In this paper, a circuit method is proposed to estimate the resonance bandwidth of transducer. A filter is used to shift the resonant frequency with its transition band. Assuming the response of sensor is Gaussian distributed near resonant frequency, we can estimate the bandwidth of resonance from the shifted frequency. According to some findings in Quarts Crystal Microbalance (QCM) theory, the resonance bandwidth of crystal is affected by the viscosity loading. So our circuit method can be used to measure the viscosity of biological tissue. Since no DSP components are involved here for spectrum analysis, our method will be a low-cost and competitive solution for the viscosity sensing in medical application.