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# Adv Electromag Waves ECE 6341

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This 25 page Class Notes was uploaded by Karolann Wiegand on Saturday September 19, 2015. The Class Notes belongs to ECE 6341 at University of Houston taught by David Jackson in Fall. Since its upload, it has received 69 views. For similar materials see /class/208289/ece-6341-university-of-houston in Electrical Engineering at University of Houston.

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Date Created: 09/19/15

ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 5 TMX SurfaceWave Solution h i R TEN 251M g 202M x I k k W x x 201 1 ZOZM 0 mg 080 1 1 kxl klz k222 kxo k02 k222 Zn jZOTlM tankx1h Z 203M TMx SurfaceWave Solution cont TRE Em 2m jZOTlM tankxlh ZoM k k Hence j X1tankxlh A 081 080 or 8r 2 j 11 jtanchlh x0 Note Assuming a real k2 a solution will only exist if kxo is imaginary TMx SurfaceWave Solution cont 1 2 2 5 Let kxO ax0 a axO k2 k0 Then we have 1 2 2 E l or 19216032 Note This must be solved numerically Properties of SurfaceWave Solution Assumptions A lossless structure A bound surfacewave solution the fields decay at x 00 Properties of SW Solution cont Property 1 k2 is real Otherwise conservative of energy is violated x I 00 Pm E Pout Z L Assume 2aL k2 a Pout Pine Properties of SW Solution cont Property 2 k2 210 Otherwise 8r imaginary no solution possible 8r 2 k jtaIKCxlh x0 1 1 k12 k222 axO k22k022 x1 Properties of SW Solution cont Property 3 kzlt k1 1 Otherwise kx1 2 k12 k222 j0x1 a 1 I th x t h n IS case 8r axo 311 Jaxl x0 j 1 tarmltax1hgt 06 tanhax1h x0 2 negative number TEX Solution for Slab h R TE 0 00 ZOTIE E 202E kxo ZTE W1 01 x k x1 TRE Z k x1 x0 k or i tankx1h Il lr kxl TEX Solution for Slab cont 12 Using kxo jax0 05x0 2 k22 02 we have i j tanchlh lur kxl L r or tankx1h kxl Graphical Solution for SW Modes Consider TMx 06x06 kxl tankx1h or axoh i kxlh tankx1h 8 I Let then Graphical Solution cont We can develop another equation by relating u and v u hk12 k2212 V hk22 k0212 Hence L12 h2 klz kzz add v2 hz kz2 k02 Graphical Solution cont u2 v2 142k12 koz 0th n12 1 Define R2 E koh2 n12 1 Note R is proportional to frequency Then Graphical Solution cont V K 112v2 2R2 R2 E koh2n12 1 TM0 v utanu Graphical Solution cont v Graph for a Higher Frequency TM0 i 7r2 Improper SW v lt 0 Proper vs Improper v axoh If v gt 0 proper SW fields decrease in x direction If v lt 0 improper SW fields increase in x direction Cutoff frequency the transition between a proper and improper mode Note This definition is different from that for a closed waveguide structure where k2 O at the cutoff frequency Cutoff frequency TM1 mode V 0 TMx Cutoff Frequency v i i i TMI R7r 7 g u R a E a E For other TM modes Further Properties of Solutions obtained rom the graphical solwutiwon Property 1 k2 CO 21th Proof v axoh wk koz Atffc v20 so kzk0 Properties of SW Solutions cont Property 2 k2 gt k1 at f gt 00 Proof 7t 37 u gtconst etc 2 2 Hence u kxlh h 12 k22 gt const k 2 k2 SO klh 1 f gt const so X gt 1 1 1 TM0 Mode The TM0 mode has three special properties TM0 1 No cutoff fc gt 0 Proof see graphical solution TM0 2 Proof Hence TM0 Mode cont 91 as f gt0 k0 1 1 2 vz utanuz u 6 6 I I hxkzz k02 z gihzac kgt 2 2 k0 E 1ik0h2 1112 5 k0 8r k0 Dispersion Plot TEX Modes kx1 luraxO 1 rt k h axoh klh an x axoh kxlh cot kxlh i r TEX Modes cont No TE0 mode f6 0 TE1 cutoff frequency at R 7f 2 In general TEX Modes cont 1 v ucotu M u hk12 k2212 v hk22 k0212 At this frequency u 0 For lower frequencies u becomes imaginary If we wish to track the TE1 ISW for lower frequencies we need to re formulate the graphical solution 25

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