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Re: [TCML] Tesla Coil + Transmitting Antenna ?

Miles Waldron wrote:
> I have always wondered if the secondary of a tesla coil
> has any interesting antenna properties, ...
> ... I believe, ... the length of the secondary tube, not the
> length of the wire wrapped around the tube, would be the
> interesting variable.

It's the height of the topload that matters the most.

The TC (with topload) is very small compared to the free space
wavelength so is accurately represented as a Hertzian dipole
and a Hertzian current loop.  The only significant parameters
concerning radiation are its operating frequency, and electric
and magnetic dipole moments.   The two dipole moments, which
represent independent radiation mechanisms, in turn depend only
on the topload height and capacitance, top voltage, secondary
cross-section area, number of turns, and secondary current.

The electric dipole dominates the far field radiation for normal
Tesla coil dimensions.  Leaving out all phase factors,

 De = electric dipole moment = omega * Ctop * Vtop * h

 omega = 2 * pi * frequency;
 h = topload height;
 Ctop = topload capacitance;
 Vtop = top voltage;

and then the vertical far-field volts/metre at low elevation
at a range r is

 Ev(r) = omega * mu * De / (4 * pi * r);

 mu = 4 * pi * 10^-7;

The actual Ev(r) could be up to twice this depending on the
Fresnel reflection coefficient of the ground, and there might
also be a small ground wave component (the formula for which
is complicated).

The source for the magnetic dipole is the coil current times
the number of turns N, times the cross-section area A of
the secondary,

 Dm = magnetic dipole moment = omega * mu * Isec * N * A;

 Isec = secondary current;

and this produces a vertical magnetic far-field, at low
elevation, of

 Hv(r) = omega * epsilon * Dm /(4 * pi * r);

 epsilon = 8.854 * 10^-12;

This component doesn't propagate very well at all because of
the strong attenuation of the associated horizontal E-field.  At
some distance (more than a km or so) the field is dominated by
Ev and its associated horizontal H-field of Ev/377 Amps/metre.

Paul Nicholson
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