EE 5337 Computational Electromagnetics (CEM)

Transcription

1 7//28 Instucto D. Raymond Rumpf (95) EE 5337 Computatonal Electomagnetcs (CEM) Lectue #6 TMM Extas Lectue 6These notes may contan copyghted mateal obtaned unde fa use ules. Dstbuton of these mateals s stctly pohbted lde Outlne Ccut/Wave Equvalence Calculatng Intenal Felds Lectue 6 lde 2

2 7//28 Ccut Wave Equvalence Lectue 6 lde 3 Ccut Wave Equvalence,,, Lectue 6 lde 4 2

3 7//28 Devaton ( of 3) We wsh to deve equatons that convet between the tansmsson lne famewok and the tansfe matx method famewok., Z, tep Extact the complex efactve ndex n and complex mpedance fom the complex popagaton constant and chaactestc mpedance Z. e jk nz n e jk z Z Lectue 6 lde 5 Devaton (2 of 3) tep 2 Relate the complex efactve ndex n and complex mpedance to the complex pemttvty and complex pemeablty. n tep 3 olve the above equatons fo the complex pemttvty and complex pemeablty. n n tep 4 Replace the complex efactve ndex n and complex mpedance wth the complex popagaton constant and chaactestc mpedance Z fom tep. j Z Z j Lectue 6 lde 6 3

4 7//28 Devaton (3 of 3) tep 5 olve the equatons fom tep 4 fo the complex popagaton constant and chaactestc mpedance Z. jk Z Lectue 6 lde 7 Calculaton of Intenal Felds Lectue 6 lde 8 4

5 7//28 Infomaton Needed The feld nsde the th laye s calculated as: ψ E z H y, z x, λz Ey, z e z W W c z H x, z λ V V e c To do ths, we must stoe W, V, and when analyzng the th laye. But how ae c and calculated? c Lectue 6 lde 9 Calculatng the Intenal Mode Coeffcents Ou scatteng matces calculate mode coeffcents that ae extenal the th laye. We need the ntenal mode coeffcents. Bounday condtons eque the felds to be contnuous acoss an nteface. Recall the bounday condton fo the fst nteface s ψ ψ W W c W W c V V c V Vc olvng fo the ntenal mode coeffcents gves c c c W W W W c V V V V Lectue 6 lde 5

6 7//28 Geneal catteng Matx Famewok Ou smulaton s eally just a sees of scatteng matces. c nc ef 2 3 L L2 L3 devce Devce n gap medum Consde ths n a moe geneal famewok as c nc N LN N N tn c tn c tn Lectue 6 lde Algothm: Fowad Pass Pogessng fom left to ght, the global scatteng matx s bult one laye at a tme. c nc c2 c2 Recod: W V λ G Lectue 6 lde 2 6

7 7//28 Algothm: Fowad Pass Pogessng fom left to ght, the global scatteng matx s bult one laye at a tme. c nc 2 c3 c3 Recod: W V λ Lectue 6 lde 3 Algothm: Fowad Pass Pogessng fom left to ght, the global scatteng matx s bult one laye at a tme. c nc G2 c3 c3 Recod: G2 2 Lectue 6 lde 4 7

8 7//28 Algothm: Fowad Pass Pogessng fom left to ght, the global scatteng matx s bult one laye at a tme. c nc G2 3 c4 c4 Recod: W V λ Lectue 6 lde 5 Algothm: Fowad Pass Pogessng fom left to ght, the global scatteng matx s bult one laye at a tme. c nc G3 c4 c4 Recod: G3 G2 3 Lectue 6 lde 6 8

9 7//28 Algothm: Fowad Pass The fnal global scatteng matx s 2 2 N N N N cef cnc 2 2 tn N N N N c GN c nc Recod: GN GN GN N c tn Lectue 6 lde 7 Algothm: Backwad Pass We ae now n a poston to calculate the mode coeffcents nsde laye N. cef GN c nc cn cn GN GN N 2 cef c nc GN GN N 2 cnc 22 cn c c c nc GN cn cn N c tn The ntenal felds can now be calculated nsde of the Nth laye. ψ E z H z xn, N λ NzN EyN, zn N N e N N zn W W c Nz H N xn, z λ N VN VN e cn yn, N Lectue 6 lde 8 9

10 7//28 Algothm: Backwad Pass We ae now n a poston to calculate the mode coeffcents nsde laye N-. cef GN 2 c nc cn cn G 2 N G N 2 N 2 cef GN2 GN2 N 2 c nc 22 N c c c c nc c nc GN 2 c c N N N N c tn The ntenal felds can now be calculated nsde of the (N )th laye. ψ E z H z xn, N λ N z E N yn, z N N N e N N zn W W c N z H N xn, z λ N VN VN e cn yn, N Lectue 6 lde 9 ummay of the Algothm Fowad Pass: Pefom smulaton as usual, buldng the global scatteng matx fom left to ght. Dung ths fowad pass, ecod W, VN, λn, and whee the ntenal feld s to be calculated. Backwad Pass: Fo each laye of nteest, calculate the extenal mode coeffcents. G G 2 ef c c c G G nc c 2 cn c 22 c and then the ntenal mode coeffcents c W W W W c c V V V V c and fnally the ntenal felds Ex, z kλz E y, z e z W W c ψ k z H x, z λ V V e c H z calculated fo each laye y, Lectue 6 lde 2 G