Radar System Engineering

SEC.11.2] COAXIAL LINES 393
Why a Matched Line?—The fraction of the incident power reflected
to the source from a section of transmission line of given VSWR is
Power reflection coefficient =
[(VSWR) – 1]’
[(VSWR) + 1]2
(3)
For the usual upper design limit of VSWR = 1.5, it is seen that the power
reflection loss is only 4 per cent, or 0.3 db, surely not serious. In highpower
systems or unpressurized airborne systems, where line breakdown
is a possibility, the strain is of course higher for a high VSWR. A ratio
of 1.5 means that for a given breakdown gradient, 33 per cent less power
can be delivered to the load than could be delivered in a matched load.
This can be a limitation.
The strongest requirement for a well-matched line arises from the
properties of the magnetron. Like all self-excited oscillators, the magnetron
exhibits an output frequency and a stability dependent upon the
load into which it works. A mismatched line represents a resistance
lower than 20 at voltage minimum, and higher than ZO at voltage maximum.
At other phases it has a reactive component which maybe either
positive or negative. As explained in Chap. 10, magnetrons are in general
designed to be stable against a VS WR of 1.5 in any phase. This is
the origin of the commonly specified upper limit for mismatch.
There is a further limitation if the mismatch occurs at the end of a
long line-for example 50 to 100 wavelengths from the magnetron. Then
as the frequency changes the number of wavelengths in the line changes,
and so also does the phase of the standing wave. The line impedance
seen at the magnetron is therefore a rapidly varying function of frequency.
If at a certain frequency the phase happens to be such that the variation
of reactance of the line with frequency is more rapid than that of the
magnetron itself, and of opposite sign, a condition results where the magnetron
has no stable frequency. In another, favorable, phase the magnetron
is stabilized. This is known as the “long line effect.’” The
result is that for long lines either (1) VS WR’S lower than 1.5 are necessary
to guarantee stable magnetron operation, or (2) a method of changing
the effective line length and hence the phase of the standing wave must
be included in the antenna line. The latter may be done by a “line
stretcher” not unlike a trombone, or in wave guide by a squeeze section
or a dielectric phase shifter.z These add an undesirable adjustment.
1102. Coaxisl Lines.-Coaxial lines consisting of concentric inner
and outer conductors are not new. At lower frequencies they have
usually consisted of cables with a solid dielectric and a braided outer
,I Micrmuaw Ma#ndrorz.s, Vol. 6, Radiation Laboratory Series.
aMicrowave Transrntision Circuits, Vol. 9, Radiation Laboratory Series.