[sdiy] Re: Leapfrog

[Magnus Danielson]

From: "jhaible" <jhaible at debitel.net>
Subject: Leapfrog (was: Re: Cauer Filter Design)
Date: Tue, 6 Jan 2004 20:09:20 +0100
Message-ID: <000601c3d488$ad600de0$8776b9d9 at debitel.net>

> > > >I would however consider doing a ortonormal leapfrog
> > > >ladder.
> [...]
> > > The only thing that worries me about this idea however is the number
> op-amps
> > > needed per section.
> 
> On a slightly related topic:
> 
> I have tried to work out a leapfrog filter design for the 25-inductor
> Hammond Line Box. This means 50 or even 75 opamps. (Yes, the long version of
> the Hammond line box is a 50-pole low pass filter!)

This is indeed one of the drawbacks of ladder/leapfrog filters.

> This was my first encounter with leapfrog circuits. After getting over the
> initial problems, it's not that difficult at all, especially for a LC circuit
> with many equal stages.

Indeed, then you've got a head-start.

> And I learned that the good old State Variable filter is nothing but the
> "leapfrog" method applied to a single LC circuit - or the other way round,
> leapfrog design means applying the "state variable" method to more complex
> RLC circuits.

Indeed. The ortonormal ladder filter has these properties, so that each
integrator output has one state, i.e. is ortogonal to that of all the other
integrator outputs. The thing which is the point with the ortonormal ladder
filter is that it is L2 scaled, so when being fead white noise, the RMS on all
integrator outputs is the same.

> Anyway, while it was interesting to read about this and do a little excercise
> on paper, I still hesitate to build a circuit where the signal would run thru
> 50 or even 75 opamps. Not sure how the ever so tiny unwanted side effects of
> an opamp will add up in a long signal chain.

I think your worries to some degree could be reduced by noting the fact that
you can do L2 optimization to acheive maximum dynamics, which should make sure
that we don't have integrator output levels which is excessively low and thus
allow for a worse signal to noise than we expected. The ortogonality of the
outputs is another thing.

> For *that* application, I guess it's easier to just use 25 cheap inductors.

Yeap.

> But as I said, this is more of a _question_ (and doubt) than a statement. Has
> anybody else on the list practical experience with "long" leapfrog designs?

I have worked with a design which had fairly long ortonormal ladder filters
(guess why I wanted to learn about them). Stuff like 48 db/Oct (6 poles per
slope) slopes and a pair (or was it only one, I don't recall now) of analog
delay-chains for timing correction. It worked very well and after some tweaking
we had something like 130 dB of dynamics in the complete system.

So, I am confident that the ortonormal ladder filters is a pretty sane design
method, given that you can take the expense of 2 op-amps (one summer and one
integrator, sadly enought you need both) per state. Hmm... or maybe one can do
with one less... Hmm! (Evil thoughs going through my brain!).

Otherwise one should look at Biquad designs using Tow-Thomas cascades. The
downside of those is that synthesis of an optimal design is not as straight
forward, you must do iterational design as far as I know. This is what we have
computers to do, to do the boring stuff for us.

Cheers,
Magnus