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86 Ladder Network Analysis
4.4. Nonadjacent Node Bridging
There are many applications where single components (e.g., R, Land C) are
connected between nonadjacent nodes of a ladder network. The bridged-T
network is often employed for servo lead/lag phase compensation and for
group time delay equalization in radio circuits. There are also a number of
narrow-band filter design methods that realize transmission loss poles by
bridging nonadjacent nodes with L or C. This section considers convenient
means for analyzing such networks without having to resort to the less
efficient nodal analysis.
4.4.1. Derivation of Bridged-T Chain Parameters. The approach for analyzing
the bridged-T structure in Figure 4.10 is to find its ABeD parameters and
then treat it as another cascaded two-port subnetwork, as described in Section
4.2. The four branch admittances may be composed of any number and kind
of components. A specific delay equalizer, bridged-T arrangement will be
considered in Section 4.4.2, and its ABCD parameters will be obtained using
the following developmen t.
Consider the separate two-port networks in Figure 4.11. The left One is the
top branch of the hridged-T, and the right one is the remaining T structure.
Paralleling these two structures produces the complete network in Figure 4.10.
It will be shown that addition of the two separate short-circuit admittance
matrices provides the short-circuit matrix of the entire bridged-T network.
To obtain the short-circuit parameters for the subnetworks, defining Equations
(3.79) and (3.80) are recalled. It is easy to see for the subnetwork in
Figure 4.lla that Yll'= Y22, =Y4' Generally, Y21 =',IV 1 when V 2 =0. IfV 1 = I,
.---__-11 Y, Ir-__-,
I I
I I I I
0---'--1 1
Y, 11--r--1 1
Y, II-~--