Measurement Techniques, Vol. 52, No. 6, 2009

ELECTROMAGNETIC MEASUREMENTS AN ELECTROSTATIC VOLTAGE COMPARATOR

A. I. Nefed’ev

UDC 531.714.75

The principles of the construction of an electrostatic dc and ac voltage comparator using a systems approach for increasing its accuracy are considered. Key words: electrostatic comparator, electrostatic and photoelectric converters, structural redundancy.

The requirements being imposed on the accuracy of ac measurements under modern conditions are increasing. An analysis of the main trends in the development of measurement techniques, carried out on the basis of a survey conducted by the Keithley Instruments Company (Cleveland, USA), has shown that there are constant requirements to increase the accuracy of measuring instruments, including measurements of voltage in ac circuits [1]. For standard measurements of ac voltage in all the developed countries, thermoelectric comparison converters are employed at the present time. The possibility of increasing the accuracy of these instruments has been largely exhausted, due to the insufficient stability of their characteristics. An estimate of the errors of standard thermoelectric converters is based on a theoretical analysis [2] and must be confirmed experimentally by international comparisons. Standard measurements of alternating voltage by several essentially independent methods based on different physical phenomena (thermal and mechanical) can be regarded as a uniquely reliable procedure, which gives a correct result (from the point of view of estimates of the systematic errors) [3, 4]. The possibility of constructing an electrostatic dc and ac voltage comparator for voltages up to 1000 V with a construction similar to weighing scales and with a sensitivity of up to 10–6, obtained from a theoretical analysis of its constructional principle, is discussed in [5]. An analysis shows that on the one hand, there are wide possibilities for increasing the accuracy of electrostatic voltage comparators, while on the other they are quite complex to construct. The development of a decentralized system for reproducing (measuring) and transferring the dimensions of units using autonomous checking and self-checking instruments is also a pressing problem [6]. The principles for constructing electrostatic voltage comparators for simultaneous comparison, described in [7, 8], shows them to be extremely promising for comparing voltages over a wide frequency band. The problem of increasing the accuracy of such comparators has been solved by using a systems approach based on structural redundancy of its components [9]. The principle considered here has been realized by constructing an electrostatic voltage comparator for voltages of up to 1000 V with an error of 0.005–0.001% and is designed to operate over a frequency band of 40 Hz – 100 kHz. The comparator consists of a measuring unit and an automatic compensator. In Fig. 1a, b, we show the construction of the measuring unit of the comparator, which includes the following subsystems: a moving part, electrostatic comparison converters, converters of the angle of rotation of the moving system into an electric signal, instruments for fastening the moving part and a liquid damper. The movable system of the comparator contains a horizontally situated beam 22, on the ends of which there are movable electrodes 16 of the electrostatic converters and flags 14. The balance arm has the form of a double-tee beam made of aluminum, on which layers of zinc and copper are successively deposited by an electrolytic method. Volgograd State Technical University, Volgograd, Russia; e-mail: [email protected]. Translated from Izmeritel’naya Tekhnika, No. 6, pp. 51–55, June, 2009. Original article submitted March 31, 2009. 650

0543-1972/09/5206-0650 ©2009 Springer Science+Business Media, Inc.

a

b Fig. 1. Construction of the measuring unit of the electrostatic voltage comparator: 1, 30) covers; 2) joint; 3) Silmin body; 4) photoresistor; 5) condenser lens; 6) light-emitting diode; 7, 8) screens; 9, 15, 16) fixed, additional, and movable electrodes; 10) stand; 11) screw; 12) handle; 13, 20) terminals; 14) flags; 17) insulator; 18, 26, 29) platforms; 19) level; 21) limiter; 22) beam; 23) base; 24) zero corrector; 25, 27, 37) brackets; 31) panel; 32–36) tension wires; 38) ring; 39) axis.

The electrostatic converter consists of a movable electrode 16 and a fixed electrode 9, an additional electrode 15, for ensuring that the electrostatic converters are identical, handles 12, terminals 13 for connecting the connecting wire, a screen 8, connected with the input of the comparator, an insulator 17, and a screen for preventing polarization of the insulator from affecting the readings of the comparator. The movable electrode 16 and the fixed electrode 9 are constructed in the form of a multicompartment cylindrical capacitor made of D16 aluminum alloy. Layers of zinc, red copper and gold are successively deposited on the electrodes by an electrolytic method. This construction of the moving system and of the electrostatic converters enables qualitatively new properties to be obtained, namely, high sensitivity due to the long length of the beam and smooth regulation of the 651

Fig. 2. Liquid damper of the vibrations of the moving part of the comparator: 40) reservoir with liquid; 41) hollow cylinder; the remaining notation is the same as in Fig. 1.

identity of the electrostatic converters, which, in the final analysis, leads to an increase in the sensitivity and accuracy of the comparator. The device for fastening the moving system contains a bracket 37 with platforms 26 placed on its ends, an axis 39, to which rings 38 and tension wires 32–36 are attached from each side. Internally the ends of the tension wires 32–34 are fixed in pairs to the axis 39 or the rings 38 using adhesives in such a way that the axis of rotation lies between the two adjacent tension wires. The movable part is retained by tension wires 36, which are at an acute angle to the horizontal plane. The tension wires 34 and 35 are situated in a horizontal plane and serve to fix the movable system with respect to the fixed electrodes. Tension wires 32 and 33 prevent the movable system from vibrating in a horizontal plane, due to mechanical interference. Moreover, they prevent the action of electrostatic forces in the electrostatic converter, directed perpendicular to the beam. Externally the ends of the tension wires 32, 33, 35, and 36 are fastened to damping springs, situated on the platforms 26. The tension wires are made of PlSr20 platinum-silver alloy and are 100 mm long. The system of tension wires is constructed using structural redundancy, where four long tension wires with a low counteracting moment, situated in pairs in mutually perpendicular planes, are used instead of a single tension wire. Qualitatively new properties of the system of tension wires are the fact that it prevents vibrations of the moving system of the comparator in nonworking planes and it enables the simplest construction of the electrostatic converters in the form of multicompartment cylindrical electrodes to be used. The use of long tension wires also helps to reduce their overall counteractinging moment. The comparator uses two converters of the angle of rotation of the movable system into an electric signal, each of which contains flags 14, fastened to the ends of the beam 22, photoresistors 4, capacitors 5, and light-emitting diodes 6. FSK-7B photoresistors and 8R3SDB-5 light emitting diodes with a wavelength of 660 nm are used in the converter. The photoresistor, the condenser lens and the light-emitting diodes are placed in a Silumin container 3. The new properties of the photoelectric converter system are the increased stability of the electrostatic comparator to transverse vibrations of the moving system. The two photoelectric converters are connected in such a way that their output signals are added when the moving system rotates in the operating direction, and are subtracted when the moving system vibrates due to the action of interference. Because of this the sensitivity of the comparator is increased and its susceptibility to mechanical interference is reduced, which is a qualitatively new property. The converter of the angle of rotation of the moving system into an electric signal is attached to supports above the electrostatic converter. The position of the diaphragms of the photoresistors is regulated by displacing the body 3 of the photoelectric converter with respect to the flags 14. Limiters 21 are used to limit the displacement of the moving system in a vertical plane. The platforms 26, to which the outer ends of the tension wires are attached, are connected to one another with brackets 25 and 27. This ensures simultaneous rotation of the platforms, which is necessary for the mechanical correction of the zero of the moving system. 652

A liquid damper of the vibrations of the moving part (Fig. 2) is combined with its fastening, and for this purpose the horizontal tension wires are made in a composite form. Their ends are connected internally through hollow polished beams 41 and tension wires 34 with high counteracting moments to the rings 38. The beams are placed in a reservoir 40, filled with ethylpolysiloxane fluid. When measuring an alternating voltage, the moving system of the comparator performs torsional vibrations, which are transmitted to the beams through the tension wires. Friction between the hollow beams and the liquid in the reservoirs leads to quenching of the torsional vibrations of the moving system. Moreover, withdrawal forces act on the beams, immersed in the liquid, and, consequently, on the moving system of the comparator, which partially compensate the weight of the moving system. As a result, the tension of the inclined tension wires is reduced, which leads to a qualitatively new property, namely, a reduction in the counteracting moment and, as a consequence, an increase in the sensitivity and accuracy of the comparator. The electrostatic converters, the device for fastening the moving system and the converters of the angular displacement of the moving system into an electric signal are placed on an aluminum base 23 (see Fig. 1), to which vertical panels 31 are attached, which form the body of the comparator. There are joints 2 on the panels for connecting an automatic compensator. Terminals 20 for connecting the low-potential connecting wire are fixed on the lower side of the base 23. Removable aluminum covers 30 enable the external ends of the tension wires to be accessed. The measuring unit is enclosed by a Π-shaped aluminum cover 1. The body of the measuring unit is fixed to the aluminum platform 18 by means of supports 10, and on this platform there is a level indicator 19 and a device 24 for smooth displacement of the bracket of the mechanical zero corrector of the movable system. The platform 29 with the screws 11 keeps the measuring unit in a horizontal position. A shock-absorbing packing 28 is placed between the platforms 18 and 29 to reduce the effect of mechanical interference on the moving system of the comparator. The beam 22 and the inner end of the terminal 20 are connected by fine momentless tape of red copper, to carry the current to the moving electrode of the electrostatic converter, which reduces the inductance of the current-conducting circuit and, consequently, the frequency error of the comparator. To ensure that the center of gravity of the moving system coincides with its axis of rotation, there is a nut on a pin at the center of the moving system which can be shifted. To balance the moving system, there are also nuts on pins close to the axis of rotation of the moving system (not shown in Fig. 1). The automatic compensator (not shown in Fig. 1) is a combination of a photoelectric converter of the angle of rotation of the moving system into an electric signal, a light amplifier and a balanced dc amplifier which sums and amplifies the signals from the two converters of the angle of rotation of the moving system. The zero of the automatic compensator is set using mechanical and electrical correctors. The procedure for measuring an alternating voltage using the comparator is as follows. Immediately before a measurement, using a mechanical corrector (not shown in Fig. 1), the moving part of the compensator is set in a horizontal position when the inputs of the electrostatic converters are short circuited. The null indicator should then be on the zero marker. The electrostatic converters are then set to be identical for an alternating voltage. To do this, the same alternating voltage is applied to both converters from an ac voltage source. If the electrostatic converters are not identical, the moving system is shifted from the zero position, which shifts the reading of the null indicator of the compensator from the zero marker. By rotating the additional electrodes of the electrostatic converters manually, the electrostatic converters are adjusted to be identical to give a zero reading on the indicator. The measured alternating voltage is then applied to one of the inputs of the measuring unit of the comparator, while a constant voltage is applied to the other input and is regulated in such a way that the null indicator shows zero. In order to eliminate errors due to asymmetry, balancing is carried out for two polarities of the dc voltage and the arithmetic mean of the results of two measurements is calculated. The dc voltage is measured using a voltage divider and dc potentiometer. The torque MA and the countering moment MB should be equal when the beam is horizontal, namely, MA = MB;

FALA = FBLB,

where FA and FB are the forces acting on the beam, and LA and LB are the lengths of its arms. 653

Electrostatic voltage comparator (EKN-1) Left EC

Right EC

G~ 745A, 746A

G– P320

VD P3027-2

DCP P3003

Fig. 3. System for the experimental investigation of the electrostatic voltage comparator by the opposition method and measuring an alternating voltage: EC is the electrostatic converter; G– and G~ are dc and ac voltage generators; VD is a voltage divider; and DCP is a dc potentiometer.

TABLE 1. Results of Measurements of the Voltage Using the Arrangement Shown in Fig. 3 Voltage, V, on the EC Frequency, kHz left

right

left

right

1

300.1521

300.1516

500.2165

500.2161

2

300.1520

300.1515

500.2160

500.2156

50

300.1518

300.1514

500.2158

500.2152

100

300.1517

300.1512

500.2556

500.2553

The forces FA and FB are obtained by differentiating the expression for the energy stored by the capacitor-electrostatic converter (EC) with respect to z: F A = U 2A ∂C A / 2 ∂z ;

FB = U B2 ∂C B / 2 ∂z .

When a zero reading is obtained on the null indicator (UNI = 0), the moments of the forces acting on the beam are balanced: U 2A L A ∂C A / ∂z

U NI = 0

= U B2 LB ∂C B / ∂z

U NI = 0

.

The error in measuring an alternating voltage U~ by the comparison method using the comparator (Fig. 3) is expressed by the formula  U − U2 ~ U + − U −  U U γ c = –av ~av or γ c =  1~  U nom . U –av 2 2   654

The comparison was carried by sequential interchange of the measurements in accordance with the algorithm U+, U1~, U–, U2~ or U1~, U+, U2~, U–. Using this method, we carried out a series of measurements of voltages of 300 V and 500 V at frequencies of 1, 2, 50, and 100 kHz. The mean values of the voltages at the outputs of the electrostatic converters are shown in the table. An analysis of the data in the table shows that the comparison error γc on changing from a dc voltage to an ac voltage does not exceed 0.0004% for voltages higher than 300 V. An independent check of the comparator was carried out using the following methods [10]: 1. A theoretical-experimental method of element-by-element determination of the components of the comparison error of the comparator and the summation of these errors statistically, assuming a uniform distribution of the terms in the tolerance field for a confidence coefficient of 0.99, calculated from the formula γ c = 1.4 γ 2fL + γ 2f + γ 2a + ψ 2t + ψ 2d + ψ 2n.c , where γƒL is the frequency error due to the inductance of the current leads in the electrostatic converter circuit, γƒL = 0.00005%; γƒ = (ƒ/ƒ0)2 is the frequency error, γƒ = 0.0001%; γa is the error due to asymmetry (eliminated systematically); ψt is the error due to the sensitivity threshold (determined experimentally), ψt = 0.0002%; ψd is the error due to zero drift (determined experimentally and mainly dependent on the stability of the dc and ac voltage calibrators), ψd = 0.0003%; and ψn.c is the error due to the nonidentical form of the characteristics of the electrostatic converters (assumed to be equal to the error ψt due to insensitivity), ψn.c = 0.0002%. Summation of the errors gives γc = 0.0006%. 2. An experimental determination of the error of the comparator by the opposition method (see Fig. 3). The difference in the comparison errors, determined using the above methods, amounted to 0.0002%. The high accuracy of the comparator is due to the fact that the units included in it acquire qualitatively new properties because of the structural redundancy, which, as a result, leads to an increase in its sensitivity. Hence, the proposed structure of the electrostatic voltage comparator guarantees high accuracy when measuring voltages in alternating-current circuits.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

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