A sigma-delta (ΣΔ) difference-of-squares LOG-RMS to digital converter for true RMS detection by merging a ΣΔ modulator with an analog LOG-RMS to DC converter based on a difference-of-squares. Chopper-stabilization, implemented through commutators running at two different frequencies, can be employed to reduce sensitivity to DC offsets and low-frequency errors, resulting in an extension of the useful input-referred dynamic range. High-order ΣΔ LOG-RMS converters can be implemented with a loop filter containing multiple integrators and feedforward and/or feedback paths for frequency compensation. The resulting implementations are ΣΔ difference-of-squares LOG-RMS to DC converters with a natural digital output and a logarithmically compressed dynamic range.