> As I mentioned earlier, I have a method to make those measurements but it's
> not practical for most hams. That's why I've been asking if anyone else has
> a less complex solution to this kind of measurement.
> 73, Rudy N6LF
Forrest Gehrke K2BT wrote a 6-part series in Ham Radio in 1983 / 1984 on phased
vertical antennas. He came up with a technique to derive the Z-parameter matrix
(self and mutual impedances 2-port matrix) without using a VNA. (If you can
measure the complete S-parameter matrix between verticals using a VNA, it's
easily converted to the Z-parameters [and vice-versa]).
His method is described in Part 3 - July 1983 issue (pg 26-34) and works for
element lengths of 1/4 wave or less. If they're longer you need to come up with
a different way to decouple the elements.
1. Start with element 1. Open-circuit all the other verticals except the pne
being measured. Open-circuited quarter-wave vertical couples weakly. Measure
the self-impedance of the excited antenna element. This provides Z11 for that
antenna. Iterate for all antenna elements (providing Z11 for each).
2. Short element 2 to ground. Measure driving point impedance of element 1.
Open-circuit element 2, short-element 3 and measure driving point impedance of
element 1. this gives Z12, Z13, and Z14 for example. Repeat for all elements.
This gives a table of measured values. For example for a 4-element array, four
measurements at element 1, four measurrments at element 2, etc. - 16 total
measurements. A passive antenna will give a symmetric Z-matrix, so the above
table has duplicated measurements which can be used to check for consistency.
Forrest was always amazed at how closely symmetric the values ended up being
after his measurements.
Extract the 2-port values for each element pair. (Z11, Z21, Z12, Z22).
For element 1 and element 2, the math is:
Z1 = E1/I1 = Z11 - (Z12)^2/Z22. This is driving point impedance of element 1
with element 2 grounded.
Then Z12 = +or- SQRT(Z22) (Z11 - Z1). You need to pick the correct root, but
it's usually pretty easy to guess.
My personal hunch would be that if there is spurious coupling from a tower or
other wire, then the Z-matricies would become non-symmetric.
-- Tom, N5EG
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