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Exam 1 - Microwave Fundamentals

Microwave Fundamentals in Electrical Engineering. Students are to show all work for proper credit. Write out all formulas used and their solutions, if assumptions are made these must be clearly stated to receive full credit. Properly label all values with the associated units, and show how your results are obtained.

Problem 1.
A fifty ohm lossless transmission line is terminated into a load impedance of Z(load) = 40 + j70 ohms. Complete the following questions in parts a and b.

a) Using a Smith Chart determine the following:
1) Plot the normalized impedance and label the value on the smith chart
2) Determine the normalized admittance and label the value on the smith chart
3) Determine the actual admittance. Y = ?
4) Determine the Voltage Standing Wave Ratio (VSWR) and label on the smith chart
5) Determine the Reflection Coefficient value

b) Verify the above values in part a, using calculations:
1) Calculated normalized impedance
2) Calculated normalized admittance
3) Calculated actual admittance
4) Calculated VSWR
5) Calculated reflection coefficient

Problem 2.
On an impedance Smith Chart, plot two curves corresponding to a value of Q = 1. Also, on the same chart plot the frequency response of a one ohm resister (normalized) in series with a capacitor. Show frequency equal to zero, frequency equal to infinite, and the direction of increasing frequency.

Problem 3.
At a frequency of 550KHz, find the length of a half wavelength dipole antenna in meters. Also, find the length of a quarter wavelength monopole antenna in meters.

Problem 4.
At a frequency of 1MHz a transmission line has the following characteristics. Find the attenuation coefficient (alpha), phase shift coefficient (beta), velocity (v), and characteristics impedance (Zo).

R = 0.3 ohms per meter
G = 0.5 micro S per meter
Bc = 0.6 milli S per meter
Inductive Reactance = 2 ohms per meter

Problem 5.
A 75ohm transmission line has a phase velocity of 200M meters per second at a frequency of 200MHz. The load is a short circuit. At a distance of 20 centimeters from the load the line looks like a(n) capacitor or inductor (circle one) whose value is _____ ? Express the answer in appropriate units (pico, micro, etc.) Solve the problem using equations and also using a Smith Chart. Show all work on the smith chart and label properly.

Exam Solutions and Calculations

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Engineering key words: RF exam, test, microwave engineering, antenna, dipole, monopole, electromagnetic, transmission line, attenuation, load impedance, resistance, smith chart, plotting, voltage standing wave ratio, VSWR, phase, short, open, normalized.

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