lecture27 - 1 ECE 303 Fall 2006 Farhan Rana Cornell...

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Unformatted text preview: 1 ECE 303 Fall 2006 Farhan Rana Cornell University Lecture 27 Rectangular Metal Waveguides In this lecture you will learn: Rectangular metal waveguides TE and TM guided modes in rectangular metal waveguides ECE 303 Fall 2006 Farhan Rana Cornell University d z x o ( ) { K K r r , 3 , 2 , 1 sin = = m e x d m E y r E z k j o z m = 1 m = 2 E y E y Parallel Plate Metal Waveguides TE Modes: 2 2 = d m k o z Dispersion relation: d z o m = 1 m = 2 H y H y x TM Modes: Dispersion relation: ( ) { K K r r , 3 , 2 , 1 , cos = = m e x d m H y r H z k j o z 2 2 = d m k o z 2 ECE 303 Fall 2006 Farhan Rana Cornell University Rectangular Metal Waveguides a b x y z Somewhat like a parallel plate metal waveguide that is closed by metal walls on the remaining two sides o ECE 303 Fall 2006 Farhan Rana Cornell University Rectangular Metal Waveguides: TE Guided Modes - I The electric field of the guided wave will satisfy the complex wave equations: ( ) ( ) r H j r E o r r r r = ( ) ( ) r E j r H r r r r = ( ) ( ) r E r E o r r r r 2 2 = ( ) ( ) r H r H o r r r r 2 2 = We look for solutions of the equation: ( ) ( ) ( ) ( ) r E r E z y x r E r E o o r r r r r r r r 2 2 2 2 2 2 2 2 2 = + + = b a y x z ( ) ( ) ( ) ( ) ( ) [ ] z k j o z e y D x C x y B x A y E r E + = r r Try separation of variables (with E-field pointing in directions transverse to the direction of propagation) Where: ( ) ( ) ( ) ( ) x k x k x C x A x x cos or sin , ( ) ( ) ( ) ( ) y k y k y D y B y y cos or sin , o z y x k k k 2 2 2 2 = + + 3 ECE 303 Fall 2006 Farhan Rana Cornell University Rectangular Metal Waveguides: TE Guided Modes - II b a y x z ( ) ( ) ( ) ( ) ( ) [ ] z k j o z e y D x C x y B x A y E r E + = r r Boundary condition: Components of E-field parallel to the metal walls must go to zero at the metal walls: , = = = b y y x E , = = = a x x y E This implies: ( ) ( ) x k x A x sin = ( ) ( ) y k y D y sin = K K , 3 , 2 1 , : where , m a m k x = = K K , 3 , 2 1 , : where , n b n k y = = So we have: ( ) ( ) ( ) ( ) ( ) [ ] z k j y x o z e y k x C x y B x k y E r E + = sin sin r r ECE 303 Fall 2006 Farhan Rana Cornell University b a y x z Rectangular Metal Waveguides: TE Guided Modes - III Another Boundary Condition:...
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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lecture27 - 1 ECE 303 Fall 2006 Farhan Rana Cornell...

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