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