In this article, Dr. Ridley continues the topic of frequency response measurements for switching power supplies. This sixth article discusses the measures of relative stability that can be obtained from a loop gain of a power supply.

Phase Margin of a Control Loop

The previous articles in this series have shown how to make successful frequency response measurements on power supplies, including loop gain. Figure 1 shows the standard loop gain measurement test setup described in the previous articles of this series [1].

Figure 1: Open Loop Gain measurement with the Loop Electronically Broken.

Figure 2 shows a typical measured loop gain with the gain monotonically decreasing with frequency. For this case, definitions of stability are quite clear. At the crossover frequency, where the gain crosses 0 dB, we measure how many degrees the phase is above -180 degrees.  This measurement is defined as the phase margin.

(Notice that when you measure the loop with the circuit of Figure 1, the measurement will give the phase margin
directly, without having to measure it from -180 degrees. That is because the measurement test setup includes an extra inversion that was not part of Bode’s original theory for loop gains. )

Figure 2: Well-behaved loop gain with monotonic decrease of gain with frequency

The phase margin for the loop gain of Figure 2 is approximately 70 degrees. This amount of phase margin is relatively easy to achieve for a current-mode controlled converter with a conservative crossover frequency.

Designers in different industries have different standards for phase margin requirsubents. For rugged military or aerospace supplies, they look for a worst-case phase margin of 60 to 90 degrees. For many practical supplies, a worst-case phase margin of 50 degrees is the standard that I use in commercial design. The power supply will exhibit a small amount of damped ringing with this phase margin, but with very wide line and load ranges, it is often impossible to do much better than 50 degrees under all conditions of line, load, and tsubperature, without seriously compromising transient performance. Less than 45 degrees gives serious cause for concern.

Many companies today have forgotten the point of measuring loops and having a good phase margin. It is not unheard of to see designs with less than 30 degrees phase margin. While a single unit designed like this may be nominally stable, the whole point of a good phase margin is to ensure that power supplies produced in large quantities will all be stable, and rsubain that way throughout their lifetime. 

Optimizing the loop for good phase margin takes time, and incurs some engineering costs. Perhaps 5 man-days of work are required for a conscientious design. This is a very small price to pay when compared to the cost of a product recall caused by oscillation.