Digital multimeters

The digital multimeter is the most used instrument on any electronics bench. It measures DC and AC voltage, DC and AC current, resistance, and usually continuity, diode forward voltage, capacitance and frequency as well. It looks simple: turn the dial, touch the probes, read the number. But every function connects the meter into your circuit in a different way, and in every function the meter disturbs the circuit a little. This lesson explains what happens inside the meter in each mode, how the meter loads the circuit, what true RMS means, and how to avoid the mistakes that give wrong readings or blown fuses.

Leo's task this week is to characterize the input stage of the pedestrian controller's push-button and loop-detector inputs. Each input has a high-value resistor divider and a filter capacitor, and Amara wants the voltages and currents at each node, the resistance of each part, and the AC ripple on the 24 V rail. Several of those measurements go wrong in instructive ways.

Inside a digital multimeter

At the heart of a bench or handheld multimeter is an analog-to-digital converter, usually a slow, very accurate integrating type that averages its input over a fixed time, often a whole number of power-line cycles so that 60 Hz hum averages to zero. In front of the converter is a signal conditioning section that turns every quantity into a small DC voltage. For DC volts, a precision resistor divider scales the input. For current, the current flows through a small shunt resistor and the meter measures the voltage across it. For resistance, the meter drives a known current through the unknown resistor and measures the voltage. For AC, a converter produces a DC voltage proportional to the RMS value of the input. The number of counts in the display, the range resistors and the shunts set what each range can show.

Measuring voltage and the loading error

In voltage mode the meter connects in parallel with the part being measured, and an ideal voltmeter would draw no current. A real one has a finite input resistance, typically 10 MΩ on DC ranges for a handheld or bench meter, and sometimes selectable to over 10 GΩ on the lowest ranges of a bench meter. When the circuit you probe has a high source resistance, that 10 MΩ forms a divider with it and the meter reads low. The rule of thumb is that the error is roughly the ratio of the source resistance to the meter's input resistance: probing a node with a 100 kΩ Thévenin resistance with a 10 MΩ meter reads about 1 % low.

Loading error is a systematic error, so it does not show up as scatter. A good habit is to estimate the Thévenin resistance of every node you probe. For the low-impedance nodes of most circuits, such as power rails, op-amp outputs and logic pins, it is far below a megohm and the meter's loading is negligible. For high-value dividers, high-impedance sensors and the gates of MOSFETs, it can dominate the measurement.

Measuring current and the burden voltage

To measure current, the meter must be inserted in series with the circuit, which means breaking the circuit and routing the current through the meter's shunt. The voltage across the shunt is called the burden voltage. On a typical handheld meter, the burden can be about 1 mV per milliampere on the milliampere range, or a few hundred millivolts at full scale on any range. In a 24 V circuit that hardly matters, but in a 3.3 V circuit, or when measuring the current into a diode or LED, a few hundred millivolts of burden can change the current you are trying to measure. Many meters list the burden voltage or shunt resistance for each range in their specification.

Current measurement is also where meters are most often damaged. The current jacks connect almost directly across the probes, so touching the probes across a voltage source with the leads in a current jack drives a large current through the shunt and fuse. Good meters have high-breaking-capacity fuses on the current inputs; cheaper ones may not. Two rules prevent almost all of this: always plan where the meter will be inserted with the circuit off, and always return the red lead to the voltage jack as soon as the current measurement is finished. Some meters beep a warning when the leads are in a current jack and the dial is set for voltage.

Measuring resistance

In resistance mode the meter's own source drives a small known current through the unknown resistor and measures the voltage across it, so the circuit must be unpowered: an external voltage adds to or subtracts from the meter's and gives a meaningless reading, and on some meters can damage the input. Discharge capacitors first. The resistor must also be isolated from parallel paths. Measuring a 100 kΩ resistor still soldered into a circuit where a 47 kΩ path runs parallel to it reads about 32 kΩ, the parallel combination. Lift one end of the part, or measure before assembly. The meter's test current flows through the probe leads and contacts too, adding a few tenths of an ohm; for low resistances, short the probes and use the meter's relative or null function to subtract the lead resistance, or use the four-wire method in lesson 8.

Diode test mode drives about a milliampere and displays the forward voltage, around 0.5 to 0.7 V for a silicon junction and higher for LEDs, some of which glow faintly. Continuity mode beeps when the resistance is below a threshold of tens of ohms; it is quick for checking wiring and finding shorts, but it cannot distinguish a 2 Ω trace from a 20 Ω fault. Capacitance mode charges the capacitor with a known current and times it; it is useful for sorting parts, but much less accurate than an LCR meter.

AC measurements and true RMS

For AC, what a meter should report is the root-mean-square value, the DC voltage that would heat a resistor equally. For a sine wave of peak Vp, the RMS value is Vp/√2 and the average of the rectified wave is 2Vp/π. Many inexpensive meters measure the average of the rectified waveform, which is easy to build, and multiply by the sine-wave form factor, π/(2√2) ≈ 1.111, so that they display RMS correctly for a pure sine. For any other waveform they are wrong. A true-RMS meter computes the RMS value directly, either with an analog RMS converter or by sampling and computing digitally, and reads correctly for distorted and non-sinusoidal waveforms within its bandwidth and crest-factor limits.

Two more specifications matter for AC. The bandwidth of the AC function is often only a few kilohertz to a few hundred kilohertz, so a meter cannot measure the amplitude of a switching regulator's 500 kHz ripple; it will read low or nothing at all. The crest factor, the ratio of peak to RMS value, is limited too: a meter rated for a crest factor of 3 may clip narrow pulses with higher peaks before computing their RMS. Finally, many meters measure only the AC component on their AC ranges, removing the DC with a coupling capacitor. To get the total RMS of a waveform with a DC level, combine the readings: V_total = √(V_DC² + V_AC²). Some meters offer an AC+DC mode that does this directly.

# True RMS versus an average-responding meter, computed from sampled waveforms
import math
N = 10000
def rms(x): return math.sqrt(sum(v * v for v in x) / len(x))
def avg_resp(x):
    m = sum(x) / len(x)                       # AC coupling removes the mean
    ac = [v - m for v in x]
    return 1.1107 * sum(abs(v) for v in ac) / len(ac)
def ac_rms(x):
    m = sum(x) / len(x)
    return rms([v - m for v in x])

waves = {
    "sine": [math.sin(2 * math.pi * k / N) for k in range(N)],
    "square": [1.0 if k < N // 2 else -1.0 for k in range(N)],
    "triangle": [4 * abs(k / N - 0.5) - 1 for k in range(N)],
    "10% pulse": [1.0 if k < N // 10 else 0.0 for k in range(N)],
}
for name, x in waves.items():
    t, a = ac_rms(x), avg_resp(x)
    print(f"{name:10s} true RMS(AC) {t:.4f}  average-responding {a:.4f}  error {100*(a/t-1):+6.1f} %")

# Loading error of a 10 Mohm meter on several source resistances
for rth in (1e3, 100e3, 320e3, 1e6):
    print(f"R_Th {rth/1e3:7.0f} kohm: reads {100*(1e7/(1e7+rth)-1):+6.2f} % of true value")

sine       true RMS(AC) 0.7071  average-responding 0.7071  error   -0.0 %
square     true RMS(AC) 1.0000  average-responding 1.1107  error  +11.1 %
triangle   true RMS(AC) 0.5774  average-responding 0.5554  error   -3.8 %
10% pulse  true RMS(AC) 0.3000  average-responding 0.1999  error  -33.4 %
R_Th       1 kohm: reads  -0.01 % of true value
R_Th     100 kohm: reads  -0.99 % of true value
R_Th     320 kohm: reads  -3.10 % of true value
R_Th    1000 kohm: reads  -9.09 % of true value

The program reproduces the table and the loading rule. Amara uses it to explain why Leo's cheap pocket meter and the bench meter disagree on the 24 V rail's ripple. The ripple is a sawtooth from the rectifier's charging pulses, close to a triangle, so the average-responding pocket meter reads a few percent low; on the sharp current pulses that flow into the capacitor, which have a high crest factor, it reads a third or more low. Lesson 6 shows how to look at that ripple directly on an oscilloscope, which is the better tool for any waveform whose shape matters.