Re: 3 probably awful beginners questions ;-)

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Paul Nicholson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

 > Les:    The effective series inductance of the system.
 > Lee:    The energy storage inductance of the system.
 > Ldc:    The low frequency inductance of the secondary.

 > Ces:    The effective shunt capacitance of the system.
 > Cee:    The energy storage capacitance of the system
 > Cdc:    The low frequency capacitance of the system.

The Les and Ces are the relevant values for calculating Fres,
and for relating base current to top voltage.  These are the correct
values to use in a simple LC circuit model.

Antonio wrote:
 > The essential behavior of a coil is correctly modeled by considering
 > only its inductance, that is the DC inductance,

Using the DC inductance takes no account of the current distribution
prevailing at high frequency, which is non-uniform.  Unless you use
the correct value of Les, the equation Vtop = 2 * pi * F * L * Ibase
does not work very well.  Just as the effective C must be arrived at by
considering the voltage distribution, so the effective L must take
account of the current distribution.

 > For a beginner, High-order modeling may be very confusing, and
 > is not necessary.

Agreed.  But Les and Ces are first order equivalents intended for use
in an LC model with only one secondary resonance represented.

It's a worthwhile exercise to set up a coil and measure Ibase and Vtop
at resonance in steady state.  Compute Les from

  Les = Vtop/(2 * pi * F * Ibase)

and see that it differs significantly from Ldc.  The measured values
of both Les and Ldc should agree with Fantc outputs to within a couple
of percent.  Large h/d coils should give an Les somewhat smaller than
Ldc.   Small h/d coils may have an Les which is rather larger than Ldc.
A flat spiral coil may give an even larger increase of Les over Ldc.

All six effective reactances listed above are well defined, and can be
measured fairly directly.   Using Ldc and a notional self-C in the way
Antonio advocates will give you an LC circuit model in which
2*pi*F=1/sqrt(LC) works correctly, but the beginner may be puzzled
why the currents and voltages don't quite relate to the reactances in
the way expected from circuit theory.  Les and Ces satisfy both
requirements.

They do not however, represent correctly the energy storage of
the resonator.  As Antonio says, you can do better with a more
complicated LC model, but Fantc provides special values of L and C
for use in the formulas E = L*Ibase^2 = C*Vtop^2.  The L and
C quantities for use here are the energy storage equivalents Lee and Cee.

The whole point of presenting these equivalents is to carry the use
of a simple LC model as far as possible, by taking proper account of
the distribution of current and voltage in the secondary.
--
Paul Nicholson
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