Double-sideband parametric conversion using non-linear resistance and capacitance

The power gain of a double-sideband up-converter using both non-linear resistance and capacitance is found. With the assumption that the second-harmonic components of resistance and capacitance are zero, it is shown that if the elements are pumped in quadrature the forward gain can be made arbitrarily high with `cold¿ tuning whilst the reverse gain is zero. Furthermore it is shown that unidirectional operation with arbitrarily high forward gain can be achieved for any up-conversion frequency ratio. Expressions are also derived for the bandwidth and noise figure of the device. Finally, it is also shown that arbitrarily high forward gain and unidirectionality appear possible when the second-harmonic components of resistance and capacitance are non-zero.