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Homework 4 - The Smith Chart

Problem 1.
Given an output impedance of 50ohms, use a Smith chart to calculate the reflection coefficients for the following impedances: (a) 100 angle 0deg, (b) 50 - j50, and (c) 0 + j75.
{ Solution } - { Smith Chart Plot }

Problem 3.
Determine the admittances using a Smith chart and by computations of the following impedances: (a) 10 - j30, (b) 100 angle +45deg, and (c) 0 - j50.
{ Solution } - { Smith Chart Plot }

Problem 5.
Given the following measured values on a 50ohm slotted transmission line with a VSWR of 2.3:1; first voltage minimum from load is 10cm, distance of second voltage minimum from load is 40cm. Determine the termination (a) as an impedance, (b) as an admittance, (c) define the values of the equivalent parallel resistance and reactance for part (b).
{ Solution } - { Smith Chart Plot }

Problem 7.
Find using a Smith Chart the impedance at a lines input with the following characteristics, 100ohms, 0.2 wavelengths in length, terminated by a 50ohm resistor.
{ Solution } - { Smith Chart Plot }

Problem 9.
A 50ohm transmission line of 0.4 wavelengths in length is terminated in an admittance of 0.01 - j0.04S. Using a Smith Chart find, (a) the input impedance, (b) the input admittance, and (c) the equivalent parallel values of resistance and reactance for part (b).
{ Solution } - { Smith Chart Plot }

Problem 11.
Utilizing a smith chart, determine the distance of a stub from the load, the length of the stub, and the stub termination given a 50ohm transmission line, a load impedance of 75 - j40ohms that is matched to a 50ohm single line matching-stub.
{ Solution } - { Smith Chart Plot }

Problem 13.
Repeat problem 11 above for a load consisting of a 100ohm resistor in parallel with a 0.0 + j50ohm reactance.
{ Solution } - { Smith Chart Plot }


Solutions and Graphics

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Engineering key words: Smith chart, impedance, admittance, coordinates, scaled parameters, SWR, wavelengths, load, reflection, analog, dBS, loss, angular, transmission, magnitude, circles, real and imaginary, stub matching, loaded, calibration, normalized, slotted line, voltage minimum, transformation, reactive, generator, short circuit, open circuit.


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