A general theory of a passive multi-port system is presented, incorporating an arbitrary number of feed and load ports. The result is a nonlinear equation system, in which the solution variables are the load admittances, connected to the load ports. The solution ensures impedance match at all feed ports at one particular frequency. It is also shown how this theory can be applied to adaptive and reconfigurable antennas, by using switches to include or exclude some of the load admittances. If, by open state of a switch, the corresponding load admittance is excluded, then the nonlinear equation system is simplified. In general, one load admittance per feed port is required to obtain complex conjugate impedance match. Then, the admittance has a real and an imaginary part, where the real part relates to a resistor, adding loss to the system. It is shown how loss-less matching can be obtained by using two, purely reactive admittances per feed port.
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