5 Transducers I

Vinay Gupta

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    Learning Objectives

 

In this module we will focus on various types of Resistive transducers.

 

Here we will study about (i) principle of operation of a resistance gauge. (ii) About theory and other basic fundamentals of Resistance Thermal Detectors (RTD). (iii) Thermistors, they are also known as Thermally resistive transducers.

 

Introduction

 

In this module we will look at Transducer. As discussed earlier, a transducer is any device that can convert energy or information from one form to another. In a measuring system the transducer or combination of transducer act as input element. They play a critical role in transforming some physical quantity to a proportional electrical signal. Therefore, selecting an appropriate transducer is important to get accurate results. While selecting a transducer first step is to understand the nature of quantity under measurement with known range of magnitudes and frequencies to be expected from the measurand. Thereafter one should examine the available transducer for the principle of measurement for the desired quantity. Transducer once identified for a measurement should be compatible with the type and range of the quantity to be measured and the output device.

 

There are various types of transducers active, passive, sensors, actuators, etc. One should also be aware of inverse transducer. It is a device that can convert an electrical quantity to non-electrical quantity. They usually are precision actuators that have an electrical input and low power non electrical output. Many data indicating and recording devices are inverse transducers. Many analog measuring instruments like ammeter or voltammeter convert electrical current into mechanical movement in the measuring dial.

 

Resistive Transducer

 

A resistive transducers belongs to the category of passive transducer. Here the resistance between the output terminals of a transducer gets varied according to the measurand. A resistive transducers are preferred over other transducer. This is because they can be used in both AC and DC circuits for resistance measurement. For any metal conductor, resistance is given by –

     where p is the resistivity of the material in -m(ohm-meter), l is the length of the conductor in meters and a is the cross-sectional area of the conductor in m2.

 

For a physical phenomenon, an input signal to the transducer leads to changes in any one of the above mentioned quantities, i.e. p,l and a.

 

For any conductor or semiconductor, any variation in force or pressure leading to change in resistance is measured via strain gauge. Changes in the resistance due variation in temperature can also be recorded by resistive transducers. Variation in light intensity i.e. for photoconductive effect, changes in resistance can be easily recorded and same is for magneto-resistive effect where changes in the magnetic field can be observed by measuring resistances. For various measurements, primarily resistive range is in the mid-range of 100 ohms-100 kohms.

 

Strain Gauges

 

A Strain Gauge is a device that is used for measuring mechanical surface strain and is one of the most extensively used electrical transducers. It can detect and covert force or any small mechanical displacements into electrical signals. Mechanical displacement with time varying form with frequencies upto 100 kHz can be detected with this device.

 

Based on the application the strain gauges can be classified into two areas

(i) Primary objective of the gauge is the measurement of strain (stress analysis) of machines and structures

(ii) Measurement of strain due to other parameter such as load, pressure acceleration and other force associated variables.

 

Based on the operating principle, gauges can be classified into mechanical, optical or electrical. Mechanical gauges are used for measuring static strain only and there application can also be extended to those measurements that can be conducted by visual means. Optical strain gauge is similar to mechanical only difference being that magnification is achieved via multiple reflectors, i.e. mirrors and prisms. Its accuracy of measurement is high and is independent of any temperature variation. In electrical strain gauges, measurement is based on changes in resistance, capacitance or inductance that are proportional to the strain transferred from the measurand to the gauge element.

 

Operating Principle of Resistance Gauge

 

Credit towards the development of an electrical resistance stain gauge goes to Lord Kelvin. In mid 19th century he expounded the theory that copper or iron wire tend to change the resistance when they are subjected to tension or compression. This change in the resistance of conductor under stress, also alters the resistivity of the conductor, this effect is also know piezo-resistive effect. Therefore strain gauges are also called piezo-resistive strain gauges.

 

As discussed earlier, the resistance of the unstrained gauge is given by equation (1). And under strained condition let us assume the resistance changes by R, length changes by L, cross-sectional area by A and resistivity by . These 4 quantities can be expressed by differentiating equation (1)-

 

Dividing both sides of the expression by R, and by taking into account small variations the above expression can be written as—

Under strained conditions, cross sectional area also changes, so the diameter of the conductor will also change

For small variations –

 

Changes in the diameter will also lead to changes in the length of the wire, is given by Poisson’s Ratio , for the given wire material –

 

For most materials, the value of the Poisson’s ratio of 0.3 is considered. From equation 5 & 6 we get –

By substituting the above expression in equation (3), we get the expression for the Gauge Factor G –

 

 

The Gauge Factor G, gives the strain sensitivity of the gauge in terms of change in resistance per unit resistance per unit strain. The 3rd term for resistance due to piezo-resistive effect can also be expressed as E, where is called longitudinal piezoresistance coefficient and E is called modulus of elasticity.

 

Resistance Temperature Detectors (RTD)

 

Resistance temperature detectors are also known as Resistance Thermometer. They are electrical transducers that enable measurement of resistance changes in terms of resistance change. The resistive element is made up of solid material, a metal, metallic alloy or a semiconductor compound. The resistivity of the metals increases with temperature whereas for semiconductors and insulators it generally decreases. Electrical resistance with temperature for various metals is expressed by the following equation –

 

?? = ?0 ( 1 + ?? + ??2 + ??3 + ⋯ ???) —————-(9)

where R0 is the resistance in at reference temperature (i.e. ice point 0 oC), Rt is resistance in at temperature t, is temperature coefficient of resistance in / /oC and , , … are coefficients determined on the basis of two or more known resistance – temperature(calibration) points.

 

For narrow range of operation, and other higher terms become negligible and expression (9) can be written as

 

Rt = R0 (1 + t) ——– (10)

 

The RTD can be used for measuring of small temperature differences as well as for wide range of temperature. The main drawback of this instrument is its large size and sophisticated instrumentation.

 

The requirements of resistance material in resistance thermometers are

  1. High temperature coefficient of resistance, to give noticeable change in resistance for small change in temperature i.e. larger sensitivity
  2. High resistivity for small wire length for high resistance
  3. Linearity of relation between resistance and temperature
  4. Stability of the electrical characteristics of the material, which is essential for good repeatability
  5. Good mechanical strength so that very fine wire can be drawn for reducing response time and gives adequate ruggedness in the construction of the device.

Platinum is the most preferred material laboratory work and industrial measurements of high accuracy. Platinum is commercial available in pure form and is relatively stable under different environment conditions. Its resistance curve is simple and holds true over wide range of temperature (- 263 0C to + 545 0C) with high precision. Its resistivity increases less rapidly at higher temperature, at the same time maintains excellent stability. The common value of resistance for a Platinum RTD ranges from 10 ohms for birdcage model to several thousand ohms for the film of RTD. The common value is 100 ohms at 0 oC with a temperature coefficient of 0.00391 per 0C.

 

Theory

 

For the sake of simplicity expression (10) can be written as

 

Rt = R0 (1 + kt) ——(11)

 

Where k is the fundamental constant, whose value is determined by measuring resistance at 0 oC and 100 oC. If R0 and R100 resistance value measured at 0 oC and 100 oC respectively. Then we get the following equation –

 

R100 = R0 (1 + 100k)

 

The above equation gives the value of k. Then, the resistance R at temperature tp oC is given by the following expression.

 

Rt = R0 (1 + ktp)      where tp is the temperature of the platinum,

 

The above equation can be written as

 

    R100 – R0 is the fundamental interval and is constant for a given temperature.

Figure 1. Circuit for Resistance thermometer

 

Platinum resistance thermometer is coupled to Wheatstone bridge or Kelvin bridge depending upon the accuracy required and the range of measurement. The modified circuit for Resistance thermometer is given in figure 1. Thermometer tube has 3 core cables, one form variable resistor, middle one from the galvanometer and third one has platinum resistance coil. The coil is in form of free spiral or is held by insulated carrier such as mica or ceramic. The diameter of the wire is 0.02 mm to 0.2 mm and the preferred thickness is 0.1 mm.

 

Thermistor

 

Thermistors are thermally sensitive resistors, resistance of a thermistor varies as a function of temperature. The thermometer element is made from semiconducting compounds. These compounds are sintered mixtures of sulphides, silicates, oxides and selenides of metals such as nickel, manganese, cobalt, copper, zinc, iron, aluminium and uranium. Depending upon their composition, the sensitivity may vary from 10-1 to 109 -cm. The resistance values of thermistor at 20 oC may lie in the range of 100 to 1M . The elements are in the form of beads, rods and discs of different sizes. The beads and discs are available with glass envelope encapsulation. The beads may be as small as 0.1 mm in diameter and may have their resistance as high as 10 k . The thermistor discs range from 2.5 to 25 mm and 0.5 to 12.5 mm in thickness where as rod type thermistors vary from 1.3 to 4.4 mm in diameter and from 6.4 mm to 51 mm in length.

 

The material used thermometry possesses high resistivity and high negative temperature coefficient of resistance. Some compound mixtures have positive coefficient. The resistance –temperature characteristics are non-linear and are governed by the relation –

 

where RT and R0 are resistance values of the thermistor at absolute temperatures at T K and T0 K respectively and is a material constant expressed in degrees Kelvin (absolute). For commonly used materials, the value of at 25 oC is 4000.

 

 

Figure 2– Resistance-temperature characteristic for thermistor materials

 

The resistance-temperature characteristic for thermistor materials is shown in figure 2. It is seen that thermistor are limited in their application as they can be used only for the range – 100 0C to + 300 0C. Some thermistors contain sintered aluminum oxide and are used up to about 1000 0C. They are quite useful for compensating electrical circuits for changes in ambient temperature.

 

The merits of thermistors over the wire-resistance elements for temperature measurements lie in their high values of temperature coefficient, relatively small size (making localized measurement possible), low thermal capacity, high speed of response and large resistance value. The time constant varies from 1s to 20s, depending on the protection tube and, when directly used it may go down to 100 ms.

 

Summary

 

In this module we studied about various types of Resistive transducers. After the briefly studying about resistive transducer we will studied in details about principle of operation of a Resistance Gauge. Thereafter, our objective was to study about Resistance Thermal Detectors (RTD). Here we studied about theory and other basic fundamentals of resistance thermometers. In the end we studied about Thermistors, they are also known as Thermally resistive transducers.

you can view video on Transducers I

References :-

  1. Electrical and Electronic Measurements and Instrumentation, Sawhney A. K., Dhanpat Rai & Sons, Reprint 1985
  2. Measurements and Instrumentation, Bakshi U.A., Bakshi A.V., Technical Publications, 2009
  3. Principles of instrumental analysis, Skoog, Douglas A., F. James Holler, and Stanley R. Crouc,. Cengage learning, Edition 2017
  4. Instrumentation, measurement and analysis. Nakra, B.C. and Chaudhry, K.K., Tata McGraw-Hill Education, 2003.
  5. Measurement and instrumentation: theory and application, Morris, A. S., & Langari, R. , Academic Press, 2012.