Impedance matrix of an antenna array in a quasi-optical resonator

The power from numerous millimeter-wave solid-state sources can be efficiently combined using quasi-optical techniques. One technique is to place an array of active radiating sources within a quasi-optical resonator. The driving point impedance of each antenna is strongly affected by the presence of all other active antennas as well as by the mode structure and Q of the resonator. The impedance matrix for an array of antennas radiating into a plano-concave open resonator is determined here through use of the Lorentz integral. The resulting expressions include the effect of diffraction loss and are valid for arbitrary reflector spacing, source frequency, array location and geometry. The result can be used for impedance matching of each active source to its antenna, facilitating design of an efficient power combining system. Simulations using the impedance matrix in conjunction with an antenna impedance model are compared with two-port measurements