A cheap multimeter on AC mode lies to you. It measures the average of the rectified signal and scales by 1.11 (the form factor for a pure sine wave). Feed it a square wave, a triangle wave, or — worst of all — a distorted current waveform from a switching power supply, and the reading can be off by 40% or more. True RMS-to-DC converters solve this by computing the actual root-mean-square value, which corresponds to real heating power in a resistive load.

The mathematical definition is V_RMS = √(average of v²(t)). Building this directly with analog circuits requires three operations: square, average, and square root. The classic implicit-computation approach (used in the AD536, AD636, AD737) cleverly avoids the explicit square root by using log/antilog feedback: it computes |V_in|²/V_out, low-pass filters it, and forces it to equal V_out. Algebraically, that means V_out = √(avg(V_in²)) — exactly RMS — with only one squaring operation and one feedback loop instead of cascading squarer + divider + square-rooter.

Real-world example: Measuring the current draw of a variable-frequency drive (VFD) motor controller. The current waveform is a chopped, harmonic-rich mess at the switching frequency. Use an AD8436 (rail-to-rail true RMS converter) fed from a Hall-effect current sensor. The chip outputs a clean DC voltage proportional to the true heating current — feed that into your ADC and you get a reading that actually predicts how hot the motor windings will get. A non-RMS meter on the same signal might read 4.2 A when the real heating-equivalent current is 6.8 A.

The crest factor trap: Every RMS converter has a specified crest factor (peak-to-RMS ratio) it can handle accurately, typically 5:1 to 10:1. For SCR-chopped loads or pulsed signals, crest factor can hit 7 or higher. Exceed the spec and the squaring stage saturates, dragging your reading low.

Rule of thumb — averaging capacitor: The output ripple and settling time are dominated by C_AV. For 1% settling error at the lowest input frequency f_min, size it as:

• C_AV ≈ 25 / (f_min × R_internal), where R_internal is the chip's internal averaging resistor (typically 25 kΩ).
• For audio (f_min = 20 Hz): C_AV ≈ 50 µF. For 60 Hz mains: ≈ 17 µF. Bigger = lower ripple but slower response.

Modern alternative: just sample the signal fast (≥10× the highest harmonic), square in firmware, and average. A 24-bit sigma-delta ADC plus a Cortex-M0 beats most analog RMS chips below 10 kHz — but above that, the analog approach still wins on power and latency.