Analytical Solution for Maximum Differential-Mode Radiated Emissions of Microstrip Trace

In this paper, a novel analytical solution was presented for estimating the maximum differential-mode (DM) radiated emission from electrically long PCB traces using transmission-line theory, travelling wave antenna, and far-field magnetic vector potential. The analytical solution was simplified for matched load in which only forward travelling wave was considered. Additionally, a simple expression for predicting maximum DM-RE from electrically short traces was obtained using proper simplifications. The results from the proposed analytical model were then compared to the results obtained from 3-D HFSS full-wave simulation and the measurement performed in a semianechoic chamber. Good agreements within ±3 dB were obtained over a wide range of frequency.