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256 Lirwur Amplifier Design Tools
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Figure 7.16.
pF and ohms
Transistor model at 4 GHz based on maximally efficient gain terminations.
parallel ohms, as shown. Kotzebue argues tbat tbis model is more accurate
than a model obtained only from S" and S22 for the input and output
branches, respectively. (See also another example of maximally efficient gain
included in Example 7.11 and Figure 7.21.)
7.3.6. Summary of Two-Port Impedance and Power Mode/s. A remarkably
compact overview of geometric models for linear network behavior is available
by the use of mapping concepts. The generalized Smith chart was shown
to constitute the base of a parabola of revolution that is the analog of the
linear two-port output power normalized to the power available at the output
port. The y-parameter model of a two-port network that utilizes two controlled
current sour~es (Figure 7.10) has available output power that is a function of
V, and two y parameters. Thus it is easy to visualize how the output power per
unit V, behaves with respect to any load admittance and its corresponding
generalized reflection coefficient.
The mapping concept enables the location, orientation, and scaling of the
generalized Smith chart in the two-port network's input admittance plane.
Location of the load reflection disk completely inside the positive G" plane
ensures stability; otherwise, all or part of the possible load admittance region
might cause negative input conductance. The stability factor was defined and
used as a valuable yardstick to indicate the amount of stability margin in
various cases, i.e., K> 1. Because input power per unit VI is just a plane
inclined in the Gin direction, there is an easily visualized relationship between
load and input impedances and efficiency.
The maximum possible efficiency and the maximum added power conditions
were examined. The unique load admittances and corresponding input
admittances were obtained for each case. Standard practice specifies a conjugate
match at the input port so that efficiency and transducer gain are
identical. In fact, a separate development showed that simultaneous conjugate
matches at both ports required exactly the load admittance that produces
maximum efficiency. In all situations, it is important to remember that
efficiency is not a function of source impedance.
Kotzebue's maximally efficient gain was defined as the efficiency when the
added power is maximized. It can be interpreted as maximizing the two-port
activity. It was also shown to be finite in most cases where the stability is only