Optimum Synthesis of Wide-Band Parametric Amplifiers and Converters

This paper derives the theoretical limitation on gain and bandwidth for parametric amplifiers and inverting-type up-converters. It shows that the transducer power gain of an amplifier or a converter can be related to the reflection coefficient of a simple matching network asG_a ≈ {ω_0} {ω₀} G_c 1/4 |p|^2whereG_aandG_care the power gain of the amplifier and the converter, respectively,ω_0andω_0 the center frequencies of the signal and the idler bands, respectively, and the reflection coefficient which is limited in bandwidth by the following formula:B/ω_0 ln 1/ρ ≤ π/2 C_1/C_0 √ω_0 /ω_0Bis the bandwidth, andC_0 + 2 C_1 cosω̄ trepresents the variable capacitance. Optimum Butterworth filters are used as the coupling networks. Condition for optimum matching is determined together with element values of the circuit. The theoretical limitation on bandwidth can be approached if the number of elements in the coupling network is increased. The design of optimum wide-band amplifiers and converters becomes straightforward, thus eliminating any cut and try process.