A bipolar four-quadrant analog multiplier based on the quarter-square technique, which is constituted from unbalanced emitter-coupled pairs, and some methods for extending the input voltage range, are described. The building blocks for the circuit consist of an unbalanced emitter-coupled pair with different emitter areas, an emitter-coupled pair with an input bias offset, and an unbalanced emitter-coupled pair with unbalanced emitter degeneration. A basic squaring circuit is realized from two identical unbalanced emitter-coupled pairs with emitter area ratio K and cross-coupled inputs and parallel-connected outputs. The quarter-square multipliers proposed in this paper can operate under low supply voltage (typically>
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K. Kimura (1994) studied this question.
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