Carl’s Random Bits
Back around 2005, I was involved in the design of a high frequency Buck regulator using a hysteric topology, sometimes referred to as a "ripple switcher". One of our ongoing problems was finding a way to model the small-signal dynamics of the system. Being a self-oscillating system, with a naturally variable switching frequency, the common PWM analysis tools failed to capture the system dynamics in a meaningful way; in particular the single-cycle response to a load step that we were attempting to optimize.
When my former company, acutechnology, began trying to raise money via VCs, we needed a "sexy" technology rather than what we had -- a solid, profitable, but conventional product line. We decided that what the world needed (or at least, what we could credibly convince the VCs that the world needed) was a much higher frequency buck (I don't recall any particular logic to our decision, but we chose to go to 20MHz). But rather than "selling smoke* to the VCs, we were acquired by a larger company (Leadis Technology).
During this timeframe, I solved the puzzle of how to analyze self-oscillating loops. The linked paper (Linear Modeling Of A Self-Oscillating PWM Control Loop) goes through the details, but basically, we could establish the small signal action of the loop by simply figuring out what the effective gain of the modulator/power stages would need to be to create the self-oscillation. Knowing the loop gain at the oscillation frequency had to be unity, we could easily define the small signal model. It sounds vaguely reasonable, but subject to many objections. But the models so derived have transient responses with excellent correlation with identical systems when modeled an a cycle-by-cycle basis.
I do not claim to be the first to use this approach - though I've found no good references to it and had to develop it myself. But the approach was inferred from small signal models published in earlier papers on self-oscillating schemes that did not explicitly define their analysis method. I firmly believe I was "re-inventing the wheel", and would be quite pleased if someone could point me to those who developed this method.
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*It wasn't all smoke and mirrors: check out the Semtech SC220 20MHz Buck Regulator released in 2012. Not the most efficient buck on the market, but by far the fastest transient response, and it uses the smallest values of external LC network, small enough to allow for air-core inductors.
Friday, June 8, 2012
Analyzing Self-Oscillating Converters