# [sdiy] Linear FM concept again

René Schmitz uzs159 at uni-bonn.de
Sun Aug 25 02:21:55 CEST 2002

```Hi Scott,

>>In an exponential VCO there are two different kinds of linear FM.
>>
>>One is an "offset linear FM" (I'm making up the term), which is a
>>linear frequency offset introduced after the exponential converter and
>>is typically used for subtle chorusey detuning.  The range might
>>typically be -10Hz to +10Hz, 0Hz by default.  The advantage it has
>>over exponential FM is that the beats-per-second doesn't change with
>>the pitch of the oscillator.
>>
>>The other is "scaling linear FM" (again, I'm making up the term) which
>>is linear FM *before* the exponential converter, effectively changing
>>its range.
>
>Ok, this is something I don't "get".  I thought that "linear FM" meant
>introducing the modulation signal such that it sums with a linear
>control signal of another VCO...  From what I'm reading, I have that
>wrong.  I don't see how summing with a signal before the expo converter
>is linear.  Help?  And thank you, Don.

The expo convertor has a linear input, where usually a reference current is fed in.
(You typically see a 1M resistor going to a reference voltage, that current being
summed into an opamps virtual ground.) This is where usually linear FM is added via
another resistor.

The benefit of this is that the peak frequency deviation is then also scaled by the
exponential pitch, and therefore the modulation index stays constant, giving a constant
spectrum, and thus timbre.

(Modulation index is defined as peak frequency deviation / carrier frequency.
The modulation index m says how many sidebands there are, they are spaced in intervals
of the modulation frequency apart. This is all from memory, so I take this with a
grain of salt.
)

Now when you want to do constant modulation index, I guess it gets tricky with linear,
because you will need an VCA to scale the ammount of modulation along with the carrier
frequency.

Say you modulate a 1kHz carrier with a modulation peak deviation of 100Hz, then a 2kHz
carrier will require a 200Hz deviation. (Just to avoid confusion, that is how far the
carrier moves, not the frequency of your modulation programe. ) So you need to make the
modulation proportionally more deeper for higher frequencies.

The expo convertor automatically accomplishes this task, so this is "scaled FM", for a
purely linear oscillator you would have to do the scaling yourself, and can use the result
for an "offset linear" method.

Cheers,
René

--
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159

```