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Class Note for ECE 3317 with Professor Jackson at UH


Class Note for ECE 3317 with Professor Jackson at UH

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This 21 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
ECE 3317 Prof David R Jackson Notes 2 Complex Vectors Adapted from notes by Prof Stuart A Long O References to equations and pages in your book Will be written in reen O Appendices A B C and D in the text book list frequently used symbols and their units O Vt is a time varying function O V is a phasor complex number O A bar underneath indicates a vector Vt V ca jb cej i I I I Phase j 5 Magnitude Real part Imaginary part ELMefsident y 61 cos jsin Hence accos b csin complex conjugate gtIlt c ajb ce39j 1 gtRe 6 za jb SU btr actior I CZ Cl a1 Job1 C1ej 1 62 a2 Job2 lczlemz multiplication Cl02Zlclllczlem1 2 division J iirilt irgtllt t lt1ljdtc Iltgtltgtt c 8 12 ejlt 2gt ch ejlt 2quot gt 12 I I j 2 Jn 7 lt lt 7 f pii39igipd DIdI L I Where n i zltl itltbgbi Note the comp9X qll r39p root Will h a v9 two possible Values T m 2 xi in quaWit12 Vt V0 cosat 14 1 I Amplitude Angular Phase Frequency f Vt ReV0 emejm Vt ReVeW 15 Vt VO cosat V 2 V0 em going from timedomain to phasor domain V0 2 R6 Vejm going from phasor domain to time domain timedomain ltgt phasor domain Vtltgt V Note Ut Vt ltgt UV 2Vt ltgt jcoV 81 However UtVt ng UV 7 ranSfOr h j each Component of a time ham TOnI C Vector function into complex v9 Gtor V t SCVX COSltQgtt x 52V COSltQgtt y 2 V2 COSltQgtt Z V x Vxej x y Vyej y 4F z Vzejqbz VCt Re V e I Q t Le V x YA Vy z 72 EEJQgtt xV COSlt I D 52V Costt D A V O at Z D p 17 Find the corresponding timedomain vector At Re A em 10 Re aw 12W 0 Re JZXCOS a j sin 01 A A 02quot 41 005 6017 ysm a The vector rotates with time wt0 Practical application A circularpolarized plane wave discussed later 5702 2 icosat kz fsinat kz E ZJ For a fixed value of z the electric field vector rotates with time Ep 1 73 Recall om example 1 1 5 AXB ECAxBy AyBx 7 1 J DCJ D WP h VP tr b9 r PfII39 b Ilt drawir IQ GhC III ilt gtr from 1 cross arid d t bracinth ir I the phasor domair I O Ct gtlt ECt if A Z 7 COS at 7 Sin2 at A Wm V02 c052wt dt ltV2ltrgtgt V2 T 1cos2at 70M 2 dt ltV2tgt V02 T 2 2 Next consider the time average of a product of sinusoids ltVt J OTVO cosat 05 IO cosat dt p17 V0 1 0 VOIO JCT cosat a cosat dt V T cosa cos2ata 0T0 Li dt ReltVI 2 V0 10 cosa ltVt1tgt V010 COS a from previous slide Hence The results directly extend to vectors that vary sinusoidally in time consider DxEx DyEy DZEZ D tReDx y ZeW etc xayaz Q DxExgtltDyEygtltDZEZgt 1 1 1 1 1 1 EReDxExERcDyEyERcDZEz R6DXE DyE DZE or ltQrEtgtReQE


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