Analysis of Arbitrarily Curved Microstrip Lines for Radiated Emission

In the context of printed circuit design, microstrip interconnects pose a great challenge in terms of radiated emission, signal integrity, and intertrace interference. Curved and bent microstrip lines are integral part of such high-frequency circuit design. In this paper, internal fields of an arbitrarily curved microstrip line are calculated using a sequential mode matching technique with piecewise circular discretization. Transverse asymmetry of the electric field is observed due to unequal curvatures of the two side edges of the microstrip line. A dynamic co-ordinate system based on Serret-Frenet reference frame is developed. A simple transmission line model is formulated in this new co-ordinate system to calculate the radiated far fields from the line. The developed model is applied to compute radiation from a sinusoidal line as well as that of a planar spiral. The model is also applied to compute the radiation efficiencies from various microstrip bends and it is observed that circular bends exhibit minimum leakage amongst others. A sinusoidal line and a planar spiral are fabricated and measured. Results are shown to be in good agreement with those predicted by the analytical model.