# 4.4 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering ECSE 352 Electromagnetic Waves and Optics 4.4 Wave equations in parallel plate waveguides References: Section 14.4 @AGK 4.4-1 Learning outcomes After taking this class you should be able to: • Explain how to find the field solutions for a general waveguide configuration elate the cut ff frequency to the field solutions Relate the cut-off frequency to the field solutions • Sketch the E and H fields for TE and TM modes in planar waveguides • Calculate the impedance for TE and TM modes • Explain what is meant by a mode ECSE 352 4.4-2 Parallel plate waveguides perfectly reflecting surface x d λ k k x k z κ m θ m RE roject - ctor onto z and x axes z 222 kk + β m =k z VIEW Project k vector onto z and x axes •D e f i n e zx kkk =+ cos mx m κθ == 22 mm k =− lectric field: sin mz m βθ Phase constant n m j z E e π ⎛⎞ ECSE 352 4.4-3 Electric field: 0 sin y EE d = ⎜⎟ ⎝⎠ Cut Cut-off frequency and wavelength off frequency and wavelength • Cut-off frequency: cm mc nd ω = 2 1 cm m n c – Phase constant is only real for ω>ω c Cut-off wavelength: hase constant is only real for 2 nd m λ = = cm m n 1 2 Phase constant is only real for λ<λ c d z TE mode: ECSE 352 4.4-4 m=1 m=2 m=3 2 m d = m d = 0 sin m jz y e d = 3 / 2 d m =

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General field solution • We derived the equation for the E-field for a TE mode in a parallel plate waveguide by considering wave interference
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## This note was uploaded on 08/17/2011 for the course ECSE 351 taught by Professor Davis during the Spring '08 term at McGill.

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4.4 - Department of Electrical and Computer Engineering...

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