# [sdiy] Through-zero FM - how much?

Ian Fritz ijfritz at comcast.net
Thu Oct 18 19:28:56 CEST 2018

```Matthew —

OK, here’s what I do. Without modulation, take the VCO’s frequency as w_0, as set by the usual expo-converter input. With linear FM, the instantaneous frequency of the VCO is w_0 multiplied by
(Init + A Cos w_m t), where
Init is in the range (-1, 1),
A is in the range (0, 1), and
w_m is the modulating frequency.

Init and A are panel controls.

In this view, the carrier frequency is
w_c = Init * w_0
and ranges from 0 to +/-1 times w_0,
so that normal unmodulated operation corresponds to
Init = 1 and A =0.

Also, the modulation depth is seen to be:
delta_w = A * w_0.

Integrating the instantaneous frequency to get the oscillators phase yields:
ph = Init * w_0 t + (A * w_0 / w_m) * Sin w_m t.

The VCO’s output is Cos(ph).

Note that Init = 0 implies a zero carrier frequency and is in no way excluded.  In fact I use it a lot. It certainly does not “go without saying” that it would not be considered.

The modulation index is defined as
m = delta_w / w_m = A * w_0 / w_m,
and in principal can have any value.

The only limits in using this approach are VCO and multiplier accuracy, range and stability. Otherwise it is completely general.

Does this help?

Ian

> On Oct 18, 2018, at 8:55 AM, mskala at ansuz.sooke.bc.ca wrote:
>
>> On Thu, 18 Oct 2018, Ian Fritz wrote:
>> I believe you are refering to the modulation index m ranging up to 8 or 10?
>>  This is not what the OP asked. The modulation index is the change in
>> carrier frequency divided by the modulation frequency.
>
> I'm interested in what the range of the modulation-amount knob and
> associated CV ought to be.  The core sees one linear control current,
> which comes from an exponential function of V/oct CV multiplied by a
> linear function of modulation CV.  I'm interested in knowing what values
> of the modulation-CV coefficient are useful.  How much deviation, compared
> to the carrier, do people want to use in practice?  At maximum deviation,
> how much does a volt of modulation CV change the frequency?
>
> It should go without saying that I mean when the carrier frequency
> is nonzero.
>
> --
> Matthew Skala
> mskala at ansuz.sooke.bc.ca                 People before tribes.
> http://ansuz.sooke.bc.ca/

```