Embedded element patterns and mutual impedance matrices in the terminated phased array environment

An embedded element pattern is the radiation pattern of a phased array when one array element is excited and all other elements are terminated in a specified impedance. Previously (Kelley, D.F. Proc. IEEE Int. Symp. Antennas and Propag Soc., vol.1, p.524-7, 2002), a relationship was derived between the mutual impedance matrix of a phased array and its short- and open-circuit embedded element patterns. Although this relationship is interesting in a theoretical sense, it is probably not of much practical value. Primarily, this is because it is difficult to obtain a "good" short or open circuit termination. Additionally, the terminal voltage (or current) at the excited element must be maintained at a value of unity with zero relative phase while the element pattern data is being collected. It is now shown that the mutual impedance matrix can also be calculated using embedded element patterns obtained using non-zero (and finite) terminations. This result is potentially more useful, because it requires that constant available power be supplied to each excited element rather than constant voltage or current maintained at the terminals.