Block diagram transformations for systems with one nonlinear element

Rules for the transformation of block diagrams representing linear systems are examined to determine their applicability for systems containing nonlinear elements. General proofs and examples are given which show that the original block diagram for any system with one input, one output, and one nonlinear element characterized by y = φ(x), where x and y are its instantaneous input and output, can always be reduced to four topologically identical and mathematically equivalent block diagrams. In these diagrams, the nonlinear element may appear as either a forward or feedback block with its input and output in either a normal or reversed cause-effect relationship.