butter and pole locations + filter information

[Kimmo Koli]

On Wed, 29 May 1996, Tom May wrote:

> 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
> 
>    (I *think* this is correct.  If anybody cares they can do it out
>    independently and we'll compare notes.)
> 
> 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.
> 
If less components are elegant then yes, otherwise the original Moog
ladder uses transistors instead diodes for a reason. The TB-303 diode
ladder is like this scematic (if input V/I conversion ie. differential
pair is omitted).

   +-----+--R--+--R--+--R--+---+---
   |     |     |     |     |   |
  Iin    C     C     C     C   R  Vout
   |     |     |     |     |   |
   +-----+-----+-----+-----+---+---
 
But the Moog filter looks like this in small signal,
  
   +-----+-R-Ibuff-+-R-Ibuff-+-R-Ibuff-+---+---
   |     |         |         |         |   |
  Iin    C         C         C         C   R  Vout
   |     |         |         |         |   |
   +-----+---------+---------+---------+---+---

where Ibuff is the current buffering (low input impedance = resistance R and 
high output impedance ) by the common-base connected ladder transistors. 
Because of the buffers all RC-time constants in the Moog-ladder are 
independent, whereas in the diode-ladder cascaded RC-networks load each other
and therefore poles are sprayed all over the s-plane.

> It must, because I get the same Vout/Vin as you(!).  And those poles
> are really sprayed all over the place.
> 
> Tom.

Seems to me, that the Moog-ladder calculations are not based on the right
small-signal equivalent circuit. The Moog filter transfer function should
be identical to OTA-based 4-pole filters like SSM2040, SSM2044 and 
CEM-filters. The different sound is due to different non-linearity inside
the filter.

Moog-ladder: 
Pre-distortion in the input (differential pair) cancels the distortion in the
active load transistors. Distortion due to transistor mismatch and base
current 'leaking' from the signal path (= distortion cancellation not 
accurate enough).

Diode ladder:
Like the Moog, but no base current distortion. Also different transfer 
function. Signal is attennuated more in the diode ladder, so worse S/N.

SSM2040:
Basic OTAs connected as voltage followers. This leads to low distortion
at low frequency (due to negative feedback), but distortion increases with 
frequency. At high Q-values large distortion concentrated near the resonance 
frequency and thus the fat sound.

SSM2044:
The folded current mirror ladder is very much like the Moog-ladder.
Of cource distortion is significantly lower due to low on-chip mismatches
compared to the discrete Moog-filter.

CEM-filter:
Like SSM2040, but uses linearized OTAs and therefore less distortion and
not a fat sound. But high S/N anyway.

Well, that's all, folks,
--------------------------------------------------------------------------------
  Kimmo Koli      			     Email: kimmo at clara.hut.fi 
  Helsinki University of Technology          URL:   http://clara.hut.fi/~kimmo
  Electronic Circuit Design Laboratory
  Otakaari 5 A 
  FIN-02150 Espoo     			     Tel:  +358 0 451 2273
  Finland      				     Fax:  +358 0 451 2269
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