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A device used for the measurement of a certain physical quantity is called a **measuring instrument**. The instruments indicate the value of these quantities, based on which we get some understanding and also take appropriate actions and decisions.

## Speed of response of a measuring instrument

The **speed of response** is a metrological characteristics function of time (dynamic characteristic) of a measuring instrument, defined as the rapidity with which an instrument or measurement system responds to changes in measured quantity.

## Types of measurement instruments

There are two main types of measuring instruments: analog and digital. The analog instruments indicate the magnitude of the quantity in the form of the pointer movement. They usually indicate the values in the whole numbers, though one can get the readings up to one or two decimal places also. The readings taken in decimals places may not always be entirely correct since some human error is always involved in reading.

The digital measuring instruments indicate the values of the physical quantity in digital format that is in numbers, which can be read easily. They can give the readings in one or more decimal places. Since there is no human error involved in reading these instruments, they are more accurate than the analog measuring instruments.

- Linear measurement instruments
- Angular measurement instruments
- Comparators
- Optical measurement instruments
- Interferometry

## Measuring instruments functions

**Indicating the value of the physical quantity:** instruments are calibrated against the standard values of the physical quantities. The movement of the pointer directly indicates the magnitude of the quantity, which can be whole numbers or also fractions. Nowadays, the digital instruments are becoming very popular, which indicate the values directly in numerical form and even in decimals thus making them easy to read and more accurate.

**Measuring instruments used as the controllers:** many instruments can be used as the controllers. For instance, when a specific value of the pressure is reached, the measuring instrument interrupts the electrical circuit, which stops the running of the compressor. Similarly, the thermostat starts or stops the compressor of the refrigeration system depending on the temperature achieved in the evaporator.

**Recording the data:** some measuring instruments can also be used to record and also store the data for real-time or later processing.

**Transmitting the data:** the measuring instruments can also be used to transfer the data to some distant places. Wires can connect the instruments kept in unsafe locations like high temperature, and their output can be taken at some distant places which are safe for human beings. The signal obtained from these instruments can also be used for operating some controls.

**Do calculations:** some measuring instruments can also carry out several calculations like addition, subtraction, multiplication, division, etc. Some can also be used to find solutions to highly complex equations.

## Measuring range of an instrument

The measuring range of an instrument is defined by the interval between the maximum and minimum values of the physical quantity that can be detected. In other words, it is the main specification, because it provides information on the suitability of the instrument to measure a given quantity, as well as to define the safety specifications declared by the manufacturer.

All other metrological characteristics of an instrument are referred to the measuring range; in fact, they can only be considered valid for the values of the quantity under examination, internal to the said range.

The measuring range can be lower than the range of the graduation (i.e., of the graduated scale): in this case the graduation contains the minimum and maximum flow rates of the instrument, or only the maximum flow rate in the event that the minimum flow rate is equal to zero; or vice versa the only minimum flow rate in the case in which the maximum flow coincides with the upper end of the graduation.

The spatial distribution law of the divisions that make up the instrument scale (scale graduation) represents the physical law on which the operating principle of the instrument is based.

The graduation may be linear (the scale divisions are equally distributed), quadratic (if the distances between two successive divisions vary according to a quadratic law), logarithmic, etcetera. In this regard, it should be noted that all instruments which are not linear graduated require particular attention in reading the measurement: in fact, the human eye hardly performs the interpolation operation in the interval between two consecutive sections if the spatial distribution law of the divisions is not linear.

The knowledge of the physical law on which the principle of operation of the measuring instrument is based allows establishing whether the instrument is, or not, suitable to provide the measurement of specific quantities. For example, if a galvanometer is linear, this instrument will be suitable only for the measurement of direct currents; if instead, the galvanometer has a quadratic law, it will be sensitive to a thermal effect and therefore suitable for the measurement of continuous and alternating currents, of any waveform.

The fundamental concept of measurement field, for the practical use of the instrument, is completed by the following further definitions:

**extension of the graduation**: set of all the divisions drawn on the scale of the instrument; the measurement field can, at most, be equal to the extension of the graduation;**minimum flow rate**: the value of the quantity to be measured below which the instrument provides indications with lower precision than the declared one;**maximum flow rate**: same definition relative to the minimum flow rate with reference to the maximum value of the quantity. Furthermore, it is the value above which the instrument provides indications of the quantity to be measured with a precision lower than the declared one;**flow rate**: maximum flow rate of an instrument whose minimum flow rate is close to zero;**nominal overload**: maximum value allowed for the quantity to be measured beyond which the instrument suffers irreversible damage; the order of magnitude of the nominal overload is approximately 3 or 4 times the maximum flow rate of the instrument.

## Performance characteristics of measurement instruments

The treatment of instrument performance characteristics generally has been broken down into the subareas of **static characteristics** and **dynamic characteristics**.

The reasons for such a classification are several. First of all, some applications involve the measurement of quantities that are constant or vary only quite slowly. Under these conditions, it is possible to define a set of performance criteria that give a meaningful description of the quality of measurement without becoming concerned with dynamic descriptions involving differential equations. These criteria are called *static characteristics*.

With static characteristics shall mean the set of metrological properties that allow an exhaustive description of the operation of a transducer, which operates under specific environmental conditions, when: slow variations of the measurand are imposed in input, in the absence of shocks, vibrations, and accelerations (unless, of course, these physical quantities are themselves the object of measurement).

Many other measurement problems involve rapidly varying quantities. Here the dynamic relations between the instrument input and output must be examined, generally by the use of differential equations. Performance criteria based on these dynamic relations constitute the dynamic characteristics.

Static characteristics also influence the quality of measurement under dynamic conditions, but the static characteristics generally show up as nonlinear or statistical effects in the otherwise linear differential equations giving the dynamic characteristics. These effects would make the differential equations analytically unmanageable, and so the conventional approach is to treat the two aspects of the problem separately.

Thus the differential equations of dynamic performance generally neglect the effects of dry friction, backlash, hysteresis, statistical scatter, etc., even though these effects influence the dynamic behavior. These phenomena are more conveniently studied as static characteristics, and the overall performance of an instrument is then judged by a semiquantitative superposition of the static and dynamic characteristics.

This approach is, of course, approximate but a necessary expedient for convenient mathematical study. Once experimental designs and numerical values are available, we can use simulation to investigate the nonlinear and statistical effects.

### Static characteristics

- Accuracy
- Precision
- Sensitivity
- Linearity
- Reproducibility
- Repeatability
- Hysteresis
- Resolution
- Threshold
- Drift
- Stability
- Tolerance
- Range or span

### Dynamic characteristics (metrological characteristics functions of time)

When the transducer must follow rapid variations of the quantity to be measured, always operating in specified environmental conditions, it is necessary to integrate the static metrological characteristics with the dynamic ones.

- Speed of response
- Response time
- Measuring lag
- Fidelity
- Dynamic error