A Phase Modulation idea (was: Nonlinear Oscillators?)

[Haible Juergen]

Sean wrote:

	>Hmm...isn't Yamaha FM based on phase modulation, as opposed to
strict
	>frequency modulation?  If so, are there any analog oscillator
designs
	>that allow phase to be controlled directly?  

Ok, this is only a very rough thought so far, but being the lazy guy I am,
I'm posting it before I've tried it myself:

Changing the phase of an oscillator by a certain amount should
be equivalent to changing the voltage of the VCO's integrating
capacitor by a certain amount, by definition. 

Someone suggested a d/dt function on an ordinary FM input, but
as he said, that's not exactly practical. But if we consider that the
VCO's capacitor performs a perfect integration on a FM *current*
(as well as on the dc current that sets the initial frequency), the
hypothetical d/dt function and the integrator function of the cap
would cancel. So how to change the capacitor voltage directly
with a modulation voltage ?

First throw would be a low impedance path that "forces" the cap
into a certain direction (opamp buffer + small resistor), but this
does not work as there is no means to mix in the normal VCO
control current.

Second throw (and this is what I want to propose here): Capacitance
voltage divider ! 
Similar as in my "linear detuning" circuit.
Feed in your modulation signal from a low impedance buffer directly 
to the VCO's integration cap by means of another capacitor !
The control current for "normal" operation will see the two caps in
parallel, so you have to recalculate your initial frequency a little.
No problem, as this will be constant for any modulation depth.
The "PM" path will see a (capacitive) voltage divider, so everything
will go straight thru, just linearly attenuated by the ratio of the two 
capacitance values. Even pulse waves (with finite rise time, of
course) will be no problem, as long as the buffer is strong enough
and can drive a capacitive load. (Not trivial, but not impossible either.)

So, where is the problem ?
Honestly, I can hardly believe that it should work. So far I have not 
considered the nonlinear effects, i.e. what happens when the capacitor
is discharged. The saw wave oscillator case would be simpler here
(though I have not explored that completely), but what about a triangle
based VCO ? For any effective linear modulation we need thru zero 
modulation, so that would be "Thru Zero PM" in that case. So probably
there is some switching and syncing required, but after all the whole scheme
is not *that* far away from phase increments during read out of a lookup
table (they also have to handle a limited adress range before there is
some "reset") - so maybe there is a realistic chance to get it working.

What do you think ?

JH.