But using that "simplification", 1/2 wave repeats terminal impedance, allows
one to ignore line matching entirely.

It could be balanced lines of 2,000 ohms, or coax of 5 ohms, both of these
according to the simplification work the same as long as they are 1/2 wave.
Additionally, it could be zip cord, or wires just strung about, as the
impedance of the feed line is not used in the simplification, and can be
modeled by a transmission like of Z ohms.

Checkout "Reference Data for Radio Engineers", Transmission lines, Mismatch
and Transducer losses. There are formulas there for this case. The
simplification ignores the mismatches at the Tx and Antenna to the line,
which causes about 4.43 dB additional "mismatch" loss, in the case of
50,450, 50. This shows up as VSWR. For a 2000 ohm line, the mismatch loss
is 10.2 dB. Some of that loss is tuned out if you have an antenna tuner.

The simplification is valid only for 50 ohm lines, or near 50 ohms, perhaps
along the way that part got dropped.
(and also because of antenna tuners, Tx out is not 50 ohms, and Antennas are
not 50 ohms)


"Richard Harrison" wrote in message
...
John Smith wrote:
"Actually not."

Actually so.

The input impedance of a 1/2-wave section of dissipationless line is a
repeat of its terminal impedance. The 50-ohm terminal impedance will be
repeated as the input impedance at the sending end of the 450-ohm line.
Likewise, the 50-ohm impedance connected to the sending end of the of
the 450-ohm line will be repeated at the output end of the 459-ohm line.
Cecil`s example is symmetrical. There are no lossless lines but
practical lines are close enough.

Best regards, Richard Harrison, KB5WZI