



Article:
Drude1902_eng.pdf
. Cite as: arXiv:1605.04196 + Graph of f vs. h/2r : Drude1902_plate1.gif . + Supplementary calculations (Open Document spreadsheet): Drude1902_Teslatrans_calcs.ods see also: Original German article: https://archive.org/details/Drude1902Testlatrans (this link gives access to a pdf file containing parts I & II and plate 1). Given here is an English translation of P K L Drude's 1902 investigation into the factors affecting the selfresonant behaviour of singlelayer coils. This work, largely ignored by the Englishspeaking world in the secondhalf of the 20th Century, is one of the earliest detailed studies of the phenomenon of selfresonance, and it marks the point at which the dependence of the fundamental selfresonant halfwavelength on the coil conductor length was established. Drude's experimental method was that of exciting coils by means of an induction loop with a variable resonating capacitor, this circuit being energised by an induction coil and a Tesla transformer with both primary and secondary spark gaps. Resonance of the coil under investigation was detected by holding an electrodeless sodiumvapour discharge tube near to the coil. Accurate frequency measurement was not possible at the time, but wavelength calibration to somewhat better than 1% was achieved by removing the coil and using the loop to excite a parallelwire transmission line with a moveable shorting strap, resonance being detected by placing the discharge tube at the voltage antinode. The selfresonance period of a coil was found to increase with the dielectric constant of the core material; but this was less than proportional to the square root of the dielectric constant (as would be the case for immersion in a homogeneous medium). The dielectric effect of the core was also greater as the height to diameter ratio is reduced, because of the increasing density of electric field lines on the inside of the coil. Hollow cylinders had less effect than solid cylinders. Wire insulation was also found to increase the selfresonance period, and the effect again increased as the height to diameter ratio was reduced. Coils were characterised by means of a function f , which is defined as the ratio of the selfresonant halfwavelength to the wire length^{[1]}. Excluding dielectric effects, f is primarily dependent on the coil height to diameter ratio (h/2r), its value being large when h/2r is small. The effect of the pitch to wirediameter ratio (g/δ) is relatively small, and the number of turns has little effect provided that there are more than 1. A graph of experimental values of f vs. h/2r , for coils on ebonite cores (ε = 2.79) and for coreless coils, is given in Plate 1 (see also the spreadsheet). In accounting for the relationship between coil parameters and selfresonance, Drude noted that when a current is induced in a disconnected longthin coil, the current will be at its maximum in the middle region and zero at the ends^{[2]}. This causes electric charge to migrate towards the coil ends, inducing a potential difference. If the resulting charge displacement is considered to be localised on two squat cylinders located at the ends of the coil, the capacitance can be calculated in terms of spherical harmonics. The resulting calculated value of f was within 5% of the observed over an h/2r range from about 2.2 to 1.0. Overtone resonances were also investigated, the node positions being located using the sodiumvapour discharge tube. It was found that overtones are not harmonically related to the fundamental resonance. Drude argued that when a coil is oscillating at its first overtone, the fact that it does not behave as two separate coils is due to the strong magnetic coupling between the two halves. When capacitance is added to a coil, such as by the addition of a conducting sphere at one end, the period of oscillation is increased, but never more than doubled. To a modern reader, this is obviously related to the groundplane effect. Drude was able to quantify the change of oscillation period by considering the resulting shift in the voltage node. In part II, Drude overcame the difficulty of calculating highfrequency inductance (i.e., the reduction due to skin effect and nonuniform current distribution) by placing fixed capacitances in parallel with coils and loops and making resonance measurements. Notes: [1] The quantity f is defined so that its value is 1 for an isolated thin straight wire. [2] An inductance factor of 2/π is introduced to account for the nonuniform current distribution. See discussion by Sederberg & McGuyer 2013 / 2015: "Translation of an article by Paul Drude in 1904." arXiv:1303.1588, section 4.5. 



