Further Generalization of the Low-Frequency True-RMS Instrument

This paper shows that the use of random uniform dither in harmonic measurement can significantly shorten both the word of the input A/D converter and the word of the applied base function (sine and/or cosine, prestored in memory), without accuracy loss. This simplifies the hardware for a precise instrument for harmonic measurement. Theoretical considerations demonstrate that the upper limit of the absolute measurement uncertainty is identical for every harmonic coefficient. It is shown theoretically, by simulation, and by experiment that a 6-bit dithered A/D converter word, an 8-bit dithered base function word, and a 6 × 8 (14-bit) multiplier word assure a measurement of 16 harmonics (16 sine and 16 cosine components) with 13-bit accuracy. The measurement of 1 × 16 harmonics is realized in a small programmable-logic-device (PLD) chip.