Microsoft Word - Article 16 - 174-1029-1-LE.docx ACTA IMEKO  February 2015, Volume 4, Number 1, 105 – 110  www.imeko.org    ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 105  Virtual quasi‐balanced circuits and method of automated  quasi‐balancing  Artur Skórkowski, Adam Cichy, Sebastian Barwinek  Institute of Measurement Science, Electronics and Control, Silesian University of Technology, Akademicka 10 Street, 44‐100 Gliwice, Poland       Section: RESEARCH PAPER   Keywords: automatic balancing; virtual instrument; quasi‐balanced circuit; LabVIEW development  Citation: Artur Skórkowski, Adam Cichy, Sebastian Barwinek, Virtual quasi‐balanced circuits and method of automated quasi‐balancing, Acta IMEKO, vol. 4,  no. 1, article 16, February 2015, identifier: IMEKO‐ACTA‐04 (2015)‐01‐16  Editor: Paolo Carbone, University of Perugia   Received January 10 th , 2014; In final form March 25 th , 2014; Published February 2015  Copyright: © 2014 IMEKO. This is an open‐access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits  unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited  Funding: This work was supported by Institute of Measurement Science, Electronics and Control, Silesian University of Technology, Poland  Corresponding author: Artur Skórkowski, e‐mail: artur.skorkowski@polsl.pl    1. INTRODUCTION  Quasi-balanced circuits are AC circuits destined for measuring impedance components. They have a special selected state, the so-called quasi-equilibrium state, which is usually a predetermined phase shift between the selected signals. The advantage of quasi-balanced circuits is the use of only one control element. The quasi-equilibrium state is an a priori assumed non-zero state – generally meant as the achievement of the determined phase shift between the selected signals of the circuit. Maximum convergence is the advantage of the circuits under consideration, whereas the lack of possibility of simultaneous measurement of both immitance components is the disadvantage, although the measurement of the second component is usually possible after uncomplicated reconfiguration of the circuit. 2. QUASI‐BALANCED CIRCUIT FOR IMPEDANCE  COMPONENTS MEASUREMENTS  There are many solutions of quasi-balanced circuits for measuring impedance components, e.g. those presented in [1…7]. Figure 1 shows an example of the circuit used for measuring a capacitance modelled by a series combination of RC [8]. Modern measuring instruments are more and more often built as virtual instruments. In analog techniques, operations on measurement signals are performed on sampled and quantized signals by software. The block diagram of the circuit (Figure 1) describing analog processing becomes then a measurement algorithm (virtual instrument). Quasi-balanced circuits can be virtualized very easily, since there are only operations of summing, amplifying or shifting signals by ±π/2 in the discussed circuits. Phase-sensitive detection can also be realized with algorithmic methods. The equations describing the selected output signals w1, w2 in the system shown in Figure 1 have the form:        2 j 2 2 j 1   eBIw eBIAVw X XX (1) where A is the voltage amplifier gain, B is the conversion factor of the current /voltage converter; VX and IX are the voltage and current of the RC object under test, respectively. ABSTRACT  A basic purpose of this research was to verify a possibility of automatic balancing in the virtual realization of a quasi‐balanced circuit  for capacitance measurements. The diagrams of a virtual quasi‐balanced instrument are presented in this paper. The tested circuit was  built using a PC computer and the DAQ card NI‐6009. The DAQ card and the calculation were controlled by the application developed  in the graphical development platform LabVIEW.  ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 106  The complex numbers in Eq. 1 can be expressed in polar from as follows:          2 j 2j2j 2 2 j 2j1j1j 1   eeIBew eeIBeVAew X XX (2) where: 21 , ww - modules of the selected signals of the circuit; �1, �2 – phases of the selected signals of the circuit; XX IV , - modules of the voltage and current of the tested RC two-port; �1, �2 - phases of the tested RC two-port. After dividing both sides of the system of equations (2) by each other one obtains the expression:   2 j 2j 2 j 2j1j 21j 2 1   eeIB eeIBeVA e w w X XX     (3) which can be brought to the form: 12 21j 2 1           eZ B A e w w X Wj (4) where: �W – angle of the phase shift between the selected signals of the circuit, XZ - modulus of the impedance of the tested RC two-port. The dependence (4) is a complex number equation and can be written as a system of two real number equations in the trigonometric form:          XXW XXW Z B A w w Z B A w w   cossin 1sincos 2 1 2 1 (5) After dividing both sides of the system of Eq. (5) by each other and trigonometric transformation, one obtains the equation describing the signal �W being detected as a function of the circuit parameters A and B as well as the tested impedance components:                          X X XX XX W ZA ZAB Z B A Z B A Re Im arccotan cos sin1 arccotan   (6) if A ≠ 0 and Re(ZX) ≠ 0. In the quasi–equilibrium state the conversion equation (6) is reduced to the form:   0 2 cotan Im00   XZAB (7) from which it is possible to calculate the passive component of the measured impedance   0 0Im A B ZX  (8) where A0 is the voltage amplifier gain in the quasi- equilibrium state, B0 is the conversion factor of the current/voltage converter in the quasi-equilibrium state. Since the discussed circuit is destined for capacitance measurements, the capacitance of the capacitor is calculated from Eq. (8). In the quasi-equilibrium state the phase angle is set to π/2. Then the capacitance of the capacitor can be determined from the relationship:   0 0 Im 1 B A Z C X X   (9) where A0 and B0 as in Equation (8). In the case of using a circuit for capacitance measurements and taking into account that X XX Cj RZ  1  , (10) Equation (6) can be rewritten as:               X X W AR C AB  1 arccotan (11) The detected signal �W is a phase shift between the selected signals w1 and w2. The equation describes the �W signal as a function of the parameters A, B and the measured impedance component. Eq. 11 is a conversion equation of the circuit of Figure 1. The amplifier’s voltage gain A or the conversion factor of the current/voltage converter’s B can be the adjusted parameter in the circuit of Figure 1. The circuit is brought to the quasi-equilibrium state by changing the value of one selected, adjustable parameter A or B. Such a process is called the process of quasi–balancing the circuit. If the measuring circuit of Figure 1 is destined for measuring the reactance of capacitors, then it is more advantageous to change the setting of the parameter B. Change of the parameter A will be more advantageous in circuits for measuring the capacitance. In both cases mentioned above a simple relation between the adjustable parameter and the quantity being measured in the quasi-equilibrium state is obtained. Such a feature is not of great importance in modern measuring instruments containing microprocessors, but in some cases (for instance in order to decrease the energy consumption in portable instruments) one still tends to simplify calculations and to reduce the balancing time of the circuit. In the case of the adjustable parameter A, the parameter B remains constant. During the whole measuring process and after achieving the quasi-equilibrium state Figure  1.  Block  diagram  of  the  quasi‐balanced  circuit  for  capacitance  measurements.  ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 107  const0  BB (12) After substituting Eq. (12) in Eq. (6) and dividing the numerator and denominator of the argument of the arccotan function in this equation by A0 one obtains                                             X X X X WA Z A A Z A A Z A A Z A A A B Re Im1 arccotan Re Im arccotan 0 0 0 00 0 (13) where �WA is the signal being detected in the case of the adjustable parameter A. The relation between the active and passive component of the series RC impedance ZX is the dielectric loss factor tg �X of this impedance     XX X Z Z  tg Im Re  (14) hence Equation (13) can be written as follows:               0 0 1 tg 1 arccotan A A A A X WA  (15) Figure 2 shows the dependence of the signal being detected, WA, on the adjustable parameter A relative to the value of A0 for different typical values of tg δX. 3. AUTOMATED QUASI‐BALANCING  Figure 3 shows a simplified structure of the virtual instrument executed in the LabVIEW graphical programming environment, according to the approach presented in [8].  The quasi–balanced circuit for capacitance measurements shown in Figure 1 was executed as a virtual instrument (Figure 3). Measurement signals, such as a voltage drop across the measured impedance and a current converted into a voltage, were applied to the data acquisition card USB NI 6009. Further conversion of the signals in the measuring channels was carried out by a program executed in the LabVIEW graphical programming environment. The amplifier voltage gain or the conversion factor of a current/voltage converter may be the adjustable parameter in this system. By amending the value of one selected adjustable parameter A or B, the system is automatically set into the quasi-equilibrium state. In the circuit for capacity measurement it is better to adjust the parameter A at a constant value of the parameter B = B0. The process of the automated quasi-balancing of the circuit shown in Figure 1 aiming at determining the capacitance CX given by Eq. (9) consists in changing the setting of A at the constant setting of B (B = B0) until the value of the signal being detected achieves π/2. The automated quasi-balancing of the circuit is performed in three steps according to the conversion characteristic presented in Figure 4:  for the optional setting A = A1 the indication of a phase- sensitive detector WA1 is determined (point 1 in Figure 4),  the setting of A is changed and for A2 ≠ A1 the indication of a phase-sensitive detector WA2 is again determined (point 2 in Figure 4),  according to the relationships presented in the system of equations (16) the setting A0 corresponding to the selected quasi–equilibrium state WA = π/2 is determined (point 0 in Figure 4).                                         0 2 0 2 2 0 1 0 1 1 1 tg 1 arccotan 1 tg 1 arccotan A A A A A A A A X WA X WA   (16)   Figure 2.   ΦWA signal vs. relative parameter A/A0 for different loss factor   tg x values.  Figure 3. The LabVIEW realization of the virtual capacitance meter.  0 15 30 45 60 75 90 0,85 0,9 0,95 1 1,05 1,1 1,15 WA A/A0 0,001 0,002 0,005 0,01 0,02 0,05 ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 108  For determining the setting A0 it is not necessary to know the loss factor tg �X, since it has a constant value in the system of equations (16) and does not appear in the solution of this system which can be presented as follows:   1122 1221 0 cotan cotan cotan cotan WAWA WAWA AA AA A    (17) Having finished the automated quasi-balancing of the circuit of Figure 1, one can determine the capacitance of the tested capacitor from Equation (9) based on the known settings B0 and A0. The exemplary results of the tests made for the virtual circuit for capacitance measurements during classical (by changes of the adjustable parameter by a given constant value) and automated quasi-balancing are given in Table 1. 4. DOUBLE QUASI‐BALANCED CIRCUITS  In general quasi-balanced circuits only allow the measurement of one impedance component, but it is possible to build circuits to measure two components of impedance, for example in parallel quasi-balanced circuits. Some quasi–balanced circuits allow the measurement of the mutual relationship between the components of the impedance, e.g. quality factor. In such systems, double quasi - balancing in two successive steps is applied. The circuit of the quasi-balanced bridge, designed to measure the quality factor of real inductors is presented in Figure 5. The symbols in Figure 1 represent respectively: R3 a standard variable resistor; VS the power supply voltage, R a potentiometer resistance; n a potentiometer setting (0 < n < 1) and I1, I2 the currents of the branches of the bridge. The object under test is modeled as a series connection of resistance RX and inductance LX. The quasi-balancing process requires two steps. In the first state of quasi-equilibrium the phase angle between VAD and VDC equals π/2. The slider of the potentiometer R is located in the position for which n = ½ and the regulatory element is a resistor R3. In the second quasi-balance state the phase angle between VDC and VCB also equals π/2. The control element is the potentiometer R. In the second quasi- balance state the n parameter is read and then the relationship for the determination of the measured quality factor QC is: n n QC 21  . (18) Based on the analysis of the bridge in Figure 5 it is possible to build a non-bridge structure, performing the same operations on the current and voltage signals of the tested impedance. The procedure of deriving a non–bridge circuit has been presented in [9]. The non-bridge circuit has the structure shown in Figure 6. This circuit processes the measurement signals according to the principle of operation of the bridge from Figure 5. The selected signals are phase shifts between w11 and w12 signals and w21 and w22 signals. It can easily be implemented as a virtual instrument. Figure 7 shows a view of the prototype of the quality factor meter built according to the previously described Figure 4.   ΦWA signal vs. parameter A for unknown loss factor tg x values  (conversion characteristic).  Table  1.  Comparison  of  selected  measurement  results  obtained  during  classical  and  automated  quasi‐balancing  of  the  circuit  for  capacitance  measurement.  The classical quasi-balance method A0 WA0 CX, µF 1.0357 90.00 0.3294 The automated quasi-balance method A1 WA1 A2 WA2 A0 WA0 CX, µF 100.0000 15.14 1.0404 89.01 1.0356 90.00 0.3294 3.9401 20.00 1.0875 80.00 1.0360 90.00 0.3295 1.9393 30.09 1.1482 70.09 1.0359 90.00 0.3295 1.5238 40.00 1.2272 60.00 1.0374 89.82 0.3299 Figure 5. Diagram of the quasi‐balanced bridge for loss factor measurement.  nVX Σ Σ IX - - PHASE DETECTOR π/2 PHASE DETECTOR π/2 + + R3 + n w11 w12 w22 w21 Figure 6.   Block diagram of a quasi‐balanced circuit with dual quasi‐ balancing.   0 15 30 45 60 75 90 WA A A0A1 A2 ΦWA1 ΦWA2 1 2 0 ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 109  concept. A coil under test was powered from the Rigol DG1022 DDS generator. The current of the object was converted to a voltage across the 1 kΩ standard resistor with accuracy class 0.01. The voltage of the object and the voltage proportional to its current were connected to the 16-bit DAQ NI USB-6251 [10]. The LabVIEW 2011 software package was used to build the virtual instrument [10]. The diagram of the virtual instrument is shown in Figure 8 and its front panel in Figure 9. The first tests were done as a simulation. The simulations confirmed the usefulness of the system to measure the quality factor of inductors. Tests of the circuit were performed for the reference inductance in the range from 0.05 H to 1 H at a frequency of 100 Hz. The results were compared with the results obtained from the meter Motech MIC-4090, for which the manufacturer declares a quality factor accuracy of 0.5%. The exemplary dependence of the errors versus the measured quality factor is shown in Figure 10. 5. CONCLUSIONS  The tests of the presented way of quasi-balancing the circuit for capacitance measurements proved that the proposed procedure is correct and showed the possibility of a significantly faster achievement of the quasi-equilibrium state than in the case of classical balance methods by changes of the adjustable parameter by a given constant value. The presented automated quasi-balance method does not reduce the accuracy of the phase detector operation and does not increase the uncertainty of determining the tested capacitor capacitance significantly. During investigations an insignificant influence of the circuit conversion characteristic shape was observed (Figure 4). Also the selection of the points on this characteristic had neglible influence on the accuracy of achieving the quasi– equilibrium state. Further investigations aim at the detailed determination of the selection of points 1 and 2 during the realization of the procedure of quasi-balancing the circuit on the accuracy of assessing the setting A0 in the quasi-equilibrium state. Further, the examination of possibilities of using the presented measuring circuit and the automated quasi- balancing procedure for determining the dielectric loss factor tg �X of an RC impedance is planned. The theory and implementation of a non-bridge quasi- balanced measuring circuit with dual quasi-balancing, designed for measurements of the quality factor have been presented as well. The main advantage of the circuit is maximum convergence and a simple measuring process. It requires two independent controls. The circuit described above has been implemented as a virtual system, using the LabView package. Simulation tests and tests carried out on real objects confirmed the usefulness of the proposed Figure 9.   Front panel of a quasi‐balanced meter with dual quasi‐balancing.   Figure 8.   Block  diagram  of  a  quasi‐balanced  circuit  with  dual  quasi‐ balancing.  Figure 7. View of the prototype of the quality factor meter realized as the  quasi‐balanced circuit with dual quasi‐balancing.   Figure 10. Error vs. the measured quality factor.  ACTA IMEKO | www.imeko.org  February 2015 | Volume 4 | Number 1 | 110  solutions. The level of errors reaches 5%, but the study was focused on the prototype, which will be even improved. REFERENCES  [1] Karandeev K. B.: “Bridge and potentiometer methods of electrical measurements”, Moscow, Peace Publishers, 1966. [2] Atmanand M.A., Jagadeesh Kumar V., Murti V.G.K: “A novel method of measurement of L and C”, IEEE Transaction on Instrumentation & Measurement, vol. 44, no. 4, August 1995, pp. 898-903. [3] Atmanand M. 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