Khớp nối giữa hai đường dây truyền tải được giới thiệu bởi sự gần gũi của họ với nhau. Khớp nối các hiệu ứng có thể được không mong muốn, chẳng hạn như nhiễu xuyên âm trong mạch in hoặc họ có thể được mong muốn, như trong Couplers hướng, mục tiêu là chuyển giao quyền lực từ một dòng khác. Tại mục 11,1-11,3, chúng tôi thảo luận các phương trình, giải pháp của họ, mô tả đường cùng và nhiễu xuyên âm [904-921]. . | 11 Coupled Lines Coupled Transmission Lines Coupling between two transmission lines is introduced by their proximity to each other. Coupling effects may be undesirable such as crosstalk in printed circuits or they may be desirable as in directional couplers where the objective is to transfer power from one line to the other. In Sections we discuss the equations and their solutions describing coupled lines and crosstalk 904-921 . In Sec. we discuss directional couplers as well as fiber Bragg gratings based on coupled-mode theory 922-943 . Fig. shows an example of two coupled microstrip lines over a common ground plane and also shows a generic circuit model for coupled lines. Fig. Coupled Transmission Lines. For simplicity we assume that the lines are lossless. Let i 1 2 be the distributed inductances and capacitances per unit length when the lines are isolated from each other. The corresponding propagation velocities and characteristic impedances are Vị 1 y LịCị Zị y Lị Cị i 1 2. The coupling between the lines is modeled by introducing a mutual inductance and capacitance per unit length Lm cm. Then the coupled versions of telegrapher s equations become C1 is related to the capacitance to ground Cig via Cl Cig Cjg so that the total charge per unit length on line-1 is Qi C1V1 - CmVz Cig Vi - Vg Cm Vi - Vz where Vg 0. . Coupled Transmission Lines 457 9V1 r ail r ỀỈ1 Sz L1 St Lm St SV2 T SI2 911 Sz St St Sil W1 r sv2 -Ị - 77 cm 77 Sz St St Sh_ 3 2 9V1 Sz St St When Lm cm 0 they reduce to the uncoupled equations describing the isolated individual lines. Eqs. may be written in the 2x2 matrix forms SV II Lm SI Sz Lm L2 St SI Cl -Cm SV Sz -Cm c2 St where V I are the column vectors For sinusoidal time dependence ejmt the system becomes dv dz II Lm Lm L2 d dz 1 c. m m G2 It proves convenient to recast these equations in terms of the forward and backward waves that are normalized with
