A Broad-Banding Theory for Varactor Parametric Amplifiers-Part I

This paper is concerned with the development of a general and rigorous broad-banding theory for varactor parametric amplifiers. We first show that the parametric device exhibits some inherent network properties which are not shared with other twoterminal active devices. When the varactor is embedded in an arbitrary passive environment, it presents an impedance that can be characterized by a positive function rather than a positive-real function. The broad-banding theory presented takes into account also the interaction between the signal and sideband circuits through the frequency coupling action of the variable capacitor. Realizability conditions on the transducer power-gain function of a varactor parametric amplifier are derived. It is shown that the prescribed transducer power-gain function must satisfy a set of restrictions derived in part from the parasitic elements of the varactor. The main results of this paper are embodied in Theorems 1 and 2 which describe a synthesis method for the realization of broad-banding parametric amplifiers using varactors. It is shown that the synthesis requires, in general, two factorizations of the prescribed transducer power-gain function.