Linear transformation converter and its application to the synthesis of nonlinear networks

A generalized approach for synthesizing a prescribed resistive nonlinear n-port is presented with the help of a linear 2nport called the linear transformation converter (LTC). It is proved that a large class of voltage-controlled (current-controlled) resistive nports can be realized by using only one LTC and an appropriate homeomorphic nonlinear n-port. The LTC is shown to be decomposable into the cascade connection of a"rotator," "reflector," and "scalor." This factorization provides not only a general realization technique, but also a geometrical interpretation of the capabilities of the 2-port LTC to transform a monotonic characteristic curve into a prescribed multivalued curve. In particular, necessary and sufficient conditions are given for realizing a multivalued two-terminal resistor by connecting an appropriate monotonic resistor across port 2 of a 2-port LTC.