[sdiy] Passive filters and impedances

[Tom Wiltshire]

Hi All,

I'm back to learning about impedances again. I've been looking at the following situations:

	http://electricdruid.net/images/PassiveFilters.png

 This shows a first order, second order, and third order passive filter, each feeding a destination which has its own impedance Rimp. Rimp might be infinity, in which case we could ignore it, or it might not.

For the first order case, I've been able to derive the transfer function by thinking of it as a potential divider with impedances. Ignoring Rimp for a moment, we have:

	Vout / Vin = (1 / sC) / (R1 + (1/sC))

This works fine. Including Rimp doesn't make it much more complicated, except that we replace  1/sC with (1/sC || Rimp)

However, I can't make the second order (or by extension third order) case work the same way. It still looks like a potential divider, with the output across C2, but the total impedance is a bit more involved. I think we have to work backwards in from the end, so we have the output across C2. We have R2 in series with C2, which is then in parallel with C1, and the result of that is in series with R1. So the total impedance is something like:

	Ztotal = R1+ (1/sC1 || (R2 + 1/sC2))			(ignoring Rimp again)

So my transfer function is:

	Vout / Vin = 1/sC2  /  (R1+ (1/sC1 || (R2 + 1/sC2)))

Is this correct? Am I on the right lines with this "potential divider" understanding of the situation?

Thanks,
Tom