Step excitation is an economically viable option for testing feedback loop stability if a network analyzer is not available.
Feedback loop stability is testable using Bode plots derived from measurements made using a network analyzer from which gain margin and phase margin can be ascertained and judged. This is all well and good, but a network analyzer might not be available. Such instruments can cost quite a lot of money so those of us who practice the profession closer to poverty-stricken levels may need something a bit more economically viable. That “something else” may be step excitation.
The basic idea is simple. You inject a small square wave disturbance into the feedback loop and examine the response to that disturbance. Where you choose to inject and where you choose to observe is yours to decide. There may be more than one point for each, but please examine the following four sketches.
Figure 1 An idealized voltage regulator with step excitation
In the first sketch, an idealized voltage regulator is perturbed ever so slightly by square wave excitation via R6 to the non-inverting input of the error amplifier, U1. The output of U1 shows an underdamped ringing waveform from which we conclude that this feedback loop’s stability is marginal at best. Not good!
Figure 2 The same regulator and excitation but showing improved stability
In the second sketch, everything is the same as before except that C2 has been removed. It looks like somebody unknown (ahem, ahem) had unwisely included C2, perhaps as an EMI suppressant of some kind but its inclusion had an adverse effect on loop stability. Gain margin and phase margin were very poor.
What the gain margin and the phase margin were numerically, I have no idea, but we are obviously better off without C2 than with it.
Figure 3 The same regulator with different step excitation
In the third sketch, capacitor C2 is back again but this time, the step excitation is applied via R6 to the error amplifier’s summing junction. The underdamped ringing waveform at the output of U1 looks even worse than it did in the first sketch.
Figure 4 The same regulator and excitation but showing improved stability
In this fourth sketch, removing C2 does the trick again. We’re going to leave C2 out. Period!
We’ve looked at a very simple case here, but we’ve injected our square wave disturbance, our step excitation, in two distinct ways. In a more complex and real-world feedback system, there may be many possible injection points. There may also be many response points to examine. You should look at ALL of them.
Your choice of injection point(s) should have no effect, or at least a negligibly small effect, on the feedback loop you are examining. In the cases above, the 1 Meg of R6 is sufficiently large for this circuit to make that so.
John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).