[TowerTalk] tower resonances

[Michael Tope]

jimlux wrote:

>Richard (Rick) Karlquist wrote:
>  
>
>>jimlux wrote:
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>>>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
>>
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>
>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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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......