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ECE 3170
Final Exam
December 16, 1999
Name ___________________________________
1.
You may use your portfolio and a calculator.
(35 out of 200 points) A 50-ohm transmission line 5.2 wavelengths long is used to connect cellular
telephone transmission circuitry (Rg = 25-ohms) to the antenna of a cell phone. The antenna has an
impedance of 60 + j 20 ohms. The generator voltage is 1V.
Find :
(a) The reflection coefficient at the input to the line
(b) The input impedance of the line
(c) The voltage standing wave ratio on the line
(d) The positive-traveling voltage on the line
(e) The power delivered to the antenna
2.
(30 out of 200 points) An air-filled 50-ohm transmission line is driven by a 25-ohm generator and is
connected to a 200-ohm load. It takes 1ms for the wave to travel from the generator to the load.
Initially the generator is turned off (zero volts). At time t=0, it is turned on to 10 V.
(a) Draw the bounce diagram for the voltage
(b) Plot the voltage at the load as a function of time for the first 4.5 ms.
(c) Plot the voltage on the line at time t=3.5 ms.
(d) If the line is driven by a high-impedance generator (Rg = infinity), and the line is broken (the load
is an open circuit), what will the voltage on the line be after some very long time?
3.
(35 out of 200 points) The DC current on a z-oriented wire is I = 5z z Amps. (The current is along the
axis of the wire and increases towards the top of the wire.). The wire is located on the z-axis and is 2m
long. Find the magnetic field at any point in space.
Note: If the integral is too difficult to do by hand, be sure you specify it completely. Give the limits
of integration, specify the function completely, and CIRCLE the variable(s) of integration
everywhere it appears in the expression.
4.
(35 out of 200 points) A parallel-polarized plane wave traveling in air is normally incident on a slab of
glass (r = 9, =1S/m, F=10 GHz). Behind the glass is water (like a fish tank). Water has(r = 80,
=3S/m). The incident electric field magnitude is 1V/m.
(a) Write an expression for the incident electric field (phasor form).
(b) Write an expression for the reflected electric field (phasor form) in the air.
5.
(5 points)
What is at least one application of electromagnetics that you may encounter in the future, and what
topic that you learned in this class will apply to it?
6.
Sketch the simplest possible transmitter and receiver system and explain what each part does. Assume
the following losses or gains:
Mixers
–2 dB
Amplifiers +10 dB
Filters
-5 dB
Loss from multipath propagation –30 dB
All lines are 50 ohms, and the antennas have an impedance of 75 ohms. The oscillator used in the
transmitter operates at 1W maximum power and 1800 MHz. The receiver can operate if –120 dB
reaches the detector. How far away can the transmitter and receiver be placed?