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Re: Parallel and Series LCR Circuit Qs
Hi Jim,
Your questions about Q are interesting and seem to be
founded in a lot of thought. Assuming the criteria for a good
TC is spark length, then the design goals should be to
achieve a high terminal voltage (without that there is no spark
or descent spark length. Therefore coil design goals are:
1. High Efficiency
2. Large ratio Cp to Cs
I do not agree with the following statement made:
"However, from what I have read (and understand) the design
dictates a large top capacity and relatively small inductance;
this resulting in white streamers showing a relatively
substantial current."
Instead, the top capacity should be large compared to secondary
coil self-capacitance. There is a design compromise that has
to be made with efficiency, coil, and secondary inductance.
All energy headed towards the secondary comes from what is
stored in the primary capacitance (Cp) at the time the spark
gap fires. That energy is:
Jp = .5 Cp Vp^2 (Joules)
At the secondary, the same equation applies:
Js = .5 Cs Vs^2
Jp = Js Eff
Therefore we have an algebraic equation to solve:
0.5 Cp Vp^2 = .5 Cs Vs^2 Eff
Vs = Vp Eff sqrt( Cp/Cs )
For maximum Vs, secondary voltage we need high
efficiency and a large Cp, and a small Cs. To get that
voltage to the top terminal, it would be best to have
Cs = Ctop or as nearly so as possible. Voltage in
Cself contributes to coil destruction and less to
spark length. I agree that a large Cs contributes to
white hot sparks, but the Cp has to increase by the
same factor.
If Eff = 1.0 then the above equation indicates the
highest secondary voltage that is possible.
Problem 1: A large Cp is difficult to charge to a high
voltage during the time of a 1/2 60 cycle period without
a very high voltage and high current transformer or
power source. Just putting in a large Cp is not the
answer because Vp won't be very high due to the
limited charging power source and short charging time.
Problem 2: A small Cs requires a high Ls, secondary
inductance to tune at a reasonably low frequency where
losses like skin effect are minimized. High Ls for
achievable Q's means high resistive losses Rloss = Ls/Q.
Kiss high efficiency good-bye with high losses.
All Coilers are trying to achieve the highest Vs and do
this by modelling and experimenting with the components
that go into a TC. It's a self arresting activity because
of parts destruction caused by high voltages and currents
that result as one achieves the long spark goal. Physics
dictates that efficiency is the price paid for a hardy TC and
in the end when design is optimized the limiting factor is
the strength and cost of materials that go into a TC.
Compounding the problem is non-linearities and the
accuracy of models. Pure experimentation is not the
answer either because results don't necessarily indicate
clearly the limiting cause for perfection and guide to
further experimental changes.
Lot's of fun, yes??? You bet it is. Sorry for the long
winded spiel and I hope this helps answer your questions.
Dick (K2YZ)
At 06:51 PM 7/22/00 -0600, you wrote:
>Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>
>
>
>----------
>> From: Tesla list <tesla-at-pupman-dot-com>
>> To: tesla-at-pupman-dot-com
>> Subject: Parallel and Series LCR Circuit Qs
>> Date: Saturday, July 22, 2000 2:09 PM
>>
>> Original poster: "Gavin Dingley" <gavin.dingley-at-astra.ukf-dot-net>
>>
>> Hi all,
>> I have a question regarding basic ac theory, something I thought I had
>> sorted, but this does not appear to be the case. I was looking at
>> building a simple crystal set and so had a look at what the ideal design
>> involves. Apparently you should use more capacity and less inductance,
>> that is, a coil wound from fairly stout wire and a large tuning
>> capacitor.
>
>In a crystal set you also have issues of impedance matching to the antenna
>and detector, which kind of throws off the classical LC calculations. A
>wire antenna shorter than a quarter wavelength (likely for AM broadcast
>band with wavelengths on the order of 300 meters), referenced against
>ground, will have an impedance that is somewhat inductive. Some crystal
>sets just use the L of the LC as the antenna, as a magnetic loop, which is
>a fairly good antenna at 1MHz kinds of frequencies. However, now, you want
>a physically large (diameter wise) inductor, to intercept the largest
>amount of RF power. A ferrite core (as in the loopstick found in most AM
>radios) has an even different effect.
>
>You also want to get the right voltages and currents to make the detecting
>junction work efficiently, so you need to trade off L and C (as well as the
>headphone impedance) for your particular detector, be it a galena crystal
>and cat whisker or a 1N34 germanium diode, or whatever.
>
>These radios are best designed by empiricism (try different stuff until it
>works).
>
>
>> Now, am I right in thinking that the Q of a parallel tuned circuit is
>> relevant to current magnification, that is, you want as much current to
>> flow through the coil and capacitor so as to have a large Q. If this is
>> so, then this explains this design for crystal sets.
>
>Q relates more to how much energy is lost in the resistance of the LC
>circuit each cycle. A Q of 100 means that 1/100th of the energy is lost
>each cycle. If you excite it with a constant amplitude sine wave, the
>amplitude in the tuned circuit will rise until the amount of loss just
>matches what is added each time. In other words, it will rise to 100 times
>the energy (10 times the voltage or current). In a crystal set, I would
>imagine the biggest loss is the headphones and the resistance of the
>detector. After all, the entire acoustic power you hear has to come from
>the incident RF power (Hmmm.. wireless transmission of power being
>converted to mechanical energy)
>
>There IS a tradeoff, higher Q means lower bandwidth (Q = Fc/BW), so a
>crystal set with a Q of 10,000 would give a lot of signal, but would only
>have a BW of 100 Hz, and the received signal would be tough to understand
>(if it were speech)
>
>> However, I am no left wondering about tesla coil secondaries. I was
>> under the opinion that a secondary resonator needed to have a fairly
>> high Q; I also thought that the secondary resonator was a series tuned
>> circuit.
>
>All true
>
>If this is the case, then there should be more inductance than
>> capacitance to get a high Q-factor.
>
>Q = sqrt ( Xl/R) = sqrt( Xc/R)
>Xl = Xc at resonance, so you can use either expression...
>
>Since the frequency is sqrt(1/(2*pi*LC)), it seems you want small C and big
>L (high Xc and Xl).... Problem is that it's hard to get high Q in an
>inductor, particularly if there are sparks hanging off loading down the
>circuit.
>
>
> However, from what I have read (an
>> understand) the design dictates a large top capacity and relatively
>> small inductance; this resulting in white streamers showing a relatively
>> substantial current.
>
>The spark is fed by energy stored in the top capacitance, so you want big C
>for that.
>
>> I once built a TC that had a large secondary inductance and small
>> capacity, as per a high Q series resonant LC circuit. This TC produced
>> nice violet streamers, indicating very little current but high voltage;
>> was this poor design?
>>
>> I guess what I'm asking is what makes a high Q in a parallel and series
>> tuned LCR circuit. Also what physical parameters does this dictate, i.e.
>> number of turns and thickness of wire in the inductance.
>
>series or parallel is the same.... lower resistance is always good (bigger
>wire, fewer turns), but you have to trade that off against the changes in
>L. Also, the big loss resistance is the sparks, not the secondary wire.
>1000 ft of 20 ga wire (1000 turns on a 4" form) is only 10 ohms. A 40 pF
>topload at 100 kHz has an impedance of 40 kOhms... If there weren't any
>other losses, the Q of this LCR would be 4000....
>
>>
>> Another question is regarding primary and secondary TC circuits. As far
>> as I understand it, the primary is a parallel tuned circuit, while the
>> secondary resonator is a series tuned circuit.
>
>sort of a combination.. The secondary is a series RL in paralle with a R
>and a C (R for the resistance of the L, another R in parallel across the
>capacitor (sparks and corona))
>