Coupled-mode theory of terminal characteristic parameters for multilayered and multiconductor lines

We have presented a full-wave coupled-mode formulation for the line parameters of multilayered and multiconductor transmission lines. It is shown that the elements of the impedance matrix for a coupled-line four-port derived from the coupled-mode equations are of the same form as those obtained by the quasi-static approach. This fact suggests that the design technique for microwave integrated circuits developed by using the impedance matrix for coupled TEM lines is also applicable in the full-wave approach. However, it should be noted that the characteristic mode impedances, the current ratios, and the voltage ratios in the present full-wave approach are obtained using the electromagnetic coupling coefficients, whereas those of the TEM lines are derived in terms of a quasi-static capacitance matrix. When the coupled conductor lines are microstrips with a negligible thickness, the electromagnetic coupling coefficients are easily evaluated by making use of the Galerkin´s moment method solutions in the spectral domain for the single microstrips in isolation. The extension of the present formulation to the multi-port system is straightforward