[sdiy] Re: Leapfrog

[jhaible]

> 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!).

My evil thoughts lead to a one opamp/state variable design.
No idea if this will be good in practice - simulations look promising,
though.

First step is that you need a signal inversion for each feedback loop. Now
you could build the whole chain with 2 inverting integrators and one
inverting
amp (3 opamps total) per two state variables, and then each feedback loop
will comprise one signal inversion, as intended. (because the feedback loops
always go over two state variables - always speaking of a LC LPF)

The really evil step is to get rid of the extra opamp by building a
non-inverting
integrator. So the whole chain will be
inverting integrator - noninverting integrator - inverting integrator -
noninverting ...
and so on.

The noninverting integrator is built by a RC lag circuit (passive) plus a
negative
impedance converter that un-dampens the RC lag circuit by loading it
with -R. This need a single opamp, which also buffers the passive circuit.
Then split the R into two R's for getting a summing input. Both R's will
load each other, so the signal is divided by 2. Set the negative impedance
converter such that you have a gain of 2 at the opamp output (where you
take the buffered signal anyway.)

My textbook says that this kind of integrator is _normally_ a bad idea
(because component tolerances might make -R larger than R), but
with the tight feedback loops of the whole circuit, stability should
be assured.

No idea if this really works - I'll post a drawing of this soon.

JH.