EEL3472_Spring2011_HO_07

EEL3472_Spring2011_HO_07 - EEL 3472 - Electromagnetic...

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Unformatted text preview: EEL 3472 - Electromagnetic Fields and Applications I Handout #7 Moore 31 January 2011 Spring 2011 Solutions to Homework Assignment #2 All CD Module Portions listed in the questions are optional. 1. Ulaby, p. 121, #2.1 2. Ulaby, p. 121, #2.2 3. Ulaby, p. 121, #2.3 4. Ulaby, p. 122, #2.5 5. Ulaby, p. 122, #2.6 6. Ulaby, p. 122, #2.7 7. Ulaby, p. 122, #2.9 8. Ulaby, p. 122, #2.12 9. Ulaby, p. 122, #2.13 10. Ulaby, p. 122, #2.14 1 Problem 2.1 A transmission line of length l connects a load to a sinusoidal voltage source with an oscillation frequency f . Assuming the velocity of wave propagation on the line is c , for which of the following situations is it reasonable to ignore the presence of the transmission line in the solution of the circuit: (a) l = 20 cm, f = 20 kHz, (b) l = 50 km, f = 60 Hz, (c) l = 20 cm, f = 600 MHz, (d) l = 1 mm, f = 100 GHz. Solution: A transmission line is negligible when l / . 01. (a) l = l f u p = ( 20 10 2 m ) ( 20 10 3 Hz ) 3 10 8 m/s = 1 . 33 10 5 (negligible). (b) l = l f u p = ( 50 10 3 m ) ( 60 10 Hz ) 3 10 8 m/s = . 01 (borderline) . (c) l = l f u p = ( 20 10 2 m ) ( 600 10 6 Hz ) 3 10 8 m/s = . 40 (nonnegligible) . (d) l = l f u p = ( 1 10 3 m ) ( 100 10 9 Hz ) 3 10 8 m/s = . 33 (nonnegligible) . Problem 2.2 A two-wire copper transmission line is embedded in a dielectric material with r = 2 . 6 and = 2 10 6 S/m. Its wires are separated by 3 cm and their radii are 1 mm each. (a) Calculate the line parameters R , L , G , and C at 2 GHz. (b) Compare your results with those based on CD Module 2.1. Include a printout of the screen display. Solution: (a) Given: f = 2 10 9 Hz , d = 2 10 3 m , D = 3 10 2 m , c = 5 . 8 10 7 S/m (copper) , r = 2 . 6 , = 2 10 6 S/m , = c = . From Table 2-1: R s = radicalbig f c / c = [ 2 10 9 4 10 7 / 5 . 8 10 7 ] 1 / 2 = 1 . 17 10 2 , R = 2 R s d = 2 1 . 17 10 2 2 10 3 = 3 . 71 / m , L = ln bracketleftbigg ( D / d )+ radicalBig ( D / d ) 2 1 bracketrightbigg = 1 . 36 10 6 H/m , G = ln [( D / d )+ radicalbig ( D / d ) 2 1 ] = 1 . 85 10 6 S/m , C = G = 1 . 85 10 6 8...
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This note was uploaded on 08/26/2011 for the course EEL 3472 taught by Professor Rakov during the Spring '08 term at University of Florida.

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EEL3472_Spring2011_HO_07 - EEL 3472 - Electromagnetic...

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