Page 382 - Engineering Electromagnetics, 8th Edition

364 ENGINEERING ELECTROMAGNETICS

across the line. A probe is moved along the line and indicates that the first
voltage minimum to the left of X is 16 cm from X.With the short circuit
removed, a voltage minimum is found 5 cm to the left of X, and a voltage
maximum is located that is 3 times the voltage of the minimum. Use the
Smith chart to determine (a) f ;(b) s;(c) the normalized input impedance
of the egg beater as seen looking to the right at point X.
10.31 In order to compare the relative sharpness of the maxima and minima of a
standing wave, assume a load z L = 4 + j0is located at z = 0. Let
|V | min = 1 and λ = 1m. Determine the width of the (a) minimum where
|V | < 1.1; (b) maximum where |V | > 4/1.1.
10.32 In Figure 10.17, let Z L = 250 , Z 0 = 50 , find the shortest attachment
distance d and the shortest length d 1 of a short-circuited stub line that will
provide a perfect match on the main line to the left of the stub. Express all
answers in wavelengths.
10.33 In Figure 10.17, let Z L = 40 − j10 , Z 0 = 50 , f = 800 MHz, and
v = c.(a) Find the shortest length d 1 of a short-circuited stub, and the
shortest distance d that it may be located from the load to provide a perfect
match on the main line to the left of the stub. (b) Repeat for an
open-circuited stub.
10.34 The lossless line shown in Figure 10.35 is operating with λ = 100 cm. If
d 1 = 10 cm, d = 25 cm, and the line is matched to the left of the stub, what
is Z L ?
10.35 A load, Z L = 25 + j75 ,is located at z = 0ona lossless two-wire line for
which Z 0 = 50 and v = c.(a)If f = 300 MHz, find the shortest distance
d (z =−d)at which the input admittance has a real part equal to 1/Z 0
and a negative imaginary part. (b) What value of capacitance C should be
connected across the line at that point to provide unity standing wave ratio
on the remaining portion of the line?
10.36 The two-wire lines shown in Figure 10.36 are all lossless and have Z 0 =
200 . Find d and the shortest possible value for d 1 to provide a matched
load if λ = 100 cm.

Figure 10.35 See Problem 10.34.