SolutionAnalysis and simulation are not helpful for practical design schedules due both to the complexity of the mathematics for analysis and the time and resources to simulate accurately. The only practical method of discovering frequency entrainment is testing for it -- and you may not catch everything. What follows are a few practical suggestion to improve the probability that your power supply design will not entrain. Here is the way I test for it. Load transients are used in the description, but testing for line transients and transients on the reference are similar. Don't forget to also test for these.
First, you want to find out what the ripple increase is for normal load transients. Starting at a 10% transient load at 50% loading, you want to measure the transient amplitude at low frequency (below the unity gain frequency) when the transient load is applied. You expect to see approximately the delta load change times the characteristic impedance of the equivalent output filter, (delta I)*(L/C). If you don't like what you see (excessive amplitude), you have to reduce the characteristic impedance, Zo, either by deceasing L or increasing C. You can then estimate what the peak-to-peak amplitude will be when you increase the frequency to that of the cross-over frequency at unity gain. You increase the switching load frequency until you get what approximates a sine wave on the voltage output and check the peak-to-peak voltage. If it is what you expected, no detrimental entrainment has occurred and the circuit is operating normally. You then sweep the load frequency up and down to makes sure no sub-harmonic or harmonic is causing entrainment. Then you repeat, increasing the load transient in 10% increments until you are switching from zero to 100% (or your specification load limits), looking for entrainment. I have observed load transient of +/- 20% entrain and cause the voltage output to swing from zero to 10 V on a 5 V power supply. One case was on the prototype (100 produced and sent to various design agencies to test) of a proposed military standard power supply. I called the design engineers to discuss the problem. They previously had no idea it was a problem, but duplicated the problem in their lab. They changed the design so the production supplies did not entrain. After running the above tests to get a feel for your design, you then have to construct a test plan that has a chance of catching most problems in a reasonable amount of test time. See the discussion at the end of Point Measurements in the estimating expert system for a discussion of this problem. You want to (must) test your design to make sure it is not susceptible to entrainment. Do not use this information for design without independent verification of the information. Editor: Jerrold Foutz |
