 TX to Ae Magnetics Self resonance -

 The Calibration of Wave-Meters for Radio-Telegraphy, by G W O Howe. Proceedings of the Physical Society of London, Vol 24, issue 1, 1st Dec. 1911*, p251-259. * The Journal is dated 1911, but the paper is headed "Read May 31 1912". Hence it is often cited with 1912 as the date. A wavemeter, consisting of a coil, a variable air capacitor, and a resonance indicator such as a gas-discharge tube or an ammeter, can be calibrated approximately by calculation if the inductance and capacitance are known. The inductance can be made independent of frequency by use of thin or stranded wire, and the air dielectric ensures that the capacitance is independent of frequency. A source of error however is the capacitance between neighbouring portions of the coil. Even when the capacitor is removed, the coil has a definite natural frequency, the ends acting as the plates of a capacitor and the central portion as an inductance, the two functions being distributed over the coil. Drude 1902 implies the existence of an equivalent circuit comprising an effective inductance and an effective self-capacitance. Drude assumes that the effective inductance is 2/π × total inductance, but it is shown that for practical purposes, the effective inductance is the same as the total inductance. If the self-capacitance calculated from the natural frequency on this basis is added to the capacitance of the variable capacitor, the remaining error in the wavemeter calibration is reduced to < 1%. A plot of the square of the self-resonant wavelength vs. parallel capacitance is a straight line that is offset by an amount equal to the self-capacitance. Thus the self-capacitance can be measured by resonating the coil against a series of known capacitances and extrapolating. Note: Howe correctly establishes that the effective inductance for the self-capacitance determination is the same as the uniform-current inductance. Drude's inductance factor of 2/π is not supported empirically. This observation however leads to a long-standing fallacy; which is due to the fact that the extrapolation measurement is made with the coil always terminated by a capacitor, the effect of which is to render the current distribution substantially uniform. It is not difficult to show that the true self-resonance frequency (SRF) of a coil is not the same as that predicted by the combination of uniform current inductance and self capacitance, but the discrepancy is later attributed to poor measurement technique by Willis Jackson. Investigators then continue to attempt to fit free-coil and extrapolated resonance measurements to the same model for many years. The issue is resolved in self-resonance and self capacitance of solenoids.  The self-capacitance of single-layer coils, W Jackson. Phil. Mag. Ser. 7, Vol. 19, 128, April 1935, p823-835. TX to Ae Magnetics Self resonance -