Explanation Given data: A lossless transmission line has 0.6 λ long and 75 Ω characteristic impedance. Reflection co-efficient angle is θ r = − 60 ° . SWR (standing wave ratio) is 1.8. Calculation: Follow the steps to design the smith chart graph, 1. Mark the point as A to represent the SWR = 1 .8 . Draw the SWR circle as shown in Figure 1. 2. Draw a straight line from the center of the Smith chart with angle − 60 ° as shown in Figure 1. 3. Read the value of point that where the drawn straight line is touch with SWR circle and name it as point B. Since it is the point where the reflection co-efficient angle is load impudence related, the point B is represents the value normalized load impedance ( z L ) . From the graph, z L = 1.153 − j 0.621 4. The line has 0.6 λ long. The total length of the scale on smith chart is 0.5 λ . Now calculate the 0.6 λ from the point C to D as 0.6 λ . Draw the line from point D to Center of the Smith chart, and find the value where the line touches with SWR circle at E . Read the value at E as 0.63 − j 0.29 , which represents the value normalized input impedance ( z i n ) . From the graph, z i n = 0.63 − j 0.29 5. Now, calculate the magnitude of the reflection co-efficient by using compass with the fixed distance of center of the Smith chart to point A , on the radially scaled parameters of reflection co-efficient for E or I, as shown in Figure 1, which reads as approximately 0.29. Thus, | Γ | = 0.29 From the Smith chart read the values as, Normalized load impedance z L = 1.153 − j 0.621 . Normalized input impedance z i n = 0.63 − j 0.29 . Write the expression to find the load impedance as follows. Z L = Z 0 z L (1) Here, Z 0 is the characteristic impedance

Fundamentals of Applied Electromagnetics (7th Edition)

7th Edition

ISBN: 9780133356984

Author: ULABY

Publisher: PEARSON

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Question

Chapter 2, Problem 59P

To determine

Find the values of reflection co-efficient magnitude (|Γ|), load impedance (ZL) and input impudence (Zin) using Smith chart.

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Chapter 2, Problem 57P

Chapter 2, Problem 62P

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