Power Consumption Reduction in High CurrentClosed Loop Hall Effect Current Sensors Using

Class D Amplifier

Aalok Dyuti SahaTexas Instruments (India) Pvt. Ltd.,

Bangalore - 560093, India.Email: aalok@ti.com

Vinod JohnDepartment of Electrical Engineering,

Indian Institute of Science, Bangalore - 560012, India.Email: vjohn@ee.iisc.ernet.in

Abstract—The closed loop hall effect current sensor is apopular current sensor because of its high bandwidth, ac and dcmeasurement, isolation. But the prime demerit of it is high powerconsumption at high currents. This is because of the losses in thelinear power amplifier driving the compensating winding current.In this paper, a novel closed loop hall effect current sensorinvolving a Class D Amplifier as power amplifier is proposed toreduce the sensor power consumption and make the sensor morecompact. This paper discusses the development of such a currentsensor, it’s stability issues, noise floor, procedures to overcomethose problems, the tradeoff between noise and bandwidth.Finally a prototype current sensor is shown and it’s performanceis compared to a similar range commercially available currentsensor. It is analysed and then verified experimentally that theproposed current sensor consumes much less power than thecommercial sensor for higher currents.

Index Terms: Closed Loop Hall Effect Current Sensor,Class D Amplifier, Sensor power consumption, Tempera-ture rise, Hall sensor.

SYMBOLS

Pcondx : Conduction loss in device xVdiode : Body-diode forward voltageVG : Applied gate-source voltageVGSth

: Gate-source threshold voltageVGSplateau

: Plateau voltage of gate-source voltageRgate : Gate resistanceCiss : Input gate capacitance∆Qplateau : Gate charge required during plateau regionigplateau

: Gate current required during plateau regionEONx

: Turn-on energy loss of device xEOFFx

: Turn-off energy loss of device xQrr : Body-diode reverse recovery chargeErrDx

: Reverse recovery energy loss of diode Dx

I. INTRODUCTION

Current sensors are used for control, monitoring or protec-tion purposes in various industries and technologies. Currentsensors are used in power electronics to provide feedbackfor control purposes, simple current monitoring, over-currentprotection, active ripple cancellation, CCM and DCM modeswitching, motor drive control and protection functions. Theyare also used in power generation operations like in controland protection of wind power, solar power stations, protectionand monitoring of the traditional power generating stations

and transmission systems, traction systems [2]. In some ofthis cases like traction systems, the measured current is high,requiring high current sensors. As CTs cannot measure DC,Hall effect current sensors are the most popular current sensorswhere such high AC as well as DC is to be measured. Openloop hall effect current sensors (OL-HECS) have limitationsdue to their nonlinearities, higher size, core heating andsaturation. Closed loop hall effect current sensors (CL-HECS)[1] gives high linearity, accuracy, higher current range for samecore size at a reasonable cost compared to fluxgate sensors andtherefore ideal for such application [2].But if the input current is high, for a CL-HECS, the com-

+-

+ -

Compensator

CompensatingCoil CurrentPrimary

Current

CoreHall

Element

+15V

-15V

Vout

Vamp

Power AmplifierStage for driving compensating winding

Fig. 1. Closed loop hall effect based Current Sensor (CL-HECS) involvingclass AB type power amplifier.

pensating current will be high too. Most commercial CL-HECS use high gain proportional compensator [3] followedby a linear power amplifier (mostly Class AB type) to drivethe compensating winding current. Theoretical maximum effi-ciency of Class AB amplifier is less than 78.5%[4]. A practicalClass AB Amplifier has an efficiency of around 50%[5]. Therest of the power dissipates as heat. This leads to necessityof larger heat-sinks in the sensor leading to accommodationproblem. To prevent this, some high current commercial CL-HECS uses the core itself as heat-sink. This puts a limit oncompensating current and core has to be derated. If compen-sating winding turns are increased to get high input currentrange with low compensating winding current, the bandwidthreduces drastically because of high inter-turn and layer to layercapacitance of the compensating winding. Also high currentdrawn from sensor dc power supply leads to increase in sizeand cost of the power supply.If instead of linear power amplifier, a class D amplifier [6] isused, then this power consumption can be reduced. A classD amplifier is a switching amplifier consisting of a pulsewidth modulator, a MOSFET based inverter[6] and an output

978-1-4673-8888-7/16/$31.00 c©2016 IEEE

filter[7] or a ripple compensating amplifier[8]. It has idealefficiency of 100%. Practically efficiency of above 90% can beachievable[5]. This paper describes a novel CL-HECS using aclass D amplifier as the compensating winding driver stage forreducing the power consumption and making the sensor morecompact.Section II briefly discusses the development and performancecharacterisation of a closed loop class D amplifier. Section IIIdiscusses the development of the CL-HECS using the aboveclass D amplifier, its stability issues, noise floor concerns, noisereduction options and finally the bandwidth of the prototypesensor is compared with a similar range commercial one. Insection IV the power loss of the proposed current sensor isfound out analytically and experimentally and compared tothe power loss of the commercial sensor. Also even higherreduction in power consumption for higher current ranges areanalysed, compared and the steady-state temperature of theprototype is shown to be within limits without explicit heat-sinks for practical operation of the sensor.

II. DEVELOPMENT AND PERFORMANCECHARACTERISATION OF THE CLASS D AMPLIFIER

InputSignal

560Ω

1

nF

R2

CF

RFR5 R4

R4R5

R3

R3

C3

C3

13.5kΩ

22kΩ

22kΩ

2.2kΩ

2.2kΩ

2.2kΩ

2.2kΩ

150pF

150pF

VF

( VS )Vi

ioS1

S4

S2

S3

D1 D2

D4 D3

Vo

+ -

LevelShifter

and Driver

Level

Shifter

and Driver

Driver Driver

Dead time logic

Dead time logic

TriangularWave

Generator

L

C

V01 V02

Fig. 2. Block Schematic of closed loop class D amplifier.

In [10], development of an open loop class D amplifier, it’snon-idealities analysis and the development of a closed loopclass D amplifier is discussed. The prototype class D amplifieris shown in Fig. 2. Fig. 3 shows the linearity of the prototype

Outp

ut vo

ltage

(V)

Input voltage (V)

Fig. 3. Linearity of the closed loop class D amplifier.

class D amplifier and the mean square error is 0.0106V, whichis 0.07% of the maximum output voltage. The linearity of thecircuit is evaluated in terms of the relationship between inputvoltage,Vi, and output voltage,Vo. The switching frequency ofthe class D amplifier is 600kHz. From the step response ofthe laboratory made class D amplifier shown in Fig. 4, the

Fig. 4. Step Response of the laboratory made prototype Class D Amplifier.

bandwidth can be approximated as 125kHz. This bandwidthand linearity is enough for the compensating winding driverof a CL-HECS.

III. DEVELOPMENT AND PERFORMANCECHARACTERISATION OF CLOSED LOOP HALL EFFECT

CURRENT SENSOR USING CLASS D AMPLIFIER

The above class D amplifier is used for compensating wind-ing driver for a ordinary CL-HECS, the schematic can be givenby Fig. 5. But this configuration leads to LC filter resonant

+

-2

13

8

LM201

4.7pF

+

-2

13

8

LM201

+

-

1k

R10

R30

R30

R20

R20

R40

4.7pF

1k

R1022k

C1

C1

1nF

1nF

1k

1k1k

100k POT

ClosedLoopClass DAmplifier

+

-2

13

8

LM201

4.7pF

+15V

-15V

VH

LC/2

C/2

V01 V02

Compensating Winding

RB

10k

10k10k

10k

Vout

+

-

R

22k

InSbHall

Element

Fig. 5. Schematic of the prototype CL-HECS.

frequency oscillations in its output. In order to identify thereason behind the oscillations, a low frequency modelling ofthe schematic of Fig. 5 is done following the steps mentionedin [9] and [10] and the block diagram is shown in Fig. 6. In

+ ++

+

- K

Current Transformer

HallElement Compensator

H-bridgeClosed loopClass DAmplifier

filter

i1(s)

Fig. 6. Block diagram of the Hall effect current sensor using Class Damplifier.

the diagram of Fig. 6, if a proportional compensator ,Kp, isused, the resulting Vout(s)

I1(s)transfer function has 6 poles and 5

zeroes. Out of these, the locus of 3 dominant poles are shownin Fig. 7. It can be seen that a complex pole-zero pair of the

2

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5

x 105

-3

-2

-1

0

1

2

3

x 105

Real Axis (seconds-1)

Imagina

ry Axis

(second

s-1 ) Increasing k p

Increasing kp

Increasing kp

Fig. 7. Variation of dominant pole-zero with increasing kp

closed loop transfer function are very close to the imaginaryaxis and moves to the right half of the s-plane for higher gainof the proportional controller. This means two branches of theroot locus completes entirely in the right half plane and createsinstability. Even if kp is made lower, it will give oscillationsin the output. This pole-zero pairs are due to the LC filter.So, LC filter prevents the use of high gain P controller or PIcontroller. So, the LC output filter is removed and the class Damplifier is operated using the inherent filtering provided bythe compensating winding coil.If the pulsed output of the H-bridge is applied directly acrossthe compensating winding, the equivalent circuit of Fig. 8is obtained. The compensating winding exhibits capacitive

22E

332E

Cp

Compensating Winding

+15V

-15V

RB

RwdgEqv.parasiticcapacitance

i i2

Lm

Fig. 8. Lumped capacitance model for the compensating winding.

behaviour for switching frequency (600kHz) and higher fre-quencies (1.8MHz, 3Mhz, 4.2MHz). So, the voltage acrossthe burden resistor contains the input current frequencies to bemeasured and also a high frequency peaky capacitive currentsuperimposed on it, which acts as a noise at the output. Inorder to reduce the noise different noise reducing methods canbe used. Their relative effectiveness can be seen in Table I.The most effective noise reduction procedures are found to

TABLE I. NOISE REDUCTION PROCEDURES

Process of noiseattenuation

Prospect of Attenua-tion

Drawbacks

Capacitivecompensation

19.5 dB attenuation forcapacitance of 22 nF

Low bandwidth (Rise time increases8 times than unfiltered for 19.5 dBattenuation) and phase shift

Ferrite beads inseries

Almost no attenuationat such low frequencies

No Attenuation

Series inductivecompensation

11 dB attenuation forinductance of 4.5 mH

LC oscillation with equivalent wind-ing capacitance and accommodationproblem

External filter ar-rangements

40 dB attenuationfor external filter of120kHz

Reduced bandwidth with reducednoise (Rise time 2.6 times for 40 dBnoise attenuation)

be using external filter arrangements along with small amountof capacitive compensation, as shown in Fig. 9. This processleads to reduction of bandwidth. So, there is a tradeoff betweenthe noise attenuation and the bandwidth. In the configurationshown in Fig. 9, if a 393 kHz external filter and 2 nF of

+

-2

13

8

LM301

15pF

10k

10k10k

10k

+

-2 1

3

8

LM301

10pF

8.2k

100pF

100pF

8.2k

V01

V02+

-Vout

22E

332E

Cp

Compensating Winding

+15V

-15V

Rburden

RwdgEqv.parasiticcapacitance

Rseries

CprobeCcomp

Fig. 9. Using Ccomp as capacitance compensation, external low pass Sallen-Key filter at the differential amplifier output.

capacitive compensation is used, we get a rise time of 1.7µs.Assuming second order system, this gives an approximatebandwidth of 235 kHz. This is close to the highest bandwidthfor any Closed loop Hall Sensor (200-250kHz) because of CTfrequency response falling at high frequencies due to inter-turn capacitance and layer-layer capacitance. If further noisereduction is required, then the bandwidth would have to befurther reduced.

The rise time of the laboratory current sensor in Fig. 10

Fig. 10. Ch 2:Step response of laboratory current sensor using 393 kHzexternal filter and 2 nF of capacitive compensation,current scale 166mV/A,time scale 1µs/div. Rise time 1.7µs for input step current of 25A.

is compared with the rise time of a commercial CL-HECSof similar range shown in Fig. 11 using step input cur-rent generated by the power electronic converter describedin [11]. Comparison between Figs. 10 and 11 shows that

Fig. 11. Step response of a commercially available CL-HECS of similarrange to a step input of 40A, time scale 5µs/div.

the laboratory current sensor has higher bandwidth than thecommercially available CL-HECS. Fig. 10 has time scale as1µs/div whereas Fig. 11 has time scale of 5µs/div. But ithas higher noise than the commercial current sensor. Hence,because of using class D amplifier as compensating windingdriver stage the bandwidth does not reduce, instead there isreduction of power loss for high current sensors.

3

IV. POWER CONSUMPTION COMPARISON OF THECURRENT SENSOR

In order to compare the class D driver stage with com-mercially available linear driver stage, the performance oflaboratory made current sensor is compared to a similar rangecommercially available CL-HECS. the driver stage of both ofthem is shown in Fig. 12. The commercially available currentsensor has a nominal input current of 500A, conversion ratioof 1:2000 and measuring range of ±800A. The laboratorycurrent sensor also has a conversion ratio of1:2000 and mea-suring range of ±900A. The control and driver circuit of thelaboratory made sensor is measured to be drawing around2W as fixed power loss. From the datasheet, the fixed powerconsumption of the commercial current sensor is taken as0.6W.

i2

M1

M4

M2

M3

D1 D2

D4 D3

+15V

-15V

VampVamp+ -

GND(a) (b)

+15V

-15V

Fig. 12. Amplifier stage for (a)laboratory setup using class D amplifier and(b)commercial current sensor using class AB amplifier respectively.

A. Power loss calculation and comparison for dc currents

Power loss in the laboratory made CL-HECS involvingClass D amplifier can be calculated starting with the com-pensating coil input current i2,

i2 = iin.n1n2

Vamp = i2(r2 +RB)

(2d− 1)VCC = Vamp

⇒ d =Vamp2VCC

+ 0.5 (1)

Conduction loss in one MOSFET M1 is given by,

PcondM1= d.i2

2.RDSon (2)

Conduction loss in complementary MOSFET M2, neglectingdead time is given by,

PcondM2= (1− d).i2

2.RDSon (3)

Conduction loss in diode D2 during dead time can be ac-counted as,

PcondD2=tdeadTsw

.i2.Vdiode (4)

Total conduction power loss can be obtained as,

Pcond = 2(PcondM1+ PcondM2

+ PcondD2) (5)

In the laboratory setup, RDSon= 18.3mΩ, Vdiode = 0.88V

, dead time tdead = 72ns, Switching period Tsw = 2µs, VG

VDS

iDS

VDS.iDS

t

t

ttvr tiftd

VCC

i2

VDS

iDS

VDS.iDS

t

t

ttir tvftd

VCC

i2

(a) (b)Fig. 13. (a)Turn on and (b)Turn off waveforms of MOSFET.

=15V, VGSth=2.1V , VGSplateau

=3V , Rgate =5.6Ω, Ciss=600pF , ∆Qplateau =0.9nC , Qrr =10nC .Following [12] we can derive, td = 506.76ps, tir =243ps, igplateau

= 2.14A, tvf = 420.6ps, tvr = 1.68ns, tif =1.198ns.So, from Fig. 13, total switching loss can be calculated as,

Psw = (4(EONm+ EOFFm

) + 2EOFFD2)fsw

= (4(0.5(tir + tvf )× i2.VCC + 0.5(tvr + tif )

× i2.VCC) + 2× 0.25Qrr.Vrr)fsw (6)

So, total power loss of the class D amplifier is given by,

PtotalD = Pcond + Psw + PNLD(7)

Power loss in the commercial CL-HECS involving class ABamplifier can be obtained from Fig. 12, for Class AB amplifiercarrying dc current,

PtotalAB= (VCC − Vamp).i2 + PNLAB

(8)

Comparison of the power lossesTaking 15V dc supply for class D in (7) and ±15V dc supplyfor class AB in (8), the power loss in the current sensors as afunction of input current is shown in Fig. 14.

0 100 200 300 400 500 600 700 800 9000

0.5

1

1.5

2

2.5

3

To

tal p

ow

er

loss in

th

e am

plif

ier

sta

ge

(W

)

Input dc current value (A)

Laboratory made setup employing class D amplifier

Commercial current sensor employing class AB amplifier

Fig. 14. Power loss comparison for laboratory sensor and commercial sensorfor dc input current.

B. Power loss calculation and comparison for ac currentmeasurement

Power loss in the laboratory made CL-HECS involvingclass D amplifier can be evaluated as follows-

4

The process is similar to DC current condition, onlyi2 = Ipeak.sin(ωt). As at a time only 2 MOSFETs are ON,

Pcondm = 2.I2rms.RDSon (9)

PcondD2=

1

2π

∫ π

0

tdeadTsw

.Ipeak.sin(θ).Vdiode.dθ (10)

Pcond = Pcondm + 4.PcondD2(11)

EONm + EOFFm = 31.87× 10−9.Vds30

.Iout[n]

0.6(12)

ErrD2= 75× 10−9.

Vds30

.Iout[n]

0.6( for Iout[n] > 0 ) (13)

Psw = 4.(

N∑n=1

(EONm + EOFFm) +

N/2∑n=1

ErrD2).finput (14)

Total loss for Class D amplifier,

PtotalD = Pcond + Psw + PNLD(15)

Power loss in the commercial CL-HECS involving Class ABamplifier can be evaluated as explained below-From Fig. 12, for Class AB Amplifier carrying AC sinusoidalcurrent,

Ploss = (VCC − |Vamp|).|i2|

So, PtotalAB=

1

2π

∫ 2π

0

(VCC − |Vamp|).I2.|sin(θ)|.dθ + PNLAB

(16)

Comparison of the power lossesTaking 15V dc supply for class D in (15) and ±15V dc supplyfor class AB in (16), the power loss in the current sensors asa function of rms value of input current is shown in Fig. 15.Therefore, both Fig. 14 and 15 shows that at higher current

0 100 200 300 400 500 6000

0.5

1

1.5

2

2.5

Tota

l pow

er

loss in the a

mplif

ier

sta

ge (

W)

Input sinusoidal current rms value (A)

Laboratory made setup employing class D amplifier

Commercial current sensor employing class AB amplifier

Fig. 15. Power loss comparison for laboratory sensor and commercial sensorfor sinusoidal input current.

range, the laboratory current sensor consumes much less poweras compared to commercial current sensor.

C. Power loss of the laboratory prototype

Fig. 16 shows the laboratory made CL-HECS using In-Sbtype Hall element (SH-400) with spinning current biasing and2000 turns compensating winding. It has 15V supply, 500 kHz

Triangularwave generator

Class D AmplierControl

Class DAmplier

Current SensorController stage

SpinningCurrent biasing

Compen-satingwinding

SH-400Hall Element

Fig. 16. The laboratory made prototype of the class D amplifier drivenCL-HECS.

switching frequency, variable kp is tuned from 968 to 48884,Rise time observed is 1.7µs for 200mV noise floor.Using this setup, the power loss measured in the sensor whilemeasuring 100A dc Current is 1.91W. This is slightly less thanthe theoretical predictions of Fig. 14. This is because the lossesin the theoretical calculations are for the worst case scenario.Due to lack of even higher current source, the experimentalverifications at higher currents is not carried out.

D. Reduction in power consumption at higher current ranges

The laboratory current sensor has 900 A range because ofsupply voltage of 15V. If supply voltage is increased to 30Vfor class D amplifier and ±30V for class AB amplifier to get±1800A current range, then the percentage reduction in powerconsumption will be much more.Fig. 17 and 18 shows the power loss comparison in such case

0 200 400 600 800 1000 1200 1400 1600 18000

1

2

3

4

5

6

7

8

9

10

Tota

l pow

er

loss in the a

mplif

ier

sta

ge (

W)

Laboratory made setup employing class D amplifier

Commercial current sensor employing class AB amplifier

Input dc current value (A)

Fig. 17. Power loss comparison for proposed current sensor involving classD Stage and commercial current sensor involving class AB Stage for higherrange of dc current.

for DC and sinusoidal currents respectively. In Fig. 17, at inputcurrent of 1200A, the power loss will reduce by 77.5% by theuse of Class D Amplifier.

E. Steady-state temperature rise

Also in commercial sensor, the main power loss is in theamplifier stage and therefore temperature increases drastically

5

0 200 400 600 800 1000 12000

1

2

3

4

5

6

7

8

Tota

l pow

er

loss in the a

mplif

ier

sta

ge (

W)

Input sinusoidal current rms value (A)

Laboratory made setup employing class D amplifier

Commercial current sensor employing class AB amplifier

Fig. 18. Power loss comparison for proposed current sensor involving classD Stage and commercial current sensor involving class AB Stage for higherrange of ac current.

with current. But in the laboratory made sensor, we can seefrom Figs. 14 and 15, the power loss in the H-bridge is verylow as compared to the fixed power loss of 2W. So, the steady-state temperature is almost fixed over the entire range of inputcurrent. The thermal image of the laboratory made setup takenduring heat-run test is shown in Fig. 19.The temperatures in Fig. 19 are taken at constant switching

Top layer Bottom layer

Fig. 19. Infrared thermal image of the laboratory setup at steady-state showingthe PCB top layer and bottom layer.

frequency of 500kHz for the class D amplifier, input sinusoidalcurrent of 100A peak-peak, the setup running for 7 hours.It is noted that the maximum temperature of the sensor is63C without any heatsink, which is well within the limit ofthe electronics. Therefore the laboratory current sensor drawsmuch lesser power and produces much lesser heat as comparedto commercial CL-HECS, at high current range.

V. CONCLUSION

An efficient CL-HECS involving a closed Loop class Damplifier as compensating winding driver stage is developed.It is seen that the laboratory made current sensor can reducepower consumption of high current sensors by upto 77.5% ascompared to commercially available closed loop Hall Effectsensors without reduction of bandwidth. Bandwidth of the lab-oratory current sensor is comparable to commercially availableCL-HECS. It can be made even better if the filter stages arereduced. Therefore it is advantageous in industrial and tractioncurrent sensors, where the input currents are high.As seen from the power loss comparison curves, the developedcurrent sensor has higher power loss than the commercial ones

at lower currents. So, the use of class D amplifier will lead toreduction of sensor power consumption only at higher currents.Therefore this is useful for current sensors used in industrialand traction applications, where the measured current is high.Also it has higher noise than the ones using linear amplifiers.This noise can be reduced at the cost of bandwidth reduction.

REFERENCES

[1] Y. Suzuki, K. Yamasawa and A. Hirayabayashi, ‘Analysis of a Zero-FluxType Current Sensor Using a Hall Element’, IEEE Translation Journalon Magnetics in Japan, vol. 1, pp. 165-170, 1994.

[2] Pavel Ripka, ‘Magnetic Sensors and Magnetometers’, Artech House,2001.

[3] P. Pejovic and D. Stankovic, ‘Transient analysis of compensated Hall-effect current transducers’, Proceedings of 21st International Conferenceon Microelectronics, 1997., vol. 2, pp 569-572, 1997.

[4] Robert Boylestad and Louis Nashelsky, ‘Electronic Devices And CircuitTheory’,Prentice Hall, 7th Edition, 1998.

[5] Jun Honda and Jonathan Adams, ‘Class D Audio Amplifier Basics’,Application Note AN-1071, International rectifier, www.irf.com.

[6] Brian E. Attwood, ‘Class D amplifier system’, US Patent 4178556, Dec.11, 1979.

[7] F.A. Himmelstoss, K.H. Edelmoser, and C.C. Anselmi, ‘Analysis of aquality class-D amplifier’, IEEE Transactions on Consumer Electronics,Vol. 42, No. 3, August 1996.

[8] F.A. Himmelstoss and K.H. Edelmoser, ‘High Dynamic Class-D PowerAmplifier’, IEEE Transactions on Consumer Electronics, Vol. 44, No. 4,November 1998.

[9] Ashish Kumar, John, V., ‘Compensator Design for Closed Loop Hall-Effect Current Sensors’, Sixth National Power Electronics Conference2013 (NPEC 2013), IIT Kanpur, India, Dec 20 - 22, 2013.

[10] Aalok Dyuti Saha and Vinod John, ‘Analysis and modelling of non-idealities in high frequency class D amplifier’, 2016 3rd InternationalConference on Electrical Energy Systems (ICEES), Chennai, 2016, pp.44-49. doi: 10.1109/ICEES.2016.7510613.

[11] Ashish K., John, V., ‘Power Electronic Converter for Characterizationof Hall-effect Current Sensors’, IEEE International Conference on PowerElectronics, Drives and Energy Systems (PEDES 2014), IIT Bombay,India, Dec 16 - 19, 2014.

[12] D. Graovac, M. Purschel, and A. Kiep, ‘Mosfet power losses calculationusing the data-sheet parameters’, Inneon application note,vol. 1, 2006.

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