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74 Ladder Network Analysis
impedance, which is always calculated for a resistance or an inductance, must
be inverted. A similar test of opposite properties is made for the capacitance
subroutine (line 9300), where it is most convenient to calculate the admittance
and invert it if the branch number is even. The Q parameter has been applied
to add a series resistance to inductors and a parallel conductance to capacitors
according to
Z=R+jX=X(d+jl);
(4.4)
Y = G +jB = B(d +j I),
(4.5)
where the decrement d is equal to I/Q (line 1150). Also, X=wL and B=wC.
Note that a lossless element may be described by Q =0 and yet avoid a
"divide-by-zero" in the decrement calculation because of the test and replacement
in line 1140, which sets Q= IEIO. There is some question as to whether
Q is frequency independent. It is always possible to calculate Q in an arbitrary
way in subroutines 9200 and 9300, where the frequency information is
available. However the decrement is determined, inversion of (4.4) or (4.5)
requires the identity
I d-jl
d +j I = d2 + I . (4.6)
This is coded in lines 9240-9260, which are potentially in common between
subroutines 9200 and 9300.
Example 4.1. Run Program B4-1 for the three examples specified in Figure
4.3. The topological input is terminated by entering 0,0, O. Note that any
number of frequencies may be analyzed sequentially once the basic information
has been input.
The input impedance is calculated last by lines 9955~9985;
discussed in Section 4.5.1.
these will be
4.1.5. Branch Topology Levels and Packing. The flexibility of the topological
description may be extended considerably by defining brancb levels, as
illustrated in Figure 4.4. The analysis program keeps track of which branch
number is being processed, and even-numbered branches are processed using
a branch impedance value. If the branch were to contain several paralleled
elements, their admittance should be calculated, added, and then inverted to
give the branch impedance. This state of paralleling admittances in an
even-numbered branch will be called level I. Suppose that the branches to be
paralleled are composed of elements in series; then these impedances should
first be added, and the separate results should be inverted, so that the level-I
operation can proceed. The state of adding series impedances to obtain
subsets to be paralleled in an even-numbered branch is called level 2. Branch
2 in Figure 4.4 contains two level-2 subset branches and one level-I branch.
The dual case is shown in branch 5 of Figure 4.4.