In this work, a numerical quasi-static approach is proposed to efficiently analyze symmetrical shielded broadside-coupled microstrip line (SBCML) structures. Based on the modified least squares boundary residual method combined with a variational technique, this approach allows accurate computation of the electrical/geometrical parameters of different SBCML configurations. The errors for the quasi-TEM electrical parameters range are less than 4%. The proposed technique was demonstrated through successful comparison with data from published works and results obtained from commercial EM simulators like CST-EMS and COMSOL.
INTRODUCTIONBroadside-coupled microstrip line (BCML) structures are frequently used in microwave and millimeterwave (mm-wave) passive/active circuits such as couplers [1, 2], baluns [3,4], antennas [5], filters [6], phase shifters [7], and impedance transformers [8]. In fact, compared to conventional edge-coupled microstrip lines, such circuits present some enhanced design parameters like tight coupling (3 dB), low VSWR, and low insertion loss. They can also produce equal even-and odd-mode phase velocities. Accurate computation of their quasi-TEM static parameters is essential for successful design of microwave systems, optical integrated circuits, and sensors. During the last years, various works have been devoted to the analysis of shielded/partial shielded and open planar transmission line configurations and to the computation of their quasi-static parameters. Existing quasi-TEM approaches include conformal mapping [9, 10], point matching method [11], neuro-fuzzy [12], method of lines [13], variational method [14,15], finite element method [16,17], orthogonal expansion method [18], quasi-static spectral domain method [19], Fourier series expansion [20], and closed-form expression [21]. From that list, the conformal mapping method is one of the most widely used. However, it is valid only over a limited range of physical dimensions and restricted configurations. On the other hand, discretization methods, like the finite element and finite difference time-domain methods, suffer from discretization errors and long CPU time, especially for very thin material layers.Recently, the quasi-TEM approach has shown several advantages like good convergence rate and accuracy, minimum memory storage and CPU time, while avoiding the need for an expansion function to solve the unknown charge density. Furthermore, it reduces the Gibbs phenomenon effect. Based on the Least Squares Boundary Residual method (LSBR), which has already been successfully and accurately applied to the characterization of multilayer isotropic and anisotropic planar transmission lines with arbitrary geometry for both the quasi-TEM and full-wave modes, the proposed method, called Modified Least Squares Boundary Residual (MLSBR), uses weighting functions (rectangular
