Relationships between active element patterns and mutual impedance matrices in phased array antennas

In the context of phased array antennas an active element pattern is the radiation pattern of an array when only one element in the array is excited and all of the others are terminated in some specified impedance, typically the output impedance of the sources that normally drive the elements. It is shown here that a combination of two types of active element patterns can be used to find the mutual impedance matrix that relates the element terminal voltages of a phased array to the terminal currents. The first type is found by forcing the terminal voltage of the active element to be unity at zero phase while the terminals of all the other elements are shorted. The second type is obtained by forcing the terminal current to be unity while the undriven feed points are open-circuited. The former is called the short-circuit active element pattern and the latter the open-circuit active element pattern.