Tom McDermott wrote:
>> 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.
>
>
<snip>
>
> 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.
>
>
That method's in the antenna book or ON4UN as well. It's a variant of
the technique for measuring the Y matrix of an arbitrary network, or,
for that matter, measuring the parameters of a power transformer
(measure with secondary open, measure with secondary shorted, etc.)
The real problem is that measurement uncertainty in the raw measurements
(feedpoint Z) combined with the arithmetic to create the matrix leads to
huge uncertainties in the resulting matrix values. I'd have to go back
to my notes of a few years ago to figure out exactly why, but it boils
down to the thing of uncertainty of (1/x) is large in an absolute sense
when the value of x is <<1, even if the relative uncertainty is small.
Not quite numerical illconditioning, but the same sort of thing.
Most of the matrices I've done from actual measurements (by me, or
gleaned from others) have been asymmetric to a certain extent (that is,
Z23 != Z32), but it's mostly due to measurement and arithmetic problems.
That is, if you have a 3 element array, you'd expect a matrix like
Z11 Z12 Z13
Z21 Z22 Z23
Z31 Z32 Z33
where Z21=Z12, Z13=Z31, Z32=Z23
But you don't get that.
Rather than rigorously compute uncertainties in the Zs given the
measurement uncertainties (preferring to leave that to the VNA
calibration designer folks who write books on it), I ran some monte
carlo style analysis putting in random errors and grinding the matrixes
(matlab makes this easy).. Yep, smallish errors in the Zmeasured makes
for serious asymmetry.
This is with using things like a MFJ-259/269 type impedance measuring
box. A nice VNA (like Tom's) has MUCH better measurement uncertainty.
Especially if you take the data from a swept frequency measurement and
use it to fit a model (for instance, over a small frequency band, a
dipole has a LCR type impedance characteristic, so you can take a bunch
of measurements over a band, and curve fit them to the LCR characteristic)
Interestingly, if you take measurement uncertainty out of the picture,
the matrix will be symmetric, even if there is something perturbing it.
The matrix won't be what you'd expect from modeling (the unperturbed
array), though.
But even assuming you can measure the Z or Y matrix, all that lets you
do is synthesize the networks to get the element currents right. But,
if there's an interaction with something else, then that "interacting
thing" has currents, so it perturbs the pattern.
What you really need is some way to actually measure the EM fields
in-situ to see if they match expectation. That's why I'm thinking the
small probe scheme might work. With small probes, you get close to
"idealized isotropic radiators" so the probe effects are small.
Jim
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