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It has recently been proposed by a few authors that the trigonometric Pythagorean identity can be used for the implementation of precision full-wave rectifiers for sinusoidal signals with advantages with respect to diode-based rectifiers for amplitudes in the hundreds of mV range. The approaches proposed so far require a 900 phase shifter and this results in the obvious limitation that the input signal frequency must be known prior to amplitude measurement. In this study, the authors propose a new precision full-wave rectifier, capable of overcoming this limitation. Starting from the sinusoidal input, a squared co-sinusoidal signal is obtained in a wide frequency range by multiplying the output signals of an integrator and of a differentiator. The signal thus obtained is added to the input signal squared, and a square root extractor is employed for obtaining a DC signal proportional to the amplitude of the input signal. A prototype capable of operating within a two decades frequency range across 3200 Hz has been realised and tested with an accuracy better than 2% and a residual ripple of less than 0.3% for input amplitudes larger than 100 mV. A configuration capable of operating in the MHz frequency range is also proposed.