Yet some more phasemodulation thoughts

[Magnus Danielson]

From: mbartkow at et.put.poznan.pl
Subject: Yet some more phasemodulation thoughts
Date: Mon, 11 Oct 1999 20:37:16 +0200


Hi MB!

> Why not use phase shifters for this job ?
> 
> Lets consider a series of OTA-based phase shifters. These have such
> advantage over others that can be linearly tuned within a wide fre-
> quency range. Applying the same control voltage as one going to VCO
> input one achieves a phase shift that is constant over pitch changes
> of the VCO. Now modulating the PS control voltage by the audio signal
> the phase of the signal is modulated as desired for the Yammy (or should
> I spell it "yummy" ?) sound :-)
> 
> The number of phase shift stages certainly determines the maximum
> modulation depth. I don't know yet, if it is better to tune the particular 
> sections to different "center" frequencies (i.e. the frequency where the 
> phase shift of the stage is pi/2), which would allow to achieve more linear
> phase/frequency characteristics and more linear phase shift dependence on
> the modulation input. On the other hand, if phase shift depends linearly
> on the frequency it is just a continuous delay line. So maybe a step-like
> phase characteristics is better, whereby all the spectral components are 
> shifted in the same way ? This is easier to build, but the shape of the
> signal is destroyed as in all nonlinear-phase systems. It might lead to
> more dramatic effect of the modulation. What do you think? 

Well, each pole/zero pair in the AP filter sections is good for 360 degree
(asymtotically) phase-shift. You would do phase shift, however, your phase
shift would be far from linear, since the phase will vary non-linear as you
tweak the AP pass the "center-frequency". Also, getting a phase filter to
preform the "appropriate" phase shifting on the overtones is also not so
nice, you would need to set up a suite of AP filters so that you get a linear
phase property.

Apart from that I come to think of CV-feedtrought and the non-linear capacitor
buildups that you end up with. Filter theory really works only for linear and
time-invariant filters. Thus if we are non-linear or have properties changing
with time, then it doesn't follow our beloved filter theory. The time-invariant
rule is just another part of the linear property.

Other than that, I think it would be nice to try at least ;)

> PS. I have got a reprint of the original J. Chowning's article on FM synthesis.
> Although he refers to it as "frequency modulation", it is obviously a phase
> modulation in his own formulas. In fact, these two are to some extent equiv-
> alent, since after appropriate scalling of the modulation depth, or index they 
> give identical output.

This would be nice to have a scan of sitting somewhere!

Cheers,
Magnus