# [sdiy] Yves Usson's Minimoog Filter

Donald Tillman don at till.com
Mon Jun 12 00:44:28 CEST 2023

```On Jun 11, 2023, at 12:27 PM, David G Dixon via Synth-diy <synth-diy at synth-diy.org> wrote:
>
> The filter works -- it just doesn't work well.

I'll recommend checking the base and emitter voltages of the ladder transistors.  Make sure those are biased reasonably.  Yves' schematic drawing is more difficult to follow in that regard.

> This is the problem I always have when I build circuits that I don't understand (and I really don't understand how this ladder filter works, and my Multisim simulations have been no help at all).

Like any diff amp, the input transistor pair converts the input signal into a balanced current pair.

Each of the transistor pairs with an emitter cap is a balanced common-base circuit.  Those are rare, so think of them as emitter followers, where the base is ac grounded, and the effective emitter resistance is inversely proportional to the transconductance, which is proportional to the current source current.  Or a variable resistance to ac ground. So each of these stages takes a current input, puts it through an RC low-pass stage with R inversely proportional to the operating current, and sends a new balanced pair of currents out from its collectors to the next stage.

So that's four w / (s + w) low-pass stages in a row.

And these are isolated stages, so that's H(s) = w^4 / (s + w)^4.

Or H(s) = w^4 / (s^4 + 4ws^3 + 6w^2s^2 + 4w^3s + w^4).

Which, by itself isn't all that interesting.  Four single poles on top of each other.

Negative feedback in this circuit, F, only affects the s^0 coefficient.  So that's:

H(s) = w^4 / (s^4 + 4ws^3 + 6w^2s^2 + 4w^3s + (F + 1) w^4)

Which causes the four poles to spread apart in the shape of an "X".  Exactly an "X".  And you get the cool resonance as two of the poles approach the Y axis.

Try that out on my Root Locus plotter:
https://till.com/articles/poledance

(I call it a "Pole Dance", but it's really somewhere between a Square Dance and a Minuet.)

-- Don
--
Donald Tillman, Palo Alto, California
https://till.com
```