[sdiy] LC filter formula questions

[jhaible]

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 ?

JH.