compensating phase shift

Yup. But be careful. You can't just slap in a filter, at any frequency, and call it a day. The filter itself has some impedance, which draws current from your switcher. A randomly chosen LC filter, with f_0 pushed up by a couple of harmonics, will most likely draw huge current spikes from the switches, due to undamped resonance.

A class D amplifier is a very tricky filtering application: the source is ideally zero ohms, and the load is often high impedance (that is, when considered at frequencies where the filter's cutoff frequency, and the switching harmonics, matter). For example, a speaker, or a motor's winding inductance.

You can't dissipate any power into zero or infinity ohms (or a reactance), no matter how you design your filter matching!!!

So, inevitably (and necessarily!), you must apply some loss to the system, to keep it behaved. So your choice of L and C is motivated, not by the load impedance, but by how much power you wish to dissipate in the (lossy) filter, and how the resulting LC values affect your load.

As an example:

Suppose you have an audio amplifier, 8 ohms load (nominal at 1kHz), a +/-20V supply (half bridge output), a 20kHz bandwidth requirement, and a 100kHz switching frequency.

Ideally, the filter would fall at 20kHz, to get maximum attenuation of switching ripple and harmonics. The values would be on the order of 1uF and

64uH. (Of course, sqrt(64uH/1uF) = 8 ohms!) In practice, you'd fudge these so that the load can act as termination for the filter, which is a one-end-shorted type -- the source is a constant voltage source, not a matched resistance. The LC values need to be skewed, so that all the termination can occur at the load end.

But if the load is itself an inductor, what do you do? You need to add an R+C in parallel with it, to provide that damping. And now your snubber will be dissipating quite a lot of signal power at the maximum frequency (not that you'd listen to 20kHz CW very often..), and accordingly, either the output amplitude is about 3dB below what you were expecting (half goes into the resistor!), or the amplifier must work twice as hard (i.e., it sees a load of about 4 ohms at 20kHz) for constant output amplitude.

So maybe we push the cutoff frequency higher, so the damping resistor doesn't burn signal power. But this pushes the filter closer to Fsw. As we approach Fsw, more and more reactive power must be handled by the filter, up to a maximum amount at Fsw. Above Fsw, reactive power goes back down, and up and down in humps, as f_0 passes each harmonic.

How much power? The nominal output power, at Fsw, is basically double the full power rating. That is, we have a 25W (sine wave, RMS) audio amplifier here; unfiltered, into an ideal 8 ohms, the square wave output would simply be 50W non stop! (20V^2 / 8 ohm = 50W.)

We can cheat this by, well, simply drawing less power at Fsw. Raise the filter impedance. But alas, more series L also means more impedance at signal frequencies. We should like to keep L under 64uH, because that's the -3dB point, for 8 ohms at 20kHz.

If we have about 25-50W available at 100kHz, but we want to dissipate only, say, 1W in the snubber, we can even calculate what f_0 we need (essentially, how many harmonics we're going to let through). 100kHz is 5 times above

20kHz, and both frequency and impedance scale as sqrt(C), keeping L constant. But a 5x reduction still burns 5-10W, so we need to go 5x further (5th harmonic); but now we've blown past the fundamental, so the power will actually be a lot less than this, now. There's 1/4th power at the 2nd harmonic, 1/9th at the 3rd, and so on; so we probably only need to filter to the 2nd harmonic to achieve this loss spec.

At the 2nd harmonic, we have maybe 6.2W available, so to dissipate 1W we need an impedance 6.2 times 8 ohms, or 49.6 ohms. L is max 64uH, so C =

0.026uF. (And an Rs+Cs in parallel with the C, where Rs = 50 ohms and Cs = 0.047uF or so.)

Which has an actual cutoff frequency of 123kHz, which is still kinda close to Fsw, so we're not terribly far off the point of 1W loss, but it will dissipate more than expected. (This obviously isn't a proper system-of-equations solution. What, you think I use my /whole/ ass for free?)

So by designing the filter impedance, and terminating it with loss, we can control peak switch current AND filter above Fsw if needed.

(By the way: FCC doesn't care about anything below 150kHz, so setting Fsw at

140kHz, and plopping down a sharp filter in the 140-280kHz range, can save you a lot of space, when it comes to passing regs! ...Just don't try this in Europe, or for any standard where they're counting all the way down to 9kHz. :^) )

Tim