Hi Carl,
Carl Noggle wrote:
All true, except that I would disagree that the spark gap resistance is
a major factor. The current in the primary of a moderate sized TC (mine,
at 1600 watts, for example) is of the order of 100 amps. Going through a
spark channel that is a fraction of a mm in dia gives a very high
current density, not too different from lightning. A plasma at these
current densities has a resistivity that is lower than any metal. A
spark gap is a remarkably good switch for high currents.
A spark gap does indeed have a negative resistance characteristic, so
the higher the primary current, the hotter the plasma channel and the
lower the arc channel resistance. However, cathode and anode voltage
drops also contribute significantly to total gap voltage drop and
losses. The gap voltage drop is the sum of the resistive channel
("positive column") voltage drop plus cathode and anode voltage drops.
The cathode drop in particular is comparatively large. Both the anode
and cathode drops appear across the plasma sheaths that "connect" the
hot positive column to the comparatively cool gap electrodes.
A TC spark gap typically has a voltage drop of 150 - 250 volts
depending on electrode materials, gap current, and electrode/gap
cooling. This is not nearly as good as a metallic conductor or even
saturated semiconductor switches. This is why an SISG (with a series
chain of saturated IGBT switches) has a higher efficiency than an
otherwise identical spark-gap switched coil.
Voltage drops across multiple spark gaps add, so instantaneous power
losses across multiple gaps tend to scale with the number of gaps. A
single gap with high velocity air flow, such as Gary Lau's
sucker/vortex gap, provides higher efficiency than multi-gap systems
since it efficiently quenches while only using a single gap.
The main source of resistance in the pri circuit is the coil wire, due
to the very shallow skin depth. The bigger the better, stranded might
help a little, the best would be a lot of small insulated wires bundled
into Litz wire, but who wants to go to that much work?
There are calculators of resistance of wire at different frequencies on
the web. Check this URL--
http://ve3efc.ca/wire_ohms.html
The R of my primary (00 wire) from this table is about 0.07 ohms, and
since the impedance of the coil is about 100 ohms, wire resistance is
not a big factor. That means that without the secondary, the primary
circuit ought to have a very high Q. I think I'll check that on my coil.
By the way, let's forget Litz wire. Looks like I overspent on wire. But
it sure is a pretty coil.
If you actually measure your primary's Q (without any secondary
present), you'll discover some interesting behavior. The primary LC
circuit does not decay exponentially, but instead decays almost
linearly due to the combination of the gap's negative resistance
characteristic and the relatively fixed gap voltage drop. For an
interesting discussion about gap losses and measured efficiency of a
single gap, search for the "Vortex Gap Loss Measurements" thread in
the Pupman archives:
http://www.pupman.com/listarchives/2000/September/msg00038.html
An interesting thing to be gleaned from the table is that the RF
resistance of any reasonable wire used for the secondary will have
hardly any increase of R at TC frequencies, so the ohmmeter resistance
of the secondary is the RF resistance. The secondary coil Q should be
high too. It seems that losses in the TC are small, and almost all the
energy should be going into the coronas. If you look though them in the
daytime, you can see quite a bit of heat distortion, even though it's
hard to see the sparks themselves.
If the radius of the wire is roughly the same as the skin depth, then
the HF resistance is approximately the same as the DC resistance.
However, TC secondaries are usually close-wound to maximize
inductance, and the RF resistance is usually significantly higher due
to "proximity effect". Similar to skin effect, this is due to magnetic
fields from adjacent windings further constraining current flow
through the wire. Proximity effect can cause boost the RF resistance
by a factor of 2-4X the DC resistance (or more). The combination of
skin and proximity effects make it challenging to wind TC secondaries
with Q's much greater than about 250 at resonant frequency. Again, the
Pupman archives have some good information - search "Proximity
Effect". Also, chapter 2, sections 18 and 19 in Terman's "Radio
Engineer's Handbook" have a good discussion and analysis of total
copper losses (including proximity effect) for single-layer air coils.
---Carl
Bert