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Homework 1 - Transmission Line Theory

Problem 1.
Find the wavelength (lambda) for the free space electromagnetic waves with frequencies: 1KHz, 100KHz, 1MHz, and 1GHz.
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Problem 2.
Find the frequency for the free space electromagnetic waves with wavelengths of: 1cm, 1m, 10m, 100m, and 1000m.
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Problem 3.
Find the characteristic impedance for an air dielectric transmission line with a D/r ratio of 8.80. Note, D equates to the physical distance between the centers of two conductors, and r equates to the radius of the conductor.
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Problem 4.
Find the characteristic impedance for an air filled concentric transmission line with a D/d ratio of 4.0. Note, D equates to the inside diameter of the outer conductor, and d equates to the diameter of the inside conductor.
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Problem 5.
Find the characteristic impedance for a coaxial cable with an inductance of 0.2uH/ft and a capacitance of 16pF/ft.
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Problem 6.
For a given length of coax cable with a distributed capacitance of 48.3pF/m and a distributed inductance of 241.56nH/ft, find the velocity factor and velocity of propagation.
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Problem 7.
Determine the reflection coefficient for a transmission line with an incident voltage of 0.2V and a reflected voltage of 0.01V.
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Problem 8.
Find the standing wave ratio (SWR) for the transmission line described in Problem 7.
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Problem 9.
Find the SWR for a transmission line with maximum voltage standing wave amplitude of Vmax = 6V, and minimum voltage standing wave amplitude of Vmin = 0.5V.
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Problem 10.
Find the standing wave ratio for a 50ohm transmission line that is terminated in a load resistance of 75ohms.
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Problem 11.
Calculate the standing wave ratio for a 75ohm transmission line that terminated in a load resistance of 50ohms.
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Problem 12.
Compute the characteristic impedance for a quarter wavelength transformer that is used to match a section of 75ohm transmission line to a 100ohm resistive load.
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Problem 13.
Using Time Domain Reflectometry (TDR), an EM pulse is transmitted down a cable with a velocity of propagation of 0.7c. The reflected signal is received 1.2us later. How far down the cable is did the EM pulse travel before it was reflected back.
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Problem 14.
Using TDR, a transmission line impairment is located 2500m from the source. For a velocity of propagation of 0.95c, calculate the elapsed time from the beginning of the pulse to the reception of the echo.
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Problem 15.
Using a time domain reflectometer, a transmission line discontinuity is located 200m from the source. If the elapsed time from the beginning of the TDR pulse to the reception of the return pulse is 833ns, determine the velocity factor.
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Homework Solutions and Calculations

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Engineering key words: transmission line, T-Line, wavelength to frequency, frequency to wavelength, conversion, impedance, admittance, parallel conductors, twin lead, coax cables, standing-wave-ratio, VSWR, reflection, amplitude, transmission, electromagnetic wave, concentric, balun, twisted pair, braid, equivalent circuit, incident wave.


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