Digital voltmeters and digital multimeters

Structure of DVMs and DMMs, ramp, dual-slope, successive-approximation and V-to-f converters, digits, counts, resolution and accuracy specifications, with worked numericals.

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Why it matters

The digital multimeter is the instrument every engineer reaches for first. Reading its specification correctly — digits, counts, resolution and "±(% of reading + digits)" — tells you whether 1.250 V on the display means 1.250 ± 0.001 V or ± 0.02 V. The dual-slope converter inside it explains why it ignores mains hum but is slow.

Key ideas

Structure of a DVM/DMM.

  • Input attenuator and range switching.
  • For current, a shunt that turns current into voltage.
  • For resistance, a constant-current source (the voltage across the unknown is read).
  • For AC, a rectifier/averaging or true-RMS converter.
  • An analogue-to-digital converter (ADC), a counter/logic, and a display.
  • Input resistance on DC voltage ranges is typically 10 MΩ, so loading is far smaller than with a 20 kΩ/V analogue meter; it is still worth checking against the source resistance.

ADC types used in DVMs.

  • Ramp (single-slope): a linear ramp is compared with the input and the time to reach it is counted. Simple, but accuracy depends on ramp linearity and clock stability; poor noise rejection.
  • Dual-slope integrating: the input is integrated for a fixed time T1 (N1 clock counts); then a reference of opposite polarity is integrated until the integrator returns to zero, taking N2 counts. Since Vin·T1 = Vref·T2, Vin = Vref·N2/N1. RC and clock frequency cancel, so accuracy depends mainly on Vref. Making T1 an integer multiple of the mains period (20 ms at 50 Hz) gives very high normal-mode rejection of hum. Slow (a few readings per second); the most common type in handheld DMMs.
  • Successive approximation (SAR): a DAC and comparator find one bit per clock cycle, so an n-bit conversion takes n clocks. Fast; used where speed matters (data acquisition, bench meters with fast reading rates). Needs a sample-and-hold and is more sensitive to noise.
  • Voltage-to-frequency (integrating): the input sets the frequency of a pulse train, counted for a fixed gate time. Also integrating, so good noise rejection.
  • Potentiometric (servo) type: a motor-driven balance against a reference.

Digits, counts and resolution.

  • An "n-digit" display shows n full digits (0–9). A ½ digit is a leading digit that can only be 0 or 1. A 3½-digit meter shows up to 1999 (2000 counts); a 4½-digit up to 19 999.
  • Resolution is the value of one count on the range in use: on the 2 V range of a 3½-digit meter it is 1 mV; on the 20 V range, 10 mV.
  • Sensitivity of a DVM is the smallest change it can show on its lowest range: S = (1/10ⁿ) × lowest full scale, where n is the number of full digits.
  • Over-range shows "1" or "OL". Choose the lowest range that does not over-range.

Accuracy specification. Usually ±(a % of reading + b digits) (or + b counts). The "digits" term is b × resolution on the range used, and dominates at low readings. A display with many digits is not automatically accurate — resolution and accuracy are different.

Other DMM features. Auto-ranging, continuity buzzer, diode test, data hold, frequency and capacitance ranges. Safety category ratings (CAT II/III/IV) describe the transient voltages the meter can survive; take the limits from the meter's specification.

Formulas

Vin = Vref·N2 / N1 (dual slope) ; T1 = N1 / fc ; T2 = N2 / fc N1 = fixed count of the integrate period; N2 = counts during de-integration; fc = clock frequency (Hz); T in s.

Vo,peak = Vin·T1 / (R·C) (integrator output at end of T1) R in Ω, C in F; must stay inside the integrator's linear range.

Resolution R = 1 / 10ⁿ (fraction of full scale) ; S = R × lowest full-scale range n = number of full digits.

Error = ±(a/100 × reading + b × resolution) (V)

Conversion time (SAR) = n × T_clock n = number of bits.

Worked examples

Example 1 — reading a 3½-digit specification. A 3½-digit DVM has accuracy ±(0.5 % of reading + 1 digit). It measures 1.250 V. Find the possible error on (a) the 2 V range and (b) the 20 V range.

  1. (a) Resolution on 2 V range = 2/2000 = 1 mV. Error = 0.005 × 1.250 + 0.001 = 6.25 + 1 = 7.25 mV, i.e. 7.25/1250 = 0.58 % of reading.
  2. (b) Resolution on 20 V range = 10 mV. Error = 6.25 + 10 = 16.25 mV, i.e. 1.3 % of reading.

Answer: (a) ±7.25 mV (±0.58 %); (b) ±16.25 mV (±1.3 %) — always use the lowest range that does not over-range.

Example 2 — dual-slope converter (GATE level). A dual-slope DVM uses a 100 kHz clock, a fixed integrate period of N1 = 2000 counts, Vref = 2.0 V, R = 100 kΩ and C = 0.2 μF. For a certain input the de-integrate count is N2 = 1250. Find (a) T1, (b) Vin, (c) the integrator output at the end of T1, (d) the effect of 50 Hz hum.

  1. (a) T1 = 2000/100 000 = 20 ms.
  2. (b) Vin = Vref·N2/N1 = 2.0 × 1250/2000 = 1.25 V.
  3. (c) Vo = Vin·T1/(RC) = 1.25 × 0.02/(10⁵ × 0.2 × 10⁻⁶) = 1.25 × 0.02/0.02 = 1.25 V.
  4. (d) T1 = 20 ms is exactly one period of 50 Hz, so a 50 Hz hum integrates to zero and is rejected.

Answer: T1 = 20 ms, Vin = 1.25 V, peak integrator output 1.25 V; 50 Hz hum (and its harmonics) is rejected.

Common mistakes

  • Treating "3½ digits" as 3500 counts; it is 1999 maximum (2000 counts).
  • Ignoring the "+ digits" term; at low readings it is the main error.
  • Confusing resolution (one count) with accuracy.
  • Expecting RC or clock frequency to appear in the dual-slope result — they cancel, which is the point of the method.
  • Thinking a high input resistance means no loading; a 10 MΩ meter on a 1 MΩ source still reads about 9 % low.
  • Measuring current with the leads left in the current jack and then switching to voltage — the shunt shorts the source and blows the fuse.

For GATE IN

Expect NAT questions on dual-slope relations (Vin from counts, integrate time, integrator peak), resolution and sensitivity of an n½-digit meter, error from a ±(% reading + digits) specification, and SAR conversion time. MCQs compare ADC types (speed versus noise rejection) and ask why integrating converters reject mains hum. Practise turning a specification into an absolute error in volts.

Quick check

  1. What is the resolution of a 4½-digit meter on its 2 V range?
  2. A dual-slope DVM has N1 = 1000 and Vref = 1 V; N2 = 640. Vin?
  3. A 10-bit SAR ADC has a 1 MHz clock. Conversion time?
  4. Why is T1 often chosen as 20 ms in India? Answers: 1. 0.1 mV (100 μV); 2. 0.64 V; 3. 10 μs; 4. it is one period of the 50 Hz mains, so hum integrates to zero.

Interview questions

All Electrical and Electronic Measurements interview questions

Try answering each one aloud before you open it.

  1. 1.What is a digital voltmeter and how does it differ from an analog voltmeter?Concept

    A digital voltmeter (DVM) is an instrument used to measure electrical potential difference between two points in a circuit. Unlike an analog voltmeter, which uses a needle and dial to display readings, a digital voltmeter provides a numerical display of voltage. Digital voltmeters are generally more accurate and provide higher precision than analog voltmeters. They also often include features like auto-ranging and data storage.

  2. 2.Explain the working principle of a digital multimeter.Concept

    A digital multimeter (DMM) is an electronic measuring instrument that combines several measurement functions in one unit. It typically measures voltage, current, and resistance. The working principle involves converting the analog signal into a digital signal using an analog-to-digital converter (ADC). The digital signal is then processed and displayed on a digital screen. DMMs are versatile and can be used for various electrical measurements.

  3. 3.What happens if a digital multimeter is used to measure a voltage beyond its maximum range?Application

    If a digital multimeter is used to measure a voltage beyond its maximum range, it may display an overload indication, such as 'OL' or a series of dashes. This is a protective feature to prevent damage to the multimeter. However, continuously applying excessive voltage can potentially damage the internal circuitry of the multimeter, leading to inaccurate readings or complete failure.

  4. 4.How does the resolution of a digital voltmeter affect its performance?Application

    The resolution of a digital voltmeter refers to the smallest change in voltage that it can detect. Higher resolution means the voltmeter can detect smaller changes in voltage, leading to more precise measurements. For example, a voltmeter with a resolution of 0.001 V can detect changes as small as 1 mV. High resolution is particularly important in applications requiring precise voltage measurements.

  5. 5.Explain the significance of input impedance in digital voltmeters.Concept

    Input impedance is the resistance that a voltmeter presents to the circuit being measured. High input impedance is significant because it minimizes the loading effect on the circuit, ensuring that the measurement does not alter the circuit's operation. Digital voltmeters typically have high input impedance, often in the range of megaohms, which makes them suitable for measuring voltage in sensitive electronic circuits.

  6. 6.Why is an analog-to-digital converter (ADC) crucial in digital multimeters?Application

    An analog-to-digital converter (ADC) is crucial in digital multimeters because it converts the analog signals, such as voltage or current, into digital signals that can be processed and displayed by the multimeter. The accuracy and resolution of the ADC directly affect the performance of the digital multimeter. A high-quality ADC ensures precise and reliable measurements.

  7. 7.Calculate the voltage reading on a digital voltmeter with a resolution of 0.01 V if the input voltage is 5.678 V.Numerical

    The digital voltmeter will display the voltage reading rounded to the nearest resolution. With a resolution of 0.01 V, the input voltage of 5.678 V will be displayed as 5.68 V.

  8. 8.A digital multimeter has a maximum current range of 10 A. What will happen if it is used to measure a current of 15 A?Application

    If a digital multimeter with a maximum current range of 10 A is used to measure a current of 15 A, it may display an overload indication or an error message. This is to protect the multimeter from damage. Exceeding the current range can cause the internal fuse to blow or damage the multimeter's circuitry, leading to inaccurate readings or failure.

  9. 9.A 3½-digit DVM measures 12.346 V. What does it display, and on which range?Numerical

    A 3½-digit meter shows at most 1999 counts. On the 2 V range 12.346 V over-ranges (display shows 1 or OL), so the 20 V range is used, where one count is 0.01 V and the display reads 12.35 V. The resolution is therefore 10 mV, and the meter's accuracy specification, ±(% of reading + digits), must be applied on top of that.

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