Pumping conditions for parametric gain with a nonlinear immittance element

Abstract

The necessary conditions for parametric amplification obtained by Penfield for the series nonlinear capacitive-linear resistive element are extended to the case when the resistive element is also nonlinear. The role played by the phase angle between the capacitive and resistive modulation, first considered by Engelbrecht for the frequency converter and the special case of quadrature pumping, is also taken into account. On the basis of the gain criteria, a figure of merit of a parametric element applicable to the pumped condition is also extended to include the type of element considered. It is demonstrated that, all things being equal, the most favorable pumping phase is that for which the capacitive variation at the pump frequency lags the resistive variation by 90° in phase. It is shown that of the nonlinear elements now being used for parametric applications, none satisfy the favorable phase condition. A convenient gain-frequency graph summarizing most of the theoretical conclusions is presented. Finally, it is also proved that for the case where the signal frequency is lower than the idler frequency, the highest frequency of operation obtainable with an existing series capacitive-resistive element can never be increased by the addition of a passive series nonlinear resistor, regardless of the pumping phase achievable by this addition.

Keywords

Affiliated Institutions

• RTX (United States) US

Related Publications