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88 Ladder Network Analysis
A similar development could be accomplished by addition of open.circuit (z)
matrices, as explained by Seshu and Balabanian (1959).
Section 3.4.3 showed how to find z and y parameters in terms of the ABCD
parameters. The ABCD parameters in terms of the y parameters are found in
an entirely analogous way. They are provided in the matrix identity
(
A B) - I(Y22 I )
C D = Y21 YIlY22-Y2IYI2 YII •
(4.34)
It is tempting to substitute (4.31)-(4.33) into each element of (4.34). It is
always worth checking algebraically to see if gross simplification or cancella·
tion of mutual terms may be accomplished. But, for analysis purposes, it
usually turns out that carrying forward the numerical results of important
stages of the computation is by far the most effective procedure.
4.4.2. A Group Delay Equalizer. Geffe (1963) has described the lowpass
group delay equalizer shown in Figure 4.12. Suppose that the five component
values have been determined, and what remains is the analysis task for this
subnetwork. Using decrement d= I/Q for each component, a comparison of
Figures 4.12 and 4.10 shows that
Y, = Y 2 =wC,(d Cl +jl), (4.35)
Y 4 =[wL,(dL\+jl)r', (4.36)
Y 3 = {[wC 2 (d c2 +jl)r' +wL 2 (d L2 +jl)} -'. (4.37)
It is important to recognize that aU parts of these calculations reside in the
component type-2 and type-3 subroutines described in Section 4.1.4. So the
bridged.T subroutine calls for the type.2 and type-3 subroutines to evaluate
the main parts of (4.35)-(4.37). This means that the bridged·T topological
input list must consist of four register pairs in the proper order, and it must
control the topological pointer N appropriately before type-2 and type-3
Note: These sections may be used only if
Resonance Tests
Type I]]a:
1. L j resonates with 1CI at
w]"",,,Ja. 2 +p2
2. ~ and