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112 Ladder Network Analysis
(b) Note the SWR definition in (4.59). Give an expression for the
partial derivative of SWR with respect to x k in terms of the
reflection coefficient and its derivative found in (a).
4.14. Consider the series dissipation resistance in an inductor:
I L wLlon
oC---i)~-"""~'fY'yr...''"'----'WM~---_oo
Find the unit-source sensitivity llQ using (4.4) and d= I/Q.
4.15. Find the unit-source sensitivities gz.' and g. for a'dissipative cascade
transmission line.
4.16. Verify numerically the three Tellegen theory examples suggested below
Equation (4.93).
4.17. Again consider the network in Figure 4.1 using only elements ZL' YI'
Z" and Y, (not Z. this time). Suppose that at some frequency
(a)
(b)
PL= 10 W, ZL=30+jI5, Y,=O.02-jO.OI,
Z,= 150-jlO, and Y,=O.OI +jO.15.
Find the exact partial derivative of Zin = V./I. with respect to
branch impedance Z, using Tellegan's theorem.
Find ,an approximate value for the same partial derivative by
first-order finite differences. Perturb Z, by 5- j I, i.e., increase Z,
to 155 - j 11 ohms.