Unformatted text preview: 13.42 CHAPTER 13. TRANSMISSION LINES the original 50 [2 cable.
a. What happens and why?
b. Based on your knowledge of transmission lines and impedance matching, describe in words how you would solve your boss’s problem. Problem 13.19: A signal generator with an internal impedance of Z, = 50 — 3'50 9
is connected to a 50 Q lossless coaxial line of length A/S, which in turn is connected
to a complex load of ZL = 100 + 3'50 9. The open-circuit voltage of the generator is lOﬁlO" volts. a. Find the reﬂection coefﬁcient at the load and the voltage standing—wave ratio. b. Calculate the input impedance of the transmission line, as seen by the generator.
c. Calculate the power delivered to the load. Hint: As one might imagine, for the
case of a lossless transmission line, the power that enters the transmission line is the
power delivered to the load. Problem 13.20: A circuit that is to be resonant at 400 M Hz is constructed of a
short-circuited, air—dielectric coaxial line. The outer conductor has an inside radius
of route, = 2.72 cm, the inner conductor has an outside radius of Timer 2 1 cm, and
both are silver plated to a thickness of 10 times the skin depth. 3. Calculate the parameters of the coax line: L, C, R, 2.3, a, A, and k. b. Develop an expression for the input impedance of the circuit as a function of fre—
quency, Z1N(f). Sketch IZINl vs. f. c. Determine the 3 dB bandwidth of this resonant circuit. (1. What is the Q of this circuit? (Divide your answer to part (c) by 400 MHz.) Problem 13.21: A 300 f2 twin—lead transmission line (effective 5,. = 1.37) is to be
used to connect a 160 MHz source to a dipole antenna with a 75 S2 input impedance.
To avoid standing waves, and consequent higher losses on the main line, an impedance
transformer (AM—transformer) is to be designed to connect between the 300-9 line
and the load. a. Derive an expression showing the impedance transformation produced by a quarter- wave section of transmission line.
b. Assuming that a piece of similar twin-lead is to be used for the transformer, what characteristic impedance must it have? What length must it have? Problem 13.22: Examine the situation of Problem 13.21 on a Smith Chart. a. Indicate in a Smith Chart the point Z L /Z0, the transformation path on the chart,
and the point ZIN/Zo. b. For a new frequency of 240 MHZ, indicate the new transformation path on the
chart and the new point Z IN /Zo. c. If the 75—!) load is replaced by a short circuit and the frequency is changed to
106.7 MHz, show the point ZSC/Zo, the path on the chart, and the point ZIN/Zo.
(1. Repeat part (c) with a frequency of 240 M H z in terms admittance admittance. ...
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- Fall '06