Digital measuring instruments
A digital instrument is not an analog instrument with a number display. Inside there is a different chain, with different errors, and a way of lying all its own: showing five solid digits of a value that is not exact in any of them.
01What changed compared with the pointer instrument
In analog instruments the measurement was a physical phenomenon: a current produced a torque on a coil and the pointer stayed where that torque balanced against the spring. Here the measurement is a number, and the whole instrument exists to produce it.
| Analog | Digital | |
|---|---|---|
| Reading | Interpreted by the operator on a scale | Numeric, no interpretation |
| Reading error | Parallax, interpolation between marks | None: the number is what it is |
| Input impedance | 20 kΩ/V typical: loads the circuit | 10 MΩ constant on all ranges |
| Varying signals | The trend is visible on the pointer | The digits dance and you cannot make sense of anything |
| Zero adjustment | Mechanical, and for the ohmmeter, every time | Automatic, internal |
| Range | Always manual | Autoranging |
| Robustness | The movement is damaged by a knock | Electronics with no moving parts |
Seeing how a quantity changes. Adjusting a trimmer to the maximum, looking for a peak, following the charging of a capacitor: the pointer shows it at a glance and the digits do not. That is why many good-quality digital multimeters have an analog bargraph below the number: it is exactly that function that was being lost.
02Architecture of a digital instrument
All digital instruments —multimeter, frequency counter, capacitance meter, scale— share the same skeleton. The first block changes, the one that translates the quantity into a voltage.
The control block looks at the result of each conversion. If the number exceeds full scale (overflow: the screen shows a lone “1” or “OL”), it goes up a range; if it falls below 10%, it goes down, and that way it makes use of all the digits. It is convenient, but it has two costs: it takes time while it searches, and on a signal that changes a lot it can end up hopping between two ranges. That is why every decent multimeter has a RANGE key to lock it by hand, which is what you should use when you are adjusting something.
03The dual-slope converter
It is the heart of almost all multimeters. It was already mentioned in A/D and D/A converters; here it is seen in detail, because it explains where its three virtues come from: accuracy, immunity to mains noise and low cost.
- R and C cancel: only Vref and the clock matter.
- The clock cancels too, because both times are measured with the same one.
- A single critical standard remains: the voltage reference.
The first ramp averages the input over t1. If t1 is an exact multiple of 20 ms, any mains interference contributes the same above and below zero: it cancels itself. This is what datasheets call NMR (normal mode rejection) and it gives 60 dB or more at 50 Hz.
Between the two ramps and the auto-zero, a complete measurement takes from 10 to 400 ms. A typical multimeter refreshes two or three times per second, and that is its physical limit, not a limitation of the display. It is no use for fast-changing signals: for those you go to the oscilloscope.
04The digital multimeter: how to read its specification
Counts and digits
A “3½-digit” multimeter has three full digits (0 to 9) and one that can only be 0 or 1: it goes up to 1999, which is 2000 counts. The “count” is the unit of resolution, and it defines what the last digit is worth on each range.
| Digits | Counts | Maximum reading | Resolution on 20 V | Instrument category |
|---|---|---|---|---|
| 3½ | 2000 | 1999 | 10 mV | Pocket multimeter |
| 3¾ | 4000 | 3999 | 10 mV | Workshop, mid-range |
| 4½ | 20,000 | 19,999 | 1 mV | Bench, laboratory |
| 6½ | 2,000,000 | 1,999,999 | 10 µV | Calibration standard |
Accuracy: not the same as resolution
Resolution is how many numbers it can display; accuracy is how close they are to the true value. It is always specified with two terms:
A 3½-digit multimeter, DC specification ±(0.5% + 3 digits). It measures on the 20 V range (resolution 10 mV) and the screen shows 12.45 V.
- 0.5% of 12.45 V = 62.3 mV
- 3 digits × 10 mV = 30 mV
- Total error: ±92.3 mV ≈ ±0.09 V
The true value lies between 12.36 V and 12.54 V. The screen shows hundredths, but the last reliable digit is the tenths one. Reporting “12.45 V” without the error is reporting too much.
Now the same measurement on the 200 V range (resolution 100 mV): 0.5% of 12.4 = 62 mV, plus 3 × 100 mV = 300 mV, total ±0.36 V. Four times worse just for leaving the range high. Always the lowest range that does not overflow.
The four traps of the digital multimeter
On AC, almost all the inexpensive ones rectify and multiply by 1.111: they are only right with a pure sine wave. With the output of a dimmer or a switching power supply the error reaches 40%. You need True RMS, as explained in AC measurements.
To measure current the instrument inserts a shunt. That resistor drops a voltage (burden voltage): typically 200 mV at full scale. In a 3.3 V circuit that drop changes what is being measured. With small currents you should use the mA range, not the 10 A one, and always check the figure in the manual.
The AC range is usually specified from 40 Hz to 400 Hz or 1 kHz. Outside that the reading drops without warning. Measuring the output of an audio amplifier at 10 kHz with an ordinary multimeter gives a number, and that number is wrong.
CAT II outlets, CAT III panels and fixed distribution, CAT IV service entrance and meter. The category is not about the voltage it measures but about the energy of a transient it can withstand without blowing up. A CAT II instrument on an industrial panel is an accident waiting to happen, and the test leads have a category too.
- Continuity with buzzer: it measures without looking at the screen, indispensable at the top of a ladder.
- Diode test: it injects ~1 mA and shows the forward drop. 0.6 V is silicon, 0.3 V germanium or Schottky, 1.8 V a red LED.
- HOLD: freezes the reading, for measuring in a place where you cannot see the screen.
- MIN/MAX: records extremes; useful for catching a motor starting spike.
- REL / relative zero: subtracts the current reading. It is the way to subtract the resistance of the test leads when measuring low values.
- Low impedance (LoZ): discharges the ghost voltages that appear through capacitive coupling in long cables and make you think a conductor is live.
05The digital frequency counter
It is the purest case of a digital instrument: it converts nothing, it counts. And what it counts is exactly what you want to measure.
Frequency counter with a 1 s timebase and a 10 ppm crystal:
- Measuring 50 Hz: N = 50, the counting error is 1/50 = 2%, and the crystal’s is 0.001%. Counting dominates. It is better to measure the period.
- Measuring 10 MHz: N = 107, the counting error is 0.00001%, and the crystal’s is 10 ppm = 0.001%, that is ±100 Hz. The crystal dominates.
That is why laboratory frequency counters have a temperature-compensated oscillator (TCXO) or an oven-controlled one (OCXO), and why the good ones have an input for an external 10 MHz standard.
The roles are reversed: the signal opens the gate and pulses of the standard clock are counted. For 50 Hz with a 10 MHz clock, 200,000 counts get in: the ±1 count error drops to 0.0005%.
Above the speed of the counter, the signal is divided by 10, 64 or 256 before being counted and the result is compensated. It is what makes it possible to reach UHF.
Modern instruments always measure the period of a whole number of cycles and calculate the frequency. It gives constant resolution in digits, regardless of the frequency.
Before the counter there is a Schmitt trigger that converts any waveform into clean pulses. Its hysteresis is what keeps superimposed noise from crossing the threshold several times per cycle. If the signal is very small, very dirty or has a DC component, the frequency counter reads anything or nothing: you have to AC-couple it and, if necessary, amplify it.
06Other digital instruments in the shop
| Instrument | What it measures and how | What to look at |
|---|---|---|
| Capacitance meter | It charges the capacitor with a constant current and measures the time, or measures the frequency of an oscillator that includes it. | Electrolytics have ±20% tolerance: an “odd” value can be normal. It does not measure series resistance (ESR), which is the most common fault. |
| ESR meter | It injects a signal of ~100 kHz and measures the resistive part. | It is the instrument that really finds the dried-out electrolytics in a switching power supply, with the capacitor still on the circuit board. |
| LCR meter | It measures the magnitude and phase of the impedance at a chosen frequency. | The test frequency matters: an inductor is not worth the same at 100 Hz as at 100 kHz. It is covered in standard-circuit measurements. |
| Digital oscilloscope | It samples and stores; then it draws. | Sampling rate, memory depth and real bandwidth. And aliasing, which on a digital instrument is a concrete danger. |
| Clamp meter | It measures the magnetic field around the conductor with a split core or a Hall sensor. | Transformer-type ones only measure AC; Hall-effect ones also measure DC. You have to clamp around only one conductor. |
| Data logger | A digital instrument with memory and a clock. | It turns a measurement into a time series: it is what lets you find the fault that shows up at three in the morning. |
Its two specifications are confused all the time. The bandwidth (for example 100 MHz) is analog: it says up to what frequency the signal reaches the converter intact. The sampling rate (for example 1 GSa/s) says how many samples per second it takes. The practical rule is that the sampling should be 5 to 10 times the bandwidth; if an instrument claims 100 MHz and 100 MSa/s, the numbers do not add up and with fast signals it will show shapes that do not exist.
07In the lab
Measure the same battery with all the multimeters in the shop and note the readings. They will differ in the last digit or in two. Look up the specification in each manual and calculate the error interval of each one: you will see that all the intervals overlap and that none contradicts the others. It is the best way to understand that one more digit is not a truer value.
Build an LED with its current-limiting resistor at 5 V. Measure the current on the mA range and note it. Then measure the voltage across the LED with and without the ammeter inserted. The difference is the instrument’s burden voltage. Repeat on the 10 A range and compare: the shunt is different.
Measure a battery with the multimeter and note it. Then bring the test lead wire close to a mains cable (without touching it) and measure again: the reading barely changes, because the dual slope averages. Repeat the same with the oscilloscope on DC: there you do see the superimposed hum. Two instruments, two different responses to the same noise.
Measure a 50 Hz signal from the generator with the frequency counter in frequency mode, 1 s gate, and note how much the last digit fluctuates. Switch to period mode and compare the stability. Then measure 1 MHz in both modes: there the advantage is reversed. Build a table with the four cases.
Check the category of the instrument and of the test leads, that the fuse is the original (not a piece of wire), that the leads do not have cracked insulation and that the selector is not on current when you are going to measure voltage. Putting a multimeter in ammeter mode across 220 V is a plain short circuit: that is why the good ones warn with a buzzer when the lead is in the current jack and the selector is on voltage.
08Common mistakes
| Symptom | Usual cause |
|---|---|
| Two multimeters give different values | Normal if the difference falls within each one’s error. It is only a problem if the intervals do not overlap. |
| The AC reading is 0 with a signal that exists | Frequency outside the bandwidth, or input DC-coupled on a small signal riding on a large value. |
| It measures voltage where nothing is connected | Ghost voltage from capacitive coupling in long cables, and the 10 MΩ input does not discharge it. Use LoZ mode. |
| The circuit stops working when the ammeter is inserted | Burden voltage of the shunt. Change range or measure the drop across a known resistor. |
| The measured resistance is higher than the resistor’s | You are measuring with the circuit powered or with another component in parallel. And at low values, the resistance of the test leads: use REL. |
| The display shows a lone “1” or “OL” | Out of range, not a fault. Go up a range. |
| The frequency counter jumps or reads double | Noisy signal crossing the Schmitt threshold twice, or insufficient amplitude. |
| The reading drifts over the months | Drift of the voltage reference. The instrument needs calibration: it is a service with a traceable standard, not a trimmer you adjust by eye. |
| With worn-out batteries the instrument measures wrong before warning | Several models lose accuracy before showing the low-battery symbol. Replace them at any suspicious reading. |
09Self-assessment
How many counts does a 4½-digit multimeter have and what is its maximum reading?
20,000 counts, and it shows up to 19,999. The “half digit” is the one on the left, which can only be 0 or 1.
A multimeter of ±(0.8% + 2 dig) on the 200 V range shows 118.5 V. What is the error?
The resolution on 200 V with 3½ digits is 0.1 V. So: 0.8% of 118.5 = 0.95 V, plus 2 × 0.1 = 0.2 V. Total error ±1.15 V: the true value lies between 117.4 and 119.7 V.
Why does the capacitor’s tolerance not matter in a dual slope?
Because the same capacitor is used to charge and to discharge. In the quotient t2/t1 the RC product cancels, and the result depends only on the voltage reference.
What integration time is appropriate in a country with a 50 Hz mains, and why?
A multiple of 20 ms (the mains period): 20, 40, 100 ms. That way the mains interference averages to zero during the first ramp. In a 60 Hz country the multiple is 16.67 ms; some instruments let you choose it.
Why does measuring 50 Hz with a frequency counter in frequency mode give a poor result?
Because with a 1 s gate 50 pulses are counted and the ±1 count uncertainty is 2%. Measuring the period with a 10 MHz standard clock, 200,000 pulses are counted and the error drops to 0.0005%.
A 10 ppm crystal measuring 10 MHz: what is the error in hertz?
10 ppm = 10 × 10−6, which on 107 Hz gives ±100 Hz. It is the accuracy floor of the instrument: no counting trick improves it.
What does it mean for a multimeter to be CAT III 600 V?
That it is designed for measuring in fixed installations —panels, distribution lines— withstanding the high-energy transients that occur there, up to 600 V nominal. It is not the same as “measures up to 600 V”: two instruments with the same voltage number can have different categories, and that is where the safety difference lies.
Why does a digital multimeter measure 12 V where nothing is connected?
Through capacitive coupling between parallel conductors: its 10 MΩ input is so high that it cannot discharge that induced voltage. The LoZ function lowers the input impedance and makes the ghost reading disappear. With an analog instrument the phenomenon does not appear, because its coil loads the circuit.
An oscilloscope claims 100 MHz of bandwidth and 100 MSa/s. What can you expect?
Trouble. With 100 MSa/s the Nyquist limit is 50 MHz: an 80 MHz signal that its input lets through will appear on the screen as a false frequency. The healthy ratio is 5 to 10 samples per cycle of the highest declared frequency.
What is the REL or relative zero function for?
To subtract the current value from all the following readings. It is used mostly on low resistances —you short the leads, press REL and so their own resistance is subtracted— and on small capacitances, to subtract that of the cable.