W4EF writes: My suspicion is that some taper does occur in air wound loading coils at > HF frequencies, but that the amount of taper doesn't follow the simple > rule that it equals the amount of taper that would occur in the length > of straight radiator replaced by the inductor. I think the degree of > taper depends on the velocity of EM wave propagation through the coil > and to some extent on the amplitude and phase of the displacement > current from the inductor to ground (It wouldn't surprise me if there is > an interdependence between the EM wave velocity and the magnitude and/or > phase of the displacement current). These two quantities are probably a > function of the length and form factor of the inductor.
Yep, and I think this issue is quite interesting. There's this paper by Corum and Corum, Reference [1] on ON4AA's inductor calculator page, that attempts to quantify the physical form-factor dependence of EM propagation characteristics on a helix. ON4AA's page is here, with some good information on the topic: http://hamwaves.com/antennas/inductance.html ON4AA's calculator uses the formulas of the aforementioned paper (among others) to make some non-trivial predictions about how coils behave. I would like to test these specific predictions quantitatively. > That said, it > would not surprise me in the least that for inductors that are > physically small relative to the overall radiator length, the amount of > current taper across the length of the inductor is negligible (i.e. > current at the top and current at the bottom are for all practical > purposes the same). I could be wrong, of course. That I will readily > concede. > If the Corum sheath-helix model is a good description of what's going on, the velocity factor of these coils can be surprisingly low in some cases. The #18AWG 10 turn per inch, 2 inch diameter miniductor that was the subject of much scrutiny should have a velocity factor around 4% at 3.8MHz. The coil modes can therefore have very short spatial wavelengths, changing things a lot over the length of the coil. According to the model, a coil shows a lot of dispersion and the characteristic impedance of propagating fields is very high (thousands of ohms) so measuring the "velocity factor" is considerably more difficult than it would be for a chunk of ordinary transmission line. To act as a simple delay line, the coil must be terminated in its characteristic impedance, which is itself a strong function of frequency. ON4AA's calculator makes the model pretty accessible, giving the characteristic impedance and the axial propagation factor Beta with fields going like E = E0*exp(i*Beta*z), with "z" the distance along the coil. The coil mode wavelength is lambda = 2*pi / Beta. It's about 3.5 meters for the coil mentioned above. I've used some rather skeptical language above ("if the model is correct, according to the model," etc.) This is not because I think the Corums' model or ON4AA's implementation and incorporation of extensions (like some of G3YNH's work: http://www.g3ynh.info/zdocs/magnetics/part_1.html) are wrong. It's simply because I haven't verified the calculation in detail nor have I been able to test the predictions to my satisfaction. I think the models have predictive power and I think quantifying current taper is potentially one of those things. But any observed current taper depends BOTH on coil mode effects and on external influences, including the antenna particulars. I think it would be most useful for the community if we can focus some testing on specific predictions from proposed mechanisms for current taper. There are a lot of possibilities, some of which are inherent to the coil and antenna setup, and some of which are plausibly dominated by measurement perturbations. I'm particularly interested in this sheath helix model for propagation on a coil. There are several rather non-trivial things it predicts. One important one is the sequence of successive coil resonances. In some sense (one that may make a certain Texan a bit unhappy with the language I'm using), the model is intended to be a self-consistent wave description of the "self-capacitance" or "inter-turn" capacitance of the coil. The coil is linked together in a complex way by the electromagnetic field around it... so you can't just draw in little fixed capacitors in between adjacent turns. But the electric field is always there when there's a time varying magnetic field. The sheath helix model is **not** only valid near self-resonance, but self-resonances are one of the easier ways to test the model. I have not yet had satisfactory results in this area, but I haven't even come close to doing anything I would consider conclusive. I've just dabbled with a couple ideas while thinking about other ways to test. I think this is a really interesting problem. I don't generally make much noise about it because it will take a lot of work on my part to convince myself one way or the other about what's happening (pure slow coil modes. vs. pure external perturbations vs. BOTH or "other"), and I have seen many discussions go sour. So mostly I stay out of it, because I don't feel like I have much meat to contribute. But I think some of this is news to some people, and it seems worth mentioning the possibility that there's rather slow EM propagation on some "typical" coils. I think it's funny and a little telling that the best piece of experimental evidence I can find that the sheath helix predictions work is on a page purporting to show the absence of such effects. But that's a story for another time, **after** I know that it's possible to reproduce the result I think I see there. K2AV says: If two responsible experimenters get opposite results in what on > surface are identical experiments, THERE IS A REASON, which means > THERE IS AN OPPORTUNITY TO DISCOVER AND ADVANCE That's exactly how I feel about it. It seems that a couple other parties, (not yet present here), feel strongly like they need to protect the ham community from the dangers of wrong thinking instead. Real, useful skepticism requires thinking the wrong thing and the right thing simultaneously for a long time while you're testing or digesting the results of tests. 73 Dan _______________________________________________ UR RST IS ... ... ..9 QSB QSB - hw? BK
