The real criteria for stability is the Nyquist_plot This is the polar representation of the Bode plots (amplitude & phase) that we normally use. (Bode & Nyquist both worked at Bell).
"Stability is determined by looking at the number of encirclements of the point at (-1,0)"
But many people forget that the Closed Loop response is directly given by the reciprocal of the distance of the Nyquist plot from (-1,0).
Amplitude & Phase margin simply measure the 'distance' from (-1,0) for 2 directions; horizontally for Amplitude Margin, and from where Nyquist cuts the unit circle for Phase Margin.
So a better criteria would be to simply close the loop and measure the peaking (or lack of it) in the closed-loop response. You can do this with a 'real life' amp if it doesn't object to frequency response measurements up to zillion MHz. If it oscillates and bursts into flames, then Nyquist has encircled (-1,0)
Unconditional stability (whether with load, feedback or device variation) is when (-1,0) is NEVER encircled evil when these evil things happen.
This used to be Electronics 101 when I were a lad en pretended to reed en rite. Apologies to yus pedants for my simplification
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That the Nyquist curve is close to the -1 point does indeed lead to peaking, but this does not mean that closed loop peaking only happens when the stability margin is low.
For example, the forward gain could have a zero (such as in TPC). This might also show up as peaking, although the system has large stability margins.
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I'll repeat ".. the Closed Loop response is directly given by the reciprocal of the distance of the Nyquist plot from (-1,0).
You are really only interested in stability margin cos of peaking and what happens when peaking becomes infinite.
As Nyquist gets closer to (-1,0), the closed loop gain increases ie it starts to peak. When Nyquist touches (-1,0), the peak is infinite and you have an oscillator. If Nyquist encircles (-1,0) you will have continuous oscillation. What happens then is that clipping or some other mechanism limits the 'gain' until the oscillation 'stabilizes' at some value.
What a zero (and other stability dodges) introduce(s) is a kink in Nyquist. If the kink brings Nyquist closer to (-1,0), you have more peaking. True stability gurus use zeros to kink Nyquist away from (-1,0) to have less peaking and make things more stable. This kink may or may not influence Amplitude or Phase margins.
If the kink doesn't change Amplitude or Phase margin much but brings other parts of Nyquist closer, you can have big 'stability' margins AND big peaking or even oscillation.
For nice simple circuits, the Phase & Amplitude Margins give you a good idea of how close Nyquist gets to (-1,0).
But it can be wrong .. especially for complicated stuff like added zeros. Remember Amplitude & Phase margin only show the 'distance' from (-1,0) for 2 points. Because of the added kinks, you have to plot the whole Nyquist to see what is happening at other points.
If you have a pathological example, do a simple Nyquist plot. It will immediately show what I'm on about.
I think you might be missing the numerator of the closed loop gain equation.
Closed loop gain, in general, has the form
Gc = Go / (1 + L),
where L is the loop gain and Go is the forward path open-loop gain. Now consider what a typical feedback circuit looks like: L is huge at low frequency (the Nyquist curve is far away) from the origin. If the closed loop gain were
Gc = 1 / (1 + L)
like you suggested, the DC gain would be close to 0 for a normal unity gain opamp connection, which is not the case.
If the forward path open loop gain equals the feedback path (like in a unity gain noninverting opamp connection) L = Go and you get
Gc = L / (1 + L).
Thus the closed loop gain at some frequency is the distance from the Nyquist plot to the origin divided by the distance to the -1 point.
Closed loop gain, in general, has the form
Gc = Go / (1 + L),
where L is the loop gain and Go is the forward path open-loop gain. Now consider what a typical feedback circuit looks like: L is huge at low frequency (the Nyquist curve is far away) from the origin. If the closed loop gain were
Gc = 1 / (1 + L)
like you suggested, the DC gain would be close to 0 for a normal unity gain opamp connection, which is not the case.
If the forward path open loop gain equals the feedback path (like in a unity gain noninverting opamp connection) L = Go and you get
Gc = L / (1 + L).
Thus the closed loop gain at some frequency is the distance from the Nyquist plot to the origin divided by the distance to the -1 point.
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I DID apologise for simplifying stuff
As far as peaking is concerned, the only case where the difference is important is if a cap across the feedback resistor limits the HF response substantially. Then you might have peaking at the -ve i/p of the amp while the output might 'hide' it cos the limited HF response. Actually, you'll still see it on the output but it might appear somewhere along the slope at very high frequencies
As this august body seems to hold limiting HF by feedback in this manner heretical, it is unlikely to be of concern.
But the stability etc still holds.
BTW, if you use a Tian probe as in the LTspice example, this will give the exact amount of peaking AT THAT POINT if you convert the Bode plot to Nyquist.
But to answer the original question, the simplest way to judge if you have the correct 'margins' is to look at 'close loop' response for peaking or lack of it.
[deleted : 2 pages of rant about where & how you should measure 'close loop' response.]
Of course there's loadsa stuff that this 'linear' analysis dun pick up .. eg most of the 'parasitic' oscillations or stuff like this Stability-analysis-EF-output-stages
But none of the simplified 'linear' analysis tools including Bode/Nyquist/Tian will pick these up either.
I'm actually amazed that LTspice's .trans is remarkably good at simulating loadsa real life problems. So do .trans as well as your Tian probes etc ... but take everything you see with a large pinch of salt.
I like very simple circuits cos than you then have some chance of making your LTspice model approach real life.
Spice does not have any additional information when making a transient simulation. So, at least at the point in time where a parasitic oscillation starts and where one still can speak of small signal behaviour, results from linear and transient analysis should not contradict.Of course there's loadsa stuff that this 'linear' analysis dun pick up ..
But none of the simplified 'linear' analysis tools including Bode/Nyquist/Tian will pick these up either.
I'm actually amazed that LTspice's .trans is remarkably good at simulating loadsa real life problems. So do .trans as well as your Tian probes etc ... but take everything you see with a large pinch of salt.
My suspicion is therefore that the small-signal analysis has not been exhaustive, if a parasitic oscillation may be seen in a transient analysis, starting out of an operating point for which the linear analysis has confirmed stability.
Matze
We agree. I meant a comparison with an amplifier with simple Miller compensation, as this is in most cases the starting point for TMC discussion (along the lines: include the OPS with this clever scheme a bit into the Miller compensation loop, keeping everything else unchanged ...).
Matze
Hi Matze,
Mike's suggestion to build a TPC amplifier, evaluate its stability, and then connect the resistor to the output instead of ground to make it into a TMC amplifier is an interesting and useful starting point. However, it is based on an oversimplification of the relationship between TPC and TMC.
Keeping the values of the compensation network components the same for TPC and TMC overconstrains the problem and may result in poorer performance for TMC than can otherwise be obtained. It is important to realize that TPC and TMC are different, even though they behave similarly in many ways and that the compensation network has a similar appearance (the T shape).
Cheers,
Bob
Mike's suggestion to build a TPC amplifier, evaluate its stability, and then connect the resistor to the output instead of ground to make it into a TMC amplifier is an interesting and useful starting point. However, it is based on an oversimplification of the relationship between TPC and TMC.
Keeping the values of the compensation network components the same for TPC and TMC overconstrains the problem and may result in poorer performance for TMC than can otherwise be obtained. It is important to realize that TPC and TMC are different, even though they behave similarly in many ways and that the compensation network has a similar appearance (the T shape).
Cheers,
Bob
Hi Bob,
I don't think so. Mike's TPC amp compensates for the overshoot by means of a series RC network across the feedback resistor, while TMC doesn't need it. So it's a different kettle of fish, i.e. not a good starting point.
Cheers,
Edmond.
Hi Edmond,
Thanks for pointing that out. I didn't realize that Mike was still using that extra network. Maybe Mike can confirm.
Cheers,
Bob
Agree.
TPC and TMC are different.
That's true there is no free lunch, but they are different in price. We can go for the one with less price.
TPC must take care of global stability, the "characteristic frequency", in most case, should be less than ULGF, so that you can have enough phase margin. ("characteristic frequency" refers to the corner frequency of the ZERO in TPC)
TMC doesn't need to take care of global stability. It just is a small loop that only involves VAS and OPS, so it has no restriction from ULGF. You can pump up the "Transition Frequency" of TMC far beyond ULGF. However, it does have its restriction, too. "Transition Frequency" should stay below 2nd Pole of output stage. (The output stage itself is 1 domain pole system. It has 2nd Pole in relatively high frequency, it's related to Ft of output device, but it is not exactly the same as Ft.)
Therefore, I always prefer TMC to TPC.
PS: The pole of OPS, you only see it when OPS is driven by current source. In TMC situation, at low frequency, VAS is pretty much a current source.
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I have not oversimpilified the relationship between TPC and "TMC". On the contrary I have proved with simulation, many years ago, that "TMC" is simply TPC localised to the second stage and the ouput stage.
I also showed that provided component values remain the same, the total loop gain enjoyed by the entire amplifier with TPC is the same as the total loop gain enjoyed by the TIS and the output stage, excluding the input stage, with "TMC".
However, recently you suggested I was "over constraining" the issue, and suggested that there were several possible values of C1, C2 and R1 of the compensator that could give the same result. This is completely untrue because you would need to find three different component values that would give
1) the same coincident pole location
2) the same location of the zero restoring single pole roll off with BOTH TPC and "TMC"
3) the same unity loop gain frequency
4) the same stability margins.
Clearly it is impossible to obtain "several" component values that accomplish all four criteria. Therefore it vital that the component values in moving from TPC to "TMC" be the same for a valid comparison.
This meets all four criteria with no difficulty whatsoever, and does not "result in poorer performance for TMC than can otherwise be obtained." Note that you make this assertion without invoking any evidence to support it.
Now, can you provide us with a "TMC" network that meets all four criteria above viz a viz a TPC network while having completely different component values? I don't think so.
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You don't need to use phase lead compensation to demonstrate that TPC and "TMC" are related.
i.e. "TMC" is just TPC constrained to the TIS and the output stage.
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Some people (Mike?) prefer expensive lunches.
That's so-called Luxury.
BTW, I find there is another way that you can use TPC.
What if you wrap up TPC with Inclusive Miller Compensation?
Hi Mike,
could you please clarify in more detail how your TMC and TPC architectures look like or provide a pointer to this information?
If you look on my small TMC analysis in the other thread, than - if I understand you right -
1. The global loop gain in a TPC topology is G_2(s).
2. The total loop gain around OPS (not exactly sure about VAS ...) is G_1(s)+G_2(s) with TMC.
What are your exact asumptions about the circuit? (In this post http://www.diyaudio.com/forums/soli...lls-power-amplifier-book-276.html#post3471007 you mention an additional zero, and Edmond is refering to an additional RC network across the feedback resistor.)
Best regards,
Matze
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Hi Matze,
If you design a TPC network with a given coincident pole location and a given location of the zero restoring a single pole roll-off and then merely connect the resistor to the output, you'll find, when you place the loop gain probe within the innermost loop enclosing the output stage, that the second stage and the ouput stage alone with "TMC" have exactly the same loop gain as the whole amplifier with TPC.
Now, with TPC, you can limit the closed loop frequency response by using a phase lead network across the feedback resistor; this is also possible with "TMC", but with TPC it, in some instances where peaking at the top end of the closed loop frequency response may occur, the phase lead network attenuates the peak.
Note that this phase lead capacitor introduces a zero in the loop gain response which appears as a pole in the closed loop frequency response.
Bob, asserts that this phase lead network may introduce RFI into the amplifier, but does not adduce any evidence to support this assertion. If a correctly designed LCR network (and Bob's are not correctly designed) is used at the output of the amplifier, it prevents RFI getting into the feedback path.
Note also that the zero I was alluding to in that post is the one that occurs in a TPC amplifier or in the loop enclosing the second stage and the output stage with "TMC". Both schemes give a double pole roll-off which reverts to a single pole roll-off due to the zero.
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Hi Mike,
Criterias #1 and #2, arbitrarily selected by you, over-constrain the problem.
We keep getting back to your insistance that the TMC network be the same as the TMC network. That is not necessary.
Cheers,
Bob
Cheers,
Bob
Hi Mike,
Can you confirm, or not, the question I raised in my post #2771. Are you still using the lead network with TPC or not?
Cheers,
Bob