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228 Impedance Matching
6.5. (a) Can a single, lossless transmission line transform 6 + j25 ohms to
7 - j20 ohms? If so, give its Zo and O.
(b) What is the input impedance of a lossless, 50-ohm transmission
line 45 degrees long and terminated by a 6 + j25-ohm load?
(c) Can the input impedance from (b) be transformed to 7 -j20 ohms
by a single lossless transmission line? If so, give its Zo and O.
6.6. Rotate load impedance Z2= 100-j150 ohms on a 50-ohm transmission
line that is 45 degrees long.
(a) What is the input impedance if the line is lossless?
(b) What is the input impedance if this length of line has a uniform
dissipation of 0.25 nepers?
6.7. Suppose that Z=R+jO ohms. Show that SWR with respect to I ohm is
R for R> I and is I/R for R< I.
6.8. A two-reactance load (an L section with g" g2' and a I-ohm resistance)
terminates an infinitely complicated bandpass matching network
driven by a resistive source. Give an algebraic (containing no integrals)
expression for an equality constraint and an inequality constraint on
the minimum possible input reflection loss, In(lllpl). The band of
interest is Wt to W2'
6.9. Prove Equations (6.48) and (6.51).
6.10. For a 100% bandwidth, what is the greatest Q L
that can be matched
with an SWR 2: I?
6.11. Derive Equations (6.57) and (6.58).
6.12. Derive Equations (6.61) and (6.62).
6.13. Find the minimum possible decrement of a single-reactance load for
optimal broadband match when lnlpl = 10 1 - w •
6.14. Estimate Fano's optimal matching solution using Equations (6.68) and
(6.69); do not iterate.
(a)
(b)
(c)
(d)
Find the optimal lowpass network that contains two reactances
and matches a 2-farad capacitor in parallel with a I-ohm resistor
over the frequency range 0 to I radians.
What is the generator resistance?
What is the range of SWR in the pass band?
What is the transducer loss at de (in dB)?
6.15. Evaluate Equations (6.68) and (6.69) for parameters a and b when
N = 3, QL = 3, and the bandwidth is 50%.