#### What is in this article?:

- When Bode Plots Fail Us
- Determining the stability of the control loop

It may come as a surprise to some that a control loop’s Bode plot does not always depict the loop stability and that the output impedance measurement, obtained non-invasively, always does. Challengers of the non-invasive phase margin measurement approach believe that the method is not always an accurate representation of loop phase margin. While this can be true for transfer functions that are more than first order, the Bode plot does not always accurately depict the control loop stability in these cases either, while the non-invasive output impedance measurement does. It is important to note, however, that the impedance must be measured at the feedback points, since downstream filters can impact the results. This is not to say that the downstream impedance is unimportant, it certainly is for Power Distribution Network (PDN) evaluations, however; the filters (and trace impedances) can mask the loop stability.

**Case study of a five output winding flyback converter**

The phase margin and gain margin do not necessarily provide an accurate assessment of the control loop stability. Let’s look at one case study of a five output winding flyback converter, where the Bode plot leads to an incorrect conclusion of stability. The Bode plot for the converter, in Fig. 1, indicates a bandwidth of 650Hz and a phase margin of 50 degrees. The small signal step load, Fig. 2, and the output impedance measurement, Fig. 3, indicate otherwise. The small signal step load shows ringing at a frequency of 850Hz, which is higher than the 650 Hz bandwidth. The small signal output impedance measurement indicates an impedance peak coinciding with the 850 Hz ringing frequency seen in the small signal step load response. Both the small signal step load and the non-invasive output impedance measurement predict a phase margin of approximately 20 degrees, which is significantly worse than the 50 degree phase margin indicated by the Bode plot. The Bode plot includes markers for the gain and phase at both the 658Hz crossover frequency and also at the ringing frequency of 850Hz.

Why are the various measurements in disagreement? In fact, maybe they are not; it’s possible the tests are simply measuring different performance aspects. The Bode plot reports the phase margin at the gain crossover frequency and the gain margin at the phase crossover frequency. These two margins do not necessarily provide a complete assessment of the control loop’s stability. This revelation is not new and is supported by the seldom- used Nichols chart. The Nichols chart is used to determine the peak response (most unstable point) from an open loop transfer function plot, as well as the crossover frequency, phase margin and gain margin. The peak response does not necessarily coincide with the gain crossover frequency. This can also be evident when using Nyquist plots and RF gain circles.