ECE3025C_Homework4_F2005_solution

ECE3025C_Homework4_F2005_solution - ECE 3025C -...

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ECE 3025C -- Electromagnetics Homework Assignment #4 – Solutions Fall 2005 Problem 1. A transmission line is being driven by a sinusoid signal of 220 MHz f = , and the line has the following properties: 1.5 H/m L μ = , and 35pF/m C = . The end of the line, i.e. open circuit, is at position 0 z = on the cable. Find the following: A. Propagation velocity in the line p v . 8 61 2 11 1.38 x 10 (m/s) (1.5 10 )(35 10 ) P v LC −− == = ⋅⋅ B. The phase constant 2/ p f v β π = for this sinusoidal signal. 6 8 2 (220 10 ) 2 / 10.02 (rad/m) 1.38 10 p fv βπ = C. The wavelength λ . 2 2 / 0.627 (m) 10.02 λπ = D. The characteristic impedance of the cable 0 Z . 6 0 12 1.5 10 207 35 10 L Z C E. The input impedance in Z at 0.5 m z =− . 0 0 0 L 0 tan( L) tan( L) for Z , this reduces to cot( L), and for L 0.5 (m) 207cot(10.02 0.5) 63.49 ⎧⎫ + = ⎨⎬ + ⎩⎭ =∞ = = = Ω L in L in in Zj Z ZZ Z Z z j F. The input impedance in Z at 0.75 m z . 0 cot( L), and for L 0.75 (m) 207cot(10.02 0.75) 73 in in Z z j = = Ω
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ECE 3025C -- Electromagnetics Homework Assignment #4 - Solutions Page 2 of 4 G. The input impedance in Z at 1.0 m z =− . 0
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ECE3025C_Homework4_F2005_solution - ECE 3025C -...

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