In this paper we analyze plane wave coupling to transmission lines rotating randomly over an infinite and perfectly conducting ground and present an efficient method to calculate average voltage. Under the assumption of small rotation quantity, the factors affecting the induced voltage and their effects are analyzed and then an efficient method to calculate the average voltage is presented when the distribution of the random rotation angles is uniform in [-π, π]. The results show that voltage variation is mainly due to the change of the source term. The effects of the source term increase linearly with the magnitude of the incident wave, change periodically with the rotation angle, and are larger in the high frequency range than in the low frequency range. The results show that the average voltages obtained by the proposed method agree well with those via the Monte Carlo method and the proposed method is much more efficient. The results also imply that the effect of random rotation is more important than that of random translation.
