Archive of the former Yahoo!Groups mailing list: MOTM

Here's some more details about "through zero" linear FM.

I can't speak to the circuit mentioned as I have not seen it. There was an
approach floating around about the same time as the this other approach
(which I will describe) that used two VCOs and a balanced modulator in order
to generate a difference frequency. This produces proper spectra for FM as
it allows the difference frequency to be negative, which is the requirement
for high modulation index FM. So I wonder if the mentioned approach is the
same? BTW if it is this approach it has a set of issues that make it
somewhat impractical for a precision VCO.

Anyway, the "preferred" approach IMHO is to implement it in the following
way. Suppose for the moment that we are starting with a conventional VCO
design that produces a triangle as its base waveform, as opposed to a
sawtooth like the 300 does. The "trick" to making a through zero VCO is
that the charging current must reverse its direction at the right moment,
the moment when the modulation has produced exactly zero Hz in the carrier
and is about to transition through zero. Reversing the current at this
point is precisely what happens in a theoretical through-zero VCO as the
change in charging current is equivalent to a phase reversal of the
waveform, and reverse phase is equivalent to negative frequency.

Thinking about it another was, if you look at the canonical digital FM
equations and think about how the digital oscillator is implemented it is
typically done with an accumulate function. When the modulation is large
enough it will actually be bigger then the increment that is added each time
to cause the base frequency in the carrier. If the modulation waveform is
negative (as it will be as it completes its cycle) the result will be a
negative number being added in the accumulate. This will momentarily cause
the accumulate to "back up". Again this is just another way at looking at
the negative frequency thing.

The VCO modified for through zero FM in the above manner is a bit more
complex circuit-wise in that you need to detect when the linear fm input
would be going through zero and keep that from happening while at the same
time cause the charging current to reverse. There is some hair on the
circuit to do this but really it is not much worse then any good precision
VCO design.

As for the motivation behind this, my memory of hearing this 24 years ago
was that it gave me goosebumps! The richness of the evolving FM spectra was
a perfect counterpoint to the normal subtractive VCF idiom. I was estatic
when the DX-7 first showed up because it was "fm in a box" but the digital
implementation never left me with quite the same first feeling. As with
most things digital it was a bit colder. That said the Nord Modular offers
"VCOs" with through zero FM and they sound pretty good - for digital that
is. Unfortunately, my through zero VCO prototype has long gone to DIY
heaven otherwise I would post examples.

Douglas