Synthesis of new nonlinear network elements

The basic problem of synthesizing a nonlinear resistor, inductor, or capacitor with a prescribed i-v, φ-i, or q-v curve is solved by introducing three new linear two-port network elements, namely the mutator, the reflector, and the scalor. The mutator has the property that a nonlinear resistor is transformed into a nonlinear inductor, or a nonlinear capacitor, upon connecting this resistor across port two of an appropriate mutator. The reflector has the property that a given i-v, φ-i, or q-v curve can be reflected about an arbitrary straight line through the origin. The scalor is characterized by the property that any i-v, φ-i, or q-v curve can be compressed or expanded along a horizontal direction, or along a vertical direction. Using these new elements as building blocks, it is shown that any prescribed single-valued (which need not be monotonic) i-v, φ-i, or q-v curve can be synthesized. Active circuit realizations for each of these new elements are given. Laboratory models of mutators, reflectors, and scalors have been built using discrete components. Oscilloscope tracings of typical mutated, reflected, and scaled i-v, φ-i, and q-v curves are given. The experimental results are in good agreement with theory at relatively low operating frequencies. The practical problems that remain to be solved are the stability and frequency limitation of the present circuits.