|First, some basic
transmission line theory:
If a line of characteristic impedance Zo is terminated in a purely resistive load that is not equal to Zo, at a frequency where the line is a quarter wave long, the impedance seen at the other end will also be purely resistive - though it's value will have been changed. If the load resistance is lower than Zo, the input resistance will be higher than Zo by the same amount (and vica verca), as the table opposite shows. In other words, the transform see-saws about Zo.
Putting two lines of equal Zo (and length) in parallel, produces a combination that is equivelent to a single line of characteristic impedence Zo/2. This is easy to demonstrate by considering the two lines as seperate circuits, with their own terminations, determining their individual transforms, then paralleling them and again considering the new overall transform.
|So using paralleled 50 ohm
lines will provide the transform possibilities shown in
the table to the left. Only the transforms reducing 50
ohms downward are tabulated, since for this application
and with current devices (usually FETs of one sort or
another) at VHF/UHF, the transform required will always be
to something less than 50 ohms for peak powers of 5 watts
So far, only pure resistive transforms have been considered, yet mixed reactive/resistive device impedances will be met in reality, and the reactive part will have to be taken into account. This can be done in practice by considering what happens if a line of less than a quarter wave is considered:
|Some ptfe cable with a Zo
of 28 ohms was available (a story in its own right) and a
resistive potentiomer was soldered across one end and
adjusted until 50 ohms was seen at the open end. The pot
value was measured and plotted below for various
percentage lengths of line relative the quarter wave
length. For all of the shortened lines, a trimmer
capacitor was used in place of the fixed capacitor
previously mentioned and varied until the purely 50 ohm
input condition was obtained.
As can be seen, the transform remains reasonably constant.