Minimum complexity decoupling networks for arbitrary coupled loads

Decoupling networks that match N coupled loads to N decoupled sources can be realized by generalized Π-networks of reactive impedances. For a set of N coupled loads, the realization of the decoupling network is not unique, and networks that involve many impedances can be difficult to lay out on circuit boards. In this paper, we establish that a decoupling network requires a minimum of N² + N impedances for N arbitrarily coupled loads, and provide examples constructed by a systematic method that realizes this lower bound.