  The cavity haloscope has been employed to detect microwave photons resonantly
converted from invisible cosmic axions under a strong magnetic field. In this
scheme, the axion-photon conversion power has been formulated to be valid for
certain conditions, either $Q_{cavity}\ll Q_{\rm axion}$ or $Q_{cavity} \gg
Q_{axion}$. This remedy, however, fails when these two quantities are
comparable to each other. Furthermore, the noise power flow has been treated
independently of the impedance mismatch of the system, which could give rise to
misleading estimates of the experimental sensitivity. We revisit the analytical
approaches to derive a general description of the signal and noise power. We
also optimize the coupling strength of a receiver to yield the maximal
sensitivity for axion search experiments.
