Electrical measurements


Before dealing with the topic of measurement of electrical quantities, it is worth to point out that, as far as you can use high-tech and high accuracy devices, no measurement can be regarded as correct. Thus, it follows that the evaluation of measurement error, in relation to the type of the used instrument, is of great importance and therefore we should carefully consider it.

Measurement errors

The process of performing a measurement is defined as the result of the relationship between a specific quantity and another homogeneous quantity chosen as unit of measure (sample). During a measurement errors always occur. They can be divided into two categories:

  • systematic errors
  • accidental errors

Systematic errors are not a result of actions of the operator, but they depend on the characteristics of the instruments and the method of measurement used.They are divided into two types: instrumental errors, which are due to the class of the measurement tool and self-consumption errors, which are due to current absorptions or voltage drops of the instruments. A source of systematic errors, for example, is when the tool interferes with the apparatus on which you are measuring a quantity. In fact, the value of the measurement is different if you get it with or without the tool. Consider the case you wish to measure the voltage with a voltmeter or the current with an amperometer, their internal resistances affect the operating conditions of the circuit on which the measurement is performed. Another common case is measurements taken with instruments out of calibration . Systematic errors are the most insidious errors because they are always in the same amount and with the same sign, therefore they are difficult to detect, but once their causes are identified, they can be easily eliminated.

Accidental errors are due both to the actions of the operator and to the environmental conditions of the measurement. The presence of these errors may randomly change the measurement result either in excess or in defect; a classic example of this type of errors is the parallax error in reading a mobile index. Another example is the error in measurements of time intervals starting and stopping a stopwatch.

This type of error can be reduced to very small entities with repeated measurements but it can not be eliminated entirely unlike the systematic errors. Thus, the result of any measurement must be interpreted , for example, repeating the same measurement and assuming that the value of the measure is between the minimum and maximum value obtained.  The greater is the number of measurements with the same result, the greater is the reliability of the measure. This means that the result of a measurement, to be properly usable, must always be associated with a value of uncertainty U, suitably defined. Therefore the value of the measure will be given by the following relationship:


Therefore, the uncertainty adequately defines the quality of the measurement and assumes an effective evaluation of all systematic errors. The value of uncertainty, according to UNI CEI ENV 13005/2000 ( regulations for uncertainty of measurement ) is classified into :

  • uncertainty of type A is based upon statistical methods (objective) or upon a series of repeated measures;
  • uncertainty of type B is based upon subjective elements such as manufacturer specifications of the instruments with relative calibration data; 
  • previous measurement data;
  • reference data in manuals, databases and scientific literature.

Practically any measure is represented by four elements: parameter, number, uncertainty, measurement unit, as shown in table 1.

Tabella 1 :

Parametronumeroincertezzaunita di misura
Tensione230± 2,5volt
Corrente32± 0,5ampere

The only exception to the uncertainty of a measurement is when you are counting discrete entities (consisting of separate elements) such as the number of people present in a room or the number of cars in a parking lot. In this case the result can be regarded as free from errors.

The previous statement introduces the concept of precision of a measurement. This concept is closely related to the quantity to be measured and the characteristics of the instrument used. The precision is defined as the smallest unit of measure that the instrument is able to appreciate. For example, if you need to measure the size of a room using a measuring tape you get an error of a few centimeters, whereas if you make the same measurement with a laser meter you get an error of less than a millimeter.

Once you obtain a certain result, you often need to approximate it or, as it is called by insiders, “to round up”. This means that you can ignore some digits taking the following factors into account:

Degree of approximation. In this case we have to apply the rule of 5. If the first digit you want to delete is less than 5, then the remaining digits remain unchanged (approximation by rounding down). Instead, if the digit you want to delete is equal or greater than 5, then you have to increases by one unit the previous digit (approximation by rounding up). Another rule you have to apply, is the determination of significant figures of a result obtained by more measures: the number of significant figures must be equal to that of the measurement less accurate. For instance, a voltage value of 45.35 V, or even 45.37 V, may be rounded up to 45.4 V; a current value of 32,34 A a can be rounded down to 32.3 A. In the case of the sum of three currents: 29.4 + 2.35 + 0.426 A, the result is 32.176 A, but you have to consider that the magnitude 29.4 limits the accuracy to the first digit after the decimal point, therefore the approximate result is 32.2 A.

 – Degree of accuracy. It is represented by the number of significant figures. It is a good practice to follow the general rule that the last significant figure of a result of a measure must be of the same order of magnitude of the uncertainty. For example, if you measure a voltage with a value of  2,145 ± 0.02V, then the result should be expressed as 2.15 V ±  0.02 V. 

Thus, executing a measurement, you must identify a possible error (uncertainty) that can be defined as absolute error εa resulting from the difference between the measured value Vm and the true value Vv. In practical applications, however, it is preferred that the value of the relative error percentage is expressed by the following equation:


that is


The value of the εr% is important. In fact, from this value you can understand that measurements can be more accurate approaching to the fulll scale in the analog instruments. For example, consider a voltmeter with a linear scale, a full scale of 250 V and an absolute error of ± 0.5 V. You made two measurements, before a measurement of 120 V and then a measurement of 230 V; εr% will be in the first case


and for the second case


It is clear that near the full scale the measure is more precise, and this is the reason why the measurement instruments are identified, according to IEC standards, with the following classes of accuracy: 0.05 – 0.1 – 0.2 – 0.3 – 0.5 – 1 – 1.5 – 2.5 – 5. This means, for example, that an analog instrument of class 1 shows a relative percentage error within ±1% for all values in the scale. The class parameter is very important in order to identify the scope of the instrument, for example:

  • classes 0,05 – 0,1 instruments: they are used as standard equipment in the laboratory;
  • classes 0.2 – 0.3 – 0.5: they are used as equipment in laboratory;
  • classes 1 – 1.5:  they are used to control systems and to calibrate the panel instruments;
  • classes 2.5 – 5: they are used with panel instruments in fixed installations for continuous measurements on the systems.
Fig.1: conventional symbols on measuring instruments.

Generally, in the analog instruments, the class parameter is directly shown in the gauge of the instrument along with other information such as the units,operating temperature, etc; instead, in the digital instruments, we can find this information in the product specifications.

Measuring instruments

The devices that make possible to establish the relationship between a specific quantity with its corresponding unit of measure are called measuring instruments. They are equipment able to compare the magnitude to be measured with the unit of measure contained inside them.

Schematically, a measuring instrument can be defined by the sequence of the following elements: a sensor, inserted in the measuring circuit, detects the value of the parameter in the measurement, a transducer transforms the type of variable detected by the sensor, such as an electromagnetic converter, an amplification stage  processes electronically or mechanically the transduced signal; the final device of reading that can be analog, in which the reading is given by an index in movement on a graduated scale, or digital, in which the reading is on a numerical display.


This scheme, typical of electric instruments, is called measuring chain and its elements can not be accommodated in the same place or at the same time. This is the case of the telemetry or tools that store and process huge amounts of data over time. Certain types of tools are able to measure different types of physical quantities, even not homogeneous, such as testers or multimeters. In fact, they can measure voltage, current, resistance, frequency.

Thus, depending on the type of final device for reading, we have two different categories of measuring instruments:

  • analog instruments
  • digital instruments

Analog instruments

The analog instruments , can be electromechanical or electronic. An electromechanical instrument is constituted by a movable element having an initial rest position. An index is attached to this movable element and it controlled by a torque proportional to the measured quantity. In contrast to this torque, there is another antagonist torque exerted by a spring, which tends to bring the movable arm in the rest position (the index towards zero). From the balance of these two torques, an angular displacement is obtained, moving forwards or backwards the index on the graduated scale. Depending on the principle underlying the electromechanical converter you may have different categories of tools:

  • permanent magnet and moving coil instruments,
  • moving iron instruments,
  • electrodynamic instruments,
  • induction instruments,
  • hot wire instruments,
  • dynamic iron instruments,
  • thermocouple instruments,
  • rectifiers instruments,
  • Hall effect instruments;

Analog electronic instruments contain circuits such as oscillators, filters, rectifiers and amplifiers, which convert the measured quantity into current in a proportional way, applying it to a magneto-electric instrument. In these instruments, the presence of amplifiers allows to obtain a high sensitivity along with a very high input impedance.

The most important technical characteristics of analog measuring instruments are:

sensitivity is the smallest measured quantity capable of generating an appreciable shift at the beginning of the scale of the instrument. In practice the sensitivity determines the lower limit of the measuring range of the instrument while the upper limit is given by the full scale;

resolution is the smallest change in the measured quantity, detected by a shift of the index. In practice, it represents the value of the last significant figure appreciable;

full scale indicates the maximum value of a magnitude that the instrument can measure and along with the sensitivity, it delimits the range of operation;

input impedance is the impedance which the instrument presents against the quantity to be measured;

accuracy class is the width of the band of uncertainty expressed as a percentage of full scale;

response time corresponds to the time that the measurement chain takes to perform the measurement. More precisely, the time elapsed from the instant in which the input varies to the time when the reading system stably assumes its final value within its limits of accuracy;

limits of use are all those variables that affect the proper functioning of the instrument such as the environmental temperature, the waveform of the input signal, the maximum values ​​of voltage and current, the position of use of the instrument, electric and magnetic fields due to external factors;

Fig.2: analog panel instruments

Digital Instruments

The digital instruments are constituted by an analog/digital converter which converts the electrical information into a binary digital signal. This signal is then decoded and applied to an appropriate numeric display on which you can read directly the value of the measure. Thanks to the modern technologies, you can have sophisticated digital instruments which are able to storage, retrieve and process the measurement data. Furthermore, they can also be interfaced with computer systems in order to set up automatic and remote system controls.

The most important technical characteristics of digital measuring instruments are:

precision defines the relative percentage error with respect to the full scale. In practice, it is similar to the accuracy class of an analog instrument;

number of digits is the slightest appreciable variation from the instrument;

measurement time is the number of measuring cycles that the tool can perform in a second;

resolution is the minimum value shown in the display with the lowest full scale. For example, a 4-digit voltmeter with the minimum full-scale of 0.1 V has a resolution of 0.01 mV. In practice this feature is equivalent to the sensitivity of an analog instrument;

input impedance is the impedance which the tool presents against the quantity to be measured;

out-of-range is the value over the scale covered by the instrument. This parameter is displayed by the instrument with an indication, such as a horizontal bar or the – sign to indicate the reverse polarity of the measurement in DC, called “half digit“. For this reason the tool is defined a 3½ digits tool;

measuring points are the number of distinct information that can be supplied by the display, including an indication of out of range. For example, a 3½ digits tool can give 1000 measuring points;

noise is represented by a random fluctuation that occurs with rapid changes in the least significant figure;

normal mode rejection (NMR) is expressed in dB and represents the ability of the instrument to distinguish the input signal to be measured from extraneous noise;

common-mode rejection (CMR) is expressed in dB and represents the ability of the instrument to distinguish the signal to be measured from the noise between input and ground.

Fig.3: digital panel instruments

In most cases, the analog and digital tools used for the measurement and control of electrical quantities, are classified according to these characteristics:

Quantity to be measured. This category consists of 1-input instruments: voltmeter, network analyzers, spectrum analyzers, amperometers, galvanometers, frequency meter, charge gauges; and 2-inputs instruments: wattmeters, varmeters, energy meters (counters), impedence meter, ohmmeters, ratiometer;

Methods of measurement. This category consists of: gauges showing the value of the measured quantity instantly without recording, recording instruments showing the progress of the measure over time by writing it on paper; and finally integrators, most commonly said counters, representing the integral of the magnitudo over time.

Fig.4: an handheld digital multimeter
Fig.4: an handheld digital multimeter

Some examples of electrical measurements

Example of a proper assessment of the ground resistance value using a digital multifunction tool.

On the display, with the selected range 200 Ω, you read a value of 20 Ω. The technical specifications on the instruction manual shows the following characteristics:

  • range = 200 Ω
  • resolution = 0.1 Ω
  • accuracy (uncertainty) ±3% of rdg (reading) + ±4 digits.

Calculate the various types of uncertainty:

  • uncertainty due to reading (dgt) = ±3% of 20 Ω = ±0,6 Ω
  • uncertainty due to the sliding of the last digit (dgt) = 0,1 Ω · ±4 digits = ±0,4Ω
  • absolute uncertainty = ±0,6 + ±0,4 = ±1 Ω
  • percent relative uncertainty = 1/20 ·100 = 5%

The correct representation of the measurement is the following: RT = 20 ± 1 Ω

Example of a proper assessment of the earth resistance value using as instrument an analog ground meter.

On the scale, with the selected range of 200 Ω, you read the value of 20 Ω. The technical specifications on the instruction manual shows the following characteristics:

  • percentage error = ±3% f.s. (full scale).

Calculate the various types of uncertainty:

  • absolute uncertainty = ±3% of 200 Ω (full scale) = ±6 Ω
  • percent relative uncertainty = 6/20 ·100 = 30%

The correct representation of the measurement is the following: RT = 20  ± 6 Ω. 

These two examples are also useful in order to understand the meaning of acceptability of measurement error and thus the validity of a measure. For example, if the measurement of earth resistance (in the above examples) is relative to a specific limit as the case of a differential switch with current Idn 1 A, in a particular environment with a contact voltage limit of 25 V and the ground resistance which must not be higher than 25 Ω; it is clear that the measurement performed with the analog tool can not be considered acceptable because the value of 25 Ω is included in the error range of the instrument

20Ω ± 6 = 14 ÷ 26 Ω.

Instead, the measurement performed with the digital instrument can be considered acceptable because the value of 25 Ω is out of range of the instrument error:

 20 Ω ± 1 = 19÷21 Ω.

Direct and indirect measurements

The measure of a given electrical quantity is defined direct when its value is obtained by directly inserting the instrument in the measuring point without having to know the value of other parameters such as, for example, the values of possible adapters. In practice, you make a direct measurement when it is directly associated with the real scope of the instrument, without inserting additional resistances in the case of voltmeters or resistance of derivation in the case of amperometers.

Consequently, since the instruments have very low full-scales, you can make direct measurements for only values of few mA or mV. Thus, most of the measurements should be considered indirect. That is, whenever you use adapters such as resistors in series or parallel (shunt), transformers that reduce the magnitude in order to make it compatible with the scope of the instrument, converters that convert a DC signal or AC signal into current or DC voltage proportionally and independently of the load.

An example could be the case you want to measure a current up to 800 A with a tool with a full scale of 5 A. In this case you must use an amperometric transformer (AT) with ratio 800/5. Then you have to choose the manufacturer and refer to the characteristics of the product, paying particular attention to the protection for any interruption of the secondary winding. This could be a source of dangerous surges and overheating. Regarding the amperometric transformers, we can find two different type of them: feed-through type, that are constituted by a winding loop in which to pass the bare conductor or isolated that must be entered directly on the instrument; and the primary winding type, that must be connected in series to the conductor on which to measure the current. Figure 5 shows the methods of insertion of the amperometric (AT) and voltmetric transformers (VT).

Fig.5: methods of insertion of the amperometric (ATs) and voltmetric transformers (VTs).

Electrical Measurements and safety

Before proceeding to make any measurement on an electrical system, it is of extreme importance that you verify the suitability of the instrument employed in relation to the characteristics of the quantity to be measured and the environment in which measurement is made. The elements that you should take into account are:

  • assessment of the quantity to be measured. It is necessary to evaluate the system in which the measurement is performed, taking into account the characteristics of the measuring instruments, of any probes and cables, especially the withstand voltage according to the categories I – 1500 V, II – 2500 V, III – 4000 V, IV – 6000 V;
  • room temperature and humidity;
  • presence of electromagnetic noise both radiated and induced;
  • assessment of ordinary or special environments (dust, liquids, flammable gases, etc.).

The measures must be performed in full compliance with the instructions contained in the user manual of the instrument, and in particular the following points must be well known to the operator.

  • the general characteristics and techniques with the operational limitations; 
  • the measurement error by using different full-scales and measurement conditions; 
  • a detailed description of the commands and how to perform a preliminary calibration; 
  • measurement procedures with connection diagrams; 
  • the safety precautions that must be taken; 
  • the breaking capacity of the fuses.

The measurement operations must be performed using only devices and accessories supplied with the instrument. You should always verify their good state of preservation, doing particular attention to the replacement of any fuse for which it is necessary to respect strictly the breaking capacity stated by the manufacturer in the user manual. Usually, in these cases, you should be tempted to replace a fuse with a common glass one (since it works as well) without thinking that this might lead to the alteration of the withstand voltage of the instrument and so resulting in serious injury to the operator as, for example, electric shock, burns, blindness.

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