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Prohle"" 227
Third, an objective function for optimizing the resistance excursions need
not be limited to gain; it might be noise figure, noise measure, or any other
function that can be formulated in terms of impedances or admittances.
Equally important, an arbitrary goal/target function may be employed so that
sloped gain functions may be matched. Like most applications of nonlinear
programming (optimization), there are several choices to be made from
experience rather than by analysis.
The optimal piecewise linear resistance function must be fitted with an even
rational polynomial, so that a matching network may be synthesized. The
Gewertz method then provides the input impedance polynomial for the
network at the load interface. Standard network synthesis techniques will
produce the LC element values.
There are two features of Carlin's broadband-matching method that distinguish
it from Fano's classical method. The discrete load impedance versus
frequency data set does not have to be identified with a resistively terminated
LC load network; i.e., load classification is not required. Also, the wellconditioned
optimization process allows sloped-gain or other arbitrary fit of
the objective function. Fano's method has been adapted by Mellor (1975) to
obtain similar results at the expense of considerable ad hoc procedures.
Network synthesis is required in these and other methods which are more
versatile than the direct design-matching method in Section 6.4.
Problems
6.1. Find four different lossless, lumped-element L-section matching networks
that transform a load impedance of 36 - j324 ohms to match a
50 +jO generator impedance.
6.2. Conjugately match a 6+j25-ohm load impedance to a 7+j20-ohm
generator using only capacitors in an L section. Obtain two different
solutions.
6.3. Plot a 2: I SWR load-locus circle on a Smith chart, and explain why
Equation (6.19) is true.
6.4. A T section is composed of the two types of L sections.
(a) Write an expression for the parallel resistance level across the
shunt reactance (X b ) as a function of the T section's terminating
resistances and transfer phase angle.
(b) A conjugately matched T section delivers I watt from a 50-ohm'
source to a 21-ohm load with a lagging current transfer phase of
155 degrees. What is the rms voltage across the shunt reactance?