Homogenization technique for transmission lines based on the Monotonicity property

The paper proposes a new homogenization technique for electrical interconnects embedded in inhomogeneous dielectrics, based on the properties of the matrices of the transmission line model. In particular, the Monotonicity property of the capacitance matrix with respect to the permittivity allows establishing a relation between the eigenvalues of the original problem and those of the equivalent homogeneous ones. The study of the sign index, a function of such eigenvalues, easily leads to the identification of two uniform values of the permittivity. The performances of the two homogeneous transmission lines associated to such values establish a lower and an upper bound to the performance of the original inhomogeneous interconnect, as shown in the examples.