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Input and Transfer Network Responses 91
1,=1+40/30=7/3. Thus B=V,=40+50X7/3=470/3. Then (4.40) shows
that I b
=3/100 and (4.38) shows that 1,= 1.970.
4.4.4. Summar)' ofNonadjacent Node Bridging. A general method for finding
the ABCD parameters of any bridged-T network was presented. Equations
for the short-circuit (y) parameters were derived in terms of the four branch
admittances. These can be converted to ABCD parameters for use in the
embedded subnetwork technique described in Section 4.2. A time delay
equalizer bridged-T network was discussed as an example. It was emphasized
that existing subroutines for RLC impedance computation could be called by
the bridged-T-component subroutine to minimize computer coding.
For T networks and more extensive subnetworks that are bridged, there
often is a need to find the internal voltages and currents. The approach above
does not provide this information and will not solve the larger problem in any
case. An efficient technique, which uses the ladder recursion scheme two extra
times to find the A and B chain parameters of the bridged subnetwork, was
described. These values, the bridging branch impedance, and the bridged
subnetwork's known output voltage and current enable the simple calculation
of the bridging current. Thus the ladder recursion scheme may proceed
through the bridged subnetwork, calculating correct v'?ltages and currents as
in the unbridged situation.
Network analysis that includes bridge subnetworks must be conducted with
the possibility that a null condition might occur. Therefore, division such as in
(4.40) should be protected by the addition of IE-9+jO to the denominator.
4.5. Input and Transfer Network Respouses
The methods described so far make it easy to obtain the input voltage and
current of a ladder network given the topological data and load power.
Several input and transfer response functions often required in practice will be
described. Quantities related to impedance and power will be defined first.
Then a definition of scattering parameters will be given as a basis for certain
wave response functions and for important applications later in this book.
Logarithms (log) in the following equations are with respect to base 10.
4.5.1. Impedance and Power Response Functions. Assume that ladder network
input voltage and current are available (see V, and I, in Figures 3.4 or
3.7, for example). Then the input impedance is
VI .
Z'=y=R,+JX,. (4.41)
I
This calculation is made in Program B4-1 by lines 9955-9985. Line 1381
detects that the input has been reached, because the component-type integer is
zero. If the next branch number is even, then the last processed branch is in