Subharmonic oscillations in DC/DC Converters

[tree]

On page 72 of http://cds.linear.com/docs/en/application-note/an19fc.pdf, it's stated that subharmonic oscillations occur for a duty cycle greater than 50%. Why don't they occur for a duty cycle less than 50%?

[T3sl4co1l]

A convenient approximation (and design choice), I think.  What matters for a peak current mode controller is if there is residual current in the inductor; if the system is designed so the flyback (or recoil or whatever) voltage equals the supply (so the switch switches Vs*2, and etc.), then current becomes continuous at >= 50% duty.

As for the oscillations themselves, the fundamental downside to a peak current mode converter (even with slope compensation and an error amplifier) is it exhibits chaos; duty cycle acts like the feedback parameter in the logistic map, and an identical bifurcation diagram can be generated from the circuit.

Tim

[tree]

As for the oscillations themselves, the fundamental downside to a peak current mode converter (even with slope compensation and an error amplifier) is it exhibits chaos; duty cycle acts like the feedback parameter in the logistic map, and an identical bifurcation diagram can be generated from the circuit.

Tim

You just enjoy confusing me to death!

[David Hess]

I thought the application note described it pretty well.  Reread the part at the beginning about S1 and S2.

[tree]

I finally figured it out. The change in duty cycle corresponds to a decrease in time for the positive slope and an increase in time, of the same amound, spent for the negative slope. The equality I1/S1 = -I2/S2, where I1 and I2 are the deltaI for the positive and negative slope, respectively. The equality is saying the exact same thing that I described in words. I2 = -S2/S1 * I1. The current perturbation will continuously increase if S2/S1 is larger than one, i.e. DC > 50%

[T3sl4co1l]

Yup, and for higher duty cycles, it bumps into a 4-cycle, then a slight bit more into 8, and so on...  Hence, bifurcation: http://en.wikipedia.org/wiki/Logistic_map

The bifurcation diagram shows the discrete points (for the map, the numerical values; for the converter, the pulse widths) that are cycled through, on the Y axis, with (average?) duty being the X axis.  It looks strange and beautiful, and doesn't make much sense at first (you can't plot it on an oscilloscope).

Tim

[David Hess]

Come to think of it not only does my DSO support roll mode but also a "scan" mode where the display record is updated in real time at slow timebases and a cursor shows the current scan position.