We demonstrate theoretically an active tunable filter with a simple two-coupled-ring structure

which yields very narrow passband based on Fano resonance in the transmission spectra.The active and tunable performances of the microring filter are achieved by the pump waveguide and micro-heating device

respectively.The formulas of the resonant transmission and the ultra narrow pass-band linewidth are derived through the coupled-mode theory.Then

the relationships between the gain and the transmission and linewidth

as well as the thermo-optic effect and the resonance wavelength of the microring waveguide are simulated useing MATLAB

respectively.The numerical calculation and simulation results show that the gain can increase transmittance and compress linewidth of the microring filter.It is also shown that the thermo-optic effect can make the resonant wavelength red shift or blue shift.