Consider the following circuit designed to obtain the root mean square (RMS) voltage of sinewaves (without any dc component).

The first stage operates as a half-wave rectifier with the input-output characteristic depicted below. The second stage consists of a multi-feedback low-pass filter (LPF) with unitary inverting gain (i.e., in the passband) and a cutoff frequency () much lower than the frequency of the input voltage signal .

Assuming , determine such that the output voltage corresponds to the RMS value of the input signal .