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Antenna design question
In message , Dave Platt
writes In article , Ian Jackson wrote: I would have thought that the feed impedance of a dipole at a wide range of frequencies/lengths (ie 'very short' to 'very long') would have been fairly typical rule-of-thumb required information for those interested in antennas. However, it does not seem to be! Oh... if rule-of-thumb is good enough for your needs, then it's not too difficult to summarize. There's a nice chart on page 2-3 of the ARRL Antenna Book. You should consider the resistive, and reactive portions of the feedpoint impedance separately. The resistive part rises from zero, up through a nominal 50 ohms or so at resonance (just under 1/2 wavelength), up to several thousand ohms at second (or anti-) resonance. If you plot the impedance-vs.- resistance relationship with the doublet length on a linear scale and the resistance on a logarithmic scale, it's not too far from being a straight line through much of this range. Between second and third resonance, the resistance drops back down to around 100 ohms... between third and fourth, up to several thousand ohms again, and so forth. As the doublet continues to get longer, the feedpoint resistance oscillates between low (odd-resonant) and high (even- or anti-resonant) values, with the oscillation becoming less and less as the doublet gets longer (think of a damped sine wave). In theory it'll eventually settle down to 377 ohms. The reactive portion of the impedance also oscillates as the doublet gets longer and longer. Between an even-numbered and odd-numbered resonance it's capacitive, dropping from thousands of ohms of negative reactance, to zero at the odd resonance. It then becomes inductive, rising to several thousand ohms just before the next even (anti-) resonant length is reached. As the even-numbered resonance length is passed it falls abruptly from very positive (inductive) to very negative (capacitive), and then begins to return slowly to zero at the next odd resonance. These excursions from positive (inductive) to negative (capacitive) continue, and also fall in their absolute value as the doublet gets longer and longer. Once the doublet is "sufficiently long" its reactance pretty much vanishes and it looks like a 377-ohm resistance. Near the resonant lengths, the value of the reactance is changing rather more rapidly than the value of the resistance. The same basic principles apply fairly well to doublets that aren't in free space, but ground reflections, mutual coupling with other antenna elements, etc. have a big effect on the actual values. Few of us have the luxury of stringing up an 80-meter longwire doublet in free space, alas :-) Yes, rule-of-thumb is more than good enough for me! I has a sneaky feeling that the feed impedance would end up at 377 ohms (impedance of free space). Many years ago, from some tables compiled by one of the many Wu's involved with antenna theory and design, I plotted Zin vs antenna length on a Smith chart. As the spiral progressively wound its way inwards with increasing antenna length, it seemed that it was heading for something between 200 and 600 ohms, so I thought to myself, "377 ohms?" Unfortunately, the table stopped when the antenna was about 5 wavelengths. I haven't seen similar tables since. -- Ian |
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