butter and pole locations

[Don Tillman]

   Date: Wed, 29 May 1996 22:51:18 -0700
   From: Tom May <ftom at netcom.com>

   Don Tillman writes:

      The generalized version (any values for the Rs and Cs) is too long for
      me to conveniently write out, but if you set all the Rs equal and all
      the Cs equal, the transfer function becomes:

	Vout              1
	---- = ----------------------------
	 Vin   s^4 + 7s^3 + 15s^2 + 10s + 1

   Curiously enough, I had just copied the Moog ladder filter patent at
   the library this morning so I just learned how these things work.  I'm
   assuming the diode ladder is similar, just replace the transistors
   with diodes and drop the resistive ladder supplying the bias voltages.
   Yep, the TB-303 circuit on Hyperreal looks pretty much like I would
   expect.  Hmm, using diodes seems a lot more elegant.

<insert a Danny Thomas "spit take">

   So the small signal circuit for a fixed control voltage would look
   like this, right?  Hardly the "all 4 poles the same" circuit that I
   had been led to believe it was!

   +--R--+--R--+--R--+--R--+---
   |     |     |     |     |
   Vin   C     C     C     C  Vout
   |     |     |     |     |
   +-----+-----+-----+-----+---


The R*land diode ladder circuit is indeed equivalent to the RC ladder
you drew.

The Moog transistor ladder is equivalent to an RC ladder with a buffer
in between each stage, so that will have four poles the same.  The
transfer function for that would be:

	Vout              1
	---- = ----------------------------
	 Vin   s^4 + 4s^3 + 6s^2 + 4s + 1

The difference between diodes and transistors here is *very*
important.


  -- Don