Derivation of a Closed-Form Approximate Expression for the Self-Capacitance of a Printed Circuit Board Trace

The electric fields that couple traces on printed circuit boards to attached cables can generate common-mode currents that result in significant radiated emissions. Previous work has shown that these radiated emissions can be estimated based on the self-capacitances of the microstrip structures on a board . In general, the determination of these self-capacitances must be done numerically using three-dimensional static modeling software. In this paper, an approximate closed-form expression for the self-capacitance of microstrip traces is derived. This expression can be used to estimate the voltage-driven common-mode emissions from boards with various microstrip trace geometries. The expression also provides insight relative to the microstrip parameters that have the greatest effect on radiated emissions.