Decomposition and synthesis of nonlinear n-ports

This paper represents a sequel to the recent work on algebraic n-ports [1]. The problem of synthesis leads naturally to a consideration of canonic decomposition of nonlinear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ports into basic building blocks. In particular, every current-controlled {voltage-controlled} resistive 2-port is shown to be realizable in a canonic form consisting of a series {parallel} connection between a reciprocal nonlinear 2-port and an element of a new class of nonlinear 2-ports called quasiantireciprocal 2-ports. This basic result is then generalized to allow the synthesis of a very large class of nonlinear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ports in terms of only two building blocks; namely, reciprocal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ports and quasi-antireciprocal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ports. Moreover, the class of quasi-antireciprocal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ports is shown to be realizable in terms of only nonlinear resistive 1-ports, reciprocal 2-ports, and gyrators.