Compensation of transimpedance op amp

I was reading an article regarding insure stability of op amp in optical application. And I do not understand the reason of below statement:

"Figure 4 depicts three different scenarios for the intersection of the closed-loop response curve with the open-loop gain curve. Stability degradation will occur when fP falls outside the open-loop gain curve. For fP1 the circuit will oscillate. If fP lies inside the open-loop gain curve, the transimpedance circuit will be unconditionally stable. This is the case for fP2 but stability is traded off for transimpedance bandwidth. The optimum solution paces fP on the open-loop gain curve as shown for fP3."




When talking about stability I am used to look at loop gain other than noise gain(or non-inverting close loop gain), here I do not understand why put the pole frequency of noise gain inside(or at the left side) the open loop gain curve will insure stability. My thinking is to look at the poles in op amp itself together with pole and zero in the feedback transfer function(reciprocal of noise gain), before the intersection frequency(GBW of loop gain), I see 1 pole from op amp, 1 pole from feedback factor, and 1 zero from feedback factor, in a sequence of increasing frequency. If setting the pole frequency of noise gain(or zero frequency of feedback gain) at intersection frequency, I see a phase of (-90)+(-90)+(-45), it is already not stable.

I knew my analysis is wrong somewhere, but I can not figure out where. Can somebody help me on this?

Intersection point at fp3 (fp3 is actually a zero of feedback factor respectively loop gain) results in +45 degree phase margin.

None of the compensation variants is exactly unstable, but phase margin with fp1 is uncomfortably low.

simbaliya said:

I was reading an article regarding insure stability of op amp in optical application. And I do not understand the reason of below statement:

When talking about stability I am used to look at loop gain other than noise gain(or non-inverting close loop gain), here I do not understand why put the pole frequency of noise gain inside(or at the left side) the open loop gain curve will insure stability.
..............
I knew my analysis is wrong somewhere, but I can not figure out where. Can somebody help me on this?

Click to expand...

The noise gain is identical to 1/Hr(s) with Hr(s)=Feedback function.
Because the loop gain
Aloop(s)=Aol(s)*Hr(s)=Aol(s)/[1/Hr(s)]

in the BODE diagram (in dB) the loop gain is Aloop(dB)=Aol(dB)-[1/Hr(dB)].

Hence, the loop gain in dB is the difference between Aol(dB) and the noise gain(dB).
At the crossing pont of both functions the loop gain is 0dB (unity) and the "rate of closure (ROC)" is an indication of stability.

Result:
Fp2: ROC = 20 dB/dec gives good stability
Fp3: ROC (real curve, rather than asymtotic)=30 dB/dec gives about 45 deg margin
FP1: ROC = 40 dB/dec gives a very poor margin near to the stability limit.

Hi FvM, if I plot the loop gain, I see firstly two poles then followed by one zero, which means there will be a frequency(before the zero frequency) where the signal phase reaches -180 degree, and loop gain magnitude more than 1, oscillating occurs at this frequency?

FvM said:

Intersection point at fp3 (fp3 is actually a zero of feedback factor respectively loop gain) results in +45 degree phase margin.

None of the compensation variants is exactly unstable, but phase margin with fp1 is uncomfortably low.

Click to expand...

simbaliya said:

Hi FvM, if I plot the loop gain, I see firstly two poles then followed by one zero, which means there will be a frequency(before the zero frequency) where the signal phase reaches -180 degree, and loop gain magnitude more than 1, oscillating occurs at this frequency?

Click to expand...

Speaking about "loop gain" the sign inversion at the inverting opamp input is included and the loop phase must start at -180 deg (at low frequencies, including DC).

Yes, I alrdy considered that in my analysis, the initial -180 plus the -180 of the two poles caused oscillating at a frequency before the zero frequency, isn't this a design issue?

LvW said:

Speaking about "loop gain" the sign inversion at the inverting opamp input is included and the loop phase must start at -180 deg (at low frequencies, including DC).

Click to expand...

simbaliya said:

Yes, I alrdy considered that in my analysis, the initial -180 plus the -180 of the two poles caused oscillating at a frequency before the zero frequency, isn't this a design issue?

Click to expand...

Yes - I understand that your circuit violates the BODE stability criterion (total loop phase 360 deg for a loop ain above 0 dB). In this case, the circuit - in closed-loop operation - will be unstable (oscillating).