[sdiy] LC filter formula questions

[Magnus Danielson]

From: "jhaible" <jhaible at debitel.net>
Subject: [sdiy] LC filter formula questions
Date: Fri, 30 May 2003 11:16:24 +0200

Hi Jürgen,

> When I build a delay line from inductors and capacitors
> (approximating a transmission line with lumped elements),
> all inductors the same value, all capacitors the same value
> except the last one, it's easy to calculate the parameters
> 
> Z (line impedance)
> 
> tg (group delay for N stages)
> 
> fc (cutoff frequency for the LPF behaviour)
> 
> 
> But what if the inductors are coupled ??
> 
> I have made some Spice simulations with variable k (between
> inductors (n) and (n+1) ), and I found that all three
> parameters change.
> 
> With increasing k (k positive), both fc and tg are increased -
> no wonder that the later version Hammond Line Boxes
> used coupled inductors!
> 
> But Z apparently changes, too. At least I see a lot of ripple
> in Spice, so I guess I need a different termination for the
> line to get a more even response. (Or will a Delay Line
> from coupled inductors always have more ripple than
> a non-coupled Line ?)
> 
> 
> Question:
> 
> Does anybody have a formula for Z, tg and fc, depending on
> k, L, C and N for a delay line with coupled inductors?
> 
> Magnus? Anybody ?

Well, I might have... but what I don't have is the time. I will keep it in the
back of my head. You should look in classic filter books since they care about
couplings. A fair assumption is that they probably didn't care an awfull lot
about it, but you can.

The coupling works both ways due to reciprocacy, so it provides some
feedforward and some feedbackwards.

Cheers,
Magnus