3. AC Voltmeters

AC voltage is harder than DC because "the voltage" means different things depending on what shape the waveform has. The number on the display is an attempt to summarize a continuous function with a single scalar, and the assumption baked into "average-responding" vs "RMS-responding" matters enormously for non-sinusoidal signals.

3.1 Average-responding AC voltmeter

Cheap AC voltmeters rectify the input (full-wave or half-wave) and feed the result to a DC voltmeter. The DC voltage is proportional to the average of the rectified waveform. For a pure sine of amplitude $V_p$, the average of the rectified signal is $V_{avg} = (2/\pi)V_p \approx 0.637 V_p$, while the RMS is $V_{rms} = V_p/\sqrt{2} \approx 0.707 V_p$.

The trick: manufacturers calibrate the scale so that for sine inputs, the meter reads RMS. The form factor (RMS/average) for a sine is $\pi/(2\sqrt{2}) \approx 1.111$, so the meter applies that fudge factor internally.

This is fine for the 50 Hz / 60 Hz line, distortion-free audio, and any other clean sinusoid. It is wrong by surprising margins for any other waveform. Triangle waves have form factor $2/\sqrt{3} \approx 1.155$; square waves have form factor 1; PWM, switching power supply ripple, audio with content, all have other ratios. A cheap multimeter applied to the AC ripple on a switch-mode supply will give a number, but probably not the right one.

3.2 RMS-responding voltmeters

The RMS is defined as $V_{rms} = \sqrt{\frac{1}{T}\int_0^T v(t)^2\, dt}$. To compute it honestly, you need to square the signal, average it, and take the square root. There are three classes of true-RMS implementation.

Thermal RMS converter. Pass the signal through a heater resistor; measure the resulting temperature with a sensor; for a paired feedback resistor, find the DC voltage that produces the same temperature. The DC voltage equals the RMS of the AC, by definition (RMS is the DC-equivalent heating voltage). Slow but extremely accurate, and completely waveform-agnostic: works for any signal up to thermal time constants. This is also the principle of the thermocouple-type RF ammeter we cover below.

Analog computational RMS chip. Specialized ICs like the Analog Devices AD536, AD636, AD736, and AD737 implement squaring (using log-antilog amplifiers or translinear circuits), averaging (with an external capacitor), and square-rooting. The AD736 is a popular choice for handheld true-RMS DMMs: low power, $\pm 0.3\%$ accuracy, works DC to ~200 kHz at full accuracy. Inside, the chip computes: $V_{out} = \sqrt{\overline{V_{in}^2}}$ The averaging time constant is set by an external capacitor. Tradeoff: large cap gives smooth reading on slowly-varying signals, small cap gives fast response.

Digital RMS computation. Sample the input with an ADC, square each sample, average, and take the square root in software. Modern bench DMMs and oscilloscopes use this approach because the same hardware also gives you the waveform. A scope's "Vrms" math measurement is just this calculation.

3.3 Crest factor

A subtle parameter that limits true-RMS instruments: the crest factor, defined as $V_{peak}/V_{rms}$. Sine has CF $= \sqrt{2} \approx 1.414$; a square has CF $= 1$; a sharp pulse train can have CF of 5, 10, 50. A true-RMS DMM has a maximum crest factor it can handle, typically 3 to 5 at full scale and higher at reduced scale. Why? The squaring stage saturates if peaks are too tall, and the result is wrong without warning.

This matters in switching power supply work. Inrush currents, gate drive currents, and rectifier conduction currents can have crest factors of 5 to 10. A handheld DMM rated CF=3 will read low. The Fluke 87V is rated CF=3 at full scale, CF=6 at half scale. The Keysight 34465A handles CF=10. Spec it deliberately.

3.4 Peak-responding voltmeter

A peak detector uses a diode and capacitor to charge to the peak of the waveform; a high-impedance buffer reads the cap. Output equals $V_{peak}$ (minus a diode drop, often compensated). Used in RF probes (where the rectified peak is a useful surrogate for amplitude) and in some specialized ham radio gear.

          D
   Vin o──►├───┬─────► Vout
              │
            ─┴─ C
              │
              ⏚

The capacitor holds the peak value; the diode prevents discharge except through the load. Often called an envelope detector: it follows the slow envelope of an AM-modulated RF signal, which is exactly what an AM radio's detector does.

3.5 Thermocouple RF ammeter

For RF current measurement (where conventional ammeters fail because of stray reactances), the thermocouple ammeter sends the unknown current through a small resistor, measuring the resistor's temperature with a thermocouple bonded to it. The thermocouple voltage is amplified and displayed. Because heating is proportional to $I^2$, the meter inherently reads true RMS regardless of waveform, and works from DC to several hundred MHz.

The cost: thermal lag (slow response, seconds), fragility (a single overload can melt the resistor), and a square-law scale (compressed at low end, stretched at high). Used in legacy ham radio transmitter ammeters and some specialized RF labs. The principle, current-to-heat-to-thermocouple-to-voltage, is the same as the thermal RMS converter, just optimized for current rather than voltage.

3.6 Multi-range AC voltmeters and range extension

Same principles as DC. For analog AC voltmeters, an attenuator at the input scales the signal down before rectification; for true-RMS chips, the input attenuator is followed by the RMS conversion. Range extension at high voltages uses precision capacitive dividers (better than resistive at high frequency because resistors have stray capacitance that ruins HF response).