Optimum Synthesis of Wide-Band Parametric Amplifiers and Converters

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Abstract
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 \approx \frac {\omega_0} {\omega_{0}\prime} G_c \aaprox \frac {1} {4 |p|^2}whereG_aandG_care the power gain of the amplifier and the converter, respectively,\omega_0and\omega_0 \primeare the center frequencies of the signal and the idler bands, respectively, and\rhois the reflection coefficient which is limited in bandwidth by the following formula:\frac {B} {\omega_0} \ln \arrowvert \frac {1} {\rho} \arrowvert \leq \frac {\pi} {2} \frac {C_1} {C_0} \sqrt{\frac {\omega_0 \prime} {\omega_0}}Bis the bandwidth, andC_0 + 2 C_1 \cos\overline{\omega} 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.

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