On Wacker’s Essential Equation in the Extrapolation Measurement Technique

The generalized three-antenna method is a standard method for measuring on-axis gain and polarization of an antenna without a priori knowledge. The cornerstone of the method is the use of the extrapolation technique and the key relationship in the extrapolation technique is Wacker’s equation. This equation expresses the received signal as a function of the separation distance between any two antennas. The derivation of Wacker’s equation is not readily available in the literature. In this paper, we provide a streamlined derivation of Wacker’s equation and address some of the common misconceptions associated with it.