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# Interm Electromag Waves ECE 6340

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This 30 page Class Notes was uploaded by Karolann Wiegand on Saturday September 19, 2015. The Class Notes belongs to ECE 6340 at University of Houston taught by David Jackson in Fall. Since its upload, it has received 71 views. For similar materials see /class/208290/ece-6340-university-of-houston in Electrical Engineering at University of Houston.

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Date Created: 09/19/15

ECE 6340 Intermediate EM Waves Fall 2008 Prof David R Jackson Dept of ECE Notes 21 Reflection from Slab TEZ E e 91 P y 5r d 1 Z T Ei E06j39kZOZe fkyy ky k0 Sinai r A J39kzoZ J39kyy k k cos6 E E0Fe 6 Notes 20 0 1 Et EEO Tejkzoze jkyy T i 1 F The origin is the reference plane for T Reflection from Stab cont Three methods 1 Wave bounce method interface reflections 2 Steadystate wave representation 3 Transverse equivalent network TEN Method 1 iquot 1 1 31nd 21711 O nl r Re ection from Slab cont 111F1 Tz 21F2 Wave Bounce Diagram JEFon 6 T1T2F23E0 6 F1 E0 9 o 0 0 80 3 O 80 A TlE0 B kzldkyA z y C 1 2T1E0e j k21 2 k1 005191 2 D 39 FZTIEOe A dtan 91 E TZFZTIEOe M Bounce Diagram cont At Z 0 r jk y 12 J39k yZA 3 j4 jk y4A T1T2r2E0e e y Note that ej2 e jkyy 2A e j2 z ye jkyy j2 y ejkyy j2 z e 6 etc So we have E 1306 1 qu T211r2e W wage 14 j V F Bounce Diagram cont Hence r r1 Tlerze J Mz T1T2F ej4 z r1 Tlerle Wz EBF1F ej4 Z r1 1 TZTIe Wz Tszfje Mz F11 Yule 1 1 Tie 1 Fej4 z 1 1 13716 129152 i Tie 12 n20 Bounce Diagram cont 1quot 1 1 1 13116 126152 io ZZe c z n20 00 1 11 Next use 2 Z IZI lt19 n20 l Z9 Hence Method 2 SteadyState Wave Representation 1 three regions 2 3 k G Ex E0e 1W E0FeJkZ Ze J W Ex 2 A6 119 BeJkZIZe J yy 39 39k G Ex TEO e y 4 unknowns F T A B 4 equations Ex and Hy must match at both interfaces Method 3 Transverse Equivalent Network TEN Method 3 cont Z I 00 TE 5 TE TE Z 5 Z 01 Z 00 E0Tlt Z TE TE TE ZOO ZOI Zoo J E 1 0 d Method 3 cont Transverse Equivalent Network TEN Z TE TE TE ZOO E ZOI ZOO E S 0 d E EOF TE TE equivalent circuit ZTE TEZ00 JZ01 tankzld L 01 TE TE Z01 1200 tankzld 202E ZLT E Method 3 cont Then we have Method 3 cont Find the transmission coefficient T 1 gt Z 2 3 TE TE F 2 TE Z 00 Z 01 9 Z 00 d i BOT Region 2 VZAejk212 AFZ 119 A ejkzlz ejkzlz Method 3 cont 1 1 Z 2 3 TE TE I1 TE Zoo 39 201 3 2 Zoo d 5 EoT VZ A 6 F2 179 At 20 VOEO1FA 1F2 Hence Method 3 cont 1 gt Z 2 3 TE TE F2 TE Zoo 5 201 3 ZOO 50 g d 5 EoT BOP Vz A e W F2 179 We then have Vd A eJ39kzld F2 ejkzld Region 3 VZ Vde szoZ d Method 3 cont 1 gt Z 2 3 TE TE F TE Zoo 39 201 a 2 Zoo d 5 EoT Hence e szozd EOTe szoz or TVdE0ejk20d A We then have T 39k d 39k d 39k d j J 21 I 6 21 20 0 Method 3 cont 1 gt Z 2 3 TE TE F TE Zoo 39 201 a 2 Zoo d 5 EoT Final result ECE 6340 Intermediate EM Waves Fall 2005 Prof David R Jackson ECE Dept Notes 21 W1 MgtIxgtbw D1 1 In Reflection from Slab TEz E XF 8 m Om 0 0 7quot Z1 XT d gt e ijOZ F e e ky k0 sm Q kz jk y Te J 026 y kzo k0 0086i Re ection from Slab cont ie ne refl39ectia39n39 and tra nsamissmn reaffiieiiesn ts F1 11 Re ection from Slab cont 111F1 Tz 21F2 5139 Bounce Diagram THon 71T2F23Eo EEO EEO kzld kyA Z y rleEoe j r271E0e 2 kzl 2 k1 cos 61 T2F271E0e 2 Bounce Diagram cont At Z 0 E FlEoejkyy T2T1F2E0612 ejkyym 3 j4 jk y4A T1T2F2Eoe e y SO E r 1306 1 qu T211r2e J Mz marge 14 X Bounce Diagram cont Hence r r1 TZTIFZe WZ gaffe 14 r1 TZTlrle Wz YT2F13614 Z F11 Tlee Wz Ef e 14 F11 Tlee Wz 1 rfe Wz Fl4ej4 z r1 1 TZTIe Wz Z We 1 y 1120 Bounce Diagram cont 00 n 1 232 21 2 Zlt1 Hence Method 2 Boundary Condition Method 1 6 Ex Eoejkzoz EOFeijOZejkyy Ex 2 Aejkzlz Bejkzlzejkyy Ex 2 TE0 ejkzozejkyy 4 unknowns F T A B 4 eqs Ex and Hy match at both interfaces Method 3 Transmission Line Theory Z ZOOTE i ZOITE ZooTE E0 i d gt EOT EOF 39 TE TE equwalent Clrcwt Z TE Z TE ZOO JZ01 tankzld 01 1 00 an 21 TE TE ZOO I ZL n I Method 3 Transmission Line Theory cont TE TE Then we have

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