Gain and directional properties of three- and four-frequency parametric devices

An examination is made of the properties of three- and four-frequency parametric devices using nonlinear resistance, capacitance and inductance, pumped at the same frequency but at different phase angles, more conventional parametric amplifiers and convertors being treated as special cases. It is shown with the aid of an equivalent circuit that there are fundamental differences between three-frequency devices with and without nonlinear resistance, only the former, for example, being capable of unidirectional operation. The difference is less marked in four-frequency devices, and it is shown that a wide range of properties are available, depending on the complication that can be tolerated.