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Relaxation Oscillators:
 
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The van Der Pol Oscillator is the first relaxation oscillator. van Der Pol
described this oscillator in a paper in 1928 in a model of human
heartbeat,
- The Heartbeat considered as a Relaxation oscillation,
and an Electrical Model of the Heart, Balth. van der Pol and J van der Mark,
(1928) Phil. Mag. Suppl. #6 pp 763--775.
Here is the second-order differential equation for a van Der Pol oscillator:
Omega controls how much voltage is injected into the system.
Alpha controls the way in which voltage flows through the system.
Think of the oscillator as having two distinct phases:
a slow recovery phase and a fast relase phase (that is
in fact where the term relaxation comes from: vaccuum tubes
quickly release or relax their voltage after slowly building
up tension.) The variable alpha controls the rate at which
the slow build up occurs. As alpha is decreased, the voltage
collects more slowly, making the slow phase take longer and hence
slowing down the oscillator.
Also notice that the amplitude of the oscillator remains constant as alpha
and/or omega vary. What changes is the shape of the voltage curve and
the frequency of the oscillator.
Vibe Hints and Experiments
- First, click on the Launch Simulator!
button in the upper left. If your browser supports Java, you
will get the Vibe simulator in a separate window. If you don't see a Launch
Simulator button, you are either browsing Vibe with Java turned off or,
alternately, Java is not working on your browser.
- Now run the oscillator with default settings for a few timesteps.
- Click the
Layer Button to run a second simulation
- This time try varying either
coupling or voltage
and then click Start to run the new simulation.
- Repeat as desired.
- You should see that peak voltage is the same whatever settings you use, but that
frequency and curve-shape change drastically.
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