161_1_Lecture_10

161_1_Lecture_10 - EE161 El EE161 Electromagnetic Waves...

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EE161 Electromagnetic Waves all 2010 Fall, 2010 Instructor: Dr. Shenheng Xu Electrical Engineering Dept., UCLA gg p , © Prof. Y. Ethan Wang
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ecture 0 Lecture 10 • Dominant Mode in Rectangular Waveguides (TE 10 Mode) • Mode Templates hase Velocity and Group Velocity • Phase Velocity and Group Velocity ispersion Relationship • Dispersion Relationship
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ummary of Solutions for TM Waves Summary of Solutions for TM Waves   0 ) , ( 2 2 y x e k 1. Use the Helmholtz equation to determine the longitudinal z c t E-field and the cutoff wavenumber subject to boundary conditions. And c z k y x e , ) , ( E j   z j z z e y x e z y x E , , , 2. Solve for transverse H-field using olve for transverse E eld using or E j z E j z y k j H z c x 2 x k H z c y 2 3. Solve for transverse E-field using 4. In the above use x k E c x 2 y k E c y 2 y TM x H Z E x TM y H Z E r k k  0 k Z TM  2 2 c k k 2 2 b n a m k c 5. The phase velocity and guided wavelength are v 2 p g
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ummary of Solutions for TE Waves Summary of Solutions for TE Waves   0 ) , ( 2 2 y x h k 1. Use the Helmholtz equation to determine the longitudinal z c t H-field and the cutoff wavenumber subject to boundary conditions. And c z k y x h , ) , (  z j z z e y x h z y x H , , , H j   H j  2. Solve for transverse E-field using olve for transverse H ld using or 1 y k E z c x 2 x k E z c y 2 H j z   H j z 3. Solve for transverse H-field using 4. In the above use y TE x E Z H x TE y E Z H 1 x k H c x 2 y k H c y 2 r k k  0 2 2 c k k 2 2 b n a m k c k Z TE 5. The phase velocity and guided wavelength are v 2 p g
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y x b a z Microwave Engineering , By Davis, M. Pozar.
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Rectangular Waveguides – Dominant Mode Dominant mode defined as the mode with lowest cutoff frequency or longest cutoff wavelength or TE 2 2 , 2 mn c b c 2 a c 2 For TE 10 : For TE 01 : b n a m For TE 11 & TM : 2 2 2 2 2 2 b a ab c b a Therefore, 11 , 01 , 10 , c c c (when a>b) or rectangular waveguides when a>b the longest and the lowest cutoff For rectangular waveguides, when a>b, the longest and the lowest cutoff frequency exist for TE 10 mode!!!
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This note was uploaded on 02/09/2011 for the course EE 161 taught by Professor Huffaker during the Spring '08 term at UCLA.

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161_1_Lecture_10 - EE161 El EE161 Electromagnetic Waves...

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