rules of thumb for R and C

To prevent the AC source from dominating or reverse biasing the current through the QCL, ${U_{AC} < U_Q}$ must always be given (in absolute values). Furthermore, as the AC voltage source together with ${R_{AC},C}$ is forming a current source, to prevent variations of QCL dynamic resistance ${X_Q}$ to influence the AC current, ${R_AC+X_C » X_Q}$ must be guaranteed. As the generator for ${U_{AC}}$ will have an impedance ${Z_{AC}}$, impedance matching demands for ${R_{AC}+X_C+X_Q=Z_{AC}}$. Putting these constraints together leads to ${I_{AC} < U_Q / Z_{AC}}$.

For the capacitor ${C}$ to let pass the AC current, ${2\pi R_{AC} C > 1 / f}$ must be true, and with ${X_C = R_{AC} / 100}$ or smaller to make sure that the impedance of the AC current source does not vary too much with frequency, it follows that roughly ${C > 8 / Z_{AC} / f}$.

For a 50 $\Omega$ generator at 10kHz, ${C}$ should therefore be of the order of 16uF or larger.

Please keep in mind that such high capacity components may have a remarkably high inductivity, so it may be useful to put a second capacitor of small value (some nF, Tantalum or similar non-polarized type) in parallel to the one calculated before.