Most experts agree that the best way of designing power supply control loops is through the use of frequency domain design methods. Some people may have studied these techniques at university in their “Control Theory” lectures but perhaps not applied directly to power supplies.

Please don’t let the phrase “Control Theory” put you off reading the rest of this article; we have come up with a way of making it not just tolerable, but perhaps even easy and fun.

Control theory was perhaps one of the subjects that I disliked most at university (second only to Maxwell’s Equations!), both as a student and as a lecturer. The reason was that it was never related to real life.

In this article we will relate everything to real power supplies. By the end of the article you should be very comfortable with the concepts of frequency domain analysis, Bode plots, gain margin, phase margin, cross over frequency and finally the power supply stability criteria. But let us first explain how and why understanding these topics are important for designing stable real life power supplies.

Frequency Domain Design

​What is frequency domain design and why is it better than the time domain when applied to power supplies?

As mentioned earlier, most experts design power supplies in the frequency domain, the main reason is that when we work in the frequency domain, we obtain a lot more information about the relative stability of our power supplies. In the time domain (i.e. when we give the power supply a step load and look at its transient response) we can never be completely certain of how far away from instability we are.

By frequency domain analysis, what I mean is that I inject a small sinusoid of a certain frequency, let’s say 10 Hz, into my power supply and then measure how the shape of this sinusoid is modified by the time it goes through the PSU and eventually comes out. This will give me the stability information that I need in order to design a nice compensator.

But how I do I inject this sine wave into my power supply? Well, assuming for now that I only have a simple proportional controller with a gain of 1, I get my PWM signal and I give its pulse-width a small wiggle/shake at for example 10Hz. This injects a 10Hz sinusoid into my power supply or my “plant”. Then I wait for this sine wave to go all the way around the system and I look at the sinusoid that comes out of the plant. By the way, in next month’s article we will go through the exact real life mechanism by which this is done in a real power supply.

​Having injected a sine wave and looking at its shape as it comes out of my power supply, I can then compare the sine wave that I put in, with the sine wave that I have got out. When we compare these two sine waves, there are only two things that can really change.

One is the height difference between the two sine waves and that gives us our “gain” and the other one is the “phase” difference between them.

For example if we injected a 1V sine wave into our system and we saw a 10V sine wave on the output then our gain at 10 Hz would be:

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