Re: TESLA COIL REVISED

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

Original poster: Terry Fritz <teslalist-at-twfpowerelectronics-dot-com>

Hi Paul,

>Hi Jaro, Gary,
>
>Jaro wrote:
>
>  > Let's compare a 1000-turn 3" diam. thin wire secondary with a
>  > 50-turn 12" diam. thick wire secondary.
>  > ...
>  > The 50-turn coil resonates at higher frequency, but it WOULD NOT
>  > have a higher resistance than one operating at a lower frequency.
>
>I'm inclined to agree with Jaro on this point.  If we're just
>looking at the coil parameters, its easy to see that the theoretical
>Q factor of the 50t coil can be much higher than the 1000t coil,
>given a few reasonable choices of wire size and coil length.
>
>For eg,
>
>turns        50              1000
>diam         12"             3"
>length       18"             18"
>wire         8 awg           26 awg
>Rdc          0.1 ohms        33 ohms
>Rac          1.3 ohms        115 ohms
>Les          365 uH          9400 uH
>Fres         2.2 Mhz         603 kHz
>
>Coil Q       3900            310
>
>The Rac includes a Medhurst phi factor for the proximity loss
>estimate.  The HF coil scores well because of the thick wire and
>the smaller spacing ratio of the winding.
>
>In practice neither coil would achieve these idealised Q factors
>due to other system losses effectively adding to the Rac of the
>resonator.  The HF coil Q is likely to go down by a factor of maybe
>10 or so, and the LF coil by maybe 2 or 4.  But even so, the HF can
>come out the winner for the unloaded system.  Indeed, if we reduce
>the turns as far as possible - to a straight tube - and put it inside
>a high Q container (a cavity) we obtain a VHF resonator capable of
>Q factors well over 1000.  I used to build commmercial VHF cavities,
>(large ones!) and casting the memory back more than 20 yrs I seem to
>remember *loaded* Q values around a couple of thousand, with
>insertion losses of around 1dB.  I'll leave it to the reader to
>estimate the unloaded Q from those figures.

I too would make a "guess" that the Q's would be far lower in 
practice.  But perhaps the lower frequency coil would not loose as much 
Q.  The 2.2MHz coil may drop to 390 but maybe the 603kHz coil would drop to 
only 150.  Hard to say since there are a lot of variables there.  Of 
course, 'sonotube' would be a poor choice for a 2.2MHz coil form :o))

It is interesting to note that if we take the numbers above at face value 
and feed the coil with 1VAC at the base, The energy in the coil is:

1/2 C V^2  ==>  1/2 C Q^2

The equivalent capacitances are 14.2pF and 7.411pF.

So E(2.2MHz) = 108.75uJ  and E(603kHz) = 0.356uJ.  Thus, the higher Q coil 
can store 300 times the energy!  This may be important in some cases.  It 
is one thing to have a lot of voltage, but having a lot of stored energy 
sure helps too!!


>As it happens I've been messing with a high Q HF CW coil at the
>weekend - I decided to rebuild the PA of my 7Mhz transmitter (a long
>story).
>
>The output stage involves a number of L and C components but the
>most critical stage is the first L and C stepping the device output
>impedance up to higher value, ...
>
>           ------ L ----- ----> to Pi network.
>          |              |
>       |  | drain        |
>       |--               C
>       |--  FET          |
>       |  |              |
>          |              |
>       ------------------------- ground
>
>The L and C here are effectively a CW TC, base driven, and loaded at
>the 'top' by the next stage - a pi network.  The arrangement steps
>up the drain output impedance (a few ohms) up to a higher value for
>the next stage.
>
>Now the efficiency is the usual
>
>    100% times (Q_unloaded - Q_loaded)/Q_unloaded
>
>and my problem is to increase Q_unloaded because it's not very good
>at the moment.  The test is to operate the thing unloaded, ie I
>disconnect the following stage and fire the thing up.  We expect
>a large voltage across the C, and the drain should see its lowest
>possible load impedance - that being the effective resistance of
>the unloaded resonator  (as load is applied to the output, the coil
>'base' impedance rises above this value to the normal operating
>level, ie the familiar see-saw effect of the 1/4 wave line [*]).

Beware that they may have had a lot of reasons to design the original 
circuit with high loss and such for protection or stability into odd 
conditions.  Or, the designers may not have had the slightest idea what 
they were doing....  I have seen it go both ways...


>Now if I repeat the above calculations for this circuit, I get
>a theoretical Les of 6.5uH and Rac of 0.08 ohms, to give an idealised
>Q of about 3600.  The measured value is unsurprisingly very much
>lower than this - around 190.  So we have lost a factor of about
>20 in going from the theoretical ideal to the real circuit.  The
>effective resistance in practice must therefore be around 1.5 ohms
>or thereabouts.  I've been trying to get this figure down so that
>I can draw more power from the device (by presenting a lower
>impedance to the drain).  Some of the extra is the device 'on'
>resistance, but much is probably coming from eddy losses in the
>poorly shielded circuit.

As the frequency goes up, the losses go way up since currents in 
surrounding junk goes way up.


>I mention all this partly to show that the practical Q values are
>always much less than the ideal unless considerable effort is put
>in, and partly as an example of a very common use for CW TCs with
>few turns aimed at high unloaded Q at HF.  You've all seen those
>nice shiny silver plated loading coils that HF transmitters
>invariably have.

They tend to turn black in these days of sulfur dioxide pollution :-p  They 
can also pump water through them...  They may not be trying to achieve some 
wonderful high Q, but rather just trying keep the coil cool enough that is 
does not melt down.  Usually, they have power to spare.  A 1% loss in a 
100kW transmitter is not a big deal, but having it go into a coil is a 
problem for the coil!


>  > Of course the higher frequency will result in shorter sparks, so
>  > this coil would be more for people who want to experiment with
>  > very high frequencies and perhaps experience beams or walls of
>  > light (brush-like discharge), instead of the sparks. And that
>  > brush-like discharge would probably be more plasma-like than the
>  > usual low-frequency sparks.
>
>Indeed.   This brings us to a more interesting topic, that of
>loading the high Q HF coil.
>
>Both the TC and the matching network above behave as a 1/4 wave
>line, having a characteristic impedance Z = sqrt(L/C) and the
>input and output impedances, Zin and Zout, are related to Z by
>
>     Zin * Zout = Z^2 = L/C
>
>Thus as Zout is reduced (heavier load) Zin increases and vica versa.
>For the TC producing a brush discharge, as the output voltage
>rises, the size of the discharge increases, so Zout reduces,
>which increases Zin, which in turn limits the power which the
>driver can put into the TC base.  Thus the system settles to an
>equilibrium involving the input power and the load discharge.
>
>The challenge for the designer is to choose an L/C ratio which
>allows the driver to transfer its full power to the load discharge.

Of course, you can use variable capacitors with motors and have the tuning 
network actively tune that load as is done in industrial plasma 
processes.  This may be needed since the load of plasmas tends to fall over 
far too wide of range for most 50 ohm power sources.

http://advanced-energy-dot-com/Upload/wp_16_tuner_topics2.pdf

http://advanced-energy-dot-com/Upload/wp_18_impedance_match3.pdf

http://www.mksinst-dot-com/cgi-bin/product.exe?pid=MWH-100

Note how the last link lists the plasma tuning range from 10 to 600 
ohms!!  These high ranges are typical...  (I know far more about those 
ranges, but "I" can't tell since it is secret...)


>It remains an open problem to predict the discharge impedance Zout
>for a given frequency, voltage, and discharge terminal shape. AFAIK,
>very few measurements of Zout are available, so there's plenty of
>experimentation to do here.  Without this information - empirical or
>theoretic, it is impossible for the CW TC builder to 'close the loop'
>at the design stage.

Unfortunately, the measurement devices used in industrial applications fall 
far short of what is needed in TC applications...  Too bad, since I have a 
bunch of them sitting under my desk :-p

>Thus, I would say L/C is at least as important as L/R for CW TC
>design, where of course R must be the total effective resistance
>(including the discharge) of the resonator, and likewise C must be
>the total capacitance, including terminal and discharge load
>capacitance.  The L/C ratios of the two example coils above are
>roughly
>
>turns        50              1000
>L/C          25e6            1260e6
>Z            5k ohms         35k ohms
>
>Regardless of Q factor and operating frequency, the low Z of the 50t
>coil makes it poorly suited for long streamer formation, and the high
>Z of the 1000t coil is probably less suitable for powering a heavy
>brush discharge.
>
>It would be easy to prepare a very high L/R coil and find that it
>produces feeble discharges due to a gross mismatch of the reflected
>load presented to the driver.  Most CW coilers build in some room to
>maneuver by installing a ferrite impedance matching transformer
>between driver and base with a selection of taps.

You can also tune it by varying the frequency which is vastly better for a 
high Q application where you need to tune it in very precisely.

http://www.mksinst-dot-com/eniAFT.html

>I think Jaro is right to point out that HF, low L/C coils are an
>under-explored area, as opposed to LF, high L/C coils aimed at
>producing long streamers.  While we're very used to dealing with
>HV LF streamer-generating coils, it pays to remember that most
>'embedded' applications of Tesla coils belong to the other category.
>
>Rather than streamer length, here the figure of merit might be
>something like volume of plasma produced per kW input, although
>plasma temperature might also be considered equally important, so
>maybe volume * temperature would be better indicator.

They want to deliver vastly lower voltages at vastly higher currents to do 
silly things like making CD's or LCD screens...


>I also think that Gary has a valid point when he warns us about the
>loss resistances rising with frequency.  It is generally harder to
>obtain high Q in practice as the frequency goes up, not so much
>for the coil itself (as we see above) but from the rest of the
>circuit, and from the interaction of the coil E and H fields with
>the surroundings.  A high Q HF coil must come equipped with a high
>Q shield too - so that the large shield eddy currents will have only
>a small impact on effective AC resistance.  It is the overall system
>Q that counts, and the coil is only a small part of it.   The VHF
>resonator achieves its very high Q largely due to the high Q of the
>containing cavity.   A poorly shielded coil such as my PA matching
>circuit will fall well short of its theoretical Q factor.
>
>I would encourage Jaro to explore the use of high Q, HF, low L/C
>Tesla coils in CW mode loaded by brush discharges. There's lots to
>be done!

Higher voltage plasma tuners can get to 15kV and they can make say 6 inch 
to foot long streamers (13.56MHz, they don't "mean" to make arcs 
;-))).  But the input power can be enormous (thousands of watts)!!  At high 
voltage and low current like that, the tuner dissipates little power.  One 
can guess that >10MHz streamers have pretty low impedance.  If you have 
3000 watts in at 15kV out for a 10 inch streamer (wild guess), the 
resistance is V^2 / P = 75kOhms (compared to ~~220K for standard 
streamers).  But if we apply John's formula...

L = 1.7 x SQRT(power) = 1.7 x SQRT(3000) = 93 inches!!

So one may perhaps conclude that streamer length per given input power 
falls dramatically at higher frequencies.  I think the real problem is the 
displacement currents to the space around the streamer start to get way too 
high to sustain a really long streamer.  But at low frequency, those 
currents fall dramatically and a little input streamer current can go 
a  "long way".  One may note that Bill's coil:

http://www.ttr-dot-com/model13.html

Does 55 foot arcs at 125kW input.  Again applying John's formula:

L = 1.7 x SQRT(125000) = 50.1 feet

So Bill's coil goes 10% further...  So one may start to detect a trend here 
that the lower the frequency, the longer the streamers.  Of course, the 
data points are precious few...

Cheers,

         Terry


>[*] This 1/4 wave impedance inversion can be regarded, equivalently,
>as a conversion from the series LCR impedance seen by the drain to
>the parallel LCR impedance seen by the load.
>--
>Paul Nicholson
>--