[Elecraft] : Resonance

[Stephen W. Kercel]

Don:

Regarding the complex impedance of an antenna at the end point, you 
raise some interesting questions.

I was always of the impression that the definition of resonance of a 
half wave radiator is the condition in which the current at the center 
is a maximum and the current at the ends is at zero. The current 
distribution in a half wave antenna is analogous to the displacement of 
a violin string, which when vibrating at resonance has zero displacement 
at the ends and maximum displacement at the center. (Such a resonance is 
easily detected with a grid dip meter, even if no feedline at all is 
connected to the radiator. Admittedly, the feedpoint would need to be 
shorted. Sweeping the grid dip meter through a range of frequencies is 
analogous to the broadband energy in the "pluck" on the violin string. 
In either case (assuming very high Q), only the energy at the resonant 
frequency actually gets coupled into the device.)

In the case of center fed half wave element, a zero value of imaginary 
component of impedance at a center feed point is a coincidental 
indication of antenna resonance rather than the definition of antenna 
resonance; it is used by amateurs because it is easy to measure, whereas 
the current distribution is almost impossible to measure directly.

If you run the "BY dipole" simulation on EZNEC at a frequency and 
radiator length for which the center feedpoint impedance is pure 
resistance, and then move the feedpoint around, the radiation pattern 
comes out just the same (within the limits of computational error) 
regardless of the feedpoint location. Also, the magnitude of the current 
distribution remains about the same, big in the center and approaching 
zero at the ends. Thus, my sense is that by the analogy to the violin 
string, the antenna is resonant at that length for that frequency 
irrespective of the feedpoint location, or the fact that the feedpoint 
impedance is complex.

Admittedly, that much of the discussion is literally academic, depending 
on how we define resonance.

However, you raise another question that is more practical than 
academic. You make the perfectly reasonable point that if I play around 
with the radiator length, I should find a length that has an end 
feedpoint impedance of some big value of R plus J0. I am sure you can do 
that, but my question to you is, what is the advantage to doing so? 
(Note: This is not intended as a smart aleck comment. If there is some 
advantage easily obtained by tweaking the radiator length, I'd really 
like to know what it is.) I do not expect that minimizing radiation from 
the transmission line is one of those advantages. Changing the radiator 
length such that you move away from the length that gives "violin string 
resonance" would make the current distribution on the radiator more 
asymmetrical and would increase the probability of feed line radiation.

This line of reasoning got me curious about something else. Elecraft 
rigs are usually rated as being able to operate normally for any load 
that has an SWR of 2 or less compared to a characteristic impedance of 
50+J0. Am I correct in assuming that that means that the rig expected to 
be able to operate normally into any complex load on or inside the SWR = 
2 circle on the Smith Chart?

Why that matters is the following. Using a high impedance quarter wave 
(approximately) transformer to Zepp feed a half wave radiator, it is 
relatively straightforward to tweak the transformer length such that the 
subsequent 50 Ohm coax has an SWR well inside the SWR = 2 circle. If so, 
the Elecraft rig should be perfectly happy, even if I seldom if ever 
actually find an impedance with a zero imaginary component.

Have I missed something in my thinking? (It would not be the first time.)

TNX & 73,

Steve Kercel
AA4AK