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No converter can operate at or above its LC resonant frequency.

There were these quasi-resonant DC to DC converters being used en group and their intended operating frequency was 100 kHz. The system of which they were a part had micro-computer control with software that was predicated on that 100 kHz frequency and I was tasked with doing a worst case analysis of the converter operation.

**Figure 1** This was the design for the quasi-resonant DC to DC converter.

The L was a transformer’s winding inductance and the C was a polypropylene capacitor. The standard resonance equation with those two values yielded a numerical result of 100 kHz, so it was assumed by everyone that 100 kHz had to be the converter’s operating frequency.

I decided to do my analysis using recursive differential equations. When I came up with an operating frequency calculation of only 80 kHz instead of 100 kHz, the project engineer thought I must have been wrong, but he couldn’t find any flaw in my work. However, the department manager got really upset with me.

He was a very intelligent man whom I had seen come up with some brilliant engineering work, but he was not long on patience, especially for my choice of analytic method. He turned to the project engineer and shouted, “Teach Dunn how this thing works!!!”.

After taking a little time to defuse myself, I undertook a SPICE analysis of the converter and, lo and behold, up came that same 80 kHz. I also saw the same waveshapes that I’d gotten from using the differential equations. With a little reflection at this point, the reason for the lower than expected operating frequency became clear.

**Figure 2** A SPICE analysis of the converter revealed the truth.

What was happening was that the on-times of the MOSFET switching cycle were adding time to what would otherwise have been a 10 µsec time period from the LC combination alone. During the MOSFET off-time, waveform curvature would follow the contour of a 100 kHz sinusoid, but that contour was interrupted and overridden during the on-times.

Any such converter is of necessity constrained by the on-time(s) of its power switch(es) to perform at an operating frequency that must be to some degree lower than the raw resonant frequency of the LC-pair alone. No converter can operate at or above its LC resonant frequency, only below that frequency.

Luckily, the software that had been written on the assumption of 100 kHz was adaptable to 80 kHz.

*John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).*

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