Calculation of Internal Inductance and AC Resistance for Finite Thickness Flat Conductors

Microstrip and stripline structures are commonly used for signal transmission in high-speed digital circuits. The Multiconductor Transmission Line (MTL) equations provide an effective description of the propagation on these structures. The current distribution on the cross-section of the circuit conductors (usually of rectangular shape) is a function of frequency and any evaluation of the per-unit-length parameters in the MTL equations should take this variation into account. This work considers the numerical calculation of the per-unit-length resistance and internal inductance from de to several hundreds of megahertz for rectangular conductors in the above structures. The problem is formulated in terms of an integro-differential equation for the total current density on the conductor cross section. The integro-differential equation is solved by the Method of Moments. All the coefficients of the complex set of algebraic equations are analytically evaluated by introducing the concept of geometrical mean distance. The proposed method is validated by comparing with the known values of resistance and internal inductance for various canonical structures.