Recent Researches in Instrumentation, Measurement, Circuits and Systems

Virtual Capacitive Sensor System NIKOLAY GOUROV, VLADISLAV SLAVOV, TASHO TASHEV FACULTY OF AUTOMATICS TECHNICAL UNIVERSITY - SOFIA 8 Kliment Ohridski blvd. 1000 - SOFIA, BULGARIA [email protected], [email protected], [email protected] Abstract: - In this paper construction of capacitive sensor virtual system is discussed. Capacitive sensors can be used to measure displacement, as its capacitance changes with the movement of the examined object. The structure, principles and characteristics of capacitive sensors are introduced in the paper. Virtual measurement system is constructed using capacitive sensors from Feedback and ELVIS II hardware platform of National Instruments. The software controlling the system is developed in LabVIEW environment. Working algorithm for describing execution of the system is synthesized. Virtual capacitive transducer system is built with educational purposes.

Key-Words: - algorithm, bridge circuit, capacitive sensor, LabVIEW, resonance, transducer, resonance method, virtual instrument Based on this dependence there are tree basic methods for realizing capacitive sensors – by varying d, A and ε. If the variation of the non-electrical quantity X leads to changes in the capacitance C of the capacitor (change of d, A or ε), the capacitance will depend on X: C = f1(X) (2) Therefore measurement of the quantity X is reduced to measurement of the capacitance C and use of the back function f1-1 to find X.

1. Capacitive Sensors Capacitive sensors are widely used in industry and science for measuring and control of variety of nonelectrical quantities. Their operational principle is based on the sensor’s capacitance changes in response to variations of the measuring quantity. These sensors find many different applications spread from moisture and humidity measurement to level, pressure and displacement measurement. They are using different operational and sensing principles to measure different quantities and even it is possible to use variety of principles to measure one and the same quantity. However in practice the application of capacitive sensors is mostly associated with displacement measurements. Measurements of rotational and translational shift and distance are very important in many engineering systems. Capacitive displacement sensors have relatively high linearity and wide range of use (from nanometers to millimeters). As mentioned above the operational principle of the capacitive sensors is based on change of their capacitance in response to the variations of the input quantity. The capacitance of the capacitor C is determined by its shape, dimensions and permittivity, therefore: C = f(d, A, ε) (1) where: d is the distance between electrodes of the capacitor, A – surface area of the electrodes; ε – permittivity of the dielectric between electrodes of the capacitor (ε= εr ε0)

ISBN: 978-960-474-282-0

area A X

moving plate

fixed plate

Fig. 1 Variable distance capacitive displacement sensor On Fig. 1 is depicted flat capacitor with variable distance between electrodes. It has one fixed and one moving electrode. The moving electrode vary the distance in response to the changes of a physical quantity (displacement). If ignore fringe effects, the capacitance can be expressed by:

C( X ) =

ε ε A = r 0 X X

εA

(3)

where: ε = the dielectric constant or permittivity er = the relative dielectric constant (in air εr ≈ 1)

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Recent Researches in Instrumentation, Measurement, Circuits and Systems

ε0 = 8.854188 10–12 F/m–1, the dielectric constant of vacuum X = the distance between plates in m A = the effective area of the plates in m2 It can be seen that the capacitance if nonlinear function of the distance (X). The sensitivity is variable and increases as x decreases, because: dC − ε r ε 0 A (4) = dX X2 Another type capacitive displacement transducer is with variable area. Such sensor is shown on Fig. 2. In this case the displacement vary surface area of the electrodes of flat capacitor and capacitance will be:

ε ε ( A − wX ) C( X ) = r 0 d

(Fig. 4) that form two capacitors. They changes there capacitances with opposite phase in respect to variations of the input quantity, which rises the sensitivity and accuracy of the sensor. 1 2

1

3

3 1, 2 - fixed plates

3 - moving plates

Fig. 4 Differential capacitive arrangements

(5)

Capacitive transducers have the following pros: high sensitivity, small size and weight, low inertia. They are relatively easy for constructing. Cons are variation of the characteristics when the working conditions are changed as temperature, humidity dust contamination of the air etc. Their accuracy is strong influenced by parasite parameters of the cables capacitance, inductance and resistance. They have low capacity (10-100 pF) and variations of the capacity are around ten times smaller.

where: w is the with of electrode (as shown on Fig.2) X – displacement (wX represents the reduction in the area due to movement of the electrode) X moving plate w d

2

fixed plate

2. Measuring Circuits To use capacitive transducers one need to measure the capacitance of the transducer or other quantity dependent from this capacitance. Because the capacitance is passive quantity, normally capacitive sensors are included as variable impedances in measurement circuit and other quantity dependent from the capacitance is measured. There are two basic ways to do that – using an AC bridge circuit or tuned circuit method (resonance method). General AC bridge circuit is depicted on Fig. 5. It consists of four impedances, an AC voltage source, and a null detector as shown.

Fig. 2 Variable area capacitive displacement sensor This means that the transducer output is linear with respect to the displacement X and the sensitivity is constant. According (1) displacement can be sensed by varying the dielectric constant of the dielectric between the plates of the capacitor. In this case (shown on Fig. 3), there is relative movement of the dielectric material between electrodes, which vary the effective dielectric constant. The output of the sensor is linear. Normally this type of transducer is used in form of two concentric cylinders for measuring the level of fluids.

dielectric ε X

variable length

Fig. 3 Variable dielectric capacitive displacement sensor To reduce or even eliminate the nonlinearity of the sensors frequently are used differential capacitive arrangements. They are basically three terminal devices

ISBN: 978-960-474-282-0

Fig. 5 Basic bridge circuit

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Recent Researches in Instrumentation, Measurement, Circuits and Systems

It is very difficult to use the bridge method when small values of capacitance are measured. In this case big influence of parasitic capacitances in the circuit can be found, which may corrupt the measurement. Therefore some other method is needed when transducers whose operation depends on their small capacitance and even smaller capacitance changes are used. If a capacitive position transducer is used, knowing the actual capacitance of the transducer is less important than knowing the relation between the input quantity being measured and the output. Thus instead of using a method which actually measures the value of the capacitance of the transducer, such as would be the case if a bridge circuit is being used, a method which uses the capacitance of the transducer to vary the parameters of an electronic circuit, and hence vary the output from that circuit, may be more usefully employed, provided the relationship between the thing being measured and the circuit output is known, of course. A circuit that uses those considerations is the inductance-capacitance resonant circuit also called tuned circuit (Fig. 7).

For this general form of AC bridge the balance, condition (null detector shows null) is as: (6)

It must be stressed that the impedance quantities in the above equation are be complex, accounting for both magnitude and phase angle. It is insufficient that the impedance magnitudes alone be balanced; without phase angles in balance as well, there will still be voltage across the terminals of the null detector and the bridge will not be balanced. Bridge circuits can be constructed to measure just about any device value desired, be it capacitance, inductance, resistance, or even “Q.” As always in bridge measurement circuits, the unknown quantity is “balanced” against a known standard, obtained from a high-quality, calibrated component that can be adjusted in value until the null detector device indicates a condition of balance. Depending on how the bridge is set up, the unknown component's value may be determined directly from the setting of the calibrated standard, or derived from that standard through a mathematical formula. A simple “symmetrical” bridge is shown on Fig. 6. It is named so because it exhibits symmetry (mirrorimage similarity) from left to right. The bridge circuit is balanced by adjusting the calibrated reactive component Cs. It is a bit simplified from its real-life counterparts, as practical symmetrical bridge circuits often have a calibrated, variable resistor in series or parallel with the reactive component to balance out stray resistance in the unknown component. But, in the hypothetical world of perfect components, this simple bridge circuit does just fine to illustrate the basic concept.

Fig. 7 LC resonant circuit The well-known formula for the frequency of resonance (fr) is:

fr =

2π LC

(7)

So if C is changed, then fr will change too. The resonant circuit can be used, together with an amplifying circuit, to form an oscillator. The oscillator produces an AC sinusoidal output at a frequency governed by the resonant frequency of the tuned circuit used in the oscillator. Therefore, if the resonant frequency of the tuned circuit is changed by changing the capacitance C, the frequency of the AC output from the oscillator will change also. The output signal of the transducer in the virtual system will be acquired, analyzed and the results will be visualized with a virtual instrument created in LabVIEW environment. A virtual instrument consists of an industrystandard computer or workstation equipped with powerful application software, cost-effective hardware such as plug-in boards, and driver software, which

Fig. 6 Bridge circuit for capacitance measurements Practically, there are different modifications of that bridge circuit to measure Capacitance as Wien bridge, Schering bridge and so on [3].

ISBN: 978-960-474-282-0

1

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Recent Researches in Instrumentation, Measurement, Circuits and Systems

Feedback’s TK2941H Capacitive transducer will be used connected in two different circuits part of TK2941A kit (Fig. 9). The module on Fig. 9 can assure the conduction of experiments using the methods described above. The output data will be acquired with National Instrument’s ELVIS II equipment and LabVIEW as an environment to create a virtual instrument to analyze and present the data [5].

together perform the functions of traditional instruments. Virtual instruments represent a fundamental shift from traditional hardware-centred instrumentation systems to software-centred systems that exploit the computing power, productivity, display, and connectivity capabilities of popular desktop computers and workstations. Although the PC and integrated circuit technology have experienced significant advances in the last two decades, it is software that truly provides the leverage to build on this powerful hardware foundation to create virtual instruments, providing better ways to innovate and significantly reduce cost. With virtual instruments, engineers and scientists build measurement and automation systems that suit their needs exactly (user-defined) instead of being limited by traditional fixed-function instruments (vendor-defined)[4].

3. Problem Formulation The structure of the virtual capacitive transducer system is shown on fig. 3. The capacitive transducer is included in a measurement circuit using one of the methods described before. The output signal is acquired by the computer with an appropriate interface. A program running on the computer calculates the necessary values, analyzes the data, and shows the results in proper form for the user. Capacitive transducer

Measurement circuit

Computer

Fig. 8 Virtual capacitive transducer block diagram

Fig. 10 Algorithm block-diagram of a virtual capacitive measurement circuit

4. Problem Solution The initial experiments conducted with the transducer and the bridge circuit showed that this approach is not suitable for our needs. The capacitance of the transducer is too small, between 20 and 40 pF, so the results were not reliable. The initial experiments using the tuned method showed stable results so the algorithm of the system was created using that method. The block diagram on fig. 10 shows the algorithm that is used to describe the execution of the virtual capacitive transducer system.

Fig. 9 Feedback’s TK2941A Instrumentation Module The problem to be solved can be divided in two steps: - to choose appropriate circuit to create the system; - to synthesize an algorithm - to create a program for data processing, analysis and results presentation;

ISBN: 978-960-474-282-0

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Recent Researches in Instrumentation, Measurement, Circuits and Systems

References: [1]. Doebelin O. E., Measurement Systems: Application and Design, McGraw-Hill, New York, 2004 [2]. Matrakov B. - editor, Electrical measurements, TU-Sofia Publishing House, 1999 (in Bulgarian) [3]. Kalchev, Measurement and Instrumentation, TU Sofia, 1998 [4]. Vladislav Slavov, Tasho Tashev, “Virtual laboratory for measurement of physical quantities”, Proceeding of the 4th International Conference on Challenges in Higher Education and Research in the 21st Century, 2006, Sozopol, pp 260-264 [5]. www.ni.com

The signal conditioning is necessary to have a precise measurement of the resonant frequency. To calculate the capacitance using formula (7) is enough to know the inductance in the resonant circuit.

5. Conclusion The reported system provides a good method of displacement measurement using capacitive sensor. The structure, principles and characteristics of capacitive sensors are introduced. Virtual measurement system is constructed. Algorithm is synthesized to describe execution of the system. The reported system will be very useful for educational process in subject “electrical measurements of non-electrical quantities”

6. Acknowledgement This work was supported and financed by the Technical University – Sofia, 2010 internal grant No.102ni101-08

ISBN: 978-960-474-282-0

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