A circuit for the square root of the sum of the squares

A piecewise-linear network can produce an output proportional to the square root of the sum of the squares of a set of input voltages, using resistors and diodes alone. The required relationship between voltages can be represented by a multi-dimensional cone; the approximation replaces this cone by an inscribed pyramid. The resulting circuits have a dynamic range equal to that of the diodes from forward conduction point to reverse breakdown. Practical circuits are given which find the root sum of two squares to within 3 per cent of the correct value with only eight diodes. Formulas show that the number of diodes depends roughly inversely on the square root of the maximum allowable per cent error.