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RE: [TCML] 1/4 wavelength theory ??
Thank you all for clarifying.
I obviously need to touch up on my tech knowledge before I go spouting
off on here. :)
Thanks for the info and links.
Shannon Weinhold
Klasdja
-----Original Message-----
From: Paul Nicholson [mailto:tcml88@xxxxxxxxxxx]
Sent: Monday, February 08, 2010 10:40 PM
To: Tesla Coil Mailing List
Subject: Re: [TCML] 1/4 wavelength theory ??
Shannon Weinhold wrote:
> This is puzzling. Isn't the 1/4 wavelength the earliest > antinode,
thereby representing the point in the resonator > where the amplitude
of the standing wave is a maximum?
>
> That would be the stance of an electrical engineer
Yes, and correctly so. The TC secondary functions as
a 1/4 wave resonator - it has all the properties expected of such,
including
- It has a characteristic impedance;
- Impedance inversion - base to top;
- A whole spectrum of resonances, but the TC
only uses the fundamental one - the 1/4 wave;
- Voltage and current antinodes pretty much
where you expect them;
The point at issue is that the natural (unloaded) 1/4 wave frequency of
the solenoid doesn't match that of the original straight wire that the
coil was wound from. This is the myth.
An example may clarify:
Take say 600 metres of wire. It is 1/4 wave resonant at 1/4 * 300e6/600
= 125kHz, or a little less if you allow 0.95 velocity factor for a
straight wire.
Now wind that wire into a solenoid, h/d ratio say 3:1.
One variation of the myth says the resonant frequency of the solenoid
remains 125kHz, ie that the wire has retained its original
straightened-out frequency.
But the reality is: the resonant frequency here will be around 200kHz.
This is easy to measure and model and there is no room for debate on
this point.
A second variation of the myth acknowledges the frequency change, but
suggests that you must now add topload C to pull the solenoid resonance
down to match the original 125kHz of the straight wire.
The reality is: nothing special happens when you do that, although you
end up with a heavily toploaded coil which is good
for matching to a breakout load. Various vague justifications
for doing this are offered - often involving a suggestion that the
voltage antinode (max) will not be at the top unless you match solenoid
frequency to straight wire frequency.
The reality is: the voltage antinode is always at the top, whatever the
toploading.
The solenoid behaves as a transmission line, although a complicated one
compared to a coax or twin line. The telegraphist's equation normally
used to describe a transmission line has to be altered a little to deal
with the solenoid but it is qualitatively the same.
When heavily loaded with top C, the coil can be modelled as a lumped LC
device with little error. Even when lightly loaded or unloaded, an LC
model can be used but the L and C used need to be carefully selected -
by modelling the thing as a transmission line and calculating suitable
equivalent lumped reactances.
JavaTC deals with all this correctly.
To summarise: The secondary is electrically a 1/4 wave, but it
doesn't resonate at the 1/4 wave frequency of the straight wire.
Making it do so by adding topload achieves nothing.
Here is an animation illustrating the voltage and current in a secondary
coil during a TC beat cycle,
http://abelian.org/tssp/pn040502/tfsm1-h1.anim.gif
The quarter-wave behaviour is clear, and you can see from the flexing of
the voltage distribution that a little bit of 3/4
wave is present too. The firing of the primary circuit excites
all the resonances of the secondary but most of the energy goes into the
1/4 wave mode. In the 'magnifier' arrangement, energy is deliberately
put into a carefully tuned 3/4 wave mode as well.
--
Paul Nicholson
--
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