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

2. Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces Digital & Analog Communications oTEM transmission lines (cables and IC/PCB traces) oDigital communications (transients) oRF communications (matching loads to amplifiers) oRLC resonators (application: e.g. filters) oTEM resonators (application: e.g. microwave filters) oMetallic waveguides  Parallel plate waveguide  Cut off and dispersion relation  Rectangular waveguides oCavity Resonators Outline Today

3. Parallel Plate Waveguides – Cut off and Dispersion 11 22 TE 1 TE 2  slope = v p =  /k z slope = v g = d  /dk z kzkz Dispersion Relations Propagation condition (k z must be real) k  Cut off frequency k z = k sin  k x = k cos 

4. TE 10 Rectangular Waveguide Mode Add Sidewalls to TE 1 Parallel Plate Waveguide  TE 10 : Surface charge  s Surface current Sidewall slots that will NOT stop current a b Power flow + + - - a b

5. Rectangular Waveguide Modes TE 10 TE 11 TM 11 b a b a b b a a What modes are these? 1)identify which lines are E and H 2)find the field that is always orthogonal to the waveguide propagation z 3)count half wavelenghts 4)determine the direction of power flow power

6. Rectangular Waveguide Modes – Cut off and Dispersion TE 11  10  20  11  01 TE 10 TE 01 TE 20  slope = v p =  /k z slope = v g = d  /dk z kzkz Dispersion Relations TM 11 Propagation condition (k z must be real) a b Cut off frequencies

7. Cutoff Frequencies: a x b m 4 3 2 1 0 TE 20 TM 20 f TE 10 Propagation Evanescence /2a = f 10  = f 20 /2b = f 01 Want b a/2 so that f 01  f 20 = /a (f 01 = /2b) Single propagating mode (if a  2b) [TE 10 ] Rectangular Waveguide Design TE m0 y TE 0n

8. Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces Digital & Analog Communications oTEM transmission lines (cables and IC/PCB traces) oDigital communications (transients) oRF communications (matching loads to amplifiers) oRLC resonators (application: e.g. filters) oTEM resonators (application: e.g. microwave filters) oMetallic waveguides  Parallel plate waveguide  Cut off and dispersion relation  Rectangular waveguides oCavity Resonators Outline Today

9. TE 10 Rectangular Waveguide Mode Add Sidewalls to TE 1 Parallel Plate Waveguide  TE 10 : Add Front and Back walls to TE 10 Rectangular Waveguide  TE 101 : y y=b y=0 x=0 x=a z y y=b y=0 x=0 x=a

10. Cavity Resonator Modes y y=b y=0 x=0 x=a z=0 z=d y

11. Cavity Resonator Time Domain Picture y y y y

12. Cavity Resonator Demo EE HH 110 mode a b d m=1 n=1 p=0