Some Properties of Multiple-Antenna-Port and Multiple-User-Port Antenna Tuners

A user port impedance range and a user port tuning range characterize an antenna tuner at a given frequency. These sets and their local dimensions are defined and studied for an antenna tuner having any number n of antenna ports and any number m of user ports. A reciprocal antenna tuner is said to have a full tuning capability if it can provide or compensate all relevant small impedance variations, under the assumption that its adjustable impedance devices can provide suitable reactance values. For reciprocal antennas and a reciprocal antenna tuner, it is proven that the local dimension of the user port impedance range is equal to m(m+1) if and only if the antenna tuner has a full tuning capability. We use this result to study an antenna tuner made of several uncoupled single-antenna-port and single-user-port antenna tuners. We also use this result to show that a new multiple-antenna-port and multiple-user-port antenna tuner has a full tuning capability.