Stable OpAmp With Phase Response >180°

[recnsci]

[quote author="Samuel Groner"]

Now why's that? I (and many textbooks) think that Nyquist told as differently--it appears however that phase response needs to be below 180° at the unity gain frequency only. Any smart guy out here who could shed some light on this? Thanks!

[/quote]

Reread those textbooks, Nyquist doesnt state that phase must be above -180
for closed loop system to be stable. It can drop below if it comes back up at
some point.
I will try to write easy-digestable version of Nyquist criterion:
Asume A(s) is Laplace domain transfer function of some amplifier. Draw
that function in s plane. Asume that feedback network is frequency invariant
with gain K. Then, closed loop system is stabile if and only if A(s)
doesn encircle (-1/K, j0) point. This holds under asumption that open
loop function A(s) doesn have poles in right half plane.

To put it in practice, lets analyse halcroamp.gif :
amplitude graph represents disctance of A(s) from (0, j0) (center of
s plane) for some angular frequency, phase graph represents angle
between positive half of real axis and line that conects some
point on A(s) and (0,j0).
So, A(s) starts at positive half of real axis, 240dB from (0, j0). When
we increase frequency, A(s) moves into lower right quadrant of s plane.
Till 500 Hz it reaches negative part of imaginary axis (phase is -90 deg).
At around 500Hz we have bump to 250dB and phase drop at -270 deg.
A(s) rushes trough whole left half plane and lands somewhere near
positive part of imaginary axis. That is, A(s) made 3/4 circle clockwise
in s plane, at pretty much constant distance from (0,j0). Past 500Hz,
phase increase (that will result in CCW direction of trajectory) but
amplitude decreases. Thus, A(s) moves trough upperleft quadrant
of s plane, and reaches again negative part of real axis (when phase
reaches -180 deg) at around 400KHz. This is important point
and we will take note that gain at this point is around 35-40 dB.
After this A(s) crosses into lower left quadrant and make lobe till it
reaches (0,j0). Angle of "entering" (0,j0) is -90 deg. We take note No2
again and say " well, only if we could buy these SPICE opamps; with
real opamps we will have some problems here".

A(s) crossed negative part of real axis at 250 dB and recrossed it at 40dB.
Now lets see whats with that (-1/K, j0) point: no feedback -> that
point is at -infinity and system is stable; apply feedback and point
start to move along real axis in positive direction; when feedback
reaches -250 dB point enters A(s) lobe and system is unstable; when
feedback reaches -40 dB point exit lobe and system again becomes stable
and it it remain stable till feedback reaches 0 dB, that is for unity
gain.

What this means in practice: closed loop amp will be stable from unity
gain till 35-40 dB of gain. Above that it will sing. In theory it will be stable
at open loop. In real world it will very much sing. This could be a bit
counter intuitive behaviour for amps, but this stuff happens in control
engeneering. Beware of Note 2. Samuel had chosen ideal amps, so
at unity gain amp is dead stable. With real opamps, unity gain
stability could be problem. Especialy if this is power amp, and output
driver is some slow device.

cheerz
urosh

 

[Samuel Groner]

Thanks for the contribution. The only question left is why this has not been used more frequently--it seems now almost trivial to design amplifiers with very low distortion.

With real opamps, unity gain stability could be problem. Especialy if this is power amp, and output driver is some slow device.

The patent suggest to use > 100 MHz opamps which might add very little additional phase shift. The plot allready includes a simple first-order output stage pole model, but obviously one would not try to run this power amplifier at unity gain. I'm anyway not interested in this specific design, just want to understand the principles behind it.

With modern high speed electronics if this funny region could be bumped up above 20 kHz while still delivering the huge loop gain margins for audio band, I could learn to like this approach.

The 400 Hz peak is perhaps artificial due to the use of ideal opamps--real amplifiers and implementations will likely have some losses to dampen that resonance. Alternatively a small capacitor bypassing the CRC-networks might provide adequate damping. On the other hand, D. Self says (when discussing two-pole compensation which can show similar o/l peaking): The open-loop gain peak at 8 kHz looks extremely dubious, but I have so far failed to detect any resulting ill-effects in the closed-loop behaviour.

Samuel

 

[bcarso]

Often transient response is an issue for non-single-pole dominated loops. For an oscillator it's a good idea though I think. For audio signals YMMV.

 

[JohnRoberts]

Thanks Urosh.

I will attempt to make sense working backwards from your statement of what this circuitry should do in practice.

What this means in practice: closed loop amp will be stable from unity
gain till 35-40 dB of gain. Above that it will sing. In theory it will be stable
at open loop. In real world it will very much sing. This could be a bit
counter intuitive behaviour for amps, but this stuff happens in control
engeneering. Beware of Note 2. Samuel had chosen ideal amps, so
at unity gain amp is dead stable. With real opamps, unity gain
stability could be problem. Especialy if this is power amp, and output
driver is some slow device.

Not only is it counter intuitive but the statement than an amplifier stable between unity and 35-40dB closed loop gain becomes unstable when you command a higher gain which attenuates the feedback even more has me talking to myself.

I could almost see the patented circuit working the opposite way in a power amp application being stable with >30dB of closed loop gain.

I'll stop rambling and go back to my pondering.

JR

 

[recnsci]

[quote author="Samuel Groner"]Thanks for the contribution. The only question left is why this has not been used more frequently--it seems now almost trivial to design amplifiers with very low distortion.
[/quote]

Not quite. More realistic circuit in LT AppNote seems (quite) marginaly stable
at some low closed loop gains and pretty much sings everywhere else.
Problem is swinging phase back over -180 deg, and keeping it there
for desired range of frequencies.
Also, Im not shure synthesis is that trivial.

And finaly, when ever in doubt about stability, ask your symulator
slave to draw root locus. There is actually just one true criterion of
stability: dont have any frickin' poles in right half plane. Nyquist criterion
is based on exactly that. While maybe more convoluted for understanding
Nyquist is great for qick analysis-on-napkin. OTOH if simulator package
has ability to draw root locus, that method wont leave any doubts.

And further more, even if stable at unity gain, I'm pretty sure this amp
will clip very ugly and posibly not even return from clipping.

John, how about this for counterinuitive-ness: from theoretical
standpint, you can have MIMO linear system with multiple poles
in right halfplane when open loop, and still have stable system at some
closed loop gains. Note that i doubt you and me will ever see this
in reality.

cheerz
urosh