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# Nonlinear circuit Stability

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#### aware_boy

##### Junior Member level 2
Hi all,

Is anyone know how to study the stability of a circuit which is in the nonlinear state? Like multiplier, or LNA with bias feed back or loop.

I would like to up this one, anyone has great ideas?

#### LvW

I am afraid, the abovementioned link will not help.
Just one possible method to proofe stability of a nonlinear system comes into my mind: Procedure of "harmonic balance".
This method works quite well for control systems which have a loop gain exhibiting a low pass overall characteristic which sufficiently attenuates the 2nd harmonic.

#### pancho_hideboo

LvW said:
This method works quite well for control systems which have a loop gain exhibiting a low pass overall characteristic which sufficiently attenuates the 2nd harmonic.
I don't think so.

(1) Both nonlinear stability analysis of Agilent GoldenGate and PSTB analysis of Cadence Spectre are based on a small signal analysis around dynamic operation points determined by large signal steady state analysis such as HB analysis or Shooting Newton analysis.
So 2nd harmonic effects are included in stability analysis since it affects operation point.

(2) In RF amplifier we can't specify clear single feed back loop.
So we don't use Loop Gain for stability study in RF amplifier.
For example see https://www.designers-guide.org/Forum/YaBB.pl?num=1218635777/0#5

(3) We have to insert probe for measuring "Loop Gain" in PSTB analysis in Cadence Spectre. We use "Loop Gain" in PSTB of Cadence Spectre.
On the other hand, we don't have to insert probe in nonlinear stablity
analysis in Agilent GoldenGate. Here we don't use "Loop Gain". We use "Eigene Values".

Of course, this nonlinear stability analysis is not perfect.
For example, K-factor evaluation based on nonlinear small small signal analysis such as PSS/PSP of Cadence Spectre is often useless.

https://www.designers-guide.org/Forum/YaBB.pl?num=1234428781
https://www.designers-guide.org/Forum/YaBB.pl?num=1243078889

rd1303

### rd1303

Points: 2

#### LvW

pancho_hideboo said:
LvW said:
This method works quite well for control systems which have a loop gain exhibiting a low pass overall characteristic which sufficiently attenuates the 2nd harmonic.

I don't think so.

Pancho_hideboo: Please, can you explain a little ? (I have the feeling, you mix two different things, which have similar names). The harmonic balance principle is a classical and proven method (described in many books on control theory) to check if a non-linear system tends to a limit cycle (oscillation) or not.

#### pancho_hideboo

LvW said:
I have the feeling, you mix two different things, which have similar names.
I don't mix up.
You can't understand "HB Analysis" correctly.

Can you correctly understand "Periodically Steady State Large Signal Analysis" such as "Harmonic Balalnce" or "Shooting Newton" in RF simulator ?

Maybe you mean "Equivalent Transfer Function Method" or "Describing Function Method" in control system theory.

This is not called as "HB analysis" in RF community.
This is called as "State Averaged Model Analysis" or "Equivalent Lowpass Model Analysis" in RF community.

Slave small signal analysis based on master large signal analysis is different from your "HB analysis" although it will be coincident to my HB analysis if I decrease accuracy or HB order.

Do you have RF theory background ?

#### LvW

Maybe you mean "Equivalent Transfer Function Method" or "Describing Function Method" in control system theory.

Hello pancho_hideboo,

You are right - my answer was directed towards the HB method based on describing functions.
But - why are you so sensitive and touchy? My only intention was to answer a question concerning "the stability of a circuit which is in the nonlinear state?".
This was a very general question - and I have tried an answer, thats all.
Regards
LvW

Just now, I have discovered that you have supplemented your former answer.
Your first answer was only: "I dont think so" - without any explanation. This gave reason to a misunderstanding. (By the way: From the beginning I didn't realize that the question was asked in the RF part of the forum).

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