[TowerTalk] tower resonances

[jimlux]

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.