Explanation Given Data: Refer to Figure P2.26 in the textbook for the given circuit. From the given circuit, Z 0 = 50 Ω R L = 75 Ω The value of frequency ( f ) is 10 MHz. Voltage standing-wave ratio on the line ( S ) is 3. Formula used: Write the expressions for voltage reflection coefficient in terms of standing-wave ratio as follows: | Γ | = S − 1 S + 1 (1) Here, S is the voltage standing-wave ratio. Write the expression for load impedance for the given circuit as follows: Z L = R L − j X C (2) Here, R L is the load resistance and X C is the load reactance. Write the expression for load reactance as follows: X C = 1 2 π f C (3) Here, f is the frequency and C is the unknown capacitance of the load capacitor. Write the expression for voltage reflection coefficient for the given circuit as follows: Γ = Z L − Z 0 Z L + Z 0 (4) Here, Z 0 is the output impedance of the lossless transmission line. Calculation: Substitute 3 for S in Equation (1) to obtain the value of voltage reflection coefficient. | Γ | = 3 − 1 3 + 1 = 2 4 = 0.5 From Equation (2), substitute ( R L − j X C ) for Z L in Equation (4) as follows: Γ = ( R L − j X C ) − Z 0 ( R L − j X C ) + Z 0 Simplify the expression as follows: Γ = ( R L − Z 0 ) − j X C ( R L + Z 0 ) − j X C Take modulus on both side of the expression as follows: | Γ | = | ( R L − Z 0 ) − j X C ( R L + Z 0 ) − j X C | = ( R L − Z 0 ) 2 + ( − X C ) 2 ( R L + Z 0 ) 2 + ( − X C ) 2 = ( R L − Z 0 ) 2 + ( X C ) 2 ( R L + Z 0 ) 2 + ( X C ) 2 Take square on both sides of the expression as follows: | Γ | 2

7th Edition

ISBN: 8220100663659

Author: ULABY

Publisher: PEARSON

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Chapter 2, Problem 26P

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Find the value of unknown capacitance C in the circuit in Figure P2.26 in the textbook.

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