HW2Solution

HW2Solution - ECE 201A Homework 2 solution 1. !...

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Unformatted text preview: ECE 201A Homework 2 solution 1. ! " ! "- + 2 j y j y x z x z E a ja e a ja e # # $ % & ! (a) ! " ! "- 1 + 2 j y j y z x z x H a ja e a ja e # # ( ) $ & % % * + ! (b) E ! and H ! fields propagating in +y direction are ! "- j y x z E a ja e # $ % ! and ! "- 1 j y z x H a ja e # ( ) $ & % * + ! . Hence the time average power density is ! " ! " ! " ! " * 2 1 1 1 1 1 Re Re Re 1 1 W/m 2 2 2 y j y j y y av x z z x y a S E H a ja e a ja e a # # & % % ,- ,- ( ) $ . $ % . & & $ % $ / / * + 1 2 1 2 ! ! ! (c) E ! and H ! fields propagating in -y direction are ! " 2 j y x z E a ja e # $ & ! and ! " 1 2 j y z x H a ja e # ( ) $ % * + ! . Hence the time average power density is ! " ! " ! " ! " * 2 1 1 1 1 1 5 Re Re 2 2 Re 4 1 W/m 2 2 2 2 j y j y y av x z z x y y S E H a ja e a ja e a a # # & & ,- ,- ( ) $ . $ & . & $ & % $ & / / * + 1 2 1 2 ! ! ! (d) Net time average power density is 2 1 5 3 1 =- W/m 2 2 y y av av av y y S S S a a % & ,- $ % $ & / 1 2 ! ! ! . (e) The part propagating in +y direction has two mutually orthogonal components with equal amplitude and 90 out of phase. So by definition this part is circularly polarized. The part propagating in - y direction has two mutually orthogonal components with unequal amplitude and 90 out of phase. So this part is elliptically polarized. 2. ! " ! " 3 10 sin x y E a ja z # & $ % ! (a) This is a perfect standing wave. We can express the same electric field as ! " 3 3 3 10 10 10 2 2 2 j z j z x y x y j z j z x y a ja a ja e e E a ja e e j j j # # # # & & & & & % % ,- ,- ,- & $ % $ & / / / 1 2 1 2 1 2 ! . As is seen this is the superposition of two waves of equal amplitude traveling in opposite directions. (b) The electric field of the wave traveling in +z direction is 3 10 2 x y j z a ja E e j # & & % ,- $ & / 1 2 ! and the electric field of the wave traveling in z directions is 3 10 2 x y j z a ja E e j # & % ,- $ / 1 2 ! . (c) The magnetic field of the wave traveling in +z direction is 3 10 2 y x j z a ja H e j # & & & ,- $ & / 1 2 ! and the magnetic field of the wave traveling in z directions is 3 10 2 y x j z a ja H e j # & & % ,- $ / 1 2 !...
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This note was uploaded on 12/02/2009 for the course ECE 000 taught by Professor O during the Spring '09 term at UCSB.

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HW2Solution - ECE 201A Homework 2 solution 1. !...

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