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Unifonn Transmission Lines 81
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ABeD L sections: the next-branch-is~odd case.
especially suited to programmable calculators, e.g., register. arithmetic for
denormalizing variables.
4.1.3. Summary ofEmbedded Two-Port Networks. The conventional use of
ABCD parameters for cascaded subnetworks has been reviewed. It was shown
that where only a few nontrivial ABCD subnetwork matrices are involved, the
usual procedure, which multiplies all branch and other ABCD matrices to
obtain the overall ABCD matrix, is quite wasteful. It usually amounts to
complex multiplications by 0+jO and 1+jO many times. The review illustrated
the mechanics of ABCD matrix multiplication, which will be applied algebraically
in Section 8.1. It was also mentioned that two recursive analyses with
extreme load impedance value would calculate the overall ladder network's
ABCD parameters should they be required for special applications.
The normalization of the two ABCD-parameter equations resulted in their
matching the form of the standard complex linear update formula. Then it
was shown that the impedance and admittance quantities appropriate to the
ladder branch were simply B/A and C/D, respectively. Thus an L section,
turned in the direction to match the next two ladder branches to be considered,
allowed the recursion to proceed. One complex linear update variable
had to be denormalized, stored, and then recalled; another had to be swapped
into a nonstandard position. The process is somewhat intricate, but is independent
of how or where the ABCD parameters were obtained. Thus the ABeD
L-section method requires programming only in one subroutine.. and this can
be done with little programming code.
4.3. Uniform Transmission Lines
Dissipative, uniform transmission lines with real characteristic impedances will
be considered (see Murdock, 1979, for the even more general case, if required).
These wi!! be treated as embedded, cascaded two-port subnetworks in
the ladder network environment, as just described, or as short- or opencircuited
stubs having only two terminals. The latter wi!! reduce to the same Z
or Y case as the dissipative lumped elements treated in Section 4.1. There are