Abstract
A novel squarer is described in which the required result is a linear combination of readily produced secondary variables.The square of a variable can be expanded in a series, where each term is derived from the preceding one by linear operations and the operations of maximum and minimum selection. ‘A converted’ variable is associated with each term of the expansion. The square is equal to a linear combination of the converted variables and the square of the last converted variable. The range of variation of successive converted variables decreases by half, and the series converges by a factor of one quarter per term.The expansion stands in direct correspondence to electronic squaring circuits which use linear elements and diode selection circuits in a cascade connection. When used in conjunction with any half squarer, the cascade squarer increases its accuracy by factors of 4, 16 … if 1, 2 … stages are used. Alternatively, a sufficient number of stages provides a complete squarer.Accuracies of ±0.1% are readily obtained in very simple circuits, and the speed of response is extremely fast.Several examples of circuits of cascade squarers are given.
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