Feedback in FM synthesis

[Magnus Danielson]

From: Don Tillman <don at till.com>
Subject: Re: Feedback  in FM synthesis
Date: Wed, 9 Aug 2000 07:53:22 -0700 (PDT)

>    Date: Tue, 8 Aug 2000 09:29:55 +0200 (MET DST)
>    From: Martin Czech <czech at Micronas.Com>
> 
>    :::John Chowning's original patent is FM.  US patent 4,018,121:
>    :::http://www.patents.ibm.com/details?pn=US04018121__
> 
>    In this patent I see the formula:
>    e=A*sin(wc*t+I*sin(wm*t))
> 
>    I think I is intended as modulation parameter independend from wm.
>    If this is the case, this formula describes PM and not FM.
> 
> Sure enough.
> 
> The Chowning patent shares a lot with his article "The Synthesis of
> Complex Audio Spectra by Means of Frequency Modulation", Journal of
> the Audio Engineering Society, 1973.  It was republished as chapter 1
> of the book "Foundations of Computer Music" edited by Curtis Roads.
> 
> In all cases his equation is, as you note, PM.  
> 
> But his block diagram ("Music V" notation) in both the article and
> the patent is clearly real FM.
> 
> So I just asked Julius Smith about this.  Julius is a professor at
> Stanford's CCRMA, worked on FM and currently works on a lot of
> physical modeling stuff, and he used to play in my rock band.  He said
> that at CCRMA they used both FM and PM implementations.
> 
> He also said that PM has an advantage because you can use feedback
> without it degenerating. 
> 
> I get the feeling that at CCRMA they used the phrase "FM" in a generic
> way to mean any situation where one digital oscillator is driving
> another.  But I'm really suprised that none of the papers that I've
> seen mention the difference between FM and PM.
> 
> Of course you know what this means; us analog oscillator builders now
> have to come up with a linear through-zero PM input.  Juergen?

Actually, I have given this some thougth... for instance, in a fairly simple
waveshaper curcuit you can do phase-shifting of sawtooth. However, my bet would
be do use a triangle oscillator, there you have all the tools to pull it both
ways. Just look at he sync-handling of the CEM 3340 for instance, it flips the
coin on the triangle generator.

Now, a triangle oscillator you can totally invert the direction of (negative
frequency really) and this is required for deeper modulation. There is one
limit in which you are making so deep modulation that you actually outbalance
the capacitors charging current, i.e. you have momentarilly stopped the phase.
If this limit is fine, a diffrentiator to append a non-scaled FM to the
sawtooth core would be fine, a very simple hack (2-3 resistors, an op-amp and
a cap) on a standard sawtooth core. A triangle core could go beyond this limit
and into deeper PM if properly setup. In many cases the triangle core has many
advantages over the sawtooth core, I am starting to see this lately.

Cheers,
Magnus