We use loop gain evaluation method for stability analysis of amplifier having clear feedback.

However what method do you use for verify stability of fairly large system circuits like MIMO(Multiple Inputs and Multiple Outputs).
There are many feedback loops. And we can't find out all possible feedback paths.

Agilent GoldenGate provides following two methods to perform Stability Analysis for judging whether the circuit is potentially stable or unstable.

Nyquist Diagram : With this method, the circuit equation is solved at each point of a frequency sweep that goes from DC to a very high value.
A Nyquist diagram is then created from this sweep and its analysis gives the value of the stability flag.
The list of frequencies is also derived from the diagram.

Eigenvalue Computation : With this method, the eigenvalues of a matrix that represents the circuit are computed.
The stability flag and the list of frequencies are computed by the analysis of those values.

So I tried this stability analysis of "Eigenvalue Computation" for post layout simulation using "extracted view".
However this analysis results didn't report any unstable mode while actual chip shows remarkable parasitic oscillation especially for bias circuits.

Transient Analysis(both traponly and gear2only) of Cadence Spectre don't show any remarkable oscillation.

Envelope Transient Analysis of Agilent GoldenGate also don't show any remarkable oscillation, here waveforms of this result are completely same as results of Transient Analysis of Cadence Spectre.

On the other hand, Transient Analysis(gear2) of Agilent GoldenGate show remarkable oscillation which is relatively close to actual phenomena.


What method do you use to verify stability of fairly large system circuits ?

buddypoor wrote on May 23^rd, 2009, 5:26am:
We can apply Nyquist Criterion even for MIMO systems using "1+G(s)" type Nyquist Diagram,
because "1+G(s)" is identical to "Characteristic Polynomial" based on State Space Formulation.
Here "G(s)" means OLTF(Open Loop Transfer Function).
http://en.wikipedia.org/wiki/State_space_representation
http://en.wikipedia.org/wiki/Nyquist_stability_criterion

However I chose "Eigenvalue Computation" method not "Nyquist Diagram".

In "Eigenvalue Computation" method, roots of "Characteristic Polynomial" based on State Space Formulation are evaluated directly.

HdrChopper wrote on May 23^rd, 2009, 10:58am:
I don't think so.

Results of Transient Analysis are very affected by initial conditions or startup conditions.
This is very true for weak parasitic oscillation.
http://www.designers-guide.org/Forum/YaBB.pl?num=1234428781/7#7

I used same initial conditions and startup pulse(voltage supply rampup) for Cadence Spectre and Agilent GoldenGate.

Transient Analysis(both traponly and gear2only) of Cadence Spectre don't show any remarkable oscillation.

Envelope Transient Analysis of Agilent GoldenGate also don't show any remarkable oscillation, here waveforms of this result are completely same as results of Transient Analysis of Cadence Spectre.

On the other hand, Transient Analysis(gear2) of Agilent GoldenGate show remarkable oscillation which is relatively close to actual phenomena.

I suspect that treatments during initial phase are different between Cadence Spectre and Agilent GoldenGate.
If circuits are in very critical "Conditionally Stable State" at DC operation points, behavior during initial phase is very important regarding whether circuits show oscillation or not.
http://www.designers-guide.org/Forum/YaBB.pl?num=1190272820

I can set very unstable conditions by decreasing decoupling capacitor value.
When I create very unstable conditions, both Cadence Spectre and Agilent GoldenGate give same oscillation waveforms.

HdrChopper wrote on May 23^rd, 2009, 8:55pm:

As conclusion, there is no general and almighty method for verification of stability of fairly large system circuits including parasitics.

buddypoor wrote on May 24^th, 2009, 1:31am:
We can't define OLTF for a multiloop system.

However we can evaluate "Characteristic Polynomial of Matrix A" like following.
Φ_A(s)=det(s*I-A)
http://en.wikipedia.org/wiki/State_space_representation

We can apply "1+G(s)" type Nyquist Diagram concept to this Φ_A(s).
Here we look whether a locus encloses origin or not instead of -1+j0.

buddypoor wrote on May 24^th, 2009, 3:25am:
Even if we use "Eigenvalue Computation" method, we can estimate stability margin by real part value of eigen values.

buddypoor wrote on May 24^th, 2009, 6:41am:
I think all issues you point out are quite right.

"1+G(s)" type Nyquist Diagram for "Characteristic Polynomial of Matrix A", Φ_A(s)=det(s*I-A) is no more than classic control theory.
However it is almost impossible to evaluate GM(Gain Margin) and PM(Phase Margin) properly.

Generally it is very difficult to grasp proper physical image and meaning in results of modern control theory compared to classic control theory.

To my regret, Agilent GoldenGate does not provide any information regarding "Controllability" and "Observabillity" of System under Analysis.
I requested enhancements for Agilent.