An Analog Squaring Technique Based on Asynchronous Sigma–Delta Modulation

Accurate analog squarers are required for different signal processing functions, such as amplitude modulation, frequency shifting, signal power estimation, and neural and image processing. Transistor-level analog squarers suffer from limited accuracy, particularly in modern deep-submicrometer technology, where the squared law of the MOS transistor in the saturation region is no longer valid. Based on the asynchronous sigma-delta modulator (ASDM), a new circuit that provides the squared value of the input signal is proposed. For slowly varying input signals, the filtered output is a replica of the squared input signal. In this brief, the proposed analog squarer is studied, and the analytical results are validated by simulation in the time domain. The effect of analog imperfections on the accuracy of the squarer is also analyzed by showing that a high signal-to-noise-plus-distortion ratio can be obtained for typical values of the mismatch and up to frequencies near half the maximum frequency of the ASDM limit cycle.