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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 4.14.3, 5.15.2, 5.4, 6.1, 6.36.4, 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 TEwave for which the Efield and the Hfield 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 Efields 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 Hfields 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 Efields 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 Hfield): 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 TEWave 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 Hfield components in terms of the incident, transmitted, and reflected Efield ycomponents, respectively, and then use the results given above in (1). Now consider an incident TMwave for which the Hfield and the Efield 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 Hfields 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 Efields 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 Hfields 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 Efield): 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 Efield components in terms of the incident, transmitted, and reflected Hfield ycomponents, 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.
 Fall '06
 RANA
 Electromagnet, Transmission line, Impedance matching, Smith chart, transmission line circuit

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