Improved analysis of implicit RMS detectors

In this paper, the output voltage of the implicit root-mean-square (RMS) detector, which is composed of two voltage-to-current converters, a multiplier/divider, and a low-pass filter and excited by an input voltage comprising a single sinusoid, is approximated using a Fourier cosine series. Using this approximation, closed-form analytical expressions for the output voltage components of the implicit RMS detector are derived. The results obtained are compared with previously published results. This comparison shows that, using the proposed approximation, an improved estimation of the RMS value and the amplitudes of the second- and fourth-harmonic components of the implicit RMS detector can be achieved for any value of the input frequency and is not restricted to large values compared with the cutoff frequency of the low-pass filter.