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This paper presents the design and analysis of an interface circuit for MEMS or biomedical sensor applications. This circuitry performs the function of an analog-to-digital converter. A first-order 1-bit sigma-delta (Σ-Δ) analog-to-digital converter is designed and simulated using Silterra 0.13μm CMOS process technology with power supply of 1.2V through Cadence. Then the circuit simulation results are transferred to MATLAB, in order to get the frequency domain power spectral density (PSD). The simulation results on noise and error analysis are compared with those from a traditional analog-to-digital converter to prove that sigma-delta is performing better in the case of weak signals acquisition.