6 Transducers II

Vinay Gupta

   Learning Objectives

In this module we will study about transformers like LVDT that can convert any linear motion into an electrical signal. This will be followed by inductive and capacitive transducers. Here we will study about transducer operation and theoretical background behind conversion of energy from one form to another.

Introduction

The main application of transducers is the measurement of non-electrical quantities by using various electrical methods. The use of electrical methods to measure any non-electrical quantity continuously and transmit data over long distances with high accuracy and sensitivity is the preferred method to record and investigate a phenomenon of interest.

Few advantages of measuring non-electrical quantities via electrical methods are

1. automatic measurement and constant readiness of the measuring apparatus
2. the possibility of non-inertial reproduction of varying value of quantity under investigation
3. it opens the possibility of automatic mathematical processing of the results of the measurement
4. instrument having wide measurement range can be easily developed

    Here onwards we will study about transducers like LVDT, Inductive transducers, etc. for measuring different types of non-electrical, mechanical motions of the object of interest. A student of electrical measurement methods should note that transducer converts energy from one from another, it may electrical, mechanical, thermal, pressure, etc. whereas a transformer is a static electrical device with inductive winding coils that can transform electrical energy inductively.

1. Linear Variable Differential Transformer (LVDT)

LVDT is an inductive transducer that converts the linear motion into an electrical signal. LVDT is a differential transformer that consists of one primary winding P and two identical secondary windings S1 and S2, would over a hollow bobbin of non-magnetic and insulating material. An illustration is shown in figure -1

Figure 1. An illustration of Linear Variable Differential Transformer (LVDT)

Both the windings have equal number of turns and are arranged concentrically and placed on side of the primary winding P. Attached to the sensing element is a soft iron core whose displacement is to be measured. It is shaped in form of cylinder or rod and slides freely in the hollow portion of the bobbin. To avoid eddy current loss, nickel-iron alloy is used as a core material, which is positioned longitudinally. Primary winding is connected to an ac source, whose voltage is varied form 5 to 25 V and frequency range is from 50 Hz to 20 kHz. When core moves in the bobbin, it varies coupling between primary and secondary windings. In the central position the coupling between the two windings is equal and so the output between the 2 coupling is also equal. As the core move towards the left of the central position, the magnetic linkage with the S1 increases and with the secondary windings S2it decreases. This increases output voltage in S1 and decreases output voltage in S2. An opposite effect will happen when core moves toward right of the bobbin. Both the windings are connecting in series position. This produces a difference in output voltages of secondary windings and gives the measurement of displacement.

Figure 2.  Variation of Differential Output Voltage With Displacement for LVDT

The differential output voltage produced with the displacement of core in LVDT is explained by the curve in figure 2. From the curve one can observe that the linearity is limited to certain range of displacement (5 mm either side of null position), beyond which curve tends to flatten out (at both ends). The range of linearity of the curve, is limited by the dimension of the transducer.

Slide -6

The net induced emf (Eo) with displacement of the movable core can be calculated from the following expression.

Where,

 = supply frequency, rad/s

Ip = primary current

Np,Ns = No. of turns of primary and secondary windings

ro,ri = outer and inner radii of the coil system

x = displacement of the core from null position

o = absolute permittivity of the space (4 x 10-7 H/m)

At null position, output voltage is not zero; some residual current exists at the output terminal but is less 1% of the maximum value of output in the linear range. In commercially available transformers, displacement from the null position varies from ± 0.01 mm to ± 25 mm.

LVDTs are used where displacement are too large for strain gauges can handles. They are used for measuring displacement from fraction of mm to a few cm. If LVDTs are to be used for displacements greater than 25 mm, then an appropriate gearing system should be used. They can also be connected to other transformers, they are often used for measuring pressure, force, weight, etc.

Slide-8

2. Inductive Transducer

An inductive transducer belongs to the category to of analog passive transducer. They normal operate on one of the following principles –

1. Variation of self inductance of the coil
2. Variation of mutual inductance of the coil
3. Production of eddy current

Let us look at these principle one by one –

Transducer Operation via Variation of Self Inductance

The self-inductance of the coil is given by the expression –

where N is the number of turns in a coil, l is the mean magnetic path length, A is cross sectional area of magnetic path and is the magnetic permeability of the material. Geometric form factor G is given A/l.

The self inductance can be varied by changing the number of turns in a coil, with permeability of magnetic material and by altering the geometrical configuration of the magnetic circuit. An Inductive transducers can be used for measuring linear as well as angular displacement.

Transducer Operation via Variation of Mutual Inductance

This type of transducers work on the principle of mutual inductance between the two coils, which further depends on the self-inductance of the coils and coefficient of coupling between them. This relationship can be understood with the following expression –

where K is the coefficient of coupling and L1& L2 are the self inductances of the coils.

Figure 3. Inductive Transducer for Measurement of Linear Displacement

   Transducers where 2 or more coils are used, the mutual inductance between the coils is varied as per the measurand. A simple example of inductive transducer for measurement of linear displacement is shown in the figure 3.

Here transducer coils are in series, so inductance is sum of self inductance of both coils and mutual inductance between them. Mathematically, inductance in this arrangement varies from L1+L2-2M to L1+L2+2M.

The displacement of the moving iron piece creates changes in the air gap of the magnetic circuit; this change is flux with the movement of the iron piece results in mutual inductance between the coil. This mutual inductance can be senses by bridge circuits.

Transducer Operation via Production of Eddy Current

Eddy currents are also called Foucault Currents. They are loops of electrical current induced within the conductors in presence of changing magnetic field. In such transducer, a conducting plate is kept near the coils carrying alternating current and eddy current is induced in the conducting plate. This plate produces its own magnetic field in opposition to the magnetic field created by the coil. Thus, currents induced in the plate reduce the net flux associated with the coil; this reduces inductance of the coil. Closer is the plate to the coil, higher is the induced eddy current and higher will be reduction in the inductance of the coil. Briefly, the inductance of the coil gets altered by the movement of the plate.

Figure 4. Measurement of Linear  Displacement via Inductive Transducer

   This mechanism is shown in the figure 4a. In such a transducer, we have a coil carrying an alternating current and a cylindrical sleeve of a conducting material that moves parallel and co-axially to the coil. Displacement of this short circuit sleeve is proportional to eddy current induced in the coil. This change in inductance of the coil is the measure of displacement, which is sensed and indicated by an ac bridge circuit. Alternatively, plate may be placed 90 degree to the axis of the coil, as shown in the figure 4b. Displacement of the plate produces change in the inductance of the coil. Sensitivity is usually low for this type of semiconductor.

3. Capacitive Transducers

A capacitive transducer is a variable capacitor whose capacitance is varied by a non-electrical quantity being measured. The capacitance C for a parallel plate capacitor is given by the following expression –

    where o is the absolute permittivity of the free space which is equal to 8.854 X 10-12 F/m; r is the relative permittivity of the dielectric, A is the are of plates in m2 and d is the distance between the 2 plates in meters.

Capacitive transducers are also analog passive transducers and capacitance in such transducers is varied by one of the following methods –

1.      By changing overlapping area of plate, A

2.      By varying relative permittivity of dielectric material between the plates

3.      By varying distance between the plates, d

Any of the above changes can be caused by physical variables like displacement, force or pressure. Change in capacitance can also be caused by change in permittivity that would be in case of measurement of levels of gases or liquid. Any change in capacitance can be measured with an ac bridge having an oscillatory circuit.

Transducer Operation via Variation of Overlapping Area of Plates

Such transducers operate on the most basic fact that the capacitance in a capacitor is proportional to the overlapping area of plates. To understand the operation of capacitive transducer let us consider that we have two parallel plates with a constant width b, as shown in figure 5a. Length l is the overlapping portion of the plates, which varies with displacement of the moving plate. Any change in displacement changes the capacitance of the system and is given by following expression –

where l is the length of overlapping portion in meters, b is the width of the plates in meters and d is separation between plates in meters.

Figure 5 .(a) Capacitive transducer by variation of overlapping area of plates. (b) Capacitance vs Displacement curve

Sensitivity, s of the system is given differential of S with respect to small change in overlapping portion of the plate.

S=   C/ l F/m ———(6)

The curve drawn for the sensitivity is between capacitance of the transducer and displacement. The curve is linear except in the initial portion, which is due to edge effect .This curve is shown in figure 5b.

The design of the transducer plates can be varied according the application. Plates can be cylindrical or parallel semi-circular plates. The equation for these designs can be derived by substituting values for the overlapping area A in previously discussed equation 5.

Transducer Operation via Variation in Distance Between The Plates

Such capacitors have two parallel plates, where one is fixed and other is a moving plate. Here capacitance is measured by varying distance d between the two plates, which is inversely proportional to the measured capacitance (see equation 4). The inverse relation curve between the capacitance and displacement is shown in figure 6.

Figure 6. Parallel Plate Capacitor

The curve is non-linear and the sensitivity of the system is high only for the initial portion of the curve. Therefore this method is best suited for extremely small displacements only. For close approximation of linearity, the transducer have a thin piece of mica, thinner than the minimum gap between the plates.

Theoretically, sensitivity of the system can be increased by increasing the area of the plates or by reducing the distance between the plates.

Transducer Operation via Variation of Permittivity of the Dielectric Material Between the Plates

In this system, dielectric material of relative permittivity r moves between the fixed parallel plates according to the displacement under measurement. Figure 7 shows the operation of the capacitive transducer with the displacement of the dielectric material. The net capacitance is given by the following expression –

Figure 7. Capacitive Transducer with dielectric Displacement

Change in displacement is proportional to the change in capacitance. This method can be used to measure displacement from 1 m to 10 mm.

Applications – capacitive transducers are used for measuring force and pressure changes which are first converted into displacement and then into change in capacitance. They are also employed to measure density, volume, level of liquid, weight, etc., but along with mechanical modifiers.

Summary

In this module we studies about transformers like LVDT that can convert any linear motion into an electrical signal. This was followed by inductive and capacitive transducers. Thereafter we studied about transducer operation and theoretical background behind conversion of energy from one form to another.

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.