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161_1_Class12 - EE161 Electromagnetic Waves Spring 2010...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 12 • Rectangular Waveguide Examples • Phase Velocity and Group Velocity Rectangular Waveguides – Dominant Mode Dominant mode defined as the mode with lowest cutoff frequency or longest cutoff wavelength 2 2 , 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = b n a m mn c π π π λ b c 2 = λ a c 2 = λ For TE 10 : For TE 01 : For TE 11 & TM 11 : 2 2 2 2 2 2 b a ab b a c + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = π π π λ 11 , 01 , 10 , c c c Therefore, λ λ λ > > (when a>b) For rectangular waveguides, when a>b, the longest and the lowest cutoff frequency exist for TE 10 mode!!! c λ The dominant mode! Single mode operation: a b c c 2 2 10 , 01 , < < ⇒ < < λ λ λ λ Only the dominant TE 10 mode is supported! Minimum mode dispersion! Rectangular Waveguides – Example 1 For an air-filled rectangular waveguide with inner dimensions 0.9 in by 0.4in., (1) calculate the cutoff frequencies for the TE 10 , TE 01 , TE 20 , TE 11 and TM 11 modes. , r c c c k ε ω ⋅ = , 2 π ω c c f = , 2 r c c c k f ε π ⋅ = 2 2 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = b n a m k c π π TE 10 , TE 01 , TE 20 , TE 11 &TM 11 c k c f 351 0254 . 4 . 0254 . 9 ....
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This note was uploaded on 05/10/2010 for the course EE 190776201 taught by Professor Yuanxunethanwang during the Spring '10 term at UCLA.

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161_1_Class12 - EE161 Electromagnetic Waves Spring 2010...

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