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Homework 3 - Line Propagation

Problem 1.
Calculate the free-space wavelength for the following frequencies and units.
Meters: 2kHz, 200kHz, 20MHz, 2GHz
Miles: 400Hz, 60Hz
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Problem 2.
A lossless transmission line has an inductance of 320nH/m and a capacitance of 57pF/m. Determine the characteristic impedance and the velocity of propagation.
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Problem 3.
The dielectric constant of mica is 6. Determine its permittivity.
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Problem 4.
The lower end of the commercial amplitude modulated (AM) band is approximately 550kHz. AM stations use quarter wave vertical antennas whose length are 0.25 lambda. Determine the length in meters of a vertical antenna operating at this lower end frequency.
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Problem 5.
A single frequency wave is propagating down a transmission line of length 200 meters with an input rms voltage of 50 volts and output rms voltage of 20 volts. Determine the total attenuation in neprs, total attenuation in dB, attenuation factor in dB/meter, and attenuation factor in nepers/meter.
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Problem 6.
A coaxial cable has the following parameters at a frequency of 1MHz. Series resistance of 0.3ohms/m, series reactance of 2ohms/m, shunt conductance of 0.5uS/m, and a shunt susceptance of 0.6mS/m. Determine alpha, beta, and gamma, the attenuation in dB/m, velocity, and output impedance (Zo).
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Problem 7.
A fifty ohm lossless transmission line is terminated into Z1 = 40 - j30. Calculate (a) the reflection coefficient at the load, (b) the reflection coefficient at distances lambda / 8 and lambda / 4 back from the load, (c) the VSWR, (d) and the input impedance for a length of 0.18 lambda.
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Problem 8.
The reflection coefficient of a load connected to a 50ohm lossless line is know to be equal to 0.5 angle pi / 4. Determine the load impedance and the voltage standing wave ratio (VSWR).
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Problem 9.
The VSWR on a 75ohm loss line is measured as S = 3. Find the magnitude of the reflection coefficient.
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Problem 11.
A lossless 75ohm coax cable has a velocity factor of 0.67. For a shorted line at a frequency of 200MHz, determine the input reactance for the following lengths;
a) 20cm
b) 40cm
c) The equivalent value of inductance or capacitance corresponding to a length of 20cm
d) The shortest length of shorted line that produces an inductive reactance of 30ohms.
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Problem 12.
Repeat your analysis for problem 11 above, but use an open line.
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Homework Solutions and Calculations

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Engineering key words: VSWR, freespace, lossless, lines, transmission, reflection coefficient, loads, balanced, lengths, short circuit, open circuit, inductance, capacitance, termination, shunt, attenuation, dB, nepers, alpha, beta, gamma, velocity factor, propagation, EM, RMS, dielectric constant, permittivity.


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