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Calorimeter



Original poster: "Gary Johnson by way of Terry Fritz <twftesla-at-uswest-dot-net>" <gjohnson-at-ksu.edu>

As some of the list knows, I have been working on a characterization of the
resistance component of the series RLC model for a Tesla secondary coil.
Wheeler gives us a nice expression for the inductance, Medhurst likewise for
the capacitance, but we do not have a similar expression for the resistance.
This resistance is the input impedance seen between the bottom connection
and ground when the secondary is operated as a magnifier (a vertical antenna
above a ground plane). Knowledge of this impedance is important when using
solid state or tube devices to drive the coil, and I believe it will also be
useful to those using classical Tesla coils.

It has taken me a long time to build the IGBT driver and develop the test
procedures, but I think things are finally working. I fabricated six coils,
one of space wound 14 gauge magnet wire, three of close wound magnet wire
(16, 18, and 20 gauge), and two of close wound 22 gauge hookup wire. In
general terms, the input impedance of the 14 gauge coil is 25 ohms, 70 to
100 ohms for the magnet wire coils, and 45 to 70 ohms for the hookup wire
coils, at voltages below breakout. Impedances rise when the spark occurs.

I assume the input impedance is a resistance that represents all the losses
in the Tesla coil.  These include:

1. Ohmic (copper) losses.
2. Dielectric losses, coil form, conductor insulation, and moisture.
3. Eddy current losses in toroid, strike ring, and ground plane (soil).
4. Radiation losses.
5. Spark losses.

Ohmic losses, as corrected for skin effect and proximity effect, account for
only 10 to 30 percent of the measured input impedance, below breakout. The
obvious question is: where is the rest of the power going? Is it heating up
the coil (dielectric losses), the surroundings (eddy currents), or the
distance (radiation)? To answer this question, I built a poor man's
calorimeter. I used sheets of the two inch thick blue styrofoam to build a
box about six feet on a side, held together with duct tape, with a panel
that can be removed to change interior components. There is a six inch
muffin fan to circulate the air and a Radio Shack indoor/outdoor thermometer
to measure temperature. It actually works reasonably well.

One interesting quirk is that below breakout, the coil gets hot first, and
then heats the air, so the peak temperature in the calorimeter will be
observed a few minutes after power is removed. Above breakout, however, the
spark heats the air first, which then heats the coil.  The air temperature
will rise more rapidly for a given amount of input power when a spark is
occurring, but the rise ends immediately when the power input stops, and the
temperature drops more rapidly as the cool coil soaks up heat from the air.

One observation is that most of the input power appears as heat inside the
calorimeter.  Radiation losses and eddy current losses are small. I realize
this has been standard wisdom for a long time, but I now fully believe it.

A second observation is that wire size has little to do with coil
performance. It is one factor out of several, and other factors are more
important in determining efficiency (power into the spark divided by the
input power). The 16 gauge coil and one of the 22 gauge coils were made as
identical as possible. They use the same coil form, same winding length, and
the same number of turns. Both are resonant at 123 kHz when using a
particular toroid. Both are tight wound but the 22 gauge coil has thicker
insulation. The 22 gauge coil has a lower input impedance and puts more
power into the spark (faster temperature rise) for a given input power. John
Freau is right when he suggests using smaller gauge wire!

A third observation, and the reason I have not been more precise with my
numbers, is that humidity appears to be the biggest factor in the input
impedance.  My lab is a large metal building in eastern Kansas. Temperatures
at the coils range from zero to 100 degrees F, and the humidity probably
ranges from 20 to 90 percent. On December 29 I measured the input impedance
of the 16 gauge coil as 87 ohms. This morning I measured 122 ohms using what
appear to be identical procedures. I put a desiccant inside the calorimeter
and watched the impedance drop to 100 ohms. (The desiccant saturated at that
point). Then I put in a humidifier and watched the impedance climb to 345
ohms. A similar test with the 22 gauge coil of identical dimensions saw the
impedance climb from 90 to 150 ohms.

A tentative conclusion from all this is that hookup wire is better than
Heavy Soderon magnet wire, at least in high humidity conditions, and that
space winding of magnet wire results in lower impedance with less variation
with humidity than tight winding.

If anyone has any suggestions for measuring and controlling humidity in my
calorimeter, and preferred test protocols, I would appreciate hearing them.

Gary Johnson