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Unilateral Scattering Gain 267
the 12-dB circle centered at 0.681 /29.88° with radius 0.324 from (7.116). This
is shown in Figure 7.21. The stability circles from Example 7.9 in Section 7.4.2
are also plotted; it is necessary to select a load on the 12-dB efficiency circle
that is in the stable region. Again, arbitrarily selecting the load nearest the
center, 0.357 /29.88°, the input reflection, by (7.32), is 0.373 / -64.46°, and
the source reflection must be the conjugate of this (see Figure 7.21) if the
plotted circle is to represent forward transducer gain. Note that the source
reflection is outside the input plane stability circle, so that stable operation is
assured. Also, the maximally efficient gain source and load reflection coeffi·
cients (f, and fd are plotted in Figure 7.21. For this device, G ME = 15.26 dB,
according to Section 7.3.5 and Program A7-4.
7.4.4, Summary of Scatteri"g Stability ami Gaill. It was noted that numerous
programs on readily available small computers exist for scattering stability
and gain calculations. It is most important to know the territory. This section
has explained the origins of the important scattering relationships for bilateral
(SI2 "" 0) networks, which apply to most real devices.
Various significant gain expressions have been identified and several underlying
assumptions have been noted. For example, the use of efficiency as
forward transducer gain can occur only when the source is chosen to be the
conjugate of the input impedance with a selected load in place. Conjugate·
image reflection terminations were given, the load reflection enabling the
maximum possible efficiency. It was remarked that concentric circles of
constant efficiency may be plotted on generalized Smith charts normalized to
the conjugate-image impedances; the interested reader is referred to Bodway
(1967).
Arbitrary efficiency and gain loci turn out to be eccentric families of circles
on the r 1 and r 2 termination Smith charts. Expressions for calculating the
location of their centers and their radii were given along with several examples.
Similar families for circles of maximally efficient gain (Section 7.3.5) are
available in the work of Kotzebue (1976). The most general expression for
forward transducer gain was given in (7.94); it may be used without any major
assumptions.
7.5. Unilateral Scattering Gain
The bilateral gain equations in Section 7.4 are greatly simplified if it is
assumed that the device is unilateral, i.e., Sl2 = O. Also, stability can no longer
be considered, because the stability factor. K in (E.2), is no longer defined. A
single scalar estimate of validity for this assumption can be calculated to
determine the relevance of unilateral analysis. Furthermore, the conceptualization
of the entire design process is considerably simplified. However, many
high-frequency transistors have substantial S12 reverse transducer gain. Readily
available computers eliminate the advantage of algebraic simplicity. How-