Figure 4

Considerations of the external circuit for the three-wave nondegenerate case. (a) This figure depicts the physical, general circuit considered in this section, containing a flux-pumped SQUID. This circuit accounts for an external source current, $i_s$, as well as external ($Y_{\mathrm{ext}}$) and local shunt ($Y_{\mathrm{sh}}$) admittances. (b) It is possible to represent the general circuit in an equivalent way that separates the external loading effects of the circuit at the “signal” (${\omega }_1$) and “idler” (${\omega }_2$) frequencies. This is done by introducing hypothetical, ideal bandpass filters at ${\omega }_1$ and ${\omega }_2$. These filters act open-circuited at their respective frequency, but short-circuited for all other frequencies. In this representation, the external admittance, $Y_{\mathrm{ext}}$, is represented at different frequencies by $Y_1$ and $Y_2$. The input admittance ($Y_{\mathrm{SQ}}$) is then based on the signal voltage response to current $i_1$, which depends upon the idler in a way that may allow for gain.