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non-dissipative circuitry



Chuck Britton wrote:

one could imagine two identical capacitors with superconducting plate
and leads. Charge one and then connect it in parallel with the
other. Calculate and account for the 'missing' electrostatic energy.

If you do it exactly as described, there will
be a lot of 'missing' (i.e. dissipated) energy
that is accounted for by the gigantic spaaaakk
that occurs when you make the connection.

By minimizing the resistance and inductance of
the leads, you can make the spaaaakk occur over
smaller and smaller timescales, but that just
makes the event more violent.

=============

But wait, there are much better ways to do things.
The rules for non-dissipating switching are simple:
-- Never close a switch that has nonzero
voltage across its terminals.
-- Never open a switch that has nonzero
current flowing through it.

One easy-to-understand version uses a variable
capacitor. The rotary version works fine
http://w3.one.net/~charlie/contest/images/Figure8.jpg
You may (but need not) consider the case where
all conductors are superconducting. As long
as the 'smooth' changes described below are
slow compared to the RC time, it doesn't much
matter whether things are strictly superconducting.

If you want to change the voltage on a given
load-capacitor from V1 to V2, you need a
driver-capacitor that is variable. Put some
large charge Q on the driver capacitor, then
adjust the capacitance Cd so that Q/Cd = V1.
Then hook the driver to the load-capacitor.
This is a non-dissipative event, because the
voltages match before (and just after) the
hookup. Then smoothly reduce the capacitance
of the driver so that the capacitance of the
two capacitors in parallel decreases and the
voltage goes up. When the voltage reaches
V2, wait a moment for the currents to stop,
then disconnect the driver.

The charge on the driver is now depleted, but
you can further adjust its capacitance Cd so
that its voltage matches the voltage of your
battery. You can then non-dissipatively
attach the driver to the battery. Then
increase the capacitance, sucking charge
out of the battery and restoring the driver
to its original state.

There are lots of additional games you can
play. For instance you can discharge the
load capacitor all the way to zero, but
you will need more than one driver.

It's quite an amusing little world, the
world of non-dissipative electrical power
handling and non-dissipative electronic
computing.

a) You can do quite a lot with just variable
capacitors (with no inductors).
b) Another style of nondissipative computing
uses inductors (with no variable capacitors).

Great fun either way. Switching power supplies
fall into category (b). You can hardly buy a
power supply these days that isn't a switcher.