ELECTRO FLD & WAVES
ELECTRO FLD & WAVES ECE 144
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This 1 page Class Notes was uploaded by Spencer Ondricka on Thursday October 22, 2015. The Class Notes belongs to ECE 144 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/227070/ece-144-university-of-california-santa-barbara in ELECTRICAL AND COMPUTER ENGINEERING at University of California Santa Barbara.
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Date Created: 10/22/15
ECE 144 ELECTROMAGNETIC FIELDS AND WAVES BOB YORK Uniform Plane Waves The Wave Equation in Lossless Sourcefree Regions Maxwell7s two curl equations can be combined to give the two vector wave equations 7 62E 7 62 V2E 7 0 V2H 7 0 6 6t 6 at A general solution to the wave equation consists of travelling waves which move with velocity 1 7 6 For timeharmonic or sinusoidal signals the wave equation becomes the Helmholtz equation V2E HE 0 and V2H k2 0 where the wave number or ro a ation constant k is given by w 27f k w 5 7 7 M v 1 Uniform Plane Waves A general solution to the wave equation is found using the Method of Separation of Variables giving E 7 E3671 Egg1 where the E vector points in the direction of propagation and is de ned such that W w 6 and is a general position vector in rectangular coordinates these can be written Ekxikykz ziy22 where hf hf k k2 The eld strengths E and E are constant vectors with the and 7 superscripts indicating propagation in the forward k direction or reverse 716 direction respectively The phasor solutions above represent uniform lane waves since the constant phase surface E constant de nes a plane surface and the eld strength is uniform everywhere The planewave solution can be substituted into Maxwell7s equations to give E X E LUMF E E 0 EXH7weE EF0 Electromagnetic waves in which both the electric and magnetic elds are perpendicular to the direction of A A 39 are called Transverse 1 t 39 TEM Waves For a wave travelling in the 2 direction in free space the above gives A 7 E 7 Egei m and H 7 aw 770 and Poynting s Theorem gives 1 Stored Electric Energy we EE 1 1 E 2 1 Stored Magnetic Energy wm EMHOQ in EEEOQ 7 1 7 7 E 2 1 Average Power Density Pave iRe E X Hgt 702 inH022 2 277 2
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