EEE445_Lectr08_RWG_CWG

EEE445_Lectr08_RWG_CWG - 3.3 Rectangular Waveguide 3.4...

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Unformatted text preview: 3.3 Rectangular Waveguide 3.4 Circular Waveguide To derive results for the TE and TM waves that can be supported by a rectangular waveguide. To derive results for the TE and TM waves that can be supported by a circular waveguide. Traditionally, TM is easier to apply the B.C., but TE is dominating. EEE 591/445 Lecture 08 1 Approximate Problem for RWG EEE 591/445 Lecture 08 2 a b , x y Assume walls are PEC Procedure for Analyzing TE and TM Waveguides Derive the BCs that apply to e z and h z . Solve Helmholtz equation subject to BCs for e z and h z . Evaluate the transverse fields. Calculate propagation constant and wave impedance. EEE 591/445 Lecture 08 3 TE mode Separation of variables by Fourier EEE 591/445 Lecture 08 4 2 2 2 2 2 2 2 2 2 2 ( , ) ( , ) ( ) ( ) 1 1 c z z c k h x y x y h x y X x Y y d X d Y k X dx Y dy + + = = + + = (3.73) (3.74) (3.75) 2 2 2 2 2 2 2 2 2 , x y x y c z z x y d X k X dx d Y k Y dy k k k H H E E y x + = + = + = EEE 591/445 Lecture 08 5 Converting a PDF into two separated ODEs Each ODE satisfies certain boundary conditions (3.76a) (3.76a) (3.77) (3.5c,d) EEE 591/445 Lecture 08 6 2 2 2 2 2 ( , ) ( sin cos )( sin cos ) BC: ( , ) cos cos , , 0,1,2,... 0,1,2,......
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EEE445_Lectr08_RWG_CWG - 3.3 Rectangular Waveguide 3.4...

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