Fundamentals of Electromagnetics with Engineering Applications
Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Chapter 10, Problem 10.1P

A matching network consists of a length of a T-line through section in series with a capacitor. Determine the length (in wavelengths) required of the through section and the capacitor value needed (at 1.0 GHz) to match a 10 j 35 Ω load impedance to the 50 Ω line.

Expert Solution & Answer
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To determine

The length of section that consists of a capacitor in series and the value of capacitor for matched network.

Answer to Problem 10.1P

The length of section is 0.294λ and the series capacitance is 1.3 pF .

Explanation of Solution

Given:

The load impedance is 10j35 Ω and the characteristic impedance of transmission line is 50 Ω . The frequency is 1 GHz .

Calculation:

The Smith chart for the matched network is shown in Figure 1.

  Fundamentals of Electromagnetics with Engineering Applications, Chapter 10, Problem 10.1P

From the Smith chart, the value of normalized load is 0.2j0.7 that is located on point a .

The normalized load at the point b is 1+j2.4 .

The length of the section of matched network is calculated as,

  d=0.5λ+0.194λ0.4λ=0.294λ

Therefore, the length of the section is 0.294λ .

The value of series capacitance is calculated as,

  j2.4=1jωCZoC=12.4ωZo

Substitute 2π×109 for ω and 50 for Zo in above equation.

  C=12.4( 2π× 10 9 )( 50)1.3×1012 F

Therefore, the capacitance is 1.3 pF .

Conclusion:

Thus, the length of section is 0.294λ and the series capacitance is 1.3 pF .

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Chapter 10 Solutions

Fundamentals of Electromagnetics with Engineering Applications

Ch. 10 - Find the scattering matrices for the simple...Ch. 10 - Cut a 50- T-line and insert a series 50- resistor...Ch. 10 - Prob. 10.14PCh. 10 - A series capacitor of value C=2.0pF is inserted in...Ch. 10 - A series inductor of value L=3.5nH is inserted in...Ch. 10 - Prob. 10.17PCh. 10 - The scattering matrix (assuming a 50- impedance...Ch. 10 - Three T-lines with the same characteristic...Ch. 10 - Consider a three-port network that is matched at...Ch. 10 - Prob. 10.21PCh. 10 - Calculate the insertion loss and the VSWR for the...Ch. 10 - Prob. 10.23PCh. 10 - Verify the scattering matrix (10.27) for the...Ch. 10 - Prob. 10.25PCh. 10 - Prob. 10.26PCh. 10 - A four-port 20-dB coupler is specified as having...Ch. 10 - Suppose the coupling for an ideal symmetrical...Ch. 10 - Suppose to port 1 of an ideal ring hybrid coupler...Ch. 10 - Prob. 10.30PCh. 10 - Prob. 10.31PCh. 10 - Prob. 10.32PCh. 10 - Suppose you join a pair of quadrature hybrid...Ch. 10 - Prob. 10.34PCh. 10 - Prob. 10.35PCh. 10 - Prob. 10.36PCh. 10 - Prob. 10.37PCh. 10 - Prob. 10.38PCh. 10 - Prob. 10.39PCh. 10 - Prob. 10.40PCh. 10 - Starting with the Figure 10.28b circuit...Ch. 10 - Starting with the Figure lO.28b circuit...Ch. 10 - Prob. 10.43PCh. 10 - Starting with the Figure 10.28a circuit...Ch. 10 - Prob. 10.45PCh. 10 - For Problem 10.45, (a) design open-ended shunt...Ch. 10 - Prob. 10.47PCh. 10 - Prob. 10.48PCh. 10 - Prob. 10.49PCh. 10 - Prob. 10.50PCh. 10 - Prob. 10.51PCh. 10 - Referring to Example 10.21 and Figure 10.48,...
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