Stability

Sounds to me like you're making it too complicated.

Simple explanation. If the phase shift of the active circuit around which negative feedback is being used is > 180 degrees at an open-loop gain greater than the desired closed loop gain, it'll be unstable.

Here endeth the lesson.

Graham

-- due to the hugely increased level of spam please make the obvious adjustment to my email address

It is not correct however. What matters is the phase shift at the gain cross over point. It is very common for a system to have more than 180 degrees of phase lag at some frequencies above and below the gain cross over point and still be stable.

What kind of crap it this?. for one thing, divide by 0 isn't going to yield much!.

Looks like trolling to me.

"If the phase shift of the active circuit around which negative feedback is being used is > 180 degrees at an open-loop gain greater than the desired closed loop gain "

Find fault with that !

No it isn't common IME and I'd like to see an example if you think so. Anyway, why confuse a simple issue ?

Graham

-- due to the hugely increased level of spam please make the obvious adjustment to my email address

Right. It's also known as "conditional stability." I do that all the time, drop 12 db/octave or more up where the gain is high, then back off and cross unity gain at some saner slope.

John

Very common in OpAmp design... pole-splitting compensation.

...Jim Thompson

This is why a control system with an integrating plant and two integrators in the controller (for good stiffness in steady state) just can't be stabilized. Because there's 270 degrees of phase shift and infinite gait at DC.

Oh wait -- I've designed several of those, with many hundreds fielded and they work just fine.

Oooh I hate counter-examples (unless it's me doing the counter-exampling).

Most GBW product slopes are 6dB / 8ve.

I'd be interested to see an example of what you claim. I dare say they are VERY conditionally stable. But why not answer the simple question which is perfectly clear and very well known ?

Graham

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Is that anything like pole-zero compensation ? I LOVE the way the phase comes back. Another little treat. My lecturers said it was too complicated to explain which of course was like a red rag to a bull. So I worked it out for myself and it's gone into many of my designs from 20 yrs ago.

Graham ;~)

due to the hugely increased level of spam please make the obvious adjustment to my email address

H_ol = (3 * s^2 + 3 * s + 1) / s^3

In the limit as s -> 0, |H_ol| -> infinity, and arg(H_ol) goes to -270 degrees.

Yet the closed loop characteristic polynomial is s^3 + 3 * s^2 + 3 * s +

So there's absolutely nothing wrong with your statement, except that it is completely wrong.

Perhaps not in audio circuits, but you'll find it it motion control all the time.

Yes.

|A(s) * R1/(R1+R2)|. Gain margin, of course, should be calculated when arg(all that) = 180.

It's even odds that you're muffing a calculation. It's easy to do with this control system stuff.

Note that few op-amps these days are unstable for any combination of R1 and R2 that you can find -- until you start trying to drive reactive loads, or accidentally load the input with a capacitance, or put some gain inside the loop, you're going to build yourself a stable amplifier.

Sno-o-o-o-ort! But don't feed that troll Eeyore/Graham, he's gone senile on us ;-)

...Jim Thompson

Never argue with a moose, they're bigger and meaner than you. Anyway, he's quite right. For instance, third order PLL loops (which have zero phase error for constant phase acceleration, as found e.g. in the Deep Space Network receivers of yore) have a phase shift of 270 degrees at low frequency.

The much-quoted Barkhausen criterion for oscillation (0 degrees loop phase, unity loop gain) is completely wrong anyway.... You can be way off Barkhausen and still have poles in the unstable half plane.

Cheers

Phil Hobbs

There is no answer to my question... I'll try to explain better...i want to calculate phase margin of an inverting opamp amplifier: phase margin should be calculated al frequency when |-A(S)*B(s)|=1 graphically i should calculate |-A(s)|, 1/|B(s)| and find freqency where |-A(s)|=1/|B(s)|: at this frequency i should calculate phase margin I think this is always true for any negative-feedback system... For an inverting amplifier at which frequency i should calculate phase margin?

Well, unless you have me plonked I _have_ answered your question.

hich

is

The word "greater" makes it wrong. The phase at the gain cross over is what matters not the phase elsewhere.

yway,

Look up PID controllers.

ent to

The ones that aren't unity gain stable are usually clearly marked as such and tend to be the really fast ones. Things like the LT1225 are not used very much in audio work. If you really want to reproduce those high notes, you need the NPTB00180s to be driven by something that works well into the low impedance loading.

One thing that may be missed by the OP is that the "input" to an op- amp should be taken as the difference between the input pins when you are working with the open loop gain of the op-amp. This is not the same as the "input" to the whole circuit. Beware of mixing up on this.

By definition it needs to be calculated each time the gain crosses unity.