Power Supply Design

Question: Can you clarify the concept of bandwidth as related to a DC-DC Converter?

Robert Erickson, Professor of Engineering at the University of Colorado and author of the text book, Fundamentals of Power Electronics (with Dragan Maksimovic), also gets questions. Here is an answer he graciously shared with me answering a recent email question from M. H.

After praising the text and providing quite a few details as background, M. H. asked the question:

Original Question: I would be very grateful if you could clarify the concept of bandwidth as related to a DC-DC converter. M.H. 05/24/2001

Professor Erickson answered:

Thank you for your comments regarding my textbook.

In response to your questions:

For small signals, the response time is directly related to the loop
crossover frequency, since the dynamics of the closed-loop system contain
poles roughly at the crossover frequency. Figure 9.14 of my second edition
is a classical plot of the second-order system response, and the horizontal
axis is wc*t, where wc is the angular crossover frequency. So one could
call wc the "bandwidth", and there is a relationship between wc, Q (or
phase margin), and settling time. These issues are treated in introductory
classical control texts such as Kuo, Ogata, or D'Azzo and Houpis.

For large signals, the situation is somewhat different. During large
transients, the duty cycle may saturate at its maximum or minimum limit,
and then slew-rate limiting occurs. The response time is then limited by
the open-loop dynamics of the converter, and the size of the inductor plays
a direct role. There can also be other factors, such as current limiting or
other circuitry, that have a similar effect.

Company data sheets usually don't give a lot of details about these things.
The best you are going to find on them is some sort of specification on
settling time, for some given load transient. To infer bandwidth from such
a specification, one must make assumptions about Q-factor, and whether
slew-rate limiting occurs.

Best wishes,

Bob Erickson

Reading this response drove me to the Erickson/Maksimovic text to look at Figure 9.14 and read the surrounding sections. Two observations came to mind.

The first observation is how essential it is that you have at least one good power electronics book in your professional library. For those that have a mathematical background through Laplace transforms the Erickson/Maksimovic text (2nd edition) is probably the best book available for power supply designers. For those with less mathematical background, I might suggest other books for your first book, but this would still be the choice for your second book because of its clear explanations -- which allow understanding the concepts even if the math is skipped.

The second observation was how Figure 9.14 and the surrounding text relates to the rule-of-thumb of 50 degrees phase margin I mentioned in the 5/22/2001 Blog on Feedback. A Q of 1 in a second-order system relates to a phase margin of 52 degrees, which in some cases may not be enough. An example is given in the text where a Q of 0.5 is more desirable resulting in a phase margin requirement of 76 degrees. The point is, a good text, with design aids such as Figure 9.14 and the surrounding explanations, allows you to intelligently modify any rules-of-thumb to better meet your actual design requirements.