Lecture 17 Metallic Waveguides Dispersion Relations

1. Lecture 17Metallic Waveguides Dispersion Relations 6.013 ELECTROMAGNETICS AND APPLICATIONS Luca Daniel

2. Outline • Review of Fundamental Electromagnetic Laws • Electromagnetic Waves in Media and Interfaces • Digital & Analog Communications • TEM transmission lines (cables and IC/PCB traces) • Digital communications (transients) • RF communications (matching loads to amplifiers) • RLC resonators (application: e.g. filters) • TEM resonators (application: e.g. microwave filters) • Metallic waveguides • Parallel plate waveguide • Cut off and dispersion relation • Rectangular waveguides • Cavity Resonators Today

3. Parallel Plate Waveguides – Cut off and Dispersion kz = k sin  kx = k cos  Propagation condition (kz must be real)  k  Dispersion Relations Cut off frequency 2 TE2 slope=vg=d/dkz TE1 1 slope=vp =/kz kz

4. TE10 Rectangular Waveguide Mode + + - - Add Sidewalls to TE1 Parallel Plate Waveguide  TE10: Surface charge s a Power flow b Surface current a Sidewall slots that will NOT stop current b

5. Rectangular Waveguide Modes b b a a b b a a b b a a TE10 TE11 power What modes are these? • identify which lines are E and H • find the field that is always orthogonal to the waveguide propagation z • count half wavelenghts • determine the direction of power flow TM11 power

6. Rectangular Waveguide Modes – Cut off and Dispersion Propagation condition (kz must be real) b a  Dispersion Relations Cut off frequencies TE20 20 11 TM11 TE11 01 TE01 slope=vg=d/dkz 10 TE10 slope=vp =/kz kz

7. Rectangular Waveguide Design y b Cutoff Frequencies: x a TEm0 TE0n m Want b a/2 so that f01 f20 = n/a (f01 = n/2b) 4 Evanescence Propagation 3 TE20 TM20 Single propagating mode (if a  2b) [TE10] 2 TE10 1 0 f 2n/2a = f20 n/2a = f10 n/2b = f01