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: /spl omega//sub 0/, /spl omega//sub 1/,/spl omega//sub 2/, and /spl omega//sub 3/; these are so related that /spl omega//sub 2/ = /spl omega//sub 0/ + /spl omega//sub 1/ and /spl omega//sub 3/ = /spl omega//sub 0/ - /spl omega//sub 1/. Here, /spl omega//sub 0/ 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, 2/spl omega//sub 0/, and individual cases are characterized by whether 2/spl omega//sub 0/, 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 /spl omega//sub 2/, but without relying on any effects due to pump harmonics. 2) Unlimited up- or down-conversion gains between /spl omega//sub 1/ and /spl omega//sub 2/ 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.