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Pseudobandpass Matching Networks 217
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Figure 6.37. Synthesized lumped-elemen! matching network for Examples 6.18 and 6.J9. [Fmm
COHee, R. M., and Joines, W. T., IEEE Trans. Circuits Syst., Vol. CAS-26, No.5, p. 321, May
1979. © 1979 IEEE.)
(6.109) are shown in Table 6.5. The synthesized network is shown in Figure
6.37. Note that the load inductance is a part of the total g2 element.
6.6.4. Summary of Pseudobandpass Matching. The narrow bandpass response
of matching L sections suggested the use of lowpass networks (cas·
caded L sections) for broadband matching witb resistance transformation. A
quadratic frequency mapping function doubled the number of network elements
while providing the appropriate correlation between the conventional
Chebyshev lowpass, flat-loss function and the pseudobandpass function.
Numerical integration over the frequency axis determined the broadband
load-reactance functional values. In practice; the two load-reactance values
are given, and trial evaluation of the one-reactance Fano integral determines
the flat-loss and ripple factors. Then a solution exists if the two-reactance
Fano integral value is less than the corresponding load function requires. If
not, a greater number of elements (n) is assumed, and the process repeated.
When the values of conventional Chebyshev constants are found acceptable,
the pole/zero locations in the conventional s' plane are computed by
formula. The quadratic frequency-mapping function then transforms these n'
values into n=2n' new values. Selection of left-half-plane poles and zeros
enables the construction of the Feldtkeller polynomials, and thus network
synthesis can proceed.
Cottee and Joines (1979) concede that the integration step can be avoided
by proceeding with trial synthesis. However. they claim that the integration
approach allows restrictions to be visualized; to that end, they include a dozen
design charts. More significantly, their article further considers distributed
(transmission line) matching networks terminated by a lumped-element load.
The transmission line elements are commensurate-all having the same length
-so that a resistively terminated network response would have harmonic