Lect25PlateWaveguides

# Lect25PlateWaveguides - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 25 2009/10/26 Parallel Metal Plate Waveguides TE and TM Guided Modes 1 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 25: Instructor: Dr. Wesley E. Swartz m = 1 m = 2 E y E y EE HHH Prelim 2 and Problem Assignments Prelim 2 Exam tomorrow night, starting at 7:30 in Phillips 101 Covers: Plane waves incident on dielectric and conductor boundaries. Effects of unmatched loads on sinusoidally driven transmission lines. Effects of a complex permittivity. Virtual work. Not included: Smith Charts, transmission line transient analysis. Bring calculators: Some numerical answers required. No Demo 9 Section this week (due to Prelim 2) . No Homework 8 (normally due tomorrow) . 2 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 25: There will be Workshop 9 Sections (Thursday, October 29) : Problem 14.4: Three dielectric layers. Problem 14.8: Two dielectric layers. Problem 13.30: Transmission line transients using a bounce diagram. Homework 9 (due November 3) : Problem 14.11: Four dielectric layers. Problem 14.14: A narrow band optical dielectric filter. Problem 13.14: Tan-tan formula versus the Smith Chart. Problem 13.8: Stub impedance match. Parallel Plate Metal Waveguides d W z 3 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 25: Consider a parallel plate waveguide (shown above). We have studied such structures in the context of transmission lines. We know that they can guide TEM waves ( T ransverse E lectric and M agnetic) in which both the electric and magnetic fields point in direction perpendicular to the propagation direction. But these structures can guide more than just the TEM waves that we have considered so far … The electric field of any guided wave will satisfy the complex wave equations: Basic Wave Equations Consider a parallel metal plate waveguide: d z x o μ ε r H r E ω × E r E 2 2 = 4 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 25: We look for solutions of the equation, where the z -dependence is that of a wave going in the z -direction, and where the E-field is pointing in the y -direction: ( ) ( ) j o = () r E j r H = × ( ) ( ) r o r H r H o 2 2 = r E r E o 2 2 = z k j z e x F y r E = ˆ Some unknown function of “x” TE Guided Modes (1) Assume a solution of the form: which represents a TE guided wave ( T ransverse E lectric) since the direction of E-field is transverse to the direction of wave propagation. d z x o z k j z e x F y r E = ˆ 5 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 25: Plugging the assumed solution into the wave equation gives: Boundary conditions for perfect conductors: r E r E o 2 2 = ( ) 0 0 = = = = d x F x F x F k x x F r E r E x z 2 z o 2 2 2 o 2 2 2 2 2 = = +

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## This note was uploaded on 11/26/2009 for the course ECE 3030 at Cornell University (Engineering School).

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Lect25PlateWaveguides - ECE 3030 Electromagnetic Fields and...

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