AW: Re: Linear FM on SEMs?

Haible_Juergen#Tel2743 HJ2743 at denbgm3xm.scnn1.msmgate.m30x.nbg.scn.de
Fri Dec 8 00:40:00 CET 1995

```>> As a rule of thump, the resistor for lin FM should always go to the
>> collector of the "reference" transistor (i.e. the one not going to the
>> VCO capacitor), regardless of the opamp/regulation configuration.
>
> That doesn't sound like linear FM to me!  You would be modulating
> the reference current, achieving a multiplicative FM.  For example,
> modulating the reference by +-1 octave would always modulate the VCO
> +-1 octave.  As I understand linear FM, one wants constant +-delta Hz
> modulation no matter what the current VCO center frequency is.  I think
> you want to connect to the "capacitor" side of the exponential converter,
> but be careful to ac couple the FM input properly to avoid detuning
> the oscillator.

That's an interesting idea.
First, what I described *is* in fact what is called linear FM throughout the
literature (and is implemented that way in many synths).
And yes, it *is* kind of multiplicative, i.e. You need the same amplitude
to modulate the VCO down to zero Hz, regardless of the original,
unmodulated frequency. That's almost always what You want when
You use lin FM (or at least that's what designers thought to be what
You want ...)

What You described would be a 3rd method which is also interesting.

Let "ki" be constants, "KOV" the (v/8ve) keyboard controll voltage,
Vm the modulation voltage, then You get this for the different options:

(1) exponential FM (at the base of either transistor):

f = ko * exp( k1 * KOV + k2 * Vm)

(2) (common, multiplying) linear FM (at the collector of the reference
transistor):

f = (ko + k2* Vm) * exp( k1 * KOV)

(3) additive linear FM (current addition at the collector of the driver
transistor's collector):

f = ko * exp( k1 * KOV) + k2 * Vm

I hope these equations are right; but please double check them!
If they are, we can see that both, (2) and (3) modulate the VCO
in a linear way (i.e. preserving the center frequency).
Option (2) has a constant modulation *index* (delta f / center f),
and option (3) has a constant delta f.

JH.

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