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Electrochemical impedance spectroscopy (EIS) is a powerful tool for characterizing biological materials, including lipid bilayers and many membrane proteins. However, traditional EIS methods are very slow at low frequencies, where these materials respond in biosensor applications. To enable dense arrays of biosensors based on tethered bilayer lipid membranes (tBLM), a new approach for EIS has been developed. This paper introduces a methodology and circuit that can rapidly perform EIS in the 1 mHz to 100 kHz frequency range. A circuit implementing this new approach has been realized in 0.5 mum CMOS technology with 3.3 voltage power supply. In the sub-hertz range where membrane protein biosensor response is most critical, the circuit can measure impedance with 8 bit resolution in 20 ms, three orders of magnitude faster than traditional integrator-based circuits. Though tailored for the low frequency spectrum in biosensor applications, the EIS circuit can be used to measure impedance in a wide range of sensory materials.