Analytical Solutions for the Radiated Emission of Parallel Microstrip Traces

A closed-form expression of the unintentional electromagnetic radiation of parallel microstrip traces is proposed. Based on transmission line theory, far-field Green's function, and concept of array factor in antenna theory, analytical solutions for the electric field radiated from a pair of parallel microstrip lines are developed. Depending on the printed circuit board material, dimension parameters, and termination impedances, the frequency and angular responses of far-field radiated emission on the upper half-plane can be analyzed by the presented method. The differential- and common-mode radiated emission solutions are validated by a full-wave simulator and test board measurements in a full-anechoic chamber.