[TCML] Freau Phase Controller - Circuit Theory

[Mike Gray <graymp89@xxxxxxxxx>]

Hi all. As I've mentioned in a separate post, I'm going to build a Freau
phase controller. So I've started looking into it, searching the archives
and reading up etc. The first thing I always do before starting something
new is make sure I understand the theory of how it works. Now I've tried
and tried but I can't seem to find any info on the actual theory behind the
phase controller. Maybe it's so simple that it doesn't need explaining! I
understand the general concept (I think), but would appreciate a fairly
detailed explanation if someone could provide it.

Here's my broken understanding. A motor run directly off mains will look
almost purely inductive. A variable inductor (variac) in series with this
will not affect the phase since the circuit is still completely inductive.
So by introducing capacitance into the circuit, you can now play with the
ratio of the reactance of the inductor and capacitor, by turning the
variac. By varying this ratio you are effectively varying the phase angle
between the voltage and current.

That's about as far I go. I've read that you should use a cap size that
gives roughly 3 to 5 volts maximum resonant rise when you're turning the
variac through its range. Larger caps will cause greater voltage rise,
presumably because they become more and more resonant with the inductance
of the variac & motor. So you're intentionally picking a cap that won't
resonate perfectly with the variac at 50Hz, but will resonate enough to
produce a small voltage rise?

What is happening it terms of voltage/current phase here? Why is this
slight resonance a good condition for controlling the phase of the circuit?
Does the max voltage rise represent the point at which the phase between
current and voltage is zero, and so ahead/behind on either side of this
point?

Lastly, I'm using a US motor (one of the small oriental ones) in the UK,
and so I've already got a variac in place to run the motor. This must
influence the design of my phase controller. The variac introduces even
more inductance into the circuit, and so I imagine I will probably need a
larger cap to compensate? Has anyone else come across this?

Cheers

Mike
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