Phased Array Feed Model Equations corresponding to two definitions of embedded beam pattern

In this report, we present the phased array feed (PAF) model equations for two definitions of embedded beam patterns. In Roshi \& Fisher (2016), we presented the PAF model by defining the embedded beam pattern as the beam pattern due to a 1 V excitation to one port and all other ports short circuited. This embedded beam pattern is referred to as voltage-embedded-beam (VEB). The embedded beam pattern can also be defined as the beam pattern due to a 1 A excitation to one port and all other ports open circuited. This definition is usually used in engineering literature and we refer to the pattern as current-embedded-beam (CEB). Here we derive the relationship between the two embedded beam patterns and present the corresponding model equations.