text: The reflection coefficient is determined by the coupling between cavity and waveguide. When the frequency of microwave is resonant frequency, the reflectance, , of the cavity is expressed as follows:
  Here  is the quality factor of the cavity including the sample,  is the quality factor of the external coupling, which is generally adjusted by iris. The total loaded quality factor of the cavity, , is defined as follows:
  The photo-generated charge carriers reduce the quality of the cavity, . When the change of quality factor is very small, the change of reflected microwave power is approximately proportional to the change of dissipation factor of the cavity. Furthermore, dissipation factor of the cavity is mainly determined by the conductivity of the inside space including the sample. Consequently, the change in the conductivity, , of the cavity contents is proportional to relative changes in microwave intensity:
  Here  is the background (unperturbed) microwave power measured coming out of the cavity and  is the change in microwave power as a result of the change in cavity conductance.  is the sensitivity factor determined by the quality of the cavity,  is the geometry factor of the sample.  can be derived by Taylor expanding of the reflectance equation:
  Here  is the resonant frequency of the cavity in Hertz unit,  is the vacuum permittivity,  is the relative permittivity of the medium inside the cavity. The relative permittivity should be considered only when the cavity is filled by solvent. When the sample is inserted into dry cavity, only vacuum permittivity should be used because most of the inside space is filled by air. The sign of  depends on whether the cavity is in the under-coupled (lower) or over-coupled (upper) regime. So, the negative signal is detected in over-coupled regime, , whereas the positive signal is detected in under-coupled regime, . No signal can be detected at critical coupling condition,  
   is determined by the overlap between the electric field and the sample position:
  Here  is the electric field in the cavity.  and  denote the total inside volume of the cavity and the volume of photo-generated carriers, respectively. If the thickness of the sample is sufficiently thin (below several μm), the electric field to photo-generated carriers would be uniform. In this condition,  is approximately proportional to the thickness of the sample. Above conductivity equation can be expressed as follows:
  Here  is the elementary charge,  is the transmittance of the sample at the excitation wavelength,  is the incident laser fluence,  is the quantum yield of photo-carrier generation per absorbed photon,  is the sum of the electron and hole mobility,  is the thickness of the sample. Because  is linearly proportional to the thickness, only the fractional absorbance of the semiconductor (between 0 and 1) should be additionally measured to determine the TRMC figure of merit  (e.g. using ultraviolet–visible spectroscopy):