  Due to the quantum nature of current flow in single-electron devices, new
physical phenomena can manifest when probed at finite frequencies. Here, we
present a semi-classical small-signal model approach to replace complex
single-electron devices by linear parametric circuit components that could be
readily used in analogue circuit simulators. Our approach is based on
weakly-driven quantum two-level systems and here we use it to calculate the
finite-frequency impedance of a single-electron double quantum dot (DQD). We
find that the total impedance is composed by three elements that were
previously considered separately: a dissipative term, corresponding to the
Sisyphus resistance, and two dispersive terms, comprised of the quantum and
tunneling capacitance. Finally, we combine the parametric terms to understand
the interaction of the DQD with a slow classical electrical oscillator which
finds applications in non-resonant state readout of quantum bits and parametric
amplification.
