# [sdiy] 2164 Korgasmatron VCF

David G. Dixon dixon at interchange.ubc.ca
Wed Sep 1 08:59:34 CEST 2010

```> > Yes, it is close to an all-pass.  Mathematically, it's a series
> combination
> > of a 12dB bandpass and a 12dB highpass.
>
> Wait.. I thought you coupled LP and HP in parallel.. that would mean
> passing every frequency fed into it... how does that compare to HP->BP
> or BP->HP? Not sure where the bandpass bit came from

Sorry.  I misspoke.  It's actually the sum of 12db HP and 12dB BP.  This is
just math, actually.  The transfer function is:

s^2 + s              s^2                 s
---------------- = ---------------- + ----------------
s^2 + (2-G)s + 1   s^2 + (2-G)s + 1   s^2 + (2-G)s + 1

where G is the gain of the resonance amplifier.  The first term is 12dB HP
and the second term is 12db BP.  When G = 0, this reduces to:

s
-----
s + 1

which is simply 6dB HP.  Of course, when G = 2, the denominator becomes zero
at the cutoff frequency (remember: s = jw and w = 1 at the cutoff frequency)
and the filter oscillates.

```