[sdiy] About this LC filter formula questions

[jhaible]

Thanks John, and list,

I know this. Really, the effects on the individual component
behaviour is quite clear. I'm after a formula for that specific
case of one special circuit (delay line built from lumped
elements, and then coupling added). Even the general
behaviour of this circuit is clear, because I've tested it
in Spice. What I need is a formula to describe this circuit.

Increase of the individual inductance *alone* would not have
the desired effect, as increasing L (with C untouched),
while increasing tg, also decreases fc. So there's a tradeoff
between your bandwidth and the number of stages needed
for a certain delay time.
*But* the coupled inductors apparently get around this dilemma,
as the coupling increases _both_ fc and tg, so less stages
are needed.

BTW, I got most of what I needed by experiment, meanwhile.
I needed to know how close I can put the inductors together
on a PCB without getting too much coupling, and to get
the remaining coupling with a positive sign at least.
I got that now.

(Not sure if I make a pcb for this, but it's tempting, because
my veroboard version is _huge_ and can be much reduced in size.
It *should* fit into a 19" enclosure. (;->)

The other question, about a formula, is just out of curiousity.
I don't plan to build a coupled 18-inductor line.

JH.



-----Ursprüngliche Nachricht-----
Von: John L Marshall <john.l.marshall at gte.net>
An: <jhaible at debitel.net>; Magnus Danielson <cfmd at swipnet.se>
Cc: <synth-diy at dropmix.xs4all.nl>
Gesendet: Samstag, 31. Mai 2003 07:38
Betreff: Re: [sdiy] LC filter formula questions


> 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
> ------------------------------------------------------------------
> Pacific Northwest Synthesizer Meeting
> August 9, 2003
> www.sound-photo.com
> ------------------------------------------------------------------
>
> ----- 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
> >
> >
>
>