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.
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