CMOS transconductance multipliers: a tutorial

Real time analog multiplication of two signals is one of the most important operations in analog signal processing. The multiplier is used not only as a computational building block but also as a programming element in systems such as filters, neural networks, and as mixers and modulators in a communication system. Although high performance bipolar junction transistor multipliers have been available for some time, the CMOS multiplier implementation is still a challenging subject especially for low-voltage and low-power circuit design. Despite the large number of papers proposing new CMOS multiplier structures, they can be roughly grouped into a few categories. This tutorial provides a complete survey of CMOS multipliers, presents a unified generation of multiplier architectures, and proposes the most recommended MOS multiplier structure. This tutorial could serve as a starting reference point (and metric) for comparison of new CMOS multiplier circuit configurations. An illustrative CMOS chip prototype verifying theoretical results is presented.