be replaced with a TPC network with the same component values plus an RC-network from the output of the amplifier to the base of the VAS. The capacitor value is the same as the TMC capacitor on the input side of the VAS (17 pF) and the resistor value is R * (1+Cout/Cin) (2.2 kohm * 6 = 13.2 kohm).
[snip]
The attached curves show loop gain for TPC + lead is in green and TMC is in red. The step response is for the TPC + lead version. The TPC version shows a little more phase lag which comes from the input stage.

Hi Megajocke,

These are interesting results, which are certainly worth to have a closer look at. So, would you be so kind to give us the exact schematics on which your graphs are based, as a verbal description alone might easily lead to errors and misinterpretation.

Thanks in advance.

Cheers,
E.
 
Hi Bob and Edmond,

A series combination of 4879 ohms and 44 pF across the 3800 ohm feedback resistor in the TPC simulation Bob posted will give the same phase lead that the TMC network itself is providing from the output directly to the VAS in the TMC version.

The loop gain around the output stage then becomes about the same for both the TPC and TMC versions with a gain crossover frequency of about 1.7 MHz. With this lead compensation network the TPC version neither has overshoot nor closed-loop frequency response peaking, just like the TMC version. See post 1200 for more details. I can post my derivation of these values if you are interested.

Regards,
Joakim

Hi Joakim,

I tried just that and indeed the overshoot has gone. That's nice! But looking at the gain and phase response of the global NFB loop, we still see that ugly phase dip around ~20kHz. Moreover, compared to TMC, the unity loop gain frequency is two times higher: 2MHz vs 1MHz for TMC, and the phase margin lower: 69 vs 91 degrees. If we adjust the TPC caps for an equal ULGF (apples to apples, you know), then the distortion of TPC is 10dB higher :sad: though the PM has become slightly better: 74 degrees.

Cheers,
E.

PS: >I can post my derivation of these values if you are interested.
Yes, please (and the schematics).
 

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Looking deeper in large signal mode, the seemingly
nice step response of the phase lead compensated
TPC amp will show itself in its whole crudity as an
ugly travesty of TMC.



Edit : The scale of step response is divided by 1000,
so the output level simulated is about 34V pk.
 

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But looking at the gain and phase response of the global NFB loop, we still see that ugly phase dip around ~20kHz. Moreover, compared to TMC, the unity loop gain frequency is two times higher: 2MHz vs 1MHz for TMC, and the phase margin lower: 69 vs 91 degrees.

Right. That's true for the feedback loop going through the LTP but the TMC version also has the feedback coming directly from the output into the VAS. If you instead look at the loop gain around the output stage they both have a crossover frequency of about 1.7 MHz and a phase margin of about 60 degrees. The TPC version has a little less phase margin because the LTP has some phase lag which I did not account for.

My thinking is that, since it's the output stage with its load that is the slow one and has the least well-controlled transfer function, this is where concern for crossover frequency and phase margin is needed most. Bringing the phase lead directly to the VAS through the TMC network or letting it pass through the LTP first shouldn't make that much of a difference as far as stability is concerned considering how well-behaved the LTP is at 2 MHz, let alone at 20 kHz where the phase dip is. If the input stage is driven into nonlinearity there will be differences of course. Is that where the worry lies?

Still there are differences in how the stages are loaded. The TPC version loads the VAS more, at least with these values in the TPC network, while the TMC version on the other hand loads the LTP more. I'll post my derivation of the component values later.

Cheers,
Joakim
 
Hi Joakim,

So it's matter where you put the gain probe. If you do it your way, then I agree with your remarks.

> If the input stage is driven into nonlinearity there will be differences of course.
> Is that where the worry lies?

Yes. If, for example, during saturation or power-up/power-down phase (or whatever reason), the gain of the LTP becomes (momentarily) much lower, then the ULGF shifts into a region where the phase maximally dips. In that case the amp will become unstable. TMC is less prone to this effect, as the TMC stuff doesn't enclose the LTP.

Cheers,
E.

edit:
>'the TMC version on the other hand loads the LTP more'
True, that is, for frequencies below 36kHz or. Above this frequency, TPC loads the LPT slightly more (at least, according my sim).
 
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Hi Jan,

The phase lead inside the feedback loop is meant to compensate (to a certain extent) for the additional phase lag (and phase dip) created by the TPC network. As a result, you get less peaking and overshoot (as far as originating from TPC). The downside is that also the unity loop gain frequency is increased. As a result, less stability.

Cheers,
E.


This is incorrect. phase lead compensation merely adds a zero in the loop gain response in the region of unity gain crossover increasing phase margin and greater stability except where gain peaking already exists, in which case the zero merely aggravates it.
 
The loop gain around the output stage then becomes about the same for both the TPC and TMC versions with a gain crossover frequency of about 1.7 MHz. With this lead compensation network the TPC version neither has overshoot nor closed-loop frequency response peaking, just like the TMC version. See post 1200 for more details. I can post my derivation of these values if you are interested.

At last someone who knows what he's talking about!

What i have discovered so far is some folks lack of knowhow when it comes to implementing TPC which has led to patently false comparisons with TMC.

The same folks have failed to appreciate that TMC is related to TPC more closely than they accept, and that TMC is a poor relative of TPC.
 
But looking at the gain and phase response of the global NFB loop, we still see that ugly phase dip around ~20kHz.

That phase dip is due to the roll off occasioned by the two coincedent poles, is completely harmless and does not even appear in the closed loop response or affect stability.

This is the trouble with not really knowing much about how to implement TPC.

No sensible comparisons can be made with TMC or much else as a result.
 
Here's what I did:

Step 1: This is the whole amplifier.

Step 2: The LTP is modeled as a transconductance amplifier with infinite bandwith while the VAS is modeled with lots of (infinite) gain and no input current.

Step 3: C1 feeds the current I0 into the virtual ground summing node at the input of the VAS and this network is used to calculate this current.

Step 4: The network in step 4 gives the same I0 if its input signals, the voltages Vfb and Vd, are the same (superposition). The loading of the output stage and the VAS is not the same as before however.

Step 5: Network used to calculate I2 in the upper branch of (4). I1 is calculated as current division between the capacitors.

Step 6: The impedances from (5) is scaled to give a network that outputs I1 instead of I2.

Step 7: The upper branch from (4) is replaced by (6) giving (7) which still gives the same I0 for the same input voltage signals as the original TMC network.

Step 8: The TMC network is replaced by the calculated TPC network and the lead link to the VAS summing node. The current I3 driving the TPC compensated VAS is then calculated.

The current I3 has two components. One is -Vin*gm for the forward path and the other one is gm * Vfb/A * (s*tau2+1)/(s*tau1+1) for the feedback path which is a lead type transfer function as tau2 > tau1.

Step 9: The lead type transfer function is implemented on the input side of the LTP instead. The circuitry to the left of the dashed line in (8) is replaced with this new network that will give the same I3 as the left part of (8) did.

The previously calculated transfer function from Vfb to I3 is identified with the one of the lead network which finally makes it possible to calculate the values of R3 and C3 that will make I3 the same as before, but now implemented with lead compensation before the input of the LTP instead of bypassing this lead feedback directly to the VAS summing node.

Finally the component values from Bob's TMC simulation are used to calculate the equivalent lead network which makes the TPC + lead version have the same feedback and forward gain for the front end as the TMC version. Thus, the closed loop gain will be the same for both.
 

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