Re: Parallel and Series LCR Circuit Qs

["Jim Lux" <jimlux-at-earthlink-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)]

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> 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))