Solid State Coil

["Tesla list" <tesla-at-pupman-dot-com>]

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

Here are some results I obtained today from my solid state driver and two
different coils.  I am trying to characterize the magnifier (a Tesla coil
driven at the base like a vertical helical antenna above a ground plane), so
there are no claims that what I am doing is optimum for 'normal' solid state
experiments. I refer to the coils as the 14 ga and 16 ga, after the wire sizes.

                              14 ga     16 ga
winding length (inches)       45.9      24.4
coil radius (inches)           7.8       9.5
turns                          387       445
winding style                 space     tight
inductance (mH)               17.2      49.4
dc resistance                  3.99      8.89
resonant frequency with toroid  209      123 kHz
input impedance (ohms)           30       90
coil form polyethylene         sheet    barrel

The driver uses 8 IGBTs rated at 1200 V, 4 in series in each leg of a half
wave switcher. It supplies a square wave to the bottom of the coil of up to
plus/minus 1500 V if everything is in perfect tune. It has survived 10 ms
bursts of 1000 V and 30 A, or around 30 kW. Think amateur radio linear with
an attitude. Today was low power testing, up to 850 W in CW mode and 2500 W
in 10 ms bursts.

The toroid has a major diameter of 24 inches and a minor diameter of 4.5
inches. It is made of 29 sections of 1/4th inch copper tubing electrically
connected with one disc, so any eddy current effects should be negligible.
(Standard wisdom is correct. Eddy currents in a solid aluminum toroid are
not important.) I stuck a 1/4th inch bolt through between two of the tubing
sections and mounted a brass knob, about 1/2 inch diameter, as a breakout
point, extending horizontal. It gets hot during operation.

When a square wave of a given voltage and the proper frequency is applied,
the current will build up, a little each cycle, until the toroid voltage
reaches the breakout level. The gradual buildup can be explained by either a
bounce diagram of a transmission line or by square wave excitation of a high
Q RLC circuit. We can think of the current being the same at all points of a
series RLC circuit, as required by Circuit Theory I.  Maxwell's claim to
fame was to recognize that current could be either conduction current (flow
of electrons) or displacement current (what happens between the plates of a
capacitor). The current entering the bottom of the coil is conduction
current, while the (same) current leaving the toroid going back to ground is
all displacement current until the spark occurs. The capacitance of the
toroid is charged and discharged each cycle. Voltage is related to charge,
and charge is related to current, so the toroid voltage at breakout is
always accompanied by a given current at the bottom of the coil. The
breakdown voltage is constant for a given coil and toroid so the input
current during spark is also constant. (Yes I understand there is some
jitter due to air currents, heating effects, etc.)

As voltage is increased, the power into the coil and into the spark will
also increase, and it is this power that determines the length of the spark.
For this particular toroid and breakout point, I observed a spark length of
5.4 times the square root of the input power in kW, in inches. So 0.85 kW
input in CW mode gave a spark length of 5 inches. The same expression held
for both coils, since the same toroid was used on each.

When power is applied for 10 ms at a time, current builds up as expected for
a linear RLC circuit for a ms or so until breakout occurs. There is a lag in
the spark process so the input current just before spark will exceed the
input current after spark. The 14 ga coil input would rise to 4.7 A at 440 V
before spark and drop to 2 A afterwards. Spark length is determined by the
peak power applied *before* spark, in the impulse mode. I think this is the
reason that conventional Tesla coils outperform the solid state coils. A
conventional system applies, say, 10 kV to the coil. Buildup occurs over a
few cycles at most. The lag in spark formation means the toroid reaches a
much higher voltage than would ever be observed with the application of a
lower voltage for a longer period of time, and the resulting spark is much
longer.

Applying power for a longer period of time, say 20 ms rather than 10 ms,
does not increase the spark length. It will make the spark thicker, however,
which might be perceived as a longer spark. 

I see two advantages to the coil with the lower input impedance: One is that
current builds up more quickly so the spark is reached sooner, for a given
input voltage. The second is that the input current during the spark is
higher, which results in a thicker, whiter spark.

Gary Johnson