Analysis of Four-Frequency Nonlinear Reactance Circuits

Several advantages of multiple-frequency nonlinear reactance circuits are described in this paper. In particular, a circuit is considered in which a nonlinear reactance couples four basic frequencies: ω₀, ω₁,ω₂, and ω₃; these are so related that ω₂ = ω₀ + ω₁ and ω₃ = ω₀ - ω₁. Here, ω₀ is taken to be the power source or pump. It is found to be desirable to allow for the possible presence of the pump harmonic, 2ω₀, and individual cases are characterized by whether 2ω₀, is present or not. The major results are as follows: 1) Unlimited amplification gain is theoretically possible at frequencies higher than the pump, by reflecting negative input resistance at ω₂, but without relying on any effects due to pump harmonics. 2) Unlimited up- or down-conversion gains between ω₁ and ω₂ are theoretically possible in the additional presence of the first pump harmonic, but without reflecting negative input or output resistance. 3) Unlimited amplification gain is theoretically possible at frequencies both lower and higher than the pump fundamental, without reflecting negative input resistance.