jimlux wrote:
>Richard (Rick) Karlquist wrote:
>
>
>>jimlux wrote:
>>
>>
>>
>>>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.
>>>
>>>
>>The true z-matrix will always be symmetric if the network is reciprocal.
>>All passive networks (not containing ferrite circulators) are
>>reciprocal. Therefore, matrix symmetry will not tell you
>>anything about whether a tower is radiating. It is, however, a check on
>>the accuracy of the measurements.
>>
>>Rick N6RK
>>
>>
>>
>
>So we can say, matrix asymmetry is ALL due to measurement and arithmetic
>problems.
>
>Hmm.. And this leads to something I was fooling with a while ago.
>Because you know the physical system has a symmetric matrix, the
>computed Z12 and Z21 are both estimates of the same parameter. I don't
>think, though, that you can just average them, at least not in the
>general case.
>_______________________________________________
>
>
>
>
If there is no unintentional mutual coupling to nearby structures and
assuming that the array elements are identical, then you should get Z11
= Z22 = Z33 to within measurement error. If you've got a nearby tower
interacting with the array, then I would expect to see differences in
Z11, Z22, and Z33 (again this assumes that Z11, Z22, and Z33 are
mechanical identical).
73, Mike W4EF......
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