[TowerTalk] Matched "Bury Flex" cables

[Jim Lux]

At 11:56 AM 7/14/2005, Jim Lux wrote:
>At 11:23 AM 7/14/2005, Tom Rauch wrote:
>
> >Unless I'm mistaken, the peak phase error caused by a line
> >mismatch occurs when the line is an odd multiple of 1/8th
> >wavelength. Phase error is zero at any multiple of 1/4 wl,
> >even or odd.
> >
> >Correct me if that is wrong, but it seems I recall that from
> >past phase analysis.
> >
> >73 Tom
>
>However, if the mismatch is reactive (i.e. the reflection coefficient is
>complex), you'd have to take that into account too. Since reactive
>mismatches are probably as common as resistive ones (if not more so), it
>bears a bit more computation.
>
>Then, the real question isn't what length of coax is the worst from a
>mismatch induced phase error standpoint, but what's the phase error impact
>of a length error, as a function of the transmission line length.  Is a 1
>inch error the same number of degrees for all line lengths?  I think not,
>but off hand, I don't know where it's worst.
>
>Standby for some data...

Turns out that there's a worst length, given a particular phase of 
mismatch, but that if you don't know the mismatch phase, and you assume 
they're all equally likely, then all lengths are the same.  That is, the 
average phase error is the same, for the same physical length error... Note 
well... this is a statistical thing.. For a given situation, there are 
always better and worse errors.

If you have a reactive mismatch, such that the reflection coefficients is 
90 degrees leading or lagging, then the worst case phase error is when the 
line is either 1/4 wavelength or 1/2 wavelength long (depending on if the 
two phases are in the same direction or not).


Interestingly, for small mismatches (say 2:1 or better or maybe even 3:1 or 
better), the length which results in the largest phase error is 
approximately 45 degrees from the length that results in the largest 
amplitude error.  In the resistive case.. odd multiples of 1/8 wavelength 
have most phase error, even multiples of 1/8th wavelength have most 
amplitude error.