[sdiy] LC filter formula questions

[John L Marshall]

The net inductance will increase. Consider the case of closest coupling,
inductance increases by the square of the turns. Double the turns equals
four times the inductance.

Take care,
John
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August 9, 2003
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----- Original Message ----- 
From: "Magnus Danielson" <cfmd at swipnet.se>
To: <jhaible at debitel.net>
Cc: <synth-diy at dropmix.xs4all.nl>
Sent: Friday, May 30, 2003 4:47 AM
Subject: Re: [sdiy] LC filter formula questions


> 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
>
>