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 Qcavity Lt Qaxion or Qcavity Gt Qaxion. 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.