

Coupled lines are often used in order to realize directional couplers or interdigitated filters. For the fast and accurate simulation of coupled coplanar lines, an analysis method with CAD capability is developed. This method allows the consideration of finite substrate and metallization thickness as well as the influence of finite ground planes.
Analysis of Multiple Coupled Coplanar Lines
Figure 61 shows the schematic description of the used analysis method based on the theory of multiconductor systems.A quasistatic finite difference method is applied to the system of multiple coupled coplanar lines that forms the coupler cross section. The use of a smart nonequidistant discretization as well as the utilization of the successive over relaxation (SOR) for the solution of the Laplace's difference equation leads to a very fast numerical determination of charge and surface current distribution on conductors. From these quantities, the distributed parameters of coupled lines, it means the capacitance, inductance and resistance matrices per unit length (Cī, Lī and Rī) can be calculated.
Figure 61. QuasiTEM mode analysis of coplanar coupled lines
The matrix of series impedance as well as the matrix of the shunt admittance per unit length of coupled section are used for the solution of the eigenvalue problem which delivers the propagation coefficients of propagating quasiTEM modes and the impedance matrix of the coupled line system. Figure 62 shows the propagation characteristics (effective dielectric constant e_{r,eff,}_{ attenuation }a and surface current distribution) calculated for the six possible quasiTEM modes of four coupled coplanar lines. Using the normalized impedances at ports, the scattering matrix of the coupled lines can be calculated.
Fig.2  Propagation Characteristics (e_{r,eff}_{ , }a) of quasiTEM modes propagating along four coupled coplanar lines (ground planes act as two additional strips)
At the present, the palette of "Coplanar Coupled Elements" consists of 2 to 10 multiple coupled coplanar lines (9 elements). IMST plans to add more elements into this palette in the future.
Table 61 shows the elements in this palette. The name of each element begins with a "C_", it follows the number of coupled center lines and the string "COUP"; for example: 2 coupled coplanar lines (C_2COUP) or three coupled coplanar lines (C_3COUP) etc. The coupled center lines are surrounded by finite ground planes. Up to 10 lines with different line widths and metallization layers as well as different slots between lines can be defined in a data item C_NL_TYP (see Coplanar Data Items).
Coplanar Coupled Elements  
Name  Physical  Analysis Method 
C_2COUP
... C_10COUP 2 to 10 Coupled Coplanar Lines 
Analysis of Multiple Coupled Coplanar Lines 
Table 51: Coplanar Transmission Lines in COPLAN and their equivalent circuit