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 μ ε , 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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## This note was uploaded on 12/14/2010 for the course EEE 445 taught by Professor Georgepan during the Fall '10 term at ASU.

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EEE445_Lectr08_RWG_CWG - 3.3 Rectangular Waveguide 3.4...

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