AW(Andre): [sdiy] analogue phase modulation

[Magnus Danielson]

From: "JH." <jhaible at debitel.net>
Subject: Re: AW(Andre): [sdiy] analogue phase modulation
Date: Thu, 11 Jan 2007 20:19:26 +0100
Message-ID: <001b01c735b5$6afbd470$0200a8c0 at jhsilent>

Jürgen,

> > This might or might not answer your question 
> 
> Excellent!
> Answers my question, and beyond.
> 
> > DX7 
> > 10 0.003
> > 20 0.013
> > 30 0.031
> > ...
> > 95 9.263
> > 99 13.119
> 
> 
> Would be interesting to know the OL number for MI of 3.14, if it's
> explicitly given in that table.

Even better, they give these two formulas prior to the table:

I = Pi*2^x
x = (33/16)-TL/8

The Output Level has a non-linear relation to TL, so that Output values of
20-99 is linear to TL according to

TL = 99 - Output Level

but for Output values of 0 to 19 the TL values shift from 127 to 81. This is a
little twist to make that range more useable I would assume. The full table is
given at page 166.

Now, this was for the DX7 where as DX21 and CX5 have other formulas. Thus,
the same operator values will not give the same modulation index and thus not
the same sound!

> But even without that, it confirms Eric's hint that "reasonable" OL
> levels mean surprisingly small MI.
> 
> 
> > The modulation index is defined on page 56 as delta_f / f_m where
> > delta_f is the frequency deviation above and below the average
> > frequency of the carrier and f_m is the modulating frequency.
> 
> ... and that _relative_ frequency deviation (delta_f / f_m) is
> identically equal to the _absolute_ phase deviation, isn't it?

It is. Here's the math for it:

O = A*sin(phi_pm)
Phi_pm = 2*pi*f0*t + MI*sin(2*pi*fmod*t)

as we derive this and divide by 2*pi we end up with

f0 + MI*fmod*cos(2*pi*fmod*t)

the maximum delta f is MI*fmod so delta_f / fmod = MI

This infact only works out exactly this was for phase modulation and not for
frequency modulation since then the 

O = A*sin(phi_pm)
Phi_pm = 2*pi*f0*t + MI*sin(2*pi*fmod*t)*t

and this would have turned out uglier.

> So those same MI numbers directly describe what I've been looking for:
> the phase excursion (in radiants), caused by the modulation.

Indeed. Now you even have formulas to go with it, at least for the higher
output levels. It seems that to cover the full range, a +/- 4.176 cycle
modulation depth is needed. A +/- 4 cycle modulation depth is acheivable by
my concept idea when using a 3 bit binary counter to acheive a 8 cycle
modulation depth rather than the 1 cycle modulation depth the original circuit
acheives (or should attempt, given the right component values :P).

Cheers,
Magnus