buddypoor wrote on Jan 19th, 2008, 8:02am:Hello Tosei,
EXAMPLE: The output A1 of opamp 1 is connected to the noninverting input of opamp 2 which has a local feedback loop with resistors R1, R2 producing a gain of 10. The output A2 of this amplifier is fed back via a resistive divider (R3:R4=1:99) to the inverting input of opamp 1 thus producing an overall positive gain of 100.
There are two realistice loop gain alternatives:
Case (1) Open the main loop at node A1 (internal loop of opamp 2 still closed)
Case (2) Open both loops at node A2.
(A third alternative opening only loop 2 with loop 1 still closed has no practical meaning).
Using PSpice and 741 opamp macros here are the simulated phase margins (ac analyses):
(1) case 1 : 44 deg and (2) case 2: 41 deg.
Now, if an additional pole at 100 kHz is introduced into the model of opamp 1 the results are as follows:
(1) case 1: 13 deg and (2) case 2: margin negative, which means “unstable”.
However, a TRAN analysis indicates that the system is stable (although the step response shows a remarkable ringing).
From this it is to be concluded that in the above example opening both loops at the same time (case 2) does NOT lead to a loop gain which gives a reliable information about the circuit behaviour. This seems to be in contradiction to some earlier statements within this topic (e.g. reply 2 and 13).
Hi Lutz,
Please let me insist one more time. I tried to replicate your example and I built a test bench using ideal opamp models which I parametrized such that they had similar open loop characteristics to the 741.
What I found (AC analysis) when adding the extra 100KHz pole to the first opamp is that for case (1) (loop broken at A1 node) the margin was little smaller than what you got but still positive, and for the case (2) (loop broken at node A2) a large negative margin, indicating
apparently the loop is not stable, and therefore in agreement with your previous statement.
However these conclusions were derived from the Bode plot of those loops, which I'm almost sure is NOT applicable for the second case. The reason for this being :
1) The phase shift characteristic (at least in my simulation) crosses the 180 point at least twice
2) If you derive the stability from the corresponding
Nyquist plot the system indicates is stable (as opposed to the Bode plot)
My TRAN simulation looked similar to what you described: heavy ringing but attenuated, indicating a very small phase margin.
Conclusion:
Previous discussions in this forum concluded the Nyquist stability criterion is the general one and is always applicable while the Bode method is not. Based on this (and on my results), statements on previous replies #2 and 13 are still valid.
The result of this is that we still have valid results from both cases which would allow us to define a single margin (not sure how) for the multi-loop system, which is the primary idea we were discussing.
I might be doing something wrong and I also do not know how you concluded case (2) was unstable, but I´m pretty sure Nyquist criterion is the one telling the truth here.
Regards
Lutz