An equivalent circuit for a non-degenerate parametric amplifier is shown in Fig. 11.1. A nonlinear capacitor is surrounded by three parallel LCR circuits, which represent the signal, idler and pump circuits, respectively.

The charge \(q\) on the nonlinear capacitance is a function of the voltage across its terminals. Using the Taylor series expansion, the charge may be expressed in the form:

\[\begin{equation} q(t) = a_1v(t) + a_2v^2(t) + a_3v^3(t) + \cdots \label{eq:charge-taylor} \end{equation}\]

When all the coefficients except the first and second terms are zero, the charge varies quadratically with the voltage,

\[\begin{equation} q(t) = Cv(t) + a_2v^2(t) \label{eq:charge-quadratic} \end{equation}\]