Topband: Impedance matching on transmission lines
MorgusMagnificen@aol.com
MorgusMagnificen at aol.com
Fri Dec 2 13:15:38 EST 2005
A lot of these questions have troubled generations of hams. In an article in
an upcoming issue of QEX I have some explanations which should resolve most of
the mysteries. In short, the reason that searches for an explanation, of why
impedance matched lines are more efficient, always end up being puzzling is
that it is NOT true. More precisely, it is approximately true that matching does
not affect efficiency. In real lines, which have small but real loss, there
is power loss due to both the standing wave and the travelling (forward) wave.
But for good lines and low SWR the difference is minute. An unmatched line
will have some reactance at its input but a conjugate match will null it out and
power will still flow with only the line loss to inhibit it. You could feed a
300ohm antenna at 1.8MHZ with 3"Heliax and have negligible line loss!
The more basic question, which my article fully answers, is why lines have an
impedance at all, which has a quite simple explanation. The line possesses
series inductance and shunt capacitance, which are typically reckoned on a
per-unit-length basis. The inductance results in a specific voltage drop per ampere
(V=LdI/dT) and the capacitance produces a specific shunt current per volt of
line voltage (I=CdV/dT). The values of L and C are uniquely fixed by the
geometry and material parameters, and the result is a fixed relationship between V
and I (i.e. an Impedance Z0) for a sine wave of current or voltage travelling
in either direction. For either of these waves the ratio is fixed and can only
have the value Z0, but two independent waves can flow simultaneously , which
allows the net line impedance (V/I) to take on any value. In other words,
bi-directional waves allow power flow to ANY value of load impedance, with the
caveat that for large mismatches and large line resistance, some additional power
will be lost by the reverse wave as it carries reflected power back to the
source.
73 and keep those lines matched,
Eric von Valtier K8LV
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