Page 378 - Engineering Electromagnetics, 8th Edition

360 ENGINEERING ELECTROMAGNETICS

50 .(b)Will other line lengths meet the requirements of part (a)? If so,
what are they?
10.10 Two lossless transmission lines having different characteristic impedances
are to be joined end to end. The impedances are Z 01 = 100 and
Z 03 = 25 . The operating frequency is 1 GHz. (a) Find the required
characteristic impedance, Z 02 ,ofa quarter-wave section to be inserted
between the two, which will impedance-match the joint, thus allowing total
power transmission through the three lines. (b) The capacitance per unit
length of the intermediate line is found to be 100 pF/m. Find the shortest
length in meters of this line that is needed to satisfy the
impedance-matching condition. (c)With the three-segment setup as found
in parts (a) and (b), the frequency is now doubled to 2 GHz. Find the input
impedance at the line-1-to-line-2 junction, seen by waves incident from
line 1. (d) Under the conditions of part (c), and with power incident from
line 1, evaluate the standing wave ratio that will be measured in line 1, and
the fraction of the incident power from line 1 that is reflected and
propagates back to the line 1 input.

10.11 A transmission line having primary constants L, C, R, and G has length
and is terminated by a load having complex impedance R L + jX L .Atthe
input end of the line, a dc voltage source, V 0 ,is connected. Assuming all
parameters are known at zero frequency, find the steady-state power
dissipated by the load if (a) R = G = 0; (b) R = 0, G = 0; (c) R = 0,
G = 0; (d) R = 0, G = 0.
10.12 In a circuit in which a sinusoidal voltage source drives its internal impedance
in series with a load impedance, it is known that maximum power transfer
to the load occurs when the source and load impedances form a complex
conjugate pair. Suppose the source (with its internal impedance) now drives
a complex load of impedance Z L = R L + jX L that has been moved to the
end of a lossless transmission line of length having characteristic
impedance Z 0 .If the source impedance is Z g = R g + jX g , write an
equation that can be solved for the required line length, , such that the
displaced load will receive the maximum power.
10.13 The incident voltage wave on a certain lossless transmission line for which
8
Z 0 = 50 and ν p = 2 × 10 m/s is V (z, t) = 200 cos(ωt − πz)V.(a)
+
Find ω.(b) Find I (z, t). The section of line for which z > 0is replaced by
+
a load Z L = 50 + j30 at z = 0. Find: (c) L ;(d) V (z); (e) V s at
−
s
z =−2.2m.
10.14 A lossless transmission line having characteristic impedance Z 0 = 50 is
driven by a source at the input end that consists of the series combination of
a 10-V sinusoidal generator and a 50- resistor. The line is one-quarter
wavelength long. At the other end of the line, a load impedance,
Z L = 50 − j50 is attached. (a)Evaluate the input impedance to the line