[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?


> 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/

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