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homework8 - 1 School of Electrical and Computer Engineering...

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Unformatted text preview: 1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 8 Due on Oct. 21, 2005 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Review sections 4.1-4.3, 5.1-5.2, 5.4, 6.1, 6.3-6.4, paperback book Electromagnetic Waves . These sections also include the material to be covered in the next two weeks of the class. Special Note: Graders have been instructed to take off points (as much as 50%) if proper units are not included in your numerical answers. You must specify the correct units with your numerical answers. Problem 8.1: (TE and TM reflections and transmissions) Consider an incident TE-wave for which the E-field and the H-field are: r k j iy i e E y r r . ˆ − and ( ) r k j iz ix i e H z H x r r . ˆ ˆ − + The E-fields of the reflected and transmitted waves are: r k j ry r e E y r r . ˆ − and r k j ty t e E y r r . ˆ − The H-fields of the reflected and transmitted waves are: ( ) r k j rz rx r e H z H x r r . ˆ ˆ − + and ( ) r k j tz tx t e H z H x r r . ˆ ˆ − + For the reflected and transmitted E-fields the reflection and transmission coefficients were calculated in the lecture notes, and are as follows: ( ) ( ) ( ) ( ) 1 cos cos 1 cos cos + − = t i i t t i i t iy ry E E θ η θ η θ η θ η ( ) ( ) ( ) ( ) 1 cos cos cos cos 2 + = t i i t t i i t iy ty E E θ η θ η θ η θ η (1) a) Find the following ratios (which are the reflection and transmission coefficients for each component of the H-field): z = 0 o i µ ε o t µ ε z x i E i H i k r i θ r θ r E r H r k r t E t H t k r t θ TE-Wave 2 i) ? = ix rx H H ii) ? = ix tx H H iii) ? = iz rz H H iv) ? = iz tz H H Hint: You can express the incident, transmitted, and reflected H-field components in terms of the incident, transmitted, and reflected E-field y-components, respectively, and then use the results given above in (1). Now consider an incident TM-wave for which the H-field and the E-field are: r k j iy i e H y r r . ˆ − and ( ) r k j iz ix i e E z E x r r . ˆ ˆ − + The H-fields of the reflected and transmitted waves are: r k j ry r e H y r r . ˆ − and r k j ty t e H y r r . ˆ − The E-fields of the reflected and transmitted waves are: ( ) r k j rz rx r e E z E x r r . ˆ ˆ − + and ( ) r k j tz tx t e E z E x r r . ˆ ˆ − + For the reflected and transmitted H-fields the reflection and transmitted coefficients were calculated in the lecture notes, and are as follows: ( ) ( ) ( ) ( ) 1 cos cos 1 cos cos + − = t t i i t t i i iy ry H H θ η θ η θ η θ η ( ) ( ) ( ) ( ) 1 cos cos cos cos 2 + = t t i i t t i i iy ty H H θ η θ η θ η θ η (2) a) Find the following ratios (which are the reflection and transmission coefficients for each component of the E-field): i) ? = ix rx E E ii) ? = ix tx E E iii) ? = iz rz E E iv) ? = iz tz E E Hint: You can express the incident, transmitted, and reflected E-field components in terms of the incident, transmitted, and reflected H-field y-components, respectively, and then use the results given...
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This note was uploaded on 09/20/2007 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell.

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homework8 - 1 School of Electrical and Computer Engineering...

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