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b. Interchange the inductor elements by resistors. In particular, com-
pute the input impedance of this circuit.

FIGURE 6.3
The magnitude (left panel) and the phase (right panel) of the characteristic root of the infinite
LC ladder.

6.9 Transfer Function for a Difference Equation with
Constant Coefficients*
In Section 6.8.1, we found the Transfer Function for what essentially was a
simple ODE. In this section, we generalize the technique to find the Transfer
Function of a difference equation with constant coefficients. The form of the
difference equation is given by:

yk() = b u k() + b u k( − 1 ) +…+ b u k( − m)
0 1 m
(6.96)
− ay k( − 1 ) − a y k( − 2 ) −…− a y k( − n)
1 2 n
Along the same route that we followed in the phasor treatment of ODE,
assume that both the input and output are of the form:

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