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*To*: tesla@xxxxxxxxxx*Subject*: Overtones and velocity factors*From*: "Tesla list" <tesla@xxxxxxxxxx>*Date*: Sun, 21 May 2006 15:25:03 -0600*Delivered-to*: testla@xxxxxxxxxx*Delivered-to*: tesla@xxxxxxxxxx*Old-return-path*: <vardan01@xxxxxxxxxxxxxxxxxxxxxxx>*Resent-date*: Sun, 21 May 2006 15:10:51 -0600 (MDT)*Resent-from*: tesla@xxxxxxxxxx*Resent-message-id*: <DWt9cgS4wmN.A.5vH.bdNcEB@chip1>*Resent-sender*: tesla-request@xxxxxxxxxx

Original poster: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx> Gerry wrote (in another thread): > about tfss270501 and md110701 spectral graphs. It appears > the first overtone is close to a 3rd harmonic frequency > (but not quite) and higher overtones seem to be noticably > lower in frequency than the 5th and 7th harmonics. Is it > true that the spectral graphs are not harmonic in nature?? True. For example here are the resonant frequencies of an unloaded coil (one of Terry's, h/d=2.92) Freq Mode Ratio 148.4kHz 1/4 wave 1.0 353.4kHz 3/4 wave 2.38 513.8kHz 5/4 wave 3.46 666.4kHz 7/4 wave 4.49 819.8kHz 9/4 wave 5.52 977.4kHz 11/4 wave 6.59 1133.1kHz 13/4 wave 7.64 As you can see, the mode frequency ratios are less than the quarter wave count. When the coil is loaded with a typical topload things change a bit, Freq Mode Ratio 97.9kHz 1/4 wave 1.0 321.4kHz 3/4 wave 3.28 490.2kHz 5/4 wave 5.0 The 1/4 wave is pulled down by a greater factor than the higher modes. There's a particular value of top C that will make the 3/4 wave exactly 3 times the fundamental - that may or may not be a good thing for a square wave drive signal. Just by luck, this example has just the right topload to make the 5/4 overtone match the 5th harmonic. I'll just say a bit about propagation velocity with respect to wire length. For the above coil, unloaded, 817 metres of wire, we have Freq Mode Overall wire velocity factor 148.4kHz 1/4 wave 1.62 353.4kHz 3/4 wave 1.28 513.8kHz 5/4 wave 1.12 666.4kHz 7/4 wave 1.04 819.8kHz 9/4 wave 0.99 977.4kHz 11/4 wave 0.97 1133.1kHz 13/4 wave 0.95 in which the velocity factor is given by 817/n * 4 * Fres/c, where n is the number of 1/4 waves in the resonance and c is the fundamental constant 300e6. Here are the figures for a coil h/d = 4.66, with 2078 metres of wire. Freq Mode Overall wire velocity factor 61.9kHz 1/4 wave 1.72 157.9kHz 3/4 wave 1.46 229.7kHz 5/4 wave 1.27 294.4kHz 7/4 wave 1.17 355.6kHz 9/4 wave 1.09 These are typical patterns, with the velocity tending towards something below c as the in-coil wavelength becomes shorter. If the velocity factor was the same for all frequencies, you would get harmonic overtones, but you can see that instead we have a lot of dispersion. This dispersion originates in the long range 'longitudinal' coupling, ie mutual L and C between remote regions of the coil. Long range coupling becomes less effective at high frequencies. The distributed mutual reactances are the same of course, but because the coil is now carrying several or many quarter wave sections, the L & C coupling to a point on the coil from some remote turn is, on average, balanced by an equal but opposite coupling from another turn at a similar range somewhere else. The longitudinal coupling becomes dominated by reactance just with neighbouring turns, h/d has less of an influence on velocity, and the winding pitch becomes more of a significant factor, eventually being dominated by the direct turn-turn coupling. I've no idea what the limiting velocity factor is or how to calculate it, but I've seen research on the topic which involves using tridiagonal matrices to represent the periodic coupling between adjacent turns. At even higher frequencies the voltage around a turn is no longer uniform and we start to get an E-field component acting across the diameter of the coil - a component which can rotate at the signal frequency. The result is circularly polarised EM waves travelling along the coil and being radiated with reasonable efficiency, beaming along the axis. In this realm the pitch and circumference become the main determining factors of the resonant modes of the structure. Bart wrote (in another thread): > I started building a Seibt Coil myself, but I have yet to > finish it. Those Seibt coils might be good ones to use for examining propagation of the various modes. > I have everything except the high voltages. High voltages - who needs 'em :) Measurements are more rewarding in the long run. Making sparks - Bah! Hope you can measure some resonant frequencies and the associated in-coil wavelengths to demonstrate the above. -- Paul Nicholson --

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