Bob Cordell's Power amplifier book

[wahab]

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.

[Edmond Stuart]

>an ugly travesty

[AndrewT]

Originally Posted by Edmond Stuart

I suppose you meant it sarcastically, didn't you?

no, it was not a sarcastic remark.
I was summarising what I think is agreed. If I am wrong then placing my post there invites correction if needed.

[Edmond Stuart]

Hi Andrew,

You weren't wrong at all, but I thought you made a sarcastic remark, because Mike's comment 'the series combination of C1 and C2 should equal the value of the capacitor you would use for single pole compensation.' is soooo obvious.

Cheers,
E.

[megajocke]

Originally Posted by Edmond Stuart

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

[Edmond Stuart]

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).

[michaelkiwanuka]

Originally Posted by Edmond Stuart

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.

[michaelkiwanuka]

Originally Posted by megajocke

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.

[michaelkiwanuka]

Originally Posted by Edmond Stuart

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.

[megajocke]

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.