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Resonant condition
Richard Fry wrote:
Could you please explain why, if the same fundamental equations given in antenna engineering textbooks and I.R.E. papers are used by modeling programs, the results of their use do not always support each other very well? I'm not aware of any cases where engineering textbooks and papers disagree with modeling programs. NEC, for example, has been very extensively tested against both theory and measurement. If there are cases where the programs seem to disagree with theory, it's very likely due to careless modeling resulting in a model which isn't the same as the textbook model. Can you cite an example of disagreement between computer model and textbook theory? If it is accepted that the radiation resistance of a short monopole is independent of the loss resistance in the loading coil and r-f ground either alone or together, then what is the basis for the variation in radiation resistance that you report? It is indeed accepted that the radiation resistance of a monopole over a perfect ground of infinite extent has the characteristics you ascribe, and computer models show this independence as they should. (I haven't yet received your model which you feel seems to show differently.) But it's neither true nor "accepted" when the ground system is much less than perfect. The variation is due to interaction between the vertical and ground system, just as the radiation resistance of a VHF ground plane antenna changes as you bend the radials downward. Altering the number, length, depth, and orientation of radials has more of an effect than simply adding loss. BTW, the equations in the Carl Smith paper I referred to earlier in this thread produce a radiation resistance of 0.113 ohms for a 1.65 MHz, 9.84' (3-m) x 0.25" OD, base driven monopole -- which is not _hugely_ different than the values calculated by EZNEC. EZNEC gives a result of 0.1095 ohm with 20 segments, converging to around 0.103 ohms with many more segments. Keep in mind that the model source position moves closer to the base as the number of segments increases. The author's result is good. If you examine the paper carefully, I'm sure you'll find that the author had to make some assumptions and approximations to arrive at his equations -- the most fundamental equations can't be solved in closed form, and many, many papers and several books were written describing various approximations to calculate something as basic as the input impedance of an arbitrary length dipole. If you do some research, you'll find that the many different approximating methods all give slightly different results. The small disagreement in the cited paper is really a measure of how good his approximations were. Modeling programs have to use numerical methods which are limited by quantization, but they have the advantage of not needing the various approximation methods required for calculation by other means. Roy Lewallen, W7EL |
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