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## May 31, 2001

### DCCM Flyback Stability

**Question:** How do I stabilize a DCCM flyback converter with multiple outputs?

**Original Question:** I have a discontinuous-current mode (DCCM) flyback converter - 12 W. The transformer has one primary, 6 identical outputs and one feedback. I am working on the compensation design - stabilization. It is hard to work out the poles and zeros. Can you recommend any reference papers on this? F. H. 05/31/2001

**Answer:** Since the inductor in the discontinuous-current mode is simply a current source, the dominate pole in the power stage is just the break point of the output capacitor and load resistor equivalents. This means your maximum phase shift is 90 degrees and the system is stable all by itself. ESR in the output capacitors add a zero and actually improve the phase shift. Since you have multiple outputs you probably want to reflect the output capacitors and load through the transformer to the input or to a single output if you want to look at the gory details of combined capacitors and load. To keep noise from being a problem I usually limit the gain in the feedback amplifier and use a high frequency capacitor to roll it off so noise and surprises at high frequency are not a problem. Just adjust things to go through unity gain about 1/10 the frequency and make sure the gain does not come back up at higher frequency. These flybacks are so stable that usually they are stable if you do nothing. The only thing that make them go unstable is adding a complex feedback with little understanding of what you are doing.(This is not true of flybacks operating in the continuous-current mode, the right-half-plane zero in these make closing the loop a challenge.)

If you only buy one book for your professional library, I recommend Erickson/Maksimovic "Fundamentals of Power Electronics" 2nd edition. This will give you the fine details to close the loop with a solid knowledge of what you are doing and will impress your boss or anyone who does a review of your design.

Also, you can crank out a fully stabilized design for this circuit in a few minutes using Ridley Engineering's Power 4-5-6. (Disclaimer: Ridley Engineering has been a sponsor of my website.)

**Follow-up Question:** Thank you for your immediate reply. I have already ordered a copy of the book you recommended. To calculate the poles and zeros, multiple output capacitors and loads can be reflected to input or a single output. **Question:** Are the poles and the zeros calculated based on the total equivalent C and R? It seems that the calculated pole/zero (reflected to the input) is different from those reflected to one of the outputs, which one is to be used? F. H. 06/04/2001

**Answer:** When you reflect the poles and zeroes, the amplitudes change proportional to the turns ratio squared, but the break points remain the same. I always reflect them to the primary, since it makes the Middlebrook Criteria, used to determine interaction with the input filter, easier to apply. After the reflection, you have a bunch of parallel filters and you need to solve for this. If they all have the same break frequency this makes it easy to approximate the results, so I usually select capacitors and other filter elements to make the break points fairly close.

Posted by Jerrold Foutz at May 31, 2001 04:29 PM