RG flow of central charge
ceff is investigated for the two boundary sine-Gordon model at the free Fermi limit. Thermodynamic Bethe ansatz approach is used to check the non-monotonic decreasing properties of
ceff, its resonance, and the modification of
ceff due to the mismatch of the periodicity of a Lagrangian parameter and that of the boundary scattering parameter. The detailed analysis uses the singularity structure of the system on the complex rapidity plane.