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Mon Dec 13 13:41:41 EST 2010

2-Scroll circuit

See [1].  The basic idea is to start with an unstable 2-pole filter
(negative damping) implemented as an SVF.  Then modify it such that
one of the state variables can have a DC bias, which shifts the center
point of the oscillation.  Then a 3rd variable is introduced.  This
takes the function of "switch state".  This can either be interpreted
as binary, or as a 1-pole filtered binary state variable with a fast
time constant.

X,Y : unstable oscillator state variables
X   : biased state varible
Z   : "switch" state.

This is a display of the X,Z plane.  The idea is to bias the
oscillator circuit in such a way that the unstable fixed point is at
the "x" mark.  Whenever the unstable oscillation crosses the
comparator cut point, the state variable is switched which projects
the point to the other plane, close to the unstable fixed point, where
the oscillation starts to grow again.


        comparator cut
            /
           /
    --x---/---  
      ^  /|
      | / |
      |/  v
    --/---x---
     /
Z

^
|
 -- > X


The variables:
  - unstable filter pole
  - unstable filter (negative) damping
  - switching speed
  - exact location of the `x' w.r.t. comparator cut line


Questions:

  - Biquad instead of SVF?  What we really want to control is the time
    it takes between state switches, independent of frequency.  This
    is propertional to ring time, not Q.


[1] ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/suykens/reports/chaos_00_125.ps.gz



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