Here the coil is placed close to the plate, and the resonant frequency is reduced from 26.6 MHz to 24.7 MHz. The Hg vapour discharge shows that the interaction is much the same as placing a small static capacitance across the coil.

According to the lumped element theory, if a capacitance equal to the self-capacitance is placed in parallel with a coil, the resonant frequency will be reduced by a factor of 1/√2. In this case, the self capacitance is 3.2 pF, and so placing that much again in parallel should reduce the resonant frequency to about 18.8 MHz. Evidently, the ground plane is not having much effect.

Various commentators, including Medhurst, attribute the self-capacitance of a coil mainly to the proximity of a groundplane. In fact, a groundplane presented broadside to the coil just adds a small ordinary stray capacitance. A groundplane presented perpendicular to the coil axis of course reduces the inductance by acting as a shorted-turn; but that is a well-understood magnetic effect, not a capacitive one.





Integer multiples of a quarter-wavelength - the ground mirror effect.

There is, however, a very pronounced ground effect that can neither be attributed to stray capacitance nor magnetic induction. This can seem highly paradoxical when performing scattering experiments (and is inexplicable using lumped-element theory), but it makes perfect sense if we refer to it as the 'transmission-line extension effect'.

If a wire is attached to one end of a coil; the fundamental scattering resonance frequency drops. The response also becomes less pronounced until the wire is long-enough, or any counterpoise to which the wire leads is large enough, to reduce the resonance frequency to roughly half its original value. It does not particularly matter how the auxiliary conductor is arranged (presuming that we are not trying to maximise radiation resistance), because what is happening is that its electrical length is being added to the electrical length of the coil. In antenna theory, this is known as the 'ground-plane mirror effect', i.e., adding a sufficiently-large counterpoise doubles the effective length of the antenna. This effect, incidentally, was noticed by Drude in 1902, when he added spherical electrodes to one end of an otherwise free coil. He attributed the effect to the shift in the voltage node and found that the SRF reduction could never be more than half its original value.

The original half-wave conductor-length resonance is nevertheless still present, it is just that it can no longer be strongly excited by scattering radiation from the coil (there is no-longer a sharp impedance discontintinuity at the grounded end). To see the original resonance, it is now necessary to measure the impedance by direct connection across the two ends of the coil. There is, of course, a line-extension effect due to connecting the coil to a circuit, and stray capacitance is added, but the direct-connection effect is much less pronounced than the ground-mirror effect. Note incidentally, that because the λ/2 wire-length resonance is the one relevant to the circuit-applications of coils, it is the theory of this (λ/2) resonance that lies behind the theory of self-capacitance prediction for the purpose of lumped-element analysis.