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
It's a bit tricky.. If the line matches the source (or the load), so
there's only a mismatch at one end, then the phase error will be equal to
the length error, because the matched (at one end) line just moves the
reference plane. So, what we're really talking about is a line which is
mismatched at both ends.
In this case, you have a wave that's reflected from one end, travels back
towards the source, then is reflected again, travelling towards the load,
where it sums with the original forward wave.
The worst case (in a phase error sense) would be if the line were 1/8
wavelength long, because the twice reflected wave would be arrive 90
degrees out of phase with the direct wave, which would result in the
largest angular change.
So this says that phase errors due to mismatch are worst when the total
phase of the mismatches and twice the transmission line length is an odd
multiple of 45 degrees. If the mismatches were resistive (so the phase of
the reflected wave is 180 degrees out), then this corresponds to the 1/8th
wavelength line.
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...
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