Bill Bowden wrote:
It would seem that a loop antenna with 100pF of winding capacitance in
parallel with a external capacitor of 200pF would resonate at the
same frequency as a antenna with no winding capacitance and a external
capacitor of 300pF, but apparently that's not the case.

The "100pF of winding capacitance" is NOT across the
entire coil as is the 200pF external capacitor. When
the operating frequency of a coil is more than ~15% of
the self-resonant frequency, the lumped circuit model
starts to fall apart. In your above example, the operating
frequency is ~60% of the self-resonant frequency so you
need to use the distributed network model (or Maxwell's
equations).

Quoting from an IEEE white paper about RF coils at:

http://www.ttr.com/TELSIKS2001-MASTER-1.pdf

"... lumped element circuit theory does not (and cannot)
accurately embody a world of second order partial
differential equations in space and time."

"The concept of coil 'self-capacitance' is an attempt
to circumvent transmission line effects on small coils
when the current distribution begins to depart from
its DC behavior. The notion has been developed by
starting with Maxwell's equations and using only the
first two terms in the Taylor series expansion for
the distributed current to obtain an expression for
the self-impedance of a generalized closed circuit.
Upon extracting Neumann's formula for the self inductance,
the remaining negative component of the reactance permits
an expression for the coil self-capacitance. These formulae
are valid for a PARALLEL combination of an inductance and
a capacitance when the operating frequency is well below
1/SQRT(L*CL). They permit a coil with a SLIGHTLY
nonuniform current distribution to be treated AS THOUGH THE
CURRENT WERE UNIFORM and the coil was shunted with a lumped
element capacitance."

The author shows how to estimate the VF and Z0 of a coil
that is operated at more than 15% of its self-resonant
frequency. It can thus be modeled as a transmission line.

The same author shows in his class notes at:

http://www.ttr.com/corum/index.htm

that the calculated self-resonant frequency of a particular
coil based on the measured self-capacitance was in error
by 65.2% when the "lumped-element assumption" was used.

The calculated self-resonant frequency based on the
transmission line distributed network model was within
5% of the measured self-resonant frequency.
--
73, Cecil http://www.w5dxp.com