Active power analog front-end based on a Wheatstone-type magnetoresistive sensor

Sensors and Actuators A 169 (2011) 83–88

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Active power analog front-end based on a Wheatstone-type magnetoresistive sensor ˜ ∗ , J. Sánchez Moreno, S. Casans Berga, A.E. Navarro Antón D. Ramírez Munoz Department of Electronic Engineering, University of Valencia, C/Doctor Moliner, 50, 46100 Burjassot, Valencia, Spain

a r t i c l e

i n f o

Article history: Received 1 January 2011 Received in revised form 24 April 2011 Accepted 27 April 2011 Available online 5 May 2011 Keywords: Power measurement Analog multiplier Magnetoresistive sensor Energy meter

a b s t r a c t In the proposed work a practical magnetoresistive wattmeter based on a commercial sensor is designed to measure active power at industrial frequencies. The electronic conditioning circuit uses differential blocks in order to preserve the sensor initial common mode rejection ratio. A 700 W power level has been reached with an uncertainty less than 1%. With few changes the proposed circuitry could be used in metering applications. © 2011 Elsevier B.V. All rights reserved.

1. Introduction In the digital era analog signal processing seems to be a rarely or obsolete electronic function. But in situations where the complexity is not a requirement or in high-speed systems the use of analog processors is a valuable solution in comparison with the cost and complexity that analog-to-digital and digital-to-analog converters offer. This is the case of analog multipliers, a classical processing function implemented in integrated building blocks that it continues generating important revenues [1]. In industrial or domestic applications the ac-power measurement is of great importance for metering purposes. Integrated analog multipliers have been used to design electronic conditioning circuits, a great number of them to process non-linear relationships [2,3]. In the sensors and instrumentation field the Wheatstone bridge is an electrical topology that allows a simple and easy way to process using an analog technique the product of two signals. Magnetic field magnetoresistive (MR) sensors have been designed in a Wheatstone type configuration and an important part of them used as current sensors measuring the magnetic field generated by this electrical signal. MR sensors offer an interesting alternative as analog multipliers in applications where processing requirements need compact and not complex solutions.

∗ Corresponding author. Tel.: +34 963544035; fax: +34 963544353. E-mail addresses: [email protected] ˜ [email protected] (J. Sánchez Moreno), [email protected] (D. Ramírez Munoz), (S. Casans Berga), [email protected] (A.E. Navarro Antón). 0924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2011.04.044

Different efforts have been dedicated to process with a MR sensor the product of the instantaneous voltage and current referred to a load. An experimental set-up was developed in [4] to measure active power in the order of various tenths of milliwatts requiring, at the same time, additional circuitry to satisfy the flipping coil requirements. MR watt-converters have been well developed and analysed using not-Wheatstone type MR topologies, [5,6]. Interesting results in power levels and frequency values of the processing signals were given using non-commercial MR sensors. Others types of watt-converters have been developed using a conversion to frequency, [7,8]. This technique required matched voltage-to-frequency converters and the use of ferrite cores to provide current signal isolation. Various limitations are related to previous non-MR power measurement methods. Resistive current shunts have ohmic losses. Hall-based wattmeters need high permeability materials like ferrites, due to the low sensitivity of the Hall current sensors used. Therefore heat, high volume and weight are obtained using these technologies [3,9].

2. Active power magnetoresistive measurement method A magnetoresistive sensor is constituted by four magnetoresistances connected in a Wheatstone bridge electrical association. Each resistance changes its value according to the surrounding magnetic field. If an electrical current I generates this magnetic field, the magnetoresistive sensor output will be proportional to the current instantaneous value. The differential output voltage of the Wheatstone bridge (Fig. 1) states that this circuit topology acts

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differential output voltage of the magnetoresistive sensor will be:

vd (t) = A · vac (t) · [S¯ · i(t) + V¯ off ] = A · Vm ·sin(ω · t) · [S¯ · Im · sin(ω · t + ϕ) + V¯ off ] = A · S¯ · Im · Vm ·sin(ω · t) · sin(ω · t + ϕ) + A · V¯ off Vm · sin(ω · t)

(5)

Considering the trigonometric formula sin(ω · t) · sin(ω · t + ϕ) =

cos ϕ − cos(2 · w · t + ϕ) 2

Eq. (5) gives to

vd (t) = Fig. 1. Differential output voltage of the Wheatstone-type magnetoresistive current sensor.

as an analog multiplier with respect to the power supply V and the measurand x related to the current I. The proportionality constant of this product is the magnetoresistive sensor sensitivity S. All these relationships are given by Eq. (1).

vd = vH − vL =

V V · (1 + x) − · (1 − x) = S · V · I 2 2

(1)

If the voltage–current pair of Eq. (1) came from a fraction of certain AC-mains voltage vac (t) and its associated current i(t) delivered to a load then the output of the sensor will contain information related to the instantaneous power processed by the load (Fig. 2). Considering that a Wheatstone sensor will have a residual output offset voltage Voff Eq. (1) could be expressed by

vd (t) = v(t) · [S¯ · i(t) + V¯ off ]

(2)

where S¯ and V¯ off are the normalized values of the sensitivity and offset output voltage of the magnetoresistive sensor, [V¯ off ] = ¯ = mV/(A · Vsup ). Taking into account a power delivered V/Vsup , [S] by an ac-mains both voltage and current will be harmonic signals of the type:

vac (t) = Vm · sin(ω · t)

(3)

i(t) = Im · sin(ω · t + ϕ)

(4)

being Vm and Im the voltage and current amplitudes of the voltage and current line signals respectively and ϕ the phase-shift between both. With the above two expressions and considering Eq. (2), the

A · S¯ · Im · Vm A · S¯ · Im · Vm · cos ϕ − 2 2 ·cos(2 · ω · t + ϕ) + A · V¯ off Vm · sin(ω · t)

(6)

Therefore, the sensor output voltage vd (t) contains one term that it is constant with respect to w and two harmonics depending on w and 2w. The constant term in w is related to the active power delivered to the load while the others two could be effectively filtered by a proper filter design. In this way, a cut-off frequency of w/10 will be enough to reach a 1% dynamic error of the low-pass filtering action [10]. On the other hand the common-mode voltage present at the output of the differential low-pass filter will be done by the expression

voC (t) = 4.07 V · sin(ω · t) − 50.4 ␮V · cos(2 · ω · t + ϕ)

(7)

The w component is dominant in amplitude but at line frequency this amplitude is low enough to be rejected by a standard instrumentation amplifier (IA). The absolute error at the output of the IA (single-ended voltage vo ) will be done by evo =

Adm · voC CMRRIA

(8)

with Adm and CMRRIA the differential gain and the common-mode rejection ratio of the IA respectively. A detailed analysis is included in an appendix at the end of the paper showing that the common-mode voltage will not influence the projected measurements. 3. Experimental measurement set-up The experimental measurement set-up is shown in Fig. 3. Between the ac-line source vac (t) and the load, a reference wattmeter was placed to measure the actual power delivered to the load. In order to have information related to the active power, the magnetoresistive sensor needs to process electrical signals involving the ac-mains voltage vac (t) and the current through the load

Fig. 2. Principle of power measurement with a Wheatstone-type magnetoresistive current sensor.

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Fig. 3. Experimental measurement set-up.

i(t). To do this, a fraction v(t) of vac (t) works as the magnetoresistive sensor power supply. On the other hand, the load current in its entirely magnitude was used as the sensor input measurand. In this experimental set-up the signal conditioning circuit has been isolated from the ac-mains by inserting an AD215 isolation amplifier (iso-amp) configured with a unity gain. However, simpler and not so expensive solutions could be adopted if a commercial wattmeter would be designed [11]. Taking into account the maximum input voltage ratings of the iso-amp (±10 V) and that for the magnetoresistive sensor (±12 V) an attenuator was placed between the line and the iso-amp. Fig. 3 shows different attenuation positions that were designed to generate various experimental measurement conditions. At the output port of the iso-amp a 200 k potentiometer was placed to compensate for the residual DC output offset of the magnetoresistive sensor. In the present work, the maximum load current was about 5 A and thus, in order to

400 Reference wattmeter

350

1 · A · S¯ · Vm · Im · cos ϕ 2

(9)

In order to have an appropriate experimental capability the mains voltage was supplied by the AC source 6834A from Agilent. This equipment gave an easy way to vary the values of the mains during the experimental procedure. The reference wattmeter used was the model 2551 from Xitron.

Theoretical

250 200 150 100 50 0 0

50

100

150

Input mains voltage (V rms ) Fig. 4. Active power vs. mains voltage with RL = 62.5 .

200

Active power relative uncertainty (%)

Active power (W)

VDC =

Experimental

300

- 50

have enough safety margin, specially with the heating of the internal sensor conductor, the part ZMC10 magnetoresistive sensor from Zetex Semiconductors was decided to use [12]. Previous section showed that the sensor output voltage is composed of three terms but only the first one is related with the active power. For this reason, a differential low-pass filter has been placed after the sensor output. Its filtering action attenuates the w and 2w components of the vd (t) voltage while preserving good commonmode rejection ratio [13]. The term involved with the active power was conditioned by an instrumentation amplifier (INA118) configured with gain G = 1000 and finally, low-pass filtered. The output of the signal chain is a DC voltage that it is stated by the equation

3 2.5 2 1.5 1 0.5 0

90

100

110

120

130

140

Input mains voltage (V rms ) Fig. 5. Active power relative uncertainty.

150

160

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D. Ramírez Mu˜ noz et al. / Sensors and Actuators A 169 (2011) 83–88 400

R L= 62.5 Ω

350

Pact,ref (W)

300 250 200 150 100 50 0

0

10

20

30

40

50

60

70

80

VDC (normalized) Fig. 6. Experimental characteristic between wattmeter readings and active power (VAC,mains ∼ [10 V. . .150 V]).

4. Experimental results and discussion With the objective to test the feasibility to measure AC mains active power, the proposed MR wattmeter was submitted to an input mains voltage sweep remaining the load in a constant value (RL = 62.5 ). Fig. 4 shows the measured active power obtained by the proposed circuit and those supplied by the reference wattmeter. Both measurement series are in good agreement in spite of a small local fluctuation in the middle of the input mains voltage range. Fig. 5 shows the obtained active power relative uncertainty. It can be seen values less than 1% corresponding to input mains voltage higher than 125 Vrms . Additionally, and increase of this uncertainty was produced if lower input voltages values are selected. This fact is due to the low level of the current measured by the MR sensor. The output voltage readings supplied by the wattmeter circuit showed a good linearity with respect to the mains active power. In Fig. 6 it is depicted how linear is the relationship between both magnitudes in the case of a 62.5  load resistance value. The linear regression procedure gave a 0.9997 correlation coefficient. In this case VDC(normalized) = VDC /A being A the input resistive divider attenuation. As a second test, the wattmeter circuit was submitted to a resistive load variation maintaining the AC-mains voltage in a constant value of 150 Vrms . In this way, Fig. 7 explains the obtained experimental inverse relationship between active power and the load resistance when this was varied from 1000  to 30 . Both, exper-

Fig. 8. Experimental characteristic between wattmeter readings and active power (RL ∼ [1000 . . .30.28 ]).

imental, theoretical and that obtained by the reference wattmeter are shown. With these conditions, the dynamic range of the magnetoresistive current bridge was of 51 dB, obtained from a 0.15 A to 4.7 A experimental measurement range and considering at least 10 mA of resolution. This value was determined by the minimum available resistance load variation. With respect to the measured power dynamic range, a 57 dB value was obtained corresponding to a 22 W to 700 W measurement range and 1 W of experimental resolution. Again, as was depicted in Fig. 3, a valuable linearity is produced by the proposed circuit that could be seen in Fig. 8 where it is shown the linear dependence between active power and the readings of the output voltage wattmeter. In this case with a correlation coefficient of 0.998. In order to work with a constant voltage AC-mains line, the circuit could be simplified extracting the isolation amplifier and putting an appropriate resistive divider attenuation. However removing the isolation amplifier will produce a significant load error due to the high attenuator output resistance (40 k in the proposed work) and the low bridge input resistance (1.2 k minimum). In order to avoid this situation a unity gain follower must be used between attenuator and sensor. 5. Conclusion In the proposed work a practical MR wattmeter based on a commercial sensor is designed to measure active power at industrial frequencies. A 700 W power level has been reached with an

Fig. 7. Active power vs. load resistance characteristic.

Fig. 9. Equivalent circuit of the magnetoresistive bridge sensor connected to the low-pass differential filter.

D. Ramírez Mu˜ noz et al. / Sensors and Actuators A 169 (2011) 83–88

uncertainty less than 1%. The MR sensing technique allows an inherent galvanic isolation without the use of ferrite cores and with no heat losses associated to shunt-based sensing techniques. With few changes the proposed circuitry finds an interesting applicability in the design of new MR based power and energy processors dedicated to metering purposes. Acknowledgements This work was supported in part by the Spanish Ministry of Science and Innovation and European Regional Development Fund under the ENE2008-06588-C04-04 project and by the Generalitat Valenciana ACOMP/2010/231 project.

87

Replacing Eqs. (A.7) and (A.8) in (A.6) will give the commonmode component at the output of the differential filter

voC =

(tRfo · Rfo + tRo · (Ro /2)) · (C1o /2) · s 1 + s · (Rfo + (Ro /2)) · C1o

· viD + viC

(A.9)

Eq. (A.9) states that the voltage viD is multiplied by a high-pass function with a corner frequency fc and gain To in its pass-band. Considering the sensor data-sheet and experimental passive components: Rfo = 56 k, tRfo = 1 % , Ro = 1.7 k, tRo = 29%,

C1o = 1 ␮F (A.10)

the corner frequency fc and gain To values will be Appendix A. Analysis of the influence of the common-mode voltage at the circuit output In order to know the influence of common-mode voltage present at the input of the differential circuit in the power measurements it could be consider the equivalent circuit of the magnetoresistive bridge sensor connected to the low-pass differential filter (Fig. 9). From Ref. [10], the common-mode component at the output of the differential filter will be done by the expression

voC = GCD · viD + GCC · viC

(A.1)

fc =

1 = 3 Hz 2 ·  · (Rfo + (Ro /2)) · C1o

(A.11)

1 (tRfo · Rfo + tRo · (Ro /2)) = 7.05 × 10−3 · 2 Rfo + (Ro /2)

(A.12)

and To =

Taking into account these filter characteristics and the expressions for voltages viD and viC :

viD (t) =

where GCD =

1 · (H11 − H12 + H21 − H22 ), 4

GCC =

1 · (H11 + H12 + H21 + H22 ) 2

(A.2)

With the configuration of the differential low-pass filter used, it could be obtained the following H functions H11

R1 + (1/s) · ((1/C1) + (1/C1 )) , = R1 + R1 + (1/s) · ((1/C1) + (1/C1 ))

H12

R1 = R1 + R1 + (1/s) · ((1/C1) + (1/C1 ))

H21 = H22 =

(A.3)

(A.4)

(A.5)

Therefore and

GCC = 1 (A.6)

Considering maximum mismatch between resistances



(R1−R1 )max = 2 · tRfo · Rfo +tRo

Ro · 2







Ro , R1+R1 = 2 · Rfo + 2 (A.7)

and 1 ∼ 2 1 + = C1 C1 C1o

the common-mode output voltage will be 1 1 · A · Vm · (To · V¯ off + 1) · sin(ω · t) − · To · A · S¯ · Im 2 4 (A.15)

The amplitudes of the w and 2w components could be obtained from the experimental values used S¯ = 0.5 mV/V · A,

Vm = 212 Vpk ,

A = 3.84 × 10−2

and then

voC (t) = 4.07 V · sin(ω · t) − 50.4 ␮V · cos(2 · ω · t + ϕ)

1 · RoL 2

R1 − R1 1 · 2 R1 + R1 + (1/s) · ((1/C1) + (1/C1 ))

(A.14)

Im = 7.07 Apk ,

with

GCD =

1 · A · Vm · sin(ω · t) 2

V¯ off = 2 mV/V,

R1 + R1 + (1/s) · ((1/C1) + (1/C1 ))

R1 ≡ Rf +

(A.13)

·Vm · cos(2 · ω · t + ϕ)

R1 + (1/s) · ((1/C1) + (1/C1 ))

1 · RoH , 2

·cos(2 · ω · t + ϕ) + A · V¯ off Vm · sin(ω · t)

voC (t) =

R1 , R1 + R1 + (1/s) · ((1/C1) + (1/C1 ))

R1 ≡ Rf +

viC (t) =

A · S¯ · Im · Vm A · S¯ · Im · Vm · cos ϕ − 2 2

(A.8)

being C1o , Rfo and Ro , the typical values of the filter and sensor resistance respectively and tRfo and tRo their resistance tolerances.

(A.16)

This is the expression of the practical common-mode voltage at the input of the IA. It is clear that the w component is the dominant in amplitude and a standard instrumentation amplifier (IA) will support and reject this common-mode voltage. The IA output voltage vo could be done by

vo = Adm · voD + Acm · voC = Adm · voD +

Adm · voC CMRRIA

(A.17)

being Adm and CMRRIA the differential gain and the common-mode rejection ratio of the IA. The absolute error of the output voltage will be evo =

Adm · voC CMRRIA

(A.18)

if it is considered the IA model INA118 with Adm = 1000, CMRRIA = 120 dB at 50 Hz and an expected output amplitude of 6 V, the relative uncertainty due to common-mode voltage will be less than 0.01%. This result shows that this factor could not be considered and does not influence the projected measurements.

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Biographies ˜ Diego Ramírez Munoz received the MSc and PhD degrees in Physics from the University of Valencia, Valencia, Spain, in 1986 and 1995 respectively. He is currently

Professor of Electronic Instrumentation in the Electronic Engineering Department at the University of Valencia. In this institution he is teaching since 1986 and he founded the Instrumentation and Measurement Systems Division in 1996. His interests are focused on analog signal processing, network theory, sensors electronic interfaces and industrial applications based in magnetoresistive sensing techniques. He belongs to IEEE from 1990 developing activities as a referee in several indexed journals and international conferences. Jaime Sánchez Moreno was born in Valencia, Spain, 1977. He received the BSc degree in telecommunications electronic engineering and the MSc in electronic engineering from the University of Valencia, Spain in 2000 and 2003 respectively. Since 2006 he has been studying PhD degree in electronic engineering in University of Valencia. Now he is a research fellow in the Electronic Engineering Department. His research interests are involved in the field of electronic instrumentation, in particular, the design and characterization of interface circuits for magnetoresistive sensors. Silvia Casans Berga was born in Valencia, Spain, 1971. She received the MSc degree in Physics in 1996, the MSc in Electronic Engineering in 1999 and her PhD degree in Electronics in 2002 all of them at the University of Valencia, Spain. Her main research areas concern about electronic instrumentation, sensors characterization and its instrumentation and application systems. Nowadays she is working as an Associate Professor at the University of Valencia teaching electronic instrumentation. Currently she participates in different projects dedicated to the development of distributed sensor networks. A. Edith Navarro Antón was born in Jávea, Alicante, Spain, 1967. She received the MSc degree in Physics in 1991 and the PhD in Electronics in 1997 both of them at the University of Valencia, Spain. Her research areas are focused on the design of distributed measurement systems and industrial projects related with electronic instrumentation. Since 1994 she works at the University of Valencia in different teaching positions. From 2000 she is working as an Associate Professor at the same university teaching microelectronics, IC technology, virtual instrumentation and instrumentation systems.