# Where to break the loop for stability testing.

#### karrrrl

Joined Aug 9, 2020
6
Specifically, I am curious why the control loop must be broken such that one side of the break is high impedance while the other side is low impedance and if this applies to more than just power electronics. I've read several app notes including TIs AN-1889 (Step 1: Setting up the Circuit, paragraph1) linked below. They all mention this fact, but do not explain why. Since the reasoning is not obvious, can someone explain the reasoning to me or at least point me in the right direction?

#### LvW

Joined Jun 13, 2013
1,438
I think, the reasoning is quite obvious:
1.) The open loop must be analyzed because the stability criterion applies to the loop gain (magnitude and phase).

2.) However, opening the loop must not change (a) the DC operating point of the whole system and (b) change or modify the loading conditions at the point where the loop is opened. (An error of app. 1...5% could be acceptable).
Otherwise, the measurement resp. simulation of the loop gain would not reflect the real operating conditions when the sysytem works with the loop is closed.

3.) Example: Lets assume that the output resistance of a gain stage under open-loop conditions is Rout=10kOhms. When the input resistance of the rest of the loop at the opening is also 10kOms, the gain under closed-loop conditions would be only 50% if compared with the gain when the loop is open.

4.) That is the reason why a simulation method was developed with "voltage/current double injection" (Middlebrook, Rosenstark).
Using this technique, the loop may be opened at any point without the mentioned loading restriction.

Last edited:

#### karrrrl

Joined Aug 9, 2020
6
3.) Example: Lets assume that the output resistance of a gain stage under open-loop conditions is Rout=10kOhms. When the input resistance of the rest of the loop at the opening is also 10kOms, the gain under closed-loop conditions would be only 50% if compared with the gain when the loop is open.
This thought experiment is what I was missing. Thank you!

#### LvW

Joined Jun 13, 2013
1,438
This thought experiment is what I was missing. Thank you!
Of course, when comparing the gain values (as I did) I am referring to the gain of the mentioned single gain stage only. But this gain stage influences both the open and the closed loop gain.