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376 Other Direct Filter Design Methods'
Figure 9.41.
1 2
Linear ~
Lossless passive
transmission ("W
bilateral SK = max ~rt
line
network
~
~ Sliding short circuit
1x 10
The measurement of SK' the maximum SWR of the input-plane image.
~
Usually, load admittances are limited to small regions of the right-half
plane. A useful upper bound on input SWR can be stated for a given load
SWR region:
(9.89)
where S"o is S" when load SL = I, and SK is the maximum SWR observed by
looking into the output terminals for all values of pure resistance connected to
the input terminals. Except for turning the network end for end, the latter is
the same as (9.86), i.e.,
(9.90)
where S" is the SWR of YML in (7.79) with respect to the nominal resistance,
and Sm" was defined in (9.88). SK may easily be measured, instead of being
calculated (see Figure 9.41). The value of SK is found by connecting all
possible reactance values to the input port. This may be done, as illustrated,
with a sliding short circuit on a transmission line or by a lossless LC resonator
tuned over an infinite range. Either way, SK is the greatest SWR value
observed at the output port.
9.5.4. Summary ofLoad Effects on Passive Networks. The geometric models
of linear two-port-network impedance and power behavior were recalled from
Chapter Seven. Bilinear mapping was extended by considering the form and
particular constants that map unit circles onto unit circles. The reflectionplane
bounds of a concentric image from another reflection plane were given.
One application was an analytic solution for the range of power delivered
from a fixed complex source to an arbitrary complex load.
Passive reciprocal networks were shown to have a simplified expression for
maximum efficiency in terms of the real-part parameter Iffi.,. It was also shown
that the relative size of the load-plane image in the input plane is a function
only of the maximum efficiency. Also, expressions for the exact SWR extreme
values of that load-plane image were stated. More often, the load-plane region
is limited to a stated SWR value. An upper bound for the input SWR of that
image was stated. Measurement methods were described for obtaining these
bounds.