y y y Field Analysis in a Lossy Dielectric Sandwiched between Flanged Rectangular Waveguide and Conducting Plane Makoto HIRANO y, Masaharu TAKAHASHI y, and Minoru ABE y. ( ) [] [],[3] y Department of Electronics and Communication Engineering, Faculty of Engineering, Musashi Institute of Technology, -8-, Tamazutsumi, Setagaya-ku, Tokyo, 58-8557 Japan [] [4],[5]. C I Vol. J8 C I No. 9 pp. 55 536 999 9 55
'99/9 Vol. J8 C I No. 9 kl = μ l " l (i = I; II; l = ; ) (TE 0 ) TE mn, TM mn C mn ;D mn z = 0 0 E II = ( E I ; 0; (a) E II y = ( E I y ; 0; (b) H II = HI ; (c) Fig. Flanged rectangular waveguide and structure of the analysis (a) Flanged rectangular waveguide (b) Structure of the analysis (a) (b) (z < = 0) (TE 0 ) (z = 0) [4] (b) I II TE z ψ I, ψ II TM z i I, i II ψ r i ψ i i + kl i i i = 0 () Hy II = HI y ; (d) II C mn ;D mn II C mn ;D mn (c),(d) C mn ;D mn 8 P k I ki z μ m;n inly mk + P C(m; n; k; l) C P mn kyi I nly mk P D(m; n; k; l) D mn m;n >< >: = ki ki z μ i0ly k P C(; 0;k;l) P k I y ki z μ m;n inl mk + P Cy(m; n; k; l) C mn + P m;n k I i mk nl + P Dy(m; n; k; l) D mn = P Cy (; 0;k;l) (3) P C (m; n; k; l), P D (m; n; k; l); P Cy (m; n; k; l), P Dy (m; n; k; l) inly mk;imk nl. (3) C mn ;D mn I ( ) E y 56
(. ) TE mn k I C mn TM mn ki yk I z " D mn (4) E II (; y; z) = 4ß Z Z ρ jk y A 0 + k k z " A sin (k z (z d)) ep ( jk ) ep ( jk y y) dk dk y (5a) Ey II (; y; z) = 4ß Z Z ρ ky k z " A jk A 0 sin (k z (z d)) ep ( jk ) ep ( jk y y) dk dk y (5b) Ez II (; y; z) = 4ß Z Z k j" kz A cos kz (z d) ep ( jk ) ep ( jk y y) dk dk y (5c) H II (; y; z) = 4ß Z Z ρ jk y A k k z μ A 0 cos (k z (z d)) ep ( jk ) ep ( jk y y) dk dk y (5d) Hy II (; y; z) = 4ß Z Z ρ jk A k yk z μ A 0 cos (k z (z d)) ep ( jk ) ep ( jk y y) dk dk y (5e) Hz II (; y; z) = 4ß Z Z jμ k k z A0 sin kz (z d) ep ( jk ) ep ( jk y y) dk dk y (5f) d = :0mm Fig. Reflection coeicient versus the number of calculated mode (a) Reflection coeicient j j (b) Phase angle i A 0 ;A C mn ;D mn 3. 3. 0GHz, " r = 5:5 j0:3 X WRJ 0 a=.9mm, b=0.mm ( ) 6 [4] 0 [5] d=0 0mm 3 (a) d=3.5mm,6mm d=mm 6 [4] 57
'99/9 Vol. J8 C I No. 9 Fig. 3 3 Occurrence rate of each mode (Freq.:0GHz,Relative permittivity: " r = 5:5 j0:3) (b) TM TM 4 TM n 4. 3 (a) d (d=.0mm) (b) (d=.0mm) (c) (d=3.5mm) (d) (d=6.5mm) (e) d (d=8.0mm) 4 (TE 0 ) Fig. 4 Incident field distribution(te 0 ). E 0 ;H 0 4 E y ;H y d=.0mm,3.5mm,6.5mm,8.0mm 58
Fig. 5 5 E II y ;HII y (d=.0mm, z=0.5mm) Field distributions on the y-plane(d=.0mm, z=0.5mm) Fig. 6 6 E II y ;HII y (d=3.5mm, z=.5mm) Field distributions on the y-plane(d=3.5mm, z=.5mm) E 0 ;H 0 5 8 > = 0;y > = 0 d=.0mm,3.5mm ( 5,6(a)) E y H y ( (b)) d=3.5mm H y d=6.5mm,8.0mm E y H ; y d=6.5mm E y d=8.0mm E y H y E y H y (a) (d) y ( 4) 9 E, H y =0 yz y=0 z 0 9 d 9, 0, E z 59
'99/9 Vol. J8 C I No. 9 Fig. 7 7 E II (d=6.5mm) y ;HII y Field distributions on the y-plane(d=6.5mm) Fig. 8 8 E II y ;HII y (d=8.0mm, z=3.0mm) Field distributions on the y-plane(d=8.0mm, z=3.0mm) H y E y E y E z H E z y 5(a) E z E y y y E y 0 H y (5e) k ;k y = 0 yz y = 0 z 0 y TEM (.0mm) H 4 5 ( 0(a)) z (3.5mm) E z ( (b)) TM 530
Fig. 9 9 (d=.0mm, z=0.5mm) Field distributions(d=.0mm, z=0.5mm) (a)h II along the y-ais (b)e II z along the y-ais 0 (d=.0mm, z=.0mm) Fig. 0 Field distributions(d=.0mm, z=.0mm) (a)h II along the y-ais (b)eii along the y- z ais d E y, H y ( ) E z E y ( (a)(b)) E y H E z y y ( (b)(d)) = 0 yz H y 0 y TM H z E y ( (a)(c)) E (6a) y = 0 z 0 TE 5. 5. d=6.5mm E y ;H y d=.0mm E y H y ( 5) d c c = p " r n z d (6) n z z (6) y y d c 0GHz (n z =) d c =6.5mm 53
'99/9 Vol. J8 C I No. 9 Fig. (d=3.5mm, z=.5mm ) Field distributions(d=3.5mm, z=.5mm) (a)h II along the y-ais (b)e II z along the y-ais Fig. (d=6.5mm) Field distributions(d=6.5mm) (a)e II y along the -ais (z=3.0mm) (b)e II y II along the y-ais (z=3.0mm) (c)h along the -ais (z=.5mm) (d)h II along the y-ais (z=.5mm) 53
Fig. 3 3 (d=8.0mm, z=3.0mm) Field distributionsd=8.0mm, z=3.0mm) (a)e II y along the -ais (b)e II y II along the y-ais (c)h II along the -ais (d)h along the y-ais d c > = 6.5mm d c < = 6.5mm 7(a)(b) d c d d c E y H y ( 3) ; y k ;k y d=8mm k = k y = r ß k = 77 j4 (7) d 6[deg./mm] 3 ( y > = 0mm) ; y y =.5mm y y=5.mm E y 3 0.3 0.43 3 y =0 y TM (=.5mm) d y y 533
'99/9 Vol. J8 C I No. 9 E y H y > = 0mm y ß= [rad] TE TM [7] d=8mm H y 8(b) 3(d) y (y=0mm) (5) 3(d) y=0mm H (5d) C 0 0:7 + j0:6 D 0:08 j0:065 TE 0 TM 5. TM 3 TM n TM E z E y TM E y ;E z E z y E y d d c E z E z y=0 z TM 6. (TE 0 ) d c d d c =0 yz TEM y d d c y=0 z TE =0 yz y TM y d c y [],,, 959. [],," EMT-9-9,99. [3],,", pp.57 59,, 989. [4],,," EMT-98-70,998. [5],,,," C--58,998. [6], ",, 99. [7],, pp.85 97,, 977.. (3) (3) P C (m; n; k; l), P D (m; n; k; l), P Cy (m; n; k; l), P Dy (m; n; k; l) i mk nly ;imk nl P C (m; n; k; l) = Z Z ( k y " 4ß k + k y k z + k k z μ jk I ^Φ mny + " k z + k z μ jk k y k I y ^Φ mn ) ^Φ kly dk dk y tan (k z d) (A a) 534
P D (m; n; k; l) = Z Z 4ß k + k y jki yk I z " ^Φmny ρ k y " k z + " k z + k z μ jk k y k I k I z " ^Φmn ^Φ kly dk dk y tan (k z d) P Cy (m; n; k; l) = Z Z 4ß k + k y jk k y k I ^Φ mny + k " k z + k k z μ (A b) ρ " k z + k z μ + k yk z μ jk I y ^Φ mn ^Φ kl dk dk y tan (k z d) P Dy (m; n; k; l) = Z Z 4ß k + k y jk k y k I yk I z " ^Φmny + k " k z ρ " + k z k z μ + k yk z μ jk I k I z " ^Φmn ^Φ kl dk dk y tan (k z d) (A c) (A d) ^Φ mny ; ^Φ mn ^Φ mny ; ^Φ mn ^Φ mny = ψ sin k I + k a k I + k j m sin k I k a k I ( j) m+ k ψ sin k I y + k y b k I y + k y j n sin ky I k + y b ky I ( j) n k y (A a) ^Φ mn = ψ sin k I + k a k I + k j m + sin k I k a k I ( j) m k ψ sin k I y + k y b k I y + k y j n sin ky I k y b ky I ( j) n+ (A b) k y 0 ab (m = k n = l > 0) B inly mk 4 = ab @ (m = k n = l = 0) 0 B inl mk = @ 0 (m j= k n j= l) ab 4 (m = k n = l > 0) 0 (m j= k n j= l C n = 0 l = 0) A (A 3a) C A (A 3b). I (z < = 0) y Ey I (; y; z) = M (; y) ep jk ψ zz I + X m;n k I C mn + ki y ki z " D mn Φ mny ep jk I zz (A 4) Φ mny Ey I n mß Φ mny = sin a 3. (5) A 0 A + a o ρ nß cos y + b b (A 5) (5) A 0 ;A C mn ;D mn A 0 = j(k + k y ) sin (k zd) " + k k I ^Φ 0y + X m;n( k k I ^Φ mny ψ k y k I y ^Φ mn C mn k k I yk I z " ^Φmny k y k I ki z " ^Φmn D mn )# (A 6a) 535
'99/9 Vol. J8 C I No. 9 A = " k z (k + k y ) sin (k zd) " k y k I ^Φ 0y + X m;n( k y k I ^Φ mny + +k k I y ^Φ mn C mn ψ k y k I yk I z " ^Φmny + k k I k I z " ^Φmn D mn )# (A 6b) 0 5 0 4 IEEE 6 IEEE 40 43 44 IEEE 536