Switching-Mode Power Supply Entrainment (1 of 7)

Problem

You have completed your design for a computer switching-mode power supply and everything checks out fine and it is installed in the computer. Then a programmer changes a software program in the computer and the computer shuts down because of out-of-tolerance voltage levels. If you are lucky, then your overvoltage protection circuits have prevented the wipe-out of every logic circuit in the computer. If your not lucky, then the wrath of your management, system engineers, and logic designers are about to descend on your serene world.

What happened?

You may be the victim of entrainment. You did check your breadboard, prototype, and first production power supply for entrainment -- didn't you?

If you did not test your power supply for entrainment, read on and become convinced that it is something you should do.

So what is entrainment?

First, it is a nonlinear phenomenon, so don't look for any simple analytical fixes. This is what Nicholas Minorsky had to say in his classic book, Nonlinear Oscillations:

"The phenomenon of synchronization or "entrainment of frequency" was the first to be studied among other nonlinear phenomena. Apparently, it was observed for the first time by Huygens (1629-1695) who reported that two clocks, which were slightly "out of step" with each other when hung on a wall, became synchronized when fixed on a thin wooden board. These effects were rediscovered more than two centuries later in electrical circuits by a number of physicists among whom one should mention Lord Raleigh, Vincent, Moller, Appleton, van der Pol, and others." [Chapter 18, Synchronization]

Anytime you see a list of names like this you know the mathematics are far from simple -- so we will avoid them and concentrate on a qualitative description. For the math lovers, Minorsky will keep you going for quite a while -- reading his references can expand it to a life-time.

For a description of entrainment, we will start by quoting Minorsky again.

"The synchronization effect can readily be observed in electronic circuits. If one applies to the grid of an electron-tube oscillator oscillating, say with a frequency of w_o, an extraneous electromotive force of frequency w, one observes the "beats" of the two frequencies. If the frequency w approaches the frequency w_o, the frequency of the beats decreases but this happens only up to a certain value of the difference |w - w_o| after which the beats disappear suddenly and there remains only the frequency w. Everything happens as if the "free" (autoperiodic) frequency w_o were "entrained" by the extraneous (heteroperiodic frequency w." [Chapter 18, Synchronization]

Now entrainment is not going to occur if there is no noise frequencies in your system, either due to a switching load (the most common stimulus), noise on the input power lines, or electromagnetic interference. However, since most practical power supply applications have these, you need to test for entrainment.

Switching-mode power supplies often have step changes in load, both positive and negative. If the step loads are periodic and the fundamental, harmonics, sub-harmonics, or beat frequencies approach the switching frequency, then the power-supply switching frequency can entrain or synchronize to the switching load and be pulled away from its natural or clocked frequency.

When entrainment or synchronization happens, sometimes the effects are minimal, but often they are dramatic. The output ripple on a 5 V logic supply can increase from 50 mV peak-to-peak to several volts peak-to-peak and over-stress or destroy the logic circuits if not protected by effective over-voltage protection. Short of this, the computer becomes useless due to excessive errors. And it can be fairly insidious, the frequency may just momentarily entrain and upset or overstress the logic with no trace that this happened or was the cause of the upset. Although the load is primarily the culprit, line noise and EMI can also cause entrainment and the increase in output ripple. Besides upsetting or overstressing the load, the power supply output capacitors and other components may be overstress.

What can make the problem worse is that systems that have successfully operated in the field for years may have entrainment invoked by a software or firmware change.

Do not use this information for design without independent verification of the information.

Editor: Jerrold Foutz