

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 matchingstub.
{ 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 }
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.
