Re: [TCML] 1/4 wavelength theory ??

[Paul Nicholson <tcml88@xxxxxxxxxxx>]

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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