Hall-E ect Current Sensors for Power Electronic ...€¦ · industrial scale helped me in the...

Hall-Effect Current Sensors for Power

Electronic Applications: Design and

Performance Validation

A Thesis

Submitted for the Degree of

Master of Sciencein the Faculty of Engineering

By

Ashish Kumar

Department of Electrical Engineering

Indian Institute of Science

Bangalore - 560 012

India

July 2014

Acknowledgements

Foremost, I express my sincere gratitude to my advisor Dr. Vinod John for the continuous

support to my M.Sc.(Engg.) study and research, for his motivation, enthusiasm, immense

practical knowledge and insightful inputs. His avant-garde thinking and step-by-step problem

solving approach helped me in growing up as a researcher. Besides the technical skills, his

exceptional patience and the human way of dealing people around are invaluable learning

additions to my life. I am blessed to have him as advisor and mentor for my research.

Besides my advisor, I would like to thank Prof. G. Narayanan for his useful suggestions.

I thank my fellow lab mates: Anirban, Anirudh, Avanish, Hedayati, Anil, Abhijit, Pavan,

Rakesh, Saichand and Nimesh in Power Electronics Group, for the stimulating discussions,

and for all the fun we have had in working together during last three years. I am thankful to

Nithya for all the helps in completing assignments, and for constantly pushing me to study.

In particular, I am grateful to Anirudh and Pallavi for introducing me to spirituality.

My sincere thank goes to M/s Electrohms Pvt. Ltd. India for their important contributions

to my laboratory hardware set-up. Their experience in manufacturing current sensors at

industrial scale helped me in the analysis and development of the Hall-effect current sensor

that I built in the laboratory. I thank Mr. Giridhar for sharing his inputs regarding industrial

requirements of the sensors.

I thank all the EE office staffs, particularly Mr. Channegowda, Mr. Kini and Mr. Pu-

rushothama for taking great care of the official formalities and purchase orders. I am thankful

to Mr. Ramchandran in the EE workshop for the help in building the hardware set-up.

i

ii Acknowledgements

I gratefully acknowledge the contributions of all the teachers, academic and non-academic,

for shaping me up what I am today. I am very grateful to my high school Mathematics tutor,

Shri Satyendra Singh for boosting self-confidence in the introvert diffident school kid. In last

fifteen years I would have not achieved the same, had he not taught me in those days. I

am thankful to my friend, Kolli Praveen Chand from the undergraduate days, for constantly

motivating me to go for higher study. I am fortunate to have Nikhil as my best friend since

school days for invariably showing faith in me, and for being always there in difficult times.

I am deeply indebted to my family for the unconditional support to my decisions at any

stage of life. My debt is due to my mother and my sister Bandana for whatever they missed

due to my absence in last three years.

Last but not the least I am grateful to the Almighty for His unconditional love, for His careful

guidance, for giving me strength, and for everything I have received or achieved.

Acknowledgements iii

Dedicated to my mother andmy sister, Bandana

Abstract

Closed loop Hall-effect current sensors used in power electronic applications require high

bandwidth and small transient errors. For this, the behaviour of a closed loop Hall-effect

current sensor is modeled. Analytical expression of the step response of the sensor using this

model is used to evaluate the performance of the PI compensator in the current sensor. Based

on this expression a procedure is proposed to design parameters of the PI compensator for

fast dynamic performance and for small transient error. A prototype closed loop Hall-effect

current sensor is built in the laboratory. A PI compensator based on the procedure devised

earlier is designed for the sensor.

A power electronic converter based current source is designed and fabricated in the labo-

ratory for validation of steady state and transient performance of Hall-effect current sensors.

A novel hardware topology is proposed, using which the same hardware set-up can produce

both step current and sinusoidal current in its designated sections without any modification

in the hardware configuration. It produces step current of controlled peak value upto 100A

and controlled rate of change with both positive and negative didt

. The step transition time

is less than 200ns. The didt

is adjustable upto a limit of 300A/µs to verify the didt

following

capability of the sensor. The same current source produces continuous sinusoidal current

of controlled magnitude upto 75A peak and controlled frequency from 1Hz to 1000Hz. The

magnitude and the frequency of the sinusoidal current can be varied on-line like a voltage

function generator. The hardware of the current source is designed to consume minimal ac-

tive power from mains during continuous sinusoidal current generation. This current source

is used in experimental verification of the steady state and the transient performance of the

designed laboratory current sensor. The transient performance of the laboratory current

sensor is observed to be superior to state-of-the-art current sensors used in power electronic

applications.

iv

Contents

Acknowledgements i

Abstract iv

List of Tables ix

List of Figures x

1 Introduction 1

1.1 Current Sensing in Power Electronics . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Current Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.2 Current Monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.3 Fault Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Hall-Effect Current Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Hall-Effect for Current Sensing . . . . . . . . . . . . . . . . . . . . . 8

1.2.2 Open Loop Hall-Effect Current Sensors . . . . . . . . . . . . . . . . . 10

1.2.3 Closed Loop Hall-Effect Current Sensors . . . . . . . . . . . . . . . . 11

1.2.4 Open Loop Hall-Effect Current Sensors using Current Transformer . 13

1.2.5 Applications in Power Electronics . . . . . . . . . . . . . . . . . . . . 14

1.3 Characteristics of Hall-Effect Current Sensors . . . . . . . . . . . . . . . . . 15

1.3.1 Steady State Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3.2 Dynamic Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4 Performance Validation of Hall-Effect Current Sensors . . . . . . . . . . . . . 17

1.5 Motivation for the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

v

vi Contents

2 Compensator Design for Closed Loop Hall-Effect Current Sensors 21

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Modeling of the Current Sensor . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.2 Derivation of Equivalent Circuit Diagram . . . . . . . . . . . . . . . . 24

2.2.3 Role of the Compensator . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Compensator Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.1 Proportional Compensator . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.2 PI Compensator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Power Electronic Converter for Characterization of Hall-Effect Current

Sensors 33

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Power Circuit Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Step Current Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.1 Falling Step Current . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3.2 Rising Step Current . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 Sinusoidal Current Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4.1 System Modeling and Current Controller Design . . . . . . . . . . . . 49

3.4.2 Scheme for Online Change in Frequency and Magnitude . . . . . . . 50

3.5 H-bridge Hardware Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.5.1 DC Bus Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.5.2 Power MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.3 IGBTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.4 Overvoltage Snubber Capacitor Cov . . . . . . . . . . . . . . . . . . . 54

3.5.5 Overvoltage Snubber Diode Dov . . . . . . . . . . . . . . . . . . . . . 55

3.5.6 Load Inductor L0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.6.1 Current and Voltage Measurement . . . . . . . . . . . . . . . . . . . 56

3.6.2 Measured Step Current Characteristics . . . . . . . . . . . . . . . . . 58

3.6.3 Sinusoidal Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.6.3.1 Current THD . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Contents vii

3.6.3.2 Power consumption . . . . . . . . . . . . . . . . . . . . . . . 66

3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4 Laboratory Current Sensor 70

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.3 Model Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 Design Example: PI Compensator . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.1 Realization of Gc(s) with Single Operational Amplifier . . . . . . . . 74

4.4.2 Realization of Gc(s) with Two Operational Amplifiers . . . . . . . . . 75

4.5 Performance Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.5.1 Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.5.2 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.5.3 Performance Comparison with State-of-the-art Current Sensor used in

Power Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.5.4 Positional Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Conclusion 85

5.1 Contributions of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2 Scope of Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

A Current Sensing Techniques 88

A.1 Ohm’s Law of Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.1.1 Shunt Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.1.2 Current Sensing MOSFETs . . . . . . . . . . . . . . . . . . . . . . . 89

A.2 Faraday’s Law of Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.2.1 Current Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.2.2 Rogowski Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.3 Magnetic Field Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

A.3.1 Hall-Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.3.2 Fluxgate Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.3.3 Magnetoresistive Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.4 Magneto-Optic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

viii Contents

A.5 Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

B Design of the Laboratory Current Sensor 93

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.2 Hall Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

B.2.1 Biasing Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.2.2 Temperature Limitation . . . . . . . . . . . . . . . . . . . . . . . . . 95

B.3 Magnetic Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.4 Compensating Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

B.5 Magnetizing Inductance Calculation . . . . . . . . . . . . . . . . . . . . . . . 98

References 100

List of Tables

1.1 Comparison of open loop and closed loop Hall-effect current sensors [22]. . . 13

3.1 Specifications of various components used in the hardware set-up. . . . . . . 53

3.2 System and controller parameters shown in Fig. 3.14. . . . . . . . . . . . . . 65

4.1 Specifications of the laboratory current sensor. . . . . . . . . . . . . . . . . . 71

4.2 Parameters of PI compensator realized with single operational amplifier. . . 74

4.3 Parameters of PI compensator realized with two operational amplifiers. . . . 77

B.1 Magnetic core details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

ix

List of Figures

1.1 Four basic categories of current sensing techniques [8]. . . . . . . . . . . . . . 2

1.2 Waveforms and frequency of currents in various applications in power electronics. 3

1.3 Fault under load test waveforms reported in [3]: IGBT current IC : 200A/div,

VCE: 100V/div, VGE: 10V/div, time: 500ns/div. The IGBT current reaches

1200A within 1µs before the short circuit fault is removed by turning off the

gate pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Hall-effect in metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Hall magnetic sensor used as current sensor. . . . . . . . . . . . . . . . . . . 9

1.6 Hall element placed in the air gap to sense the magnetic flux density in the gap. 10

1.7 Open loop Hall-effect current sensor. . . . . . . . . . . . . . . . . . . . . . . 11

1.8 Closed loop Hall-effect current sensor. . . . . . . . . . . . . . . . . . . . . . . 12

1.9 An open loop Hall-effect current sensor combined with current transformer [22]. 14

1.10 Definitions of the step response parameters of a current sensor [22]. . . . . . 16

2.1 Closed loop Hall-effect current sensor: (a) photograph of the magnetic core

with Hall element (b) schematic. . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Equivalent circuit model of closed loop Hall-effect current sensor. . . . . . . 25

2.3 Block diagram representation of a closed loop Hall-effect current sensor: (a)

signal propagation in the Hall element channel (b) overall block diagram model. 26

2.4 Asymptotic bode plot of ‖H(jω)‖ with proportional compensator. . . . . . . 28

2.5 Step response: i2(t) for a fixed ωn and different values of ζn. . . . . . . . . . 30

2.6 Effect of variation in ωn with ζ1 = 1 (a) step response of i2(t) (b) bode

magnitude plot of ||H(jω)||. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

x

List of Figures xi

3.1 Configuration of the power electronic converter based current source for per-

formance validation of current sensors. . . . . . . . . . . . . . . . . . . . . . 35

3.2 Power circuit of the hardware set-up for characterization of Hall-effect current

sensors (a) series connected auto-transformer, step-down transformer, diode

bridge rectifier and dc electrolytic capacitor to produce variable dc voltage Vd,

(b) the circuit topology to produce reference step current iLs(t) and sinusoidal

current i0(t) in the branch P1-P2 and P3-P4 respectively. . . . . . . . . . . . 36

3.3 Equivalent power circuit of the hardware setup to produce step current and

sinusoidal current in the branch P1-P2 and P3-P4 respectively. . . . . . . . . 37

3.4 Symbolic representation of top view of the hardware setup: Solid and dotted

lines represent positive and negative dc bus plate respectively. IGBT and

MOSFET modules are placed carefully to reduce the loop inductance created

by the branch P1-P2 of positive dc bus plate and negative dc bus plate. . . . 38

3.5 Modification in the hardware to accommodate the current sensor under test

for step response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6 Equivalent circuit arrangement for step current generation. . . . . . . . . . . 40

3.7 Four modes of operation of the falling step current generation circuit. The

step current iLs(t) is observed in the Mode-III. . . . . . . . . . . . . . . . . . 41

3.8 Equivalent circuit during the conduction interval of Dov. . . . . . . . . . . . 42

3.9 Waveforms of the gate pulses g1-g4 along with i0(t), ic1(t), iLs(t), vce1(t), iCov(t)

and cCov(t) during the four modes in generation of falling step current. The

fall time of iLs(t) is exaggerated, though it is negligible compared to Ton in

practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.10 For a fixed value of dc bus voltage Vd and the total stray inductance Ls (a)

plot of fall time tf vs. voltage overshoot across the IGBT IG1 using (3.10)

with different values of peak current ILs0, (b) plot of capacitor Cov vs. tf using

(3.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.11 Four modes of operation of the rising step current generation circuit. The

step current iLs(t) is observed in the Mode-III. . . . . . . . . . . . . . . . . . 45

3.12 Waveforms of the gate pulses g1-g4 along with i0(t), ic1(t), iLs(t), vce1(t), iCov(t)

and cCov(t) during the four modes in generation of rising step current. The

rise time of iLs(t) is exaggerated, though it is negligible compared to discharge

time constant of the load current i0(t). . . . . . . . . . . . . . . . . . . . . . 47

xii List of Figures

3.13 Equivalent circuit: sinusoidal reference current generation in the branch P3–P4. 48

3.14 Block diagram of closed loop PR current controlled inverter. . . . . . . . . . 49

3.15 Adaptive scheme for online change in frequency of the output current (a) block

diagram of frequency adaptive proportional-resonant controller based on two

integrators in continuous time domain [66], (b) online change in frequency ω0

and magnitude I∗m of the current command generated in FPGA using external

potentiometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.16 Hardware set-up to generate step current and continuous sinusoidal current

(a) top view of components placement on heat sink with dc bus copper plates

(b) internal details of the power device modules. The positive and the negative

dc bus plates are shown in red and blue color respectively. . . . . . . . . . . 52

3.17 Effect of reverse recovery effect of Dov on the falling step current iLs(t) (a)

silicon based diode , (b) zero reverse recovery SiC SBD diode [75]. . . . . . . 55

3.18 Air core toroidal cage inductor L0 (a) the six coils are connected in series

symmetrically to result in a toroidal cage shape, (b) series connection of the

six coils [67], [68]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.19 Top view of the hardware set-up fabricated in the laboratory. . . . . . . . . . 57

3.20 Large bandwidth YOKOGAWAr current probe [82] inserted in the branch

P1-P2 to capture the produced step current. . . . . . . . . . . . . . . . . . . 58

3.21 Experimental waveforms of step current iLs(t) produced in the branch P1-P2

and IGBT voltage overshoot for different values of snubber capacitor Cov.

The peak value ILs0 is fixed at 48A for both falling and rising step current

generation. (a) - (c): falling step current iLs(t) and corresponding IG1 voltage

vce1(t), (d) - (f): rising step current iLs(t) and corresponding IG4 voltage

vce4(t). (a) Cov: 95nF, (b) Cov: 48nF, (c) Cov: 15nF, (d) Cov: 95nF, (e) Cov:

48nF, (f) Cov: 15nF. iLs(t): 20A/div, vce1(t): 20V/div, vce4(t): 20V/div,

time: 200ns/div. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.22 Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t).

ILs0: 48A, Cov: 15nF, Rov: 50Ω. (a) falling step current, (b) rising step

current. iLs(t): 20A/div vCov(t): 20V/div time: 200ns. . . . . . . . . . . 61

List of Figures xiii

3.23 Experimental waveforms of step current iLs(t) produced in the branch P1-P2

and IGBT voltage overshoot for different values of peak current ILs0. The

snubber capacitor Cov is fixed at 15nF for both falling and rising step current

generation. (a) - (c): falling step current iLs(t) and corresponding IG1 voltage

vce1(t), (d) - (f): rising step current iLs(t) and corresponding IG4 voltage

vce4(t). (a) ILs0: 10A, (b) ILs0: 25A, (c) ILs0: 48A, (d) ILs0: 10A, (e) ILs0:

25A, (f) ILs0: 48A. Time scale: 200ns/div. The fall time tf and the rise time

tr are independent of ILs0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.24 Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t).

ILs0: 48A, Cov: 15nF, Rov: 50Ω. (a) falling step current, (b) rising step

current. iLs(t): 20A/div vCov(t): 20V/div time: 200ns/div. . . . . . . . 63

3.25 Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t)

during discharge period of mode-IV. ILs0: 48A, Cov: 15nF, Rov: 50Ω. (a)

falling step current, (b) rising step current. iLs(t): 20A/div vCov(t): 20V/div

time: 10µs/div. The capacitor Cov voltage shoots upto 88V, and gets dis-

charged within 2µs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.26 Bode magnitude plot of the open loop transfer function at 1Hz, 10Hz, 100Hz

and 1000Hz resonant frequency of the PR current controller. In all four cases

the bandwidth is 1.28kHz, and the phase margin is 68.5. . . . . . . . . . . . 66

3.27 Experimental waveforms of the controlled output current i0(t) and the error

ierr(t) at fundamental frequency of (a) 1Hz, (b) 10Hz, (c) 100Hz and (d)

1000Hz. The output current i0(t) contains 20kHz switching components. . . 67

3.28 Experimentally observed THD of output current i0(t) in frequency range 1Hz

- 1000Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.29 Experimental waveforms of line-to-line voltage Vab(t) of 3-φ power supply and

the input line current Ia(t) drawn by the laboratory current source during

150A pk-pk sinusoidal current generation at 50Hz. The hardware set-up draws

315W active power from mains power supply. . . . . . . . . . . . . . . . . . 69

4.1 Overall schematic of the laboratory current sensor with PI compensator. The

single OpAmp based PI compensator is later replaced by two OpAmp based

PI compensator in the final design. . . . . . . . . . . . . . . . . . . . . . . . 71

xiv List of Figures

4.2 Comparison of simulation and experimental results of step response of the

laboratory current sensor for three different values of the damping factor ζn

and constant ωn. The step excitation is 20A. (a)-(c): Vout(t) from the simu-

lation model, (d)-(f): Vout(t) from the experimental hardware. (a), (d) ζn =

0.56, ωn = 592 rad/s; (b), (e) ζn = 1.80, ωn = 592 rad/s; (c), (f) ζn = 14.28,

ωn = 592 rad/s; vertical scale: 4A/div, time scale: 2ms/div. . . . . . . . . 72

4.3 Circuit realization of PI compensator, Gc(s) using single operational amplifier

with current booster amplifier at the output stage. vH(s) is the output voltage

of the Hall element. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.4 Comparison of simulation and experimental Vout(t) waveforms for large ωn

with a 20A step primary current. Ch-2 displays Ch-1 with 10x magnified

vertical scale about the steady state value (a) response of the simulation model

(b) experimental result. Kp = 392, Ki = 1714134. Ch-1: 500mV/div, Ch-2:

50mV/div, time scale: 200µs/div. . . . . . . . . . . . . . . . . . . . . . . . . 75

4.5 Experimental results: low frequency sinusoidal current measurement with the

laboratory current sensor using single OpAmp PI compensator: Kp = 392, Ki

= 1714134. Ch-2 (5A/div): reference current, Ch-4 (5A/div): current sensor

output. time scale:(a) 25ms/div, (b) 2.5ms/div. . . . . . . . . . . . . . . . . 76

4.6 Circuit realization of PI compensator, Gc(s) using two operational amplifiers

with class-B power amplifier at output stage. . . . . . . . . . . . . . . . . . . 76

4.7 Experimental waveform of Vout(t), when PI compensator is realized with two

operational amplifiers for a 20A step primary current. Ch-2 displays Ch-1

with 10x magnified vertical scale about the steady state value. Kp = 15510,

Ki = 2.54x109. Ch-1: 500mV/div, Ch-2: 50mV/div, time scale: 200µs/div. . 77

4.8 Small signal frequency response measurement of the laboratory current sensor.

||Vout(jω)i1(jω)

|| with gain normalized to one. . . . . . . . . . . . . . . . . . . . . . 78

4.9 Output of the laboratory current sensor with 75A peak sinusoidal excitation

at 100Hz. Vertical scale: 37A/div, time: 5ms/div. . . . . . . . . . . . . . . . 79

4.10 Step response measurement of the laboratory current sensor with 40A step

excitation: (a) with energized Hall element (b) without energized Hall ele-

ment. Reference step current is produced by the laboratory hardware set-up.

Vertical scale: 10A/div, time: 1µs/div. . . . . . . . . . . . . . . . . . . . . . 80

List of Figures xv

4.11 Step response of the laboratory current sensor after de-energizing the Hall

element circuit, captured for the duration of 20ms. The step excitation is

40A. Vertical scale: 10A/div, time: 1µs/div. . . . . . . . . . . . . . . . . . . 81

4.12 Comparison of step response measurement with 87A step current generated

using the laboratory current source (a) response of the laboratory current

sensor (b) response of commercial current sensor [79]. Vertical scale : (a)

20A/div (b) 18A/div; Time scale: 5µs/div. . . . . . . . . . . . . . . . . . . 82

4.13 Effect of position of the primary conductor with respect to the air gap on the

step resonse of the laboratory current sensor: (a) five different positions in the

aperture of the toroidal core; output of the sensor at the position (b) C (c) S

(d) W (e) N and (f) E. The step excitation is 40A, and the direction of the

current is out of plane of the paper. The inner diameter of the toroid is 30mm,

and the conductor diameter is 3mm. Minimum disturbance is observed at the

centre. Vertical scale : 20A/div ; Time scale: 1µs/div. . . . . . . . . . . . . 84

B.1 Photograph of 300A closed loop Hall-effect current sensor built in the laboratory. 93

B.2 (a) Working principle of a Hall element, (b) photograph of InSb Hall element

chip [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

B.3 Output characteristics of SH-400 Hall sensor [35] with constant current drive

and constant voltage drive. Variation in (a) output voltage VH and (b) offset

voltage Vos with respect to ambient temperature. The constant voltage drive

results in less variation in VH and Vos compared to constant current drive. . 95

B.4 Input characteristics of SH-400 Hall sensor [35] (a) input resistance of a Hall

element, (b) variation in input resistance Rin with ambient temperature. . . 96

B.5 Constant voltage drive circuit for SH-400 Hall element (a) the circuit used in

the laboratory current sensor (b) effect of variation in input resistance Rin on

the bias voltage Vc. The resistor R is chosen as 1.2kΩ to maintain Vc around

1.30V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.6 Input voltage derating curve of SH-400 [35] for constant voltage drive. The

input voltage Vc must stay within the curve envelop. . . . . . . . . . . . . . . 97

B.7 Dimensions of (a) the toroidal core and (b) the Hall element SH-400 [35]. All

dimensions are in mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

xvi List of Figures

B.8 (a) The Hall element SH-400 inserted in the air gap, (b) cross section of a

high sensitive InSb Hall element [34]. The ferrite substrate of SH-400 reduces

the effective air gap length. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Chapter 1

Introduction

Current sensors are widely used in industrial electronics and scientific instruments. Their

major applications include particle accelerator, beam instrumentation, plasma research, elec-

trical surgical analysers, CT scan machine, lightning discharge, EMI industry, high voltage

surge current testing, automotive electronics, electric drives, power converters and power

systems. Bandwidth, precision, construction, compactness and galvanic isolation require-

ment vary based on the applications. Output of the sensors may be used to monitor current

or as feedback signal in a control loop. Galvanic isolation and voltage insulation level are

other important criteria of selection of current sensors in high voltage high current appli-

cations. In most of the applications only ac sensing suffices the requirement, while in few

but critical applications the sensor is required to sense both dc and ac with sufficiently large

bandwidth. Sensors used in pulsed operations are expected to have very small rise time, of

the order of 1ns. Current sensing techniques used in the aforementioned applications are

enlisted in Fig. 1.1 with dc/ac current sensing capability and galvanic isolation property.

These techniques can be broadly classified into four categories [8]:

• Ohm’s Law of resistance

• Faraday’s Law of induction

• Magnetic field sensors

• Magneto-optic effect.

These techniques are discussed briefly in Appendix A. A comprehensive survey of existing

techniques is given in [8]-[14]. Performance of current sensors using these techniques is

evaluated comparatively and enlisted in [8], [10] and [11].

1

2 Chapter 1. Introduction

Figure 1.1: Four basic categories of current sensing techniques [8].

1.1 Current Sensing in Power Electronics

Current sensors find frequent use in power electronic applications. It includes current/torque

control of electric motors, current control in grid connected converters, UPS, resonant con-

verters, current mode control of dc-dc converters, short-circuit protection of power devices,

inrush current measurement in power system etc. Few waveforms of electric currents in

power electronic applications are depicted in Fig. 1.2. Waveform shape, magnitude and fre-

quency of electric currents in power converters are required to determine efficiency, harmonic

distortion, electromagnetic compatibility, semiconductor switch stress etc. The ultimate ob-

jective of power electronic study is to convert electric energy into useful form in the most

efficient manner. The efficient power conversion requires both voltage and current data. Un-

like voltage sensors the current sensors, when integrated to power conversion system, often

need to intrude to the current carrying circuit, which may affect the actual current sensing.

1.1. Current Sensing in Power Electronics 3

Switched Reluctance Motor

50Hz Fundamental

time

Induction Motor, DC-AC Inverter

50Hz Fundamental

250Hz - 10kHz Switching

time

Resonant DC-AC Converter

100kHz - 1MHz Fundamental

time

Current Mode Controlled DC-DC Converter

DC + 10kHz - 200kHz Switching

time

Inrush capacitor switching current in HVDC system

timetime

Inrush current drawn by incandescentlight bulbs

Figure 1.2: Waveforms and frequency of currents in various applications in power electronics.


A number of current sensing techniques exist these days. A particular technique may be se-

lected for use in a power electronic system based on its required role. Application of current

sensors in power electronics may be broadly categorised into three types: current control,

current monitor and fault protection.

1.1.1 Current Control

Electric current is essential driving factor in electromechanical energy conversion. Interac-

tion with magnetic field creates electromagnetic force or torque, which facilitates conversion

of mechanical energy into linear or rotary motion respectively. Applications of electric mo-

tors range from huge marine electric propulsion motor to tiny spindle motor in hard disk of

computer, from heavy duty drilling motor in mines to light rotary motor in domestic sewing

machine. Most of these applications require controlled torque and speed, which, in turn,

require control of electric currents. Apart from electromechanical energy converters electric

power may be further converted using power electronic converters from dc to ac, ac to dc,

dc to dc or ac to ac based on applications. These converters are the main constituents in

solar and wind energy conversion, grid-integration, power conditioners and various utility

equipments. Size of the converters ranges from tiny regulator module in an electronic gad-

get to large power conditioner in HVDC applications. In most of these converters current

controllers are required to produce current of desired shape and frequency.

Isolated current sensors, specially Hall-effect current sensors are widely used in current

control of electric drives, grid-interactive converters, active power filters and other high power

low voltage power electronic systems. In high power converters the switching frequency is

of the order of 10kHz. Bandwidth of Hall-effect sensors is typically 200kHz [22], and can

be employed in the feedback of these converters. In addition to high bandwidth the Hall-

effect sensors have dc/ac measuring capability, and provide galvanic isolation as well. Their

construction is robust, and can be used in field applications. In non-isolated dc-dc converters

shunt resistors are frequently used in current mode controllers and other current control

schemes, while Magneto-Resistive (MR) sensors and miniature Hall-effect current sensors

find place in isolated dc-dc converters.

1.1. Current Sensing in Power Electronics 5

1.1.2 Current Monitor

In most of the power electronic systems the current is needed to be monitored to validate the

theoretical analysis with experimental results. The bandwidth of the sensor in monitoring

application is usually higher compared to that used in current controllers. High bandwidth

current sensors are called current probe, and have special signal conditioning circuit to reject

unwanted measurement noise. These probes have special output port to be used in oscillo-

scopes. Hall-effect current sensors are widely used to monitor currents in electric motors and

power converters. Typical bandwidth of these sensors is 200kHz, which is sufficient enough

to capture dc/ac current with switching ripples [22]. In resonant converters the fundamental

frequency of the current may go as high as 1MHz, and current transformers find frequent use

in these converters. Four special applications involving current monitoring are given below:

PCB based power converters

In printed circuit boards there are always pace constraint and limitation on heat dissipation.

The current sensors used in PCB are expected to be compact in size, and work satisfactorily

with natural cooling. Shunt resistors are very common in PCB current sensing, but they

dissipate considerable heat at large current. Linear Hall IC based sensors and Magneto-

Resistive (MR) sensors have inherent galvanic isolation, and are usually employed, where

high bandwidth and dc/ac measurement capabilities are required. These sensors are available

commercially with current measuring range upto 100A, and consume minimal power even

at large currents. Linear IC based current sensors have typical bandwidth of 100 kHz [24],

while MR sensors bandwidth is relatively high, upto 2 MHz [25]. Shunt resistors, linear

Hall ICs, senseFETs, Magneto-Resistive sensors and current transformers are used without

signal conditioning circuit to monitor currents in automotive and low power electronics [10].

Current transformer based sensors are also used in PCB based dc-dc converters to measure

average inductor current [12]. To be operated in an ambient temperature of 250 C, a novel

bidirectional saturated current transformer based sensor is used in [4]. The sensor is mounted

on the leg of a discretely packaged SiC device, and can measure dc and sinusoidal ac upto

1kHz and 50A.


Switch current

To determine the switching losses in semiconductor devices the switching current needs to

be monitored. With the advent of modern power devices capable of switching as fast as

in 10ns, the current sensor’s response time and didt

rating must be sufficient to capture that

current [14]. Owing to inherent galvanic isolation and high bandwidth, Rogowski coil based

current sensors are usually employed in industry to observe switching current, but intrusion

of the coil in the switching circuit inserts inductance, and hence affects the actual switching

current waveforms. It also increases the voltage overshoot across the switching device. Co-

axial current transformer is a practical solution used to monitor switching current in high

power converters with minimal insertion inductance [7].

Pulse current

Capacitive discharge and surge current testing need current sensors designed for pulse cur-

rent monitoring. Current transformers and Rogowski coils are usually employed in these

applications [15]. In HVDC systems the current level may go as high as 500kA. Fibre-Optic

current sensors are used to monitor bi-directional dc upto 500kA with high level voltage

isolation and good immunity to electromagnetic interference [9]. In low voltage applications

SMD shunt resistors are also used to monitor pulse current, but their use is often limited

by the pulse heat dissipation represented by I2t rating [12]. A combination of Hall-effect

sensor and current transformer is used in designing a current probe capable of measuring

both dc and ac upto 40A current and bandwidth from dc to 30MHz [6]. Owing to small

size and high bandwidth, MR sensors find frequent use in brushless dc motors and switched

reluctance motors to sense square shaped current [9].

EMI test

Electromagnetic Interference (EMI) test is an important application, where the current as

low as 10 µA and frequency as high as 200MHz may be required to be monitored [2]. These

current probes are normally designed using current transformers.

1.2. Hall-Effect Current Sensors 7

1.1.3 Fault Protection

The dynamic performance of current sensors plays crucial role in fault protection system of

motors and power converters. The protection system sends shut-down signal on either over-

current or short-circuit fault. Output of the current monitors, discussed in previous section,

can be used in over-current protection. In short-circuit protection of power semiconductor

devices the sensor must respond very fast, as the devices can survive the fault current lasting

for only few µs. A typical high power IGBT short-circuit current is shown in Fig. 1.3 [3].

The IGBT current reaches 1200A within 1µs before the short circuit fault is removed by

turning off the gate pulse. The didt

tracking capability of the sensors must be sufficiently

high to track the short-circuit current. Shunt resistors, current transformers and Hall-effect

current sensors are usually employed in short-circuit protection of power electronic circuits

[3]. These days some IGBTs have in-built sense resistor in the output path to be used for

over-current and short-circuit protection. Integration of current sensor in modern power

device modules is briefly discussed in [14].

Figure 1.3: Fault under load test waveforms reported in [3]: IGBT current IC : 200A/div,

VCE: 100V/div, VGE: 10V/div, time: 500ns/div. The IGBT current reaches 1200A within

1µs before the short circuit fault is removed by turning off the gate pulse.

1.2 Hall-Effect Current Sensors

Hall-effect based sensing devices are widely used in keyboards, position sensors, proximity

sensors, speed sensors, magnetic card readers, flow rate sensors, automotive sensors, current


sensors etc. General features of Hall-effect based sensing devices are : true solid state, long

life, high speed operation, no moving part, broad temperature range (-40C to +150C) and

highly repeatable operation [23]. In addition to these features, Hall-effect current sensors

utilize the static and dynamic magnetic field measurement capability of Hall-effect based

magnetic sensors to measure both dc and ac. The magnetic field produced by the current

to be measured is sensed by a Hall-effect magnetic sensor, whose output gives indirect mea-

surement of the current. More details about Hall-effect based sensing devices and their

applications in current sensors are given in [23], [33], [22]. The operating principle of Hall-

effect current sensors used in power electronic applications is briefly discussed in the following

sections.

1.2.1 Hall-Effect for Current Sensing

A Hall element, also called Hall-effect magnetic sensor, is a transducer, which produces

output voltage in response to applied magnetic field. It is made of semiconductor or metal

alloys. It uses the Hall-effect phenomenon of metals and semiconductors to sense the applied

magnetic field.

e-

e-

e-

CurrentSource

+

-

BiasingCurrent

OutputVoltage

Magnetic Field(Perpendicular to

Hall Element)

Figure 1.4: Hall-effect in metals.

The Hall-effect was discovered in 1879 by Edwin Herbert Hall. When a magnetic field B

is applied to a metal or semiconductor, and if the charge carriers are moving with a speed v

(by applying an electromotive force), they experience Lorentz force, F = qv ×B, and drift

towards the direction of force. The accumulation of these carriers create electric potential


across the two parallel sides of the Hall element as shown in Fig. 1.4. This potential is

directly proportional to perpendicular component of the magnetic field BH and the biasing

current IC . The resultant output voltage is given as:

VH = RHICBH

where RH is called Hall-coefficient. It is constant for a wide range of BH , and varies with

temperature. If the biasing current IC is maintained constant, the output voltage gives direct

measurement of the applied magnetic field. Structure, fabrication and characteristics of Hall

elements are discussed in detail in [29]-[33].

Hall Element

Figure 1.5: Hall magnetic sensor used as current sensor.

If the relationship between an electric current and the magnetic field produced by the

current is known, the same Hall element can be used to measure this current also.

For example, it is known that the magnetic field produced at distance d by a conductor

carrying Ip current is:

B =µ0

2πdIp

provided the distance d is very small. If a Hall element is placed perpendicular to this

magnetic field as shown in Fig. 1.5, and biased with a constant current IC , the sensor output

voltage can be given as:

vH = RHICµ0

2πdIp

.


In this way, vH gives measurement of the current Ip. To make vH linearly dependent on

Ip, the distance d must be maintained constant. This type of current sensing technique is

used in PCB based current sensors, where current carrying track and Hall element both are

mounted on fixed positions.

1.2.2 Open Loop Hall-Effect Current Sensors

In another arrangement the Hall element is placed in the air gap of a magnetic core as shown

in Fig. 1.6(a). The air gap is kept very small compared to length of the core. The magnetic

core acts like a flux concentrator. Permalloy Fe-80%Ni provides very low coercive magnetic

field Hc in the wide operating temperature (-40C - +140C), and is normally used for the

magnetic core in Hall-effect sensors [28]. It improves linearity and accuracy of the sensor.

Magnetic Core

Hall Element

+

-

Magnetic Core

Current Carrying Wire

HallElement

Figure 1.6: Hall element placed in the air gap to sense the magnetic flux density in the gap.

Ignoring fringing effect in the air gap, the magnetic field in the gap can be assumed to

be uniform and perpendicular to the plane of the Hall element as shown in Fig. 1.6(b). The

magnetic field in the air gap can be expressed as:

Bg =µ0

lgIp = BH

Normally the distance d in Fig. 1.5 is of the order of few centimetres, whereas in this

case lg is in few millimetres only. It makes the magnetic field produced over Hall element for

the same value of Ip much larger compared to that in previous arrangement. In this way the

sensitivity of the current sensor is improved. Also, very high permeability of the core keeps

the magnetic flux confined within itself and air gap only. If the air gap is very small, the


+

-

Magnetic Core

Current Carrying Wire

HallElement

Amplifier

Figure 1.7: Open loop Hall-effect current sensor.

position of the current carrying wire in the empty inner space of the core does not affect the

flux distribution significantly, and hence, the expression of Bg [26], [27]. This fact can be

utilized to build a clamp-on current sensor, which is very convenient for monitoring currents

in industrial applications [9].

The output voltage of the Hall element consists of two components: common mode

vcom and differential mode vH . Only vH responds to the changing magnetic field [30]. The

magnitude of vH is of the order of mV even for a large current. A differential amplifier with

high CMRR is required at the output of the Hall element to bring the amplified output

voltage vamp into proper measuring range. Normally, operational amplifiers are used to

amplify vH . In high precision applications instrument amplifiers are used. This configuration

of the sensor, shown in Fig. 1.7, is known as open loop Hall-effect current sensor. As evident

from the configuration the output signal is a voltage signal. The losses in the amplifier and

in the magnetic core contribute to its total power consumption.

1.2.3 Closed Loop Hall-Effect Current Sensors

In open loop current sensors when the current is large, the core flux becomes high, and may

saturate. The operating point may deviate from the linear range of B-H curve, resulting

in nonlinear vH . Also, the saturation flux density Bsat of the core puts restriction on the

upper limit of the measured current. For example, if the core is Ne-Fe alloy with saturation

flux density 600mT @250C, and air gap length of 0.5mm, the maximum current that can be

measured will be ≈ 239A. But the B-H curve becomes highly nonlinear near to Bsat. To

avoid non-linearity the current sensor should be operated near to zero flux density of the

core.

To maintain zero flux in the core the open loop configuration is modified to accommo-


+

-

+

-

Compensator

CompensatingCoil CurrentBurden

Resistor

PrimaryCurrent

Magnetic Core

HallElement

Figure 1.8: Closed loop Hall-effect current sensor.

date a compensating winding as shown in Fig. 1.8. Instead of amplifying and measuring

vH directly, it is passed through a compensator Gc(s), whose output is fed back through

compensating winding to produce counter magnetic flux in the core to nullify the total flux.

The voltage drop across this burden resistor RB reflects the measured current Ip. This con-

figuration is known as closed loop Hall-effect current sensor. Due to operation near zero core

flux they are also known as zero flux type Hall-effect current sensor [37].

The compensator Gc(s) is usually implemented with operational amplifiers. A current

booster amplifier is employed at the output stage of the compensator to cater the high value

of I2. The output signal in this configuration is current, due to which the power consumption

increases with the magnitude of the primary current. But, the linearity and the accuracy of

these sensors are much better compared to the open loop configuration [22]. Designing of

these sensors mainly involves proper choice of the compensator Gc(s), number of turns in the

compensating winding and value of the burden resistor. Biasing of the Hall element requires

careful design of the electronic circuitry considering the effect of ambient temperature [30].

The working principle of closed loop Hall-effect sensors is discussed in Chapter 2, and the

designing issues in Appendix B.

Few important performance parameters of the open loop and the closed loop current

sensor are compared, and enlisted in Table 1.1. These days closed loop Hall-effect current

sensors are available upto 10000A measuring capability. Typically the bandwidth is from

DC to 200kHz, while in few designs the bandwidth of 300kHz can be achieved [22]. If cost

and power consumption are not in consideration, closed loop sensors are preferred over the


Table 1.1: Comparison of open loop and closed loop Hall-effect current sensors [22].

Open loop Closed loop

Output signal voltage current

Power consumption low high

Design challenges moderate complex

Cost low high

Construction robust delicate

Bandwidth high high

Accuracy moderate high

open loop sensors.

1.2.4 Open Loop Hall-Effect Current Sensors using Current Trans-

former

In open loop current sensors the Hall element is solely responsible for measurement of both

low and high frequency primary current. Its performance gets deteriorated at high frequency

due to thermal drift, non-linearity and limited bandwidth of the Hall-element and the ampli-

fier circuit [12]. These effects are minimized in closed loop sensor by using the compensating

winding, where Hall-effect takes care of low frequency measurement, and current transformer

effect comes into picture for high frequency measurement [1]. But, the power consumption

increases due to output current signal. A novel configuration was proposed in [5], where

the output voltage of the Hall element and the current transformer winding are amplified

and added using an electronic adder to get the final output voltage signal proportional to

the primary current. This configuration was further modified in [6] to get a bandwidth of

30MHz.

Similar to the above configurations, a novel configuration is designed and commercialized

by LEM Inc., as shown in Fig. 1.9. It uses the low frequency measurement capability of open

loop sensors and high frequency accuracy provided by current transformer. The two outputs

are added electronically to get the final output voltage signal. The detailed working principle


+

-

Amplifier

PrimaryCurrent

Magnetic Core

HallElement

+

ElectronicAdder

Figure 1.9: An open loop Hall-effect current sensor combined with current transformer [22].

of these sensors can be found in [22]. Its performance and cost are comparable to closed loop

sensors. As the output signal is voltage, its power consumption is lower compared to closed

loop sensors.

1.2.5 Applications in Power Electronics

Hall-effect current sensors are widely used in power electronic applications as key element

of control loops (e.g. current, torque, force, speed, position) or in current display systems.

Owing to inherent galvanic isolation, the toroidal structure and dc/ac measuring capability

with high bandwidth, these sensors get an advantage over other current sensing techniques.

The applications of Hall-effect current sensors in power electronics are listed below, though

the list is not exhaustive.

Typical applications include [9], [22]:

• electric drives, for the control of phase currents and torque

• frequency converters, for the control of output current and dc bus current

• grid-interactive inverters, for control of grid currents

• power factor correction circuits, for monitoring of mains current

• power conditioners, for the control of fundamental and harmonic currents

• uninterrupted power supply (UPS) or other battery operated equipment, for the control

of charge and discharge currents

• servo-motors used in robotics, for high performance speed and position control

• special wide bandwidth power supplies used in radar

1.3. Characteristics of Hall-Effect Current Sensors 15

• automotive electronics, for motor drives and battery current control

• protection of power semiconductor devices from output short-circuit fault

• electric traction systems, trackside circuit breaker and rectifier protection, rolling stock

traction converters and auxiliary power supplies

• energy management systems, switching power supplies, electrolysis equipment, and other

applications.

A comprehensive set of criteria for selection of current sensors based on their applications

is given in [22].

1.3 Characteristics of Hall-Effect Current Sensors

Hall-effect current sensors measure dc/ac and complex current waveforms with galvanic

isolation. There is always a limitation on the primary current that can be measured without

any thermal/electrical failure. The accuracy and the linearity parameters are important in

high precision applications like speed/position control of servo motor drives. The operating

range of ambient temperature should also be specified to protect the Hall element and internal

electronic components. The dynamic performance affects the performance of the current

control loop, in which they are employed. The characteristics of Hall-effect current sensors,

or in general any dc/ac current sensor, can be broadly represented by two behaviours:

1.3.1 Steady State Behaviour

Steady state behaviour can be characterized by the nominal current rating, measurement

accuracy, linearity error, power consumption and the ambient temperature range [79]. The

nominal current rating can go upto 10000A. Closed loop sensors have better accuracy (error

less than 1%) compared to open loop counterparts (error of the order of few percent) [22].

Normally these sensors can operate from -40C to +85C ambient temperature. In automo-

tive applications the upper limit can be raised upto +125C, but the bandwidth goes down

due to increased core losses and reduced margin of heat dissipation in internal electronics.

1.3.2 Dynamic Behaviour

Dynamic behaviour of Hall-effect current sensors can be characterized by its bandwidth and

step response. Fig. 1.10 shows typical parameters defined in [22] to characterize step response


of a current sensor. Response time tres and didt

following capability are often used to quantify

the step response.

• Bandwidth: Higher bandwidth results in better step response of the sensor. Bandwidth

Rise time

Responsetime

Reaction time

Figure 1.10: Definitions of the step response parameters of a current sensor [22].

of Hall-effect sensors is often limited by the processing electronics and core losses. Typical

bandwidth of open loop and closed loop sensors is 50kHz and 200kHz respectively.

• Response time tres: A current sensor’s response to a step current with controlled rate of

change is characterized by the response time. It is the delay between the primary reference

current reaching 90% of its final value and the sensor’s output reaching 90% of its final value.

During this measurement the reference current shall behave as a step current. For closed

loop and open loop sensors its typical value is 1µs and 5µs respectively.

•di

dtfollowing: It characterizes the sensor’s ability to follow a fast change in primary

current. It is mainly governed by high frequency disturbance created by external conductors.

The routing of sensor output wires and paths of the PCB track at the output limit the didt

following capability of the sensor. The output wiring should have minimal loop area to

improve didt

rating [22]. This characteristic is important in monitoring current for short

circuit protection of power devices. Typical value of didt

following capability of Hall-effect

current sensors is 50A/µs.

The dynamic performance of Hall-effect current sensors is strongly affected by the location

1.4. Performance Validation of Hall-Effect Current Sensors 17

of the primary conductor with respect to the air gap in the magnetic core. Increasing the air

gap reduces the effect of nonlinearity caused by the non-homogeneity of the magnetic core

material, but larger air gap leads to unwanted sensitivity to the position of the measured

conductor. Fringing of the field in the gap reduces natural shielding of the toroid from

unwanted external magnetic field [9], [26], [27].

1.4 Performance Validation of Hall-Effect Current Sen-

sors

A current source is required to verify the transient and the steady state performance of

Hall-effect current sensors. To verify the transient performance of a current sensor having

response time less than a specified value, the current source must be able to produce a step

excitation current having step transition time much less than the specified response time,

so that it would emulate step input to the sensor. It should also generate a step current

with controlled rate of change to find out the parameters shown in Fig. 1.10. The didt

of the

step current should be greater than the rated value to check the limitation in accurate didt

following.

To check the -3dB bandwidth of the sensor a network analyzer can be used to excite the

sensor, and the response plot can be obtained for frequency ranging upto order of MHz. The

excitation current in network analyzer is of the order of 100mA, which is very small compared

to typical current rating of the current sensor. The measurement by network analyzer gives

small signal frequency response of the sensor. Usually the nominal current rating of Hall-

effect sensors used in power electronic applications is of the order of 100A. It follows the need

of dc and sinusoidal current generation of large magnitude and frequency upto sufficiently

large value to obtain the large signal frequency response of the sensor. Heat-run is standard

testing of current sensors used in industries to check thermal reliability of the sensors. In this

test the sensor is kept in a temperature controlled chamber at ambient temperature of +85C

for 24 hours-48 hours. The sensor is continuously excited with sinusoidal current of rated

current magnitude and frequency of 50Hz, corresponding to typical fundamental frequency

sensing requirements. For this test also the current source must produce sinusoidal current

of rated current magnitude and frequency of 50Hz. The linearity and the accuracy of the

sensor output must be verified for the dc excitation at rated value. To verify all these

steady state characteristics the current source should be able to produce dc and sinusoidal


reference current at the rated value with variable frequency upto sufficiently large value.

While generating continuous sinusoidal current it should draw minimal active power from

the mains supply to reduce the electricity consumption during the heat-run test.

1.5 Motivation for the Work

Semiconductor power devices and magnetic elements are essential constituents of a power

electronic converter. With the advent of modern sophisticated technologies for fabrication

and design of power semiconductor devices there has been immense research going on to

manufacture high speed devices required for high switching frequency power converters.

High switching frequency reduces the size and cost of reactive components significantly, and

increases the converter power density that is desirable in space applications, bearing less

drives, automotive industries, grid-tie inverters, offshore wind power generation, oil and gas

exploration and biomedical instruments. In most of these applications current controllers

are required in speed and torque controllers, switching regulators, power flow controllers

and active power filters. Current sensors play critical role in the feedback path of high

performance closed loop current controlled power converters. With high speed semiconductor

devices the bandwidth of the current sensor is required to be above the switching frequency

to implement a stable current controller.

Research to develop prototype current sensors in laboratory, with improved bandwidth

and response time, required for high frequency applications is also gaining importance [6].

Bandwidth of high current open loop Hall-effect current sensors is less than 50kHz due to

non-linearity and thermal drift of the Hall element at high frequency. It is a challenge to

further improve its bandwidth, as the output solely depends upon the characteristics of the

Hall element. Due to this reason open loop current sensors are used mostly to measure dc

and low frequency ac with sufficient linearity and accuracy.

In closed loop sensors the output depends upon the Hall element for dc and low frequency

measurement upto typically 1kHz. Beyond this range the current transformer action comes

into picture, and the sensor output depends upon the characteristics of the current trans-

former (CT) structure of the sensor. Typical bandwidth of closed loop Hall-effect current

sensors is 200kHz. Its bandwidth can be further improved by careful design of the CT struc-

ture, comprising of air gap size, magnetic core material, position of the Hall element in the

air gap, compensating coil winding strategy, intra- and inter-winding parasitic capacitance,

1.5. Motivation for the Work 19

mutual coupling with the primary conductor, layout of the PCB track at the output stage

and the output stage wiring. Thus, closed loop Hall-effect current sensors have scope to

improve its bandwidth, and to make it suitable for high frequency power converters.

Keeping the above aspects for improvement in consideration, this research work mainly

comprises of two parts:

• to develop a methodology for compensator design of a closed loop Hall-effect current

sensor, keeping its step response characteristics as design attributes,

• to fabricate a controllable current source in laboratory for experimental verification of

the steady state and the transient performance of the current sensor.

Chapter 2, Compensator design for closed loop Hall-effect current sensors. It

introduces the mathematical modeling of closed loop Hall-effect current sensors and the role

of the compensator. It describes the proposed methodology for compensator design of a

closed loop Hall-effect current sensor based on its step response characteristics as the design

attributes.

Chapter 3, Power electronic converter for characterization of Hall-effect current

sensors. It describes the design of a power electronic converter for characterization of steady

state and transient performance of Hall-effect current sensors. A novel hardware topology is

proposed, using which the same hardware set-up can produce both controlled step current

and controlled sinusoidal current in its designated sections without any modification in the

hardware configuration.

Chapter 4, Laboratory current sensor. This chapter covers the experimental verification

of performance of the prototype closed loop Hall-effect current sensor built in the laboratory.

Compensator of the laboratory current sensor is designed based on the procedure devised in

Chapter 2, and its performance is validated by the hardware set-up developed in Chapter 3.

Appendix A briefly discusses existing current sensing techniques.

Appendix B describes the design of the closed loop Hall-effect current sensor fabricated in

the laboratory.


1.6 Summary

An objective of this research work is to design high performance closed loop Hall-effect cur-

rent sensors and to verify its performance. Existing current sensing techniques in power

electronics are classified based on the applications. Working principle of existing Hall-effect

current sensors is discussed briefly. Applications of these sensors in power electronic ap-

plications is listed. Steady state and dynamic characteristics of Hall-effect current sensors

are discussed. To validate these characteristics a current source is suggested with required

details. Performance of open loop and closed loop Hall-effect current sensors is compared,

and found that closed sensors have higher bandwidth, and it can be further improved by

careful design of the current transformer structure.

Chapter 2

Compensator Design for Closed Loop

Hall-Effect Current Sensors

2.1 Introduction

Current sensors are widely used in power electronic systems including switched mode power

converters, electric machine drives, grid connected power converters, etc. A number of

these applications require current measurement with galvanic isolation. Current transformers

cannot measure direct currents and have large error at low frequency alternating currents. A

modified current transformer structure using Hall element, also known as Hall-effect current

sensor is commonly used in isolated current measurement applications. This study involves

analysis to develop high performance dc/ac current sensor with performance comparable to

commercially available current sensors [79].

Analysis of closed loop compensated Hall-effect current sensors was reported in [36]-

[39]. In [38] it was shown that high gain of proportional compensator results in significant

improvement in steady state performance of these sensors. High frequency model employing

control component and system identification presented in [39] further helped in analysis

upto MHz range. However, modeling of the current sensor with the objective of designing

its compensator parameters is little reported.

In this chapter operational principle of closed loop Hall-effect current sensors is discussed.

An equivalent circuit is derived using some practical assumptions, which facilitates the anal-

ysis of these sensors. Closed form analytical expressions of step response are derived for the

current sensor with a proportional and a PI compensator. This is used to show the effect of

changing the control parameters on the dynamic performance. Based on these expressions

a procedure is devised to tune the parameters of PI compensator for high precision current

21

22 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors

measurement. A prototype current sensor is built in laboratory and tested to validate the

analysis. The experimental results are discussed in Chapter 4.

Symbols and abbreviations

i1 : Primary current, current to be measured

i2 : Secondary current, compensating current

n1 : Number of primary turns

n2 : Number of secondary turns

φc : Magnetic flux in the core

λ2 : Flux linked with secondary coil

Bg : Magnetic flux density in air gap

Hg : Magnetic field intensity in air gap

lg : Air gap length

Hm : Magnetic field intensity in the core

lm : Mean length of the core

Ac : Cross-sectional area of the core

µr : Relative permeability of the core

r2 : Winding resistance of secondary coil

RB : Burden resistance

vH : Hall element output voltage

Kh : Sensitivity of Hall element

BH : Perpendicular component of the magnetic

field over the Hall element

Gc(s) : Compensator transfer function

Vout : Voltage drop across the burden resistor

2.2 Modeling of the Current Sensor

A closed loop Hall-effect current sensor is shown in Fig. 2.1. A Hall element is inserted in

the air gap. A conductor carrying current i1 creates magnetic flux in the core and the air

gap. The Hall element produces voltage vH in response to the air gap magnetic field, which

is further amplified by the compensator Gc(s) in order to produce counter magnetic flux in

2.2. Modeling of the Current Sensor 23

+

-

+

-

Compensator

CompensatingCoil Current

BurdenResistor

PrimaryCurrent

Magnetic Core

HallElement

HallElement

Magnetic Core

CompensatingCoil

Figure 2.1: Closed loop Hall-effect current sensor: (a) photograph of the magnetic core with

Hall element (b) schematic.

the core due to compensating coil current i2. This ensures that excitation of the magnetic

core is small and lies in linear region of the B-H curve of the core material.

2.2.1 Assumptions

To model the current sensor the following assumptions are made:

1. Relative permeability of the magnetic core is very high.

2. Leakage inductance and inter-winding capacitance of the compensating winding are

ignored.

3. Position of the conductor with respect to central axis of the core does not affect the

magnetic flux distribution.

4. Presence of the Hall element in the air gap does not disturb the field distribution in

the air gap.

5. Fringing effect in the air gap is ignored.

Hall-effect current sensors are mostly used to sense switching ripple currents of switching

converters, grid frequency currents and their harmonics. Typical bandwidth of Hall-effect

current sensors is 200kHz. Switching frequency in power electronic converters may go upto


100kHz. The non-idealities associated with the sensor become significant in the frequency

range greater than hundreds of kHz. Hence, the above assumptions are relevant from the

perspective of power electronic applications.

2.2.2 Derivation of Equivalent Circuit Diagram

Applying Ampere’s circuital law, and ignoring reluctance offered by the magnetic core we

get

n1i1 − n2i2 = Hmlm +Hglg ≈ Hglg (2.1)

Using the assumptions 4 and 5, the core flux can be expressed as:

φc = BgAc (2.2)

=µ0Acn2

lg

n1

n2

i1 − i2

=Lm

n2

im (2.3)

where

im =

(n1

n2

i1 − i2), and Lm =

(n22µ0Ac

lg

)(2.4)

im is magnetizing current, and Lm is magnetizing inductance, both referred to secondary

side. The voltage induced in secondary winding can be written as:

V2 =d

dtλ2 =

d

dt(n2φc) =

d

dt(Lmim)

= Lmd

dtim (2.5)

As per configuration of the current sensor set-up shown in Fig. 2.1,

Vamp(t) + V2(t) = (r2 +RB)i2(t) (2.6)

Vamp(s) = Gc(s)vH(s) (2.7)

Based on (2.3)-(2.6) the equivalent circuit model of the current sensor can be represented as

shown in Fig. 2.2.

Output voltage of the Hall element, vH , is given by:

vH = KhBH = KhBg = Kh

φc

Ac

(2.8)

2.2. Modeling of the Current Sensor 25

+-

+

-

+ -

Figure 2.2: Equivalent circuit model of closed loop Hall-effect current sensor.

Using (2.3), vH can be expressed as:

vH = Kh

Lm

n2Ac

im (2.9)

vH is the feedback signal corresponding to im. It passes through the compensator, Gc(s) to

change Vamp(s), and in turn, reduces φc. The signal propagation through the Hall element

channel is shown in Fig. 2.3(a). Using (2.7), (2.8) the equivalent circuit can be represented

in s−domain as a block diagram in Fig. 2.3(b).

2.2.3 Role of the Compensator

For accurate measurement of i1 the secondary current i2 should be ideally equal to n1

n2i1.

In other words, the magnetizing current, im, and hence the core flux φc, should be brought

down close to zero. Role of the compensator Gc(s) may be understood with the equivalent

circuit shown in Fig. 2.2. The voltage source Vamp is a function of vH and Gc(s) as expressed

in (2.7). At low frequency the reactance associated with Lm becomes very small. In absence

of Vamp(t) the magnetizing inductance draws huge im, and hence, the error in i2(t) becomes

large at low frequency. The compensator Gc(s) generates sufficient voltage Vamp to reduce

V2 across Lm, and hence im. At high frequency the reactance of Lm is high, and Gc(s) does

not need to play any compensator’s role to make im small. The CT action takes over Gc(s)

at high frequency.

Role of Gc(s) is clearly visible in the block diagram in Fig. 2.3(b) also. This is a unity

feedback closed loop reference tracking control system. The forward path consists of two

parallel paths, namely the current transformer channel and the Hall element channel. The


Magnetic CoreHall Element +

-

Sensitivity ofHall Element

Compensator

(a)

+ +

+

HallElement

Compensator

BurdenResistor

(b)

Figure 2.3: Block diagram representation of a closed loop Hall-effect current sensor: (a)

signal propagation in the Hall element channel (b) overall block diagram model.

forward gain must be very high in the desired range of frequency. The Hall element channel,

enclosed with dotted line, is responsible for the high gain required in low frequency range,

while the block “n2s” provides the required high gain in high frequency range. The effect of

Gc(s) may be explained analytically as follows:

Using block diagram in Fig. 2.3(b),

i2(s)

i1(s)=n1

n2

H(s)

1 +H(s)

(2.10)

and the measurement error function is given by

im(s)

i1(s)=n1

n2

1

1 +H(s)

(2.11)

2.3. Compensator Design 27

where

H(s) =1

r2 +RB

n22µ0Ac

lgs+

n2µ0Kh

lgGc(s)

=

Lm

r2 +RB

s+Kh

n2Ac

Gc(s)

=Lm

RL

(s+KmGc(s)) (2.12)

and

r2 +RB = RL,Kh

n2Ac

= Km (2.13)

Based on (2.11), to bring im close to zero, H(s) must be large over the whole frequency

range. H(s) can be further split into two parts as:

H(s) =Lm

RL

s+LmKm

RL

Gc(s)

= HCT (s) +HHE(s) (2.14)

In (2.14) HCT (s) reflects current transformer action, while HHE(s) accounts for the compen-

sation provided by the Hall element. At low frequencies ‖HCT (jω)‖ is very small. Without

HHE(s) the magnitude of H(s) also becomes small. Due to the same reason current trans-

formers are not used to measure direct and low frequency ac. The compensation HHE(s)

is chosen such that its magnitude is large at low frequency, which can be done by proper

selection of Gc(s).

2.3 Compensator Design

In closed loop Hall-effect current sensors the magnetic core should be excited close to zero

core flux. The constituent, ‖HCT (jω‖ of ‖H(jω)‖ is very large at high frequency, but almost

negligible near dc. It urges the choice of Gc(s) to be such that it results in large value of

‖HHE(jω)‖ at low frequency.

The compensator Gc(s) can be chosen as either of the following classical compensators:

A) Proportional (P)

B) Proportional-Integrator (PI)


2.3.1 Proportional Compensator

Using Gc(s) = Kp turns (2.12) into:

H(s) =Lm

RL

(s+KmKp)

=

LmKmKp

RL

( s

KmKp

+ 1

)(2.15)

‖H(jω)‖ has finite value, K for ω < KmKp. It results in constant non-zero value of im,

which reflects as steady state deviation in i2 from i∗2 = n1

n2i1.

∥∥∥∥∥∥ im(jωn1

n2i1(jω)

∥∥∥∥∥∥ =1

1 + LmKm

RLKp

(2.16)

An obvious choice of Kp should result in large magnitude of H(s) in the flat region shown

in Fig. 2.4.

(rad/sec)

0 dB

Figure 2.4: Asymptotic bode plot of ‖H(jω)‖ with proportional compensator.

The value of Kp may be selected based on the dynamic performance of the compensated

current sensor. A step response is a simple choice to measure the dynamic performance.

For a step jump in i1(t) at t = 0, i.e. i1(s) =I1

swith zero initial condition, and using


(2.10), (2.15) we get,

i2(s) =n1

n2

I1s

(H(s)

1 +H(s)

)=n1

n2

I1(s+KmKp)

s(s+KmKp + RL

Lm)

=n1

n2

I11

(1 + RL

KmKpLm)× 1

s

+n1

n2

I11

(1 + KmKpLm

RL)×

1

(s+KmKp + RL

Lm)

⇒ i2(t) =n1

n2

I11

(1 + RL

KmKpLm)

+n1

n2

I11

(1 + KmKpLm

RL)e−(KmKp+

RLLm

)t (2.17)

Eq.(2.17) shows that there is always a steady state error in i2(t). A very high value of

Kp is preferred to confine the error to a chosen tolerance limit. The maximum value of Kp

is limited by the practical implementation of Gc(s) using operational amplifiers.

2.3.2 PI Compensator

Using Gc(s) = Kp +Ki

sin (2.12) we get,

H(s) =Lm

RL

(s2 +KmKps+KmKi)

s(2.18)

=Lm

RL

(s2 + 2ζHωns+ ω2n)

s(2.19)

where

ζH =KmKp

2ωn

(2.20)

ωn =√KmKi (2.21)

The compensator parameters Kp and Ki can be decided, if ζH and ωn are known. These

values are chosen based on magnitude frequency response of H(s) in conjunction with step


response of the compensated system. As discussed earlier ||H(jω)|| should be kept high

throughout the frequency range of interest to minimize error in alternating current measure-

ment.

For a step jump in i1(t) at t = 0 with zero initial condition, i1(s) = I1s

. Using (2.10),(2.18)

we get,

i2(s) =n1I1n2s

s2 +KmKps+KmKi

s2 + (KmKp + RL

Lm)s+KmKi

(2.22)

=n1

n2

I1

1

s−

RL

Lm

s2 + (KmKp + RL

Lm)s+KmKi

(2.23)

=n1

n2

I1

1

s−

RL

Lm

s2 + 2ζnωns+ ω2n

(2.24)

where

ζn =KmKp + RL

Lm

2ωn

(2.25)

and ωn is given by (2.21).

The second term in (2.24) represents the fractional error in i2(s). Based on the damping

factor ζn the step response may become under damped (ζn < 1), critically damped (ζn = 1)

or over damped (ζn > 1). Fig. 2.5 shows the step response in these conditions for a fixed

value of the natural frequency ωn.

Figure 2.5: Step response: i2(t) for a fixed ωn and different values of ζn.

To avoid large peak undershoot in i2(t) we can select ζn ≥ 1, but this would increase the

settling time. A high value of ζn requires high Kp as expressed in (2.25). Implementation


of PI compensator using operational amplifiers puts limitation on maximum value of Kp.

Choosing ζn = 1 avoids that complexity and provides lower settling time. Using ζn = 1 in

(2.24) we get

i2(s) =n1

n2

I1

1

s−

RL

Lm

(s+ ωn)2

(2.26)

Inverse Laplace transform of (2.26) gives

i2(t) =n1

n2

I1

(1− RL

Lm

te−ωnt

)(2.27)

i2(t) has minimum value, I2minat t = tmin, where

tmin =1

ωn

(2.28)

I2min=n1

n2

I1

(1− RL

eωnLm

)(2.29)

In (2.29) e is the base of natural logarithm. Plot of i2(t) in (2.27) is shown in Fig. 2.5. It is

evident from (2.27) that the steady state error is always zero for DC measurement.

Very low values of tmin and the error in i2(t) are desired for fast dynamics response. It

can be achieved with large value of ωn as shown in (2.28) and (2.29). Fig. 2.6(a) shows the

effect of increasing ωn in the step response. It can be seen that high value of ωn results in

reduced error with low settling time.

Figure 2.6: Effect of variation in ωn with ζ1 = 1 (a) step response of i2(t) (b) bode magnitude

plot of ||H(jω)||.


If Kp and Ki are selected such that

KPKm RL

Lm

we can approximate ζH in (2.20) as equal to ζn, i.e.

ζH ' 1 (2.30)

Bode magnitude plot of ||H(jω)|| is shown in Fig. 2.6(b) for ζH = ζn equal to 1. Increase

in the value of ωn increases the minimum value of ||H(jω)||. This reduces the error in

measurement of sinusoidal i1(t) throughout the frequency range of interest. ωn is selected

based on either the value of tmin or the maximum undershoot allowed using (2.28) or (2.29).

The PI compensator parameters Kp and Ki are calculated using (2.21) and (2.25) with

ζn = 1. The system parameters Lm, RL and Km are expressed in (2.4) and (2.13).

2.4 Conclusion

An equivalent circuit of closed loop compensated Hall-effect current sensors is derived based

on the assumptions relevant from perspective of power electronic applications. This is used

to develop a model of the current sensor. Role of the compensator in the sensor is explained

using the derived equivalent circuit and block diagram model. In low frequency range the

compensator along with the Hall element plays dominant role, while at high frequency the

current transformer action takes over. Dynamic performance of the current sensor with

proportional and PI compensator is analyzed. The sensor with proportional compensator has

inherent non-zero steady state error, while the PI compensator always results in zero steady

state error for dc measurement. Even though the derived model represents low frequency

behaviour of the sensor, its use in the tuning procedure has major impact on the behaviour

of the sensor immediately after the rising edge of the step response. Choosing ζn = 1 reduces

undershoot in the step response while having fast settling time. A tuning procedure based

on analytical expression of the step response is proposed for the PI compensator. A high

value of ωn ensures fast dynamic response as well as good steady state performance.

Chapter 3

Power Electronic Converter for

Characterization of Hall-Effect

Current Sensors

3.1 Introduction

Hall-effect current sensors, used in power electronic applications, are typically specified in

terms of rated current, rise time, settling time, reaction time, didt

limitation and bandwidth

[79]. A step current waveform contains more harmonic components than other waveforms,

and can be used to validate dynamic performance of a current sensor [6]. The steady state

performance can be validated using dc and sinusoidal current excitation. Small signal band-

width of these sensors can be measured using commercial frequency response analyzer, but

excitation current of the order of 100mA can only be obtained, while the nominal current

rating of Hall-effect sensors can be of the order of 100A. In most of the applications these

sensors are used to sense dc and alternating current of grid frequency along with its harmon-

ics. To characterize the steady state performance of the sensors their frequency response

must be validated with excitation current of rated magnitude, and frequency ranging from

dc to sufficiently large frequency.

Earlier works, reported in [43]-[47], focus on developing high frequency 100A sinusoidal

current source using transconductance amplifier with small signal variable frequency sinu-

soidal voltage input. Successful attempt was made in [47] to produce stable accurate 100A

current and in the frequency range from 0.1Hz to 1kHz using computer controlled commer-

cial equipment in conjunction with software-controlled digitizing voltmeter. It was further

used in [48] to validate the performance of the AC-DC current developed in the laboratory.

33

34 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors

Though the operation of the current source was simple, it was difficult to be reproduced in

a laboratory. A number of novel methods were proposed in [49], [52], [53] to characterize

current transducers at high frequencies of the order of 100Mz, but no experimental set-up

were developed. A single phase low current AC source with frequency ranging from 50Hz

to 500Hz was used in [50] to validate the metrological performance of the sensor. In [54] a

test rig was fabricated in laboratory, generating step current of 40ns rise time with 540A

peak current to validate transient performance of Rogowski current transducer. Experimen-

tal results for characterization of current transformers and Hall-effect current transducers in

presence of harmonic distortions are reported in [55]-[58] in the frequency range from 30Hz

to 800Hz and 15A peak current. But, little is reported to date on hardware, which can be

used to validate both transient as well as steady state performance of Hall-effect current

sensors without any modification.

This chapter describes the design of a current source capable of producing step current

with controlled peak value and transition time, as well as sinusoidal current of adjustable

magnitude and frequency. The hardware is configured such that it does not require any

modification while changing over from step current generation to sinusoidal current and

vice versa. As the magnitude of excitation current needs to be large, the current source

is designed using power electronic circuits. It can produce step rise and step fall current

of 100A peak having rise/fall time less than 200ns. Apart from producing step current the

current source also produces sinusoidal current of magnitude 150A peak-peak, and frequency

in the range 1Hz - 1000Hz. The upper limit of the magnitude and the frequency is sufficient

to characterize most of the sensors used in industrial electronics operating at grid frequency

and its harmonics. Like a voltage function generator the magnitude and the frequency of

the produced current can be varied on-line. It facilitates on-line recording of magnitude and

phase plot of the sensor with respect to the excitation current.

The current sensor can be enclosed inside a temperature and humidity controlled cham-

ber, and its performance can be validated at rated operating conditions. Testing of the

sensor at the rated conditions also gives total amount of power consumed by its internal

electronic and magnetic components. The sinusoidal reference current can be used for heat

run test of current sensors, where the sensors are excited with sinusoidal current of rated

magnitude and 50Hz frequency in a thermal chamber at elevated ambient temperature for

time duration of the order of 24 hours. During this heat run test the current source consumes

minimal power from the mains power supply to reduce overall electricity cost of the test.

3.2. Power Circuit Topology 35

Temperature and HumidityControlled Chamber

Temperature and HumidityControlled Chamber

+15V -15V0+24VThre

e P

hase

41

5V

L-L

50

Hz/

60

Hz

Pow

er

Sup

ply

P1 P2

P3

P4

Power Electronics BasedCurrent Source

Auxiliary Power Supply

CurrentSensor

CurrentSensor

P1-P2 : Transient Current Calibration Branch

P3-P4 : Continuous Current Calibration Branch

Figure 3.1: Configuration of the power electronic converter based current source for perfor-

mance validation of current sensors.

3.2 Power Circuit Topology

The power electronic current source produces reference step current and sinusoidal current

in two different branches P1-P2 and P3-P4 respectively as shown in Fig. 3.1. The conductors

in these branches are mounted with screws, and can be detached to insert the sensor under

test. The hardware includes a 3-φ auto-transformer, step-down transformer and diode bridge

rectifier with dc electrolytic capacitor bank Cd to produce a variable dc voltage Vd across the

terminals DC+ and DC− as shown in the Fig. 3.2(a). Auxiliary dc power supply of +15V,

-15V, 0V, +24V are also required for internal gate drivers, protection cards, sensing cards

and digital controller platform etc.

The internal power circuit of the current source is shown in Fig. 3.2(b) for reference sinu-

soidal current and step current generation. An IGBT leg and a MOSFET leg are connected

in parallel to the dc bus. The circuit resembles a single phase H-bridge voltage source in-

verter constituting power MOSFETs M1, M2 and IGBTs IG1, IG2. The choice of using two

different devices (IGBT and Power MOSFET) is explained in sections 3.5 and 3.6.3. The


+

+

Current Sensor(step response)

Current Sensor(frequency response)

Autotransformer Step-down transformer Diode Bridge Rectifier

0 - 415V 450V : 50V

41

5V

L-L +

Figure 3.2: Power circuit of the hardware set-up for characterization of Hall-effect current

sensors (a) series connected auto-transformer, step-down transformer, diode bridge rectifier

and dc electrolytic capacitor to produce variable dc voltage Vd, (b) the circuit topology to

produce reference step current iLs(t) and sinusoidal current i0(t) in the branch P1-P2 and

P3-P4 respectively.

3.2. Power Circuit Topology 37

P

N

A B

Figure 3.3: Equivalent power circuit of the hardware setup to produce step current and

sinusoidal current in the branch P1-P2 and P3-P4 respectively.

load is an air core inductor L0. An RCD over-voltage clamp is connected across the IGBT

leg, which is used to observe step current iLs(t) in the branch P1 − P2. The MOSFET leg is

protected with a de-coupling capacitive snubber Cs. The reference sinusoidal current i0(t)

is observed in the branch P3−P4. The power circuit is reproduced in Fig. 3.3 to simply the

visualization. It must be noted here that at a time only one type of reference current (step

or sine) can be produced by the current source.

The hardware is configured in such a way that no modification is required to changeover

from sinusoidal current generation mode to step current generation mode or vice versa. The

branches P1 − P2 and P3 − P4 are screw mounted, and can be detached to accommodate

the current sensor under test. Typical value of insertion impedance of Hall-effect current

sensor, used in power electronic applications, is below 100nH. It can be seen in Fig. 3.3

that insertion of current sensor in the branch P3 − P4 does not affect the total inductance

of the load significantly, as the load inductor L0 is much larger compared to the insertion

impedance of current sensor. But the insertion impedance becomes comparable, when the

sensor is inserted in the branch P1 − P2 of positive dc bus plate, and has direct impact on

the total loop stray inductance of the dc bus. It causes large voltage overshoot across the

IGBT during turn-off. Moreover, the positive dc plate needs to be modified to accommodate

the current sensor in the branch P1 − P2, and hence the positive and the negative dc bus

plates cannot be placed lateral to each other. It further increases total loop stray inductance

across the dc bus. A careful approach to design the layout of dc bus plates and placement of


semiconductor devices is required. After that the snubber elements can be chosen properly

to minimize the voltage overshoot across the semiconductor devices.

+

+Lo

op

Indu

ctan

ce

sinusoidal current

step c

urr

ent

+

+

Power MOSFET module

IGBT module

RCD snubber

Figure 3.4: Symbolic representation of top view of the hardware setup: Solid and dotted

lines represent positive and negative dc bus plate respectively. IGBT and MOSFET modules

are placed carefully to reduce the loop inductance created by the branch P1-P2 of positive

dc bus plate and negative dc bus plate.

The layout of dc bus plates along with connection of semiconductor devices is symbolically

sketched in Fig. 3.4. The layout of devices ensures that the additional stray inductance due

to the branch P1−P2 appears only across the IGBT leg, and not across the MOSFET leg. It

is shown later that only the IGBT leg is switched to observe step current, and undergoes large

voltage overshoot during the turn-off due to additional dc bus stray inductance. Considering

this the voltage rating of IGBT is chosen much higher compared to dc bus, while the power

MOSFETs voltage rating is relatively low. Low voltage power MOSFETs have very low ON

resistance Rds compared to those of high voltage rating. A SiC SBD diode is selected as the

snubber diode Dov owing to its zero reverse recovery feature. It is shown in the following

sections that these properties are advantageous in producing sharp step current and reducing

conduction losses in sinusoidal current generation.

The choice of two different devices (IGBT and MOSFET) and working principle of the

3.3. Step Current Generation 39

circuit (Fig. 3.3) are explained below.

3.3 Step Current Generation

IGBT Module

DC Bus Capacitor

Positive BusPlate

Positive BusPlate

Negative BusPlate

Current Sensor

+- +-

P1 P2

+

-

MOSFET Module

Figure 3.5: Modification in the hardware to accommodate the current sensor under test for

step response.

Step electric current may be produced as either rising or falling current. Producing

perfect step change in an electric current is impossible due to inherent stray inductance Ls

associated with current carrying elements in the circuit. But, the duration of change can

be minimised to emulate a step current, though it results in very high didt

producing large

voltage drop over the inductive path, which can damage the circuit elements. In this section

a non-destructive method is proposed to generate both rising and falling step current with

rise/fall time less than 200ns, and adjustable step current value. Its didt

can be varied by

using suitable snubber capacitor Cov.

A 3-dimensional representation of the hardware set-up in step current generation mode

is shown in Fig. 3.5. As mentioned earlier the U-shape cut in the positive dc bus plate to

accommodate the current sensor in the branch P1-P2 increases the loop area, and in turn,

the total dc bus stray inductance as shown in Fig. 3.6(a). The equivalent circuit is depicted

in Fig. 3.6(b). Here, Ls represents total stray inductance as seen by the IGBT module. It

includes the insertion impedance offered by the current sensor also. The current iLs(t) flowing

in the branch P1-P2 is the required stimulus for step response measurement of the current


sensor under test. The semiconductor switches can be switched in a particular sequence to

generate either falling or rising step current. The operation of this circuit is explained in the

following sections to generate the step current.

P

N

A B

P

N

A B

Figure 3.6: Equivalent circuit arrangement for step current generation.

3.3.1 Falling Step Current

A falling step current is produced in the branch P1-P2 using the over-voltage RCD snubber.

The circuit operates in four modes, shown in Fig. 3.7.

1) Mode-I: All the four switches are OFF. The capacitor Cov gets charged to dc bus voltage.

To avoid large inrush current, the dc bus voltage is increased slowly using autotransformer

at the AC input side till it reaches Vd.

2) Mode-II: The top IGBT IG1 and the bottom MOSFET M2 are switched ON. The load

inductor L0 starts getting charged, and the current i0(t) increases linearly as expressed in

(3.1).

ILs0 =VdL0

Ton, (3.1)

where Ton is the ON period of IG1.

3) Mode-III: The load current i0(t) is sensed using a current sensor. When it attains a

specified value ILs0, the IGBT IG1 is turned OFF. As soon as the voltage across IG1 rises

to dc bus voltage Vd, the diode D4 starts free-wheeling the inductor current i0, and the

IGBT current ic1 starts falling. Owing to very small turn-off time of the IGBT used in the

hardware, the DC bus current iLs can be assumed to stay constant at ILs0 till ic1 falls to

zero. The fall time of ic1 is governed by the turn-OFF characteristics of the IGBT, and is

neglected to simplify the further analysis. When IG1 starts turning off, the snubber diode

Dov turns ON, and Cov starts getting charged from its initial pre-charged voltage Vd till iLs


P

N

A B+

-

P

A B

P

A B+

-

P

A B+

-

+

-

+

-

+

-

+

-

Figure 3.7: Four modes of operation of the falling step current generation circuit. The step

current iLs(t) is observed in the Mode-III.

comes down to zero. The voltage vce1 across IG1 is equal to the capacitor voltage vCov as

long as Dov is conducting. The free-wheeling diode D4 along with L0 appears as short circuit

after IG1 turns off.

4) Mode-IV: The snubber diode Dov stops conducting. The capacitor Cov starts getting

discharged through the resistor Rov till its voltage comes down to the dc bus voltage Vd. Due

to ON-state voltage drop across M2 and D4, the free-wheeling current i0(t) also comes down

to zero in a while.

The above four modes complete the sequence to generate the falling step current. It is a

single pulse operation, and the modes are not repeated. The falling step current is observed

in mode-III, and the response may be captured in a high bandwidth oscilloscope in single

sequence capture mode. As it is one cycle process, the power consumption during step current

generation is not considered while designing the hardware set-up.

The factors governing the characteristics of the falling step current in the mode-III are

analyzed below. At the start of mode-III the current iLs(t) is ILs0, and IG1 is turned off.


The diode Dov starts conducting, till iLs(t) comes down to zero. The equivalent circuit during

+

+

+Figure 3.8: Equivalent circuit during the conduction interval of Dov.

the decay of iLs(t) can be represented as in Fig. 3.8. The switching transients of diodes and

IGBTs are ignored during the analysis. Assuming that iLs(t) starts falling at t = 0, the

equivalent circuit in Fig. 3.8 can be used to derive the expression of iLs(t) and vCov(t), valid

for conduction interval of Dov.

iLs(t) = ILs0 cosω0t−

VCov − Vdω0Ls

sinω0t, (3.2)

vCov(t) = Vd +ILs0

ω0Cov

sinω0t+ (VCov − Vd) cosω0t (3.3)

where

ω0 =1√LsCov

, . (3.4)

and VCov is the initial voltage across Cov.

The fall time tf is calculated, when iLs(t) comes down to zero and Dov stops conducting.

It results in

tf =1

ω0

tan−1(ILs0ω0Ls

VCov − Vd

)(3.5)

The gate pulses g1-g4 along with i0(t), ic1(t), iLs(t), vce1(t), iCov(t) and iCov(t) are shown

in Fig. 3.9 during the four modes.

The capacitor Cov is pre-charged to Vd. Putting VCov = Vd results in

iLs(t) = ILs0 cosω0t, (3.6)

vCov(t) = Vd +ILs0ω0Cov

sinω0t, (3.7)

tf =π

2ω0

=π

2

√LsCov, (3.8)


Figure 3.9: Waveforms of the gate pulses g1-g4 along with i0(t), ic1(t), iLs(t), vce1(t), iCov(t)

and cCov(t) during the four modes in generation of falling step current. The fall time of iLs(t)

is exaggerated, though it is negligible compared to Ton in practice.

which makes tf independent of ILs0.

With proper choice of Cov and using (3.1), (3.8) the current iLs(t) flowing in the branch

P1-P2 can be made fall to zero in a fixed duration tf from a peak value ILs0. Confining the

fall time tf to a minimal value we can emulate iLs(t) as a step input required to excite the

current sensor in Fig. 3.5.

The voltage vce1(t) across the IGBT IG1 attains maximum value at t = tf , given by

VOV 1 = Vd + ILs0

√Ls

Cov

(3.9)


Figure 3.10: For a fixed value of dc bus voltage Vd and the total stray inductance Ls (a) plot

of fall time tf vs. voltage overshoot across the IGBT IG1 using (3.10) with different values

of peak current ILs0, (b) plot of capacitor Cov vs. tf using (3.8).

In practical implementation, the dc bus voltage Vd is fixed, and the stray inductance Ls

depends only on the layout arrangement of the devices, the bus plates and sensor insertion

inductance. The peak current ILs0 is fixed, and must be below the rated current of the IGBT.

As shown in (3.8) Cov is left to be decided to generate a current of peak ILs0 with fall time

tf . Eq. (3.8) suggests that tf can be reduced by using low capacitance Cov, but reduction

in Cov raises the peak voltage VOV 1 across the IGBT as shown in (3.9). A proper value of

Cov must be chosen to keep VOV 1 below the voltage rating specified by the manufacturer.

• Selection of Cov: Using (3.8), (3.9) the voltage overshoot (VOV 1 – Vd) can be expressed

as:

(VOV 1 − Vd) =πILs0Ls

2tf(3.10)

Fig. 3.10(a) shows the variation in the fall time tf with the overshoot in voltage across

IG1 for a fixed value of peak current ILs0. A family of curves is plotted for different values

of ILs0 using (3.10). The designer may, first, decide the permissible overshoot (VOV 1 − Vd)based on the device voltage rating. With this overshoot, minimum value of tf is found out

with curve of the largest ILs0. Using Fig. 3.10(b) a suitable value of the capacitor Cov is

selected for a fall time greater than or equal to the value of tf found earlier. The capacitor

Cov experiences high dvdt

just after IG1 turns off completely. Metallized film polypropylene

(MFP) capacitors have capability to withstand high voltage pulses [84], [85].

• Selection of Rov: The resistor Rov of the RCD snubber comes into picture in the mode-

IV, when Cov starts getting discharged. In the following sections it is shown that this

RCD snubber is used in generation of reference sinusoidal current also using pulse width


N

P

A B+

-

P

A B+

-+

-

P

A B+

-+

-

P

A B+

-+

-

Figure 3.11: Four modes of operation of the rising step current generation circuit. The step

current iLs(t) is observed in the Mode-III.

modulated power converter configuration. Rov must be chosen sufficiently small to ensure

that the snubber capacitor Cov is fully discharged before next turn-off. At the same time the

discharge transient should be overdamped to prevent undesired switch voltage oscillations,

imposing a minimum value of Rov [61].

3.3.2 Rising Step Current

The same circuit, shown in Fig. 3.3 to produce falling step current, is used for rising step

current generation. The switches are modulated in a slightly different way. The circuit

is operated in four consecutive modes to produce the current. In this case, the sense of

direction of the currents iLs(t) and i0(t) is reverse compared to that in falling one as shown

in Fig. 3.11. The bottom IGBT IG4 is switched to produce rising step current in the branch

P1-P2 during mode-III. The four modes are explained below:

1) Mode-I: Keeping all the four switches OFF the capacitor Cov gets charged to dc bus

voltage Vd.

2) Mode-II: The top MOSFET M1 and the bottom IGBT IG4 are switched ON. The load

inductor L0 starts getting charged, and the current i0(t) increases linearly as expressed in


(3.1).

3) Mode-III: When i0(t) attains a specified value ILs0, the IGBT IG4 is turned OFF. As

soon as the voltage across IG4 rises to dc bus voltage Vd, the diode D1 starts free-wheeling

the inductor current i0, and the IGBT current ic1 starts falling. When IG4 starts turning off,

the snubber diode Dov turns ON, and Cov starts getting charged from its initial pre-charged

voltage Vd till iLs rises to ILs0. The voltage vce4 across IG4 is equal to the capacitor voltage

vCov as long as Dov is conducting. The free-wheeling diode D1 along with L0 appears as

short circuit after IG4 turns off.

4) Mode-IV: The snubber diode Dov stops conducting. The capacitor Cov starts getting

discharged through the resistor Rov till its voltage comes down to the dc bus voltage Vd. Due

to ON-state voltage drop across M1 and D1, the free-wheeling current i0(t) also comes down

to zero in a while.

Similar to the falling step current the equations governing the characteristics of iLs(t) are

given below:

iLs(t) = ILs0(1− cosω0t), (3.11)

vCov(t) = Vd +ILs0ω0Cov

sinω0t, (3.12)

tr =π

2

√LsCov, (3.13)

Here also, the rise time tr is independent of ILs0. Waveforms of the gate pulses g1-g4 along

with i0(t), ic1(t), iLs(t), vce4(t), iCov(t) and cCov(t) during the four modes in generation of

rising step current are shown in Fig. 3.12.

The procedure to select Cov for a desired rise time tr is similar to that discussed in the

previous section, and can be decided using (3.11), (3.12) and (3.13) for a particular value of

ILs0 and tr.

3.4 Sinusoidal Current Generation

The circuit shown in Fig. 3.3 is used to generate reference sinusoidal current i0(t) in the

branch P3-P4. Ignoring the snubber elements the circuit can be redrawn as shown in Fig. 3.13.

The topology is similar to single phase full bridge voltage source inverter with pure inductive

load. The power MOSFETs M1 & M2 along with IGBTs IG1 & IG4 constitute a hybrid

structure to reduce overall switching loss in the devices based on a hybrid PWM strategy

for full bridge inverter proposed in [62]. The MOSFET leg is switched at high frequency,

3.4. Sinusoidal Current Generation 47

Figure 3.12: Waveforms of the gate pulses g1-g4 along with i0(t), ic1(t), iLs(t), vce1(t), iCov(t)

and cCov(t) during the four modes in generation of rising step current. The rise time of

iLs(t) is exaggerated, though it is negligible compared to discharge time constant of the load

current i0(t).


while the IGBT leg is switched at the fundamental frequency of the output current i0(t). It

gives a space to raise the fundamental frequency of the reference current i0(t) to a higher

value, which may not be feasible with both legs consisting of IGBTs only. For example, to

produce a fundamental current of 1kHz frequency, the IGBT leg needs to be switched at

1kHz, and the MOSFET leg may be switched at 20kHz. The switching ripple observed in

iL(t) will have 20kHz component. Had both legs made of IGBT only, they would have had

to be switched at 10kHz by unipolar PWM method, resulting in higher switching losses.

The hybrid PWM principle and its frequency spectrum are described in detail in [62],

and the spectrum is shown to be similar to unipolar PWM method with triangular carrier.

P

N

A B+

Figure 3.13: Equivalent circuit: sinusoidal reference current generation in the branch P3–P4.

As the objective is to produce a current for measurement purpose only, an inductor is

chosen as the load to avoid any active power consumption by load. In this way, the mains

needs to supply active power required for losses in semiconductor devices only, and the

reactive power required by the inductor gets delivered by the dc bus electrolytic capacitor

bank.

The current sensor inserted in the branch P3–P4 as shown in Fig. 3.2(b) induces an

insertion impedance, which can be neglected in comparison to relatively large value of L0.

The total inductance across the bridge can be taken equal to L0. The winding resistance of

L0 is denoted by r0. An equivalent circuit is drawn in Fig. 3.13 with relevant details. Cd is

capacitance of the dc bus electrolytic capacitors.

3.4. Sinusoidal Current Generation 49

3.4.1 System Modeling and Current Controller Design

Average model of the inverter modulated with hybrid PWM method is derived in [62], and

is similar to sine-triangle unipolar PWM method. The average output voltage, vAB(t) can

be expressed in terms of modulation index m(t) and dc bus voltage Vd as:

vAB(t) = m(t)Vd (3.14)

In s-domain the output current i0(t) can be written as:

I0(s) =VAB(s)

sL0 + r0(3.15)

The output current i0(t) is sensed and compared with the reference current command gen-

erated in a microprocessor. A proportional-resonant current controller, proposed in [63],

[64] is used in the closed loop structure, as shown in Fig. 3.14. Kp and Kr are gains of the

current controller; Vp is the PWM gain; Hc is gain of the standard current sensor used in the

feedback path. The controlled output current tracks the output of this sensor only. Hence,

it must be chosen as state-of-the-art current sensor used for precise measurement.

+-

Current Sensor

Current Controller PWM InverterCurrent

CommandOutput Current

Figure 3.14: Block diagram of closed loop PR current controlled inverter.

The open loop transfer function of the closed loop system, shown in Fig. 3.14, is expressed

as:

OL(s) =VdHc

Vp

(1

sL0 + r0

)(Kp +

sKr

s2 + ω20

)(3.16)

The current controller must be able to make the output current track the current command in

a broad frequency range. The semiconductor devices always have a upper limit on switching

frequency to avoid thermal failure. This, in turn, puts upper limit on the fundamental

frequency of the closed loop controlled current. In the higher frequency range the controller


gains, used in (3.16), should be selected carefully to avoid instability due to low switching-

to-fundamental frequency ratio. A design procedure is proposed in [65] to evaluate optimal

controller parameters in this condition.

3.4.2 Scheme for Online Change in Frequency and Magnitude

The sinusoidal current command i∗0(t) = I∗m sinω0t is generated using a look-up table of sine-

cosine function stored in an FPGA. Its operating frequency is swept in the frequency range

of interest. Varying the frequency ω0 and the magnitude I∗m online, preferably by changing

a knob setting, will be convenient for the user to record the magnitude and phase shift with

respect to the reference current at a particular frequency to get the current sensor frequency

response.

A frequency adaptive continuous time structure of proportional-resonant controller is

proposed in [66] to mitigate the sensitiveness to frequency variations of the signals to be

controlled. It does not require the online computation of explicit cosine functions. The

structure is shown in Fig. 3.15(a), and is used in implementing digital PR controller to track

harmonics currents for an active power filter [66].

The above idea is followed by a scheme proposed in this section, and shown in Fig. 3.15(b)

to generate the sinusoidal current command of frequency ω0. The output of the potentiometer

POT1, filtered by a low pass filter, is per-unitized and integrated to produce θ = ω0t, which is

fed as the memory address to the look-up table of sine function stored in the FPGA. The unit

reference sinusoid sinω0t is further multiplied by the desired magnitude I∗m to generate final

current command I∗m sinω0t. Here, the current magnitude I∗m is generated using another

external potentiometer POT2. Square of the frequency of the current command, ω2o is

fed to the frequency adaptive PR controller block shown in Fig. 3.15(a). In this way, the

resonance frequency of the PR current controller is always equal to the frequency of the

current command. It ensures that the output current i0(t) tracks the current command i∗0(t)

with zero steady error while varying its frequency ω0 online by changing the variable terminal

of the external potentiometer.

3.5. H-bridge Hardware Design 51

Per-unitizationin FPGA

Look-up Table for sine function

+VCC

0

To Proportional-Resonant Controller

Current Command

SquareFunction

POT1Low Pass

Filter

Per-unitizationin FPGA

+VCC

0

POT2Low Pass

Filter

Figure 3.15: Adaptive scheme for online change in frequency of the output current (a) block

diagram of frequency adaptive proportional-resonant controller based on two integrators in

continuous time domain [66], (b) online change in frequency ω0 and magnitude I∗m of the

current command generated in FPGA using external potentiometers.

3.5 H-bridge Hardware Design

In a power converter, layout of the two dc bus plates are usually designed to overlap each

other completely to minimise the total dc bus stray inductance. In this hardware set-up

the dc plates cannot overlap each other, as the current sensor under test must be accom-

modated in P1-P2 branch of the positive dc bus plate. This modification increases the total

stray inductance, and causes large voltage overshoot across the IGBT during step current

generation. The layout of dc bus plates is designed carefully to minimize the stray induc-

tance. The actual layout of dc bus plates with branches P1 − P2 and P3 − P4 along with

placement of IGBT, MOSFET modules on the heat sink are shown in Fig. 3.16 as top view


O

+

-

ElectrolyticSCapacitor

PG86DI

33000MFD5S100V

R1 Y1 B1+

-

R1 Y1 B1

+

-

IGBTSModule

SEMiX101GD066HDs

100A5S600V

DiodeSRectifier

SKKD42F

40A5S1200V

R2Y2B2+-

R2 Y2 B2

+

-

PowerSMOSFETSModule

SK115MD10

80A5S100V

R1 Y1 B1R2Y2B2

+

- +-+-

P1

P2

Heat Sink

T+ T-

Figure 3.16: Hardware set-up to generate step current and continuous sinusoidal current (a)

top view of components placement on heat sink with dc bus copper plates (b) internal details

of the power device modules. The positive and the negative dc bus plates are shown in red

and blue color respectively.


of the laboratory hardware setup. Three legs of each of IGBT and MOSFET modules can be

connected in parallel to increase the peak value of the reference step and sinusoidal current.

Six electrolytic capacitors are connected in parallel across dc bus to supply high rms ripple

current required by the inductive load. The RCD over-voltage snubber is connected across

the terminals T+-T−.

Specifications of various components used in the hardware set-up are enlisted in Table

3.1.

Table 3.1: Specifications of various components used in the hardware set-up.

Components Specifications Technology

Cd 33000µF, 100V Electrolytic [78]

Cs 2.2µF, 1000V Snubber

IG1, IG4 100A, 600V Field-stop Trench-gate [76]

MS1, MS4 80A, 100V Trench-gate [77]

Rov 50Ω, 10W Metal Film

Cov 1200V, 15nF Metallized Film Polypropylene

Dov 1200V, 20A SiC Schottky Barrier Diode [75]

L0 72µH, 70Arms Air-core Toroidal-cage [67]

3.5.1 DC Bus Capacitor

In sinusoidal current generation mode the dc bus voltage Vd has direct impact on overall

losses in the power converter. As the load is inductive, the reactive power will be supplied

by the dc bus capacitor bank. Losses in the semiconductor devices and capacitor banks

are drawn as active power from the main power input. Smaller Vd results in lower losses in

semiconductor devices during continuous operation. It also reduces the cost of electrolytic

dc bus capacitors, power devices and magnetic components. Vd is fixed at 40V in sinusoidal

current generation. During step current generation Vd is fixed at 15V to lower the voltage

overshoot across IG1 and IG4 during their turn-OFF. A parallel bank of six electrolytic


capacitors of voltage rating 100V is connected across the dc bus. Its rms ripple current

rating is suitably selected to deliver required reactive power to the inductive load.

3.5.2 Power MOSFETs

Low voltage rated power MOSFETs have relatively smaller ON-resistance Rds compared

to high voltage power MOSFET of the same current rating. During sinusoidal current

generation only the nature of current waveform is the matter of interest. A low voltage

power MOSFET with required current rating reduces the conduction loss during sinusoidal

current generation. Selection of 40V dc bus in sine current generation mode is followed

by the selection of a trench-gate Power MOSFET module of rating 100V, 80A. Three such

devices are connected in parallel to form one MOSFET leg.

3.5.3 IGBTs

The switching characteristics of IGBTs come into picture when IG1 or IG4 turns off to

generate falling or rising step current respectively in the branch P1 - P2. To emulate step

current the IGBT current should come down to zero instantaneously, which is not feasible

with practical devices. To minimize the transition interval the IGBT must have very fast

turn-off characteristic along with small tail current. Field-stop trench-gate IGBTs have the

desired turn-off behaviour [69], [70], [71]. IG1 sees a voltage overshoot during the turn-off.

To survive this overshoot the voltage rating of the IGBT must be sufficiently high compared

to 15V dc bus voltage in the step current generation mode. Also, high voltage IGBTs have

fast turn-off characteristics compared to low voltage IGBT of the same current rating. A

field-stop trench-gate IGBT module of 600V voltage rating [76] is used in the hardware.

3.5.4 Overvoltage Snubber Capacitor Cov

In the step current generation mode, the diode Dov and the overvoltage snubber capacitor

Cov are connected across the IGBT leg to limit the voltage overshoot during the turn-off.

The capacitor Cov experiences high dvdt

just after IG1 or IG4 turns off completely. Metallized

film polypropylene (MFP) capacitors have capability to withstand high voltage pulses [84],

[85]. A sufficiently high voltage rating of 1200V MFP capacitor is used in this application.


Figure 3.17: Effect of reverse recovery effect of Dov on the falling step current iLs(t) (a)

silicon based diode , (b) zero reverse recovery SiC SBD diode [75].

3.5.5 Overvoltage Snubber Diode Dov

The reverse recovery effect of Dov on the falling step current waveform is depicted in

Fig. 3.17(a). To emulate a step current the diode Dov should have zero reverse recovery.

Silicon carbide based Schottky barrier diodes are well known for zero reverse recovery at

ambient temperature [74], [72], [73], shown in Fig. 3.17(b). A 1200V rated SiC diode [75] is

used in the hardware.

C1

C1

C2

C2

Figure 3.18: Air core toroidal cage inductor L0 (a) the six coils are connected in series

symmetrically to result in a toroidal cage shape, (b) series connection of the six coils [67],

[68].


3.5.6 Load Inductor L0

In sinusoidal current generation the load inductor L0 is another major constituent of the

overall loss. As the operating current is very high, even a small winding resistance of L0

results in high copper loss. To avoid magnetic core loss and the core saturation at large cur-

rent L0 is designed as a toroidal cage air core inductor, based on the the guidelines reported

in [67], [68]. At large current the magnetic field produced by L0 may interfere with the

neighbouring electromagnetic equipments. The toroidal cage shape, shown in Fig. 3.18(a),

ensures confinement of the magnetic field inside the cage, and hence, it reduces the EMI

significantly.

3.6 Experimental Results

In this section, the analyses done in sections 3.3 and 3.4 are verified with the hardware

set-up of the current source fabricated in the laboratory. Photograph of the hardware set-up

(top view) is shown in Fig. 3.19. In P1-P2 branch a current probe is inserted to record the

produced step current. The probe is removed when the current source is operated to produce

sinusoidal current in the branch P3-P4 (not shown here).

3.6.1 Current and Voltage Measurement

The purpose of the current source, fabricated in the laboratory, is to validate the performance

of Hall-effect current sensors. But, to validate the analysis involved in designing the current

source itself, large bandwidth current probes and voltage probes are required to capture

current and voltage drops having very small transition time.

Current sensing

The load current i0(t) is sensed using a state-of-the-art current sensor [79]. During sinusoidal

current generation, the output of the load current sensor used in the feedback path, is

compared with the reference current signal generated in the FPGA to nullify the error by

the current controller. In this way the characteristics of the produced sinusoidal current

follows that of the load current sensor. In step current generation, didt

of the load current is

much smaller than the step current. The sensor [79] can respond fast enough to send cut-off

signal to turn-off the IGBT gating pulse.

3.6. Experimental Results 57

Figure 3.19: Top view of the hardware set-up fabricated in the laboratory.

The produced step current in the branch P1-P2 has very small transition time, of the

order of 100ns. To capture this current a YOKOGAWAr current probe [82] having rise time

less than 3.5ns is inserted in the branch P1-P2 as shown in Fig. 3.20. It can measure upto

50A dc. All experimental waveforms of the step current, shown in this section, are captured

using this probe.

Voltage sensing

In step current generation, to capture the voltage overshoot across the IGBT during its

turn-off a large bandwidth voltage probe is needed. A Tektronixr high voltage differential

voltage probe [83] having rise time less than 14ns is used. It is also used to capture the

voltage drop waveform across different sections of the dc bus plates to estimate the stray

inductance associated with that particular section.

We are mainly interested in the magnitude and shape of the current produced by the current

source rather than the voltage waveforms. We may choose the dc bus voltage Vd considering

factors like voltage overshoot, total loss etc. in the hardware set-up. As discussed in section


YOKOGAWAcurrent probe

Digital storage oscilloscope

Positive dc bus plate

Figure 3.20: Large bandwidth YOKOGAWAr current probe [82] inserted in the branch

P1-P2 to capture the produced step current.

3.3, the voltage overshoot across the IGBT during step current generation directly depends

upon Vd, a 15V dc bus is chosen to confine the overshoot within the IGBT voltage rating.

Moreover, during sinusoidal current generation the total power consumption depends on Vd.

The dc bus is fixed at 40V in this case to avoid over-modulation switching region of the

power converter at the maximum output operating frequency for the selected value of L0.

3.6.2 Measured Step Current Characteristics

As expressed in (3.8) and (3.13), the fall time tf and the rise time tr of the step current

depend upon the total stray inductance Ls and snubber capacitor Cov. Once the hardware

set-up is fabricated, Ls gets fixed based on layout of dc bus plates and switching devices.

The capacitor Cov may be changed in discrete steps to see the effect of its variation on the

produced step current iLs. The dc bus voltage is fixed at 15V, and the load inductor L0 is

72µH. The transition intervals tf and tr are observed for different values of Cov and the peak

current ILs0. As discussed earlier tf and tr should vary with Cov, but must be completely

independent of ILs0.

Experimental waveforms of the step current along with voltage drop across the corre-

sponding switching IGBT are depicted in Fig. 3.21, showing the effect of variation in Cov on

tf and tr of the falling and the rising step current iLs(t) produced in the branch P1-P2. The


peak current is fixed at 48A, as the current probe [82] can measure upto 50A dc. The cur-

rents and voltage drops are shown in accordance with the circuits of Fig. 3.7 and Fig. 3.11.

The transition intervals tf and tr decrease with decrease in Cov, which validates the relation

expressed in (3.8) and (3.13). As expected, tf of the falling current and tr of the rising

current are observed to be equal for the same set of values of Vd, Ls, ILs0 and Cov.

During turn-off of the IGBT, the peak IGBT voltage drop is expressed to be dependent

on Vd, Ls, ILs0 and Cov, in (3.9). The IGBT voltage waveforms vce1(t) and vce4(t) are

expected to have one peak, but two peaks are observed, shown in Fig. 3.21(a)-(f). This may

be explained with Fig. 3.22, which shows the step current iLs(t) along with IGBT current

ic1(t), the diode current iDov(t) and vce1(t) as per the circuit of Fig. 3.7 during falling current

generation with 95nF Cov. The dc bus current iLs(t) falls with two different slopes, which

causes two different peaks in vce1(t). As direct measurement of the IGBT current ic1(t) is

not feasible in this hardware set-up, the currents iLs(t) and iDov(t) are captured with two

current probes, and their mathematical difference is used to get waveform of ic1(t).

In the analyses done in section 3.3 all the semiconductor devices were assumed to have

ideal switching characteristics. The IGBT current fall time was neglected, but in practice

the current takes certain time to come down near to zero, and relatively more time to

come completely to zero due to inherent tail current, as shown in Fig. 3.22(a). The diode

Dov also takes finite time to turn on. While ic1(t) comes down to zero, Dov is not fully

turned on. During this interval the dc bus current iLs(t) does not find path to flow through

Cov, and starts decreasing according to turn-off and turn-on characteristics of IG1 and Dov

respectively. It falls with certain didt

, depending on its initial value ILs0, but independent of

Cov. It produces the first peak in vce1(t), which may be observed in Fig. 3.22(b). After Dov

is fully turned on, iLs(t) starts falling under the influence of Ls and Cov, as per the circuit of

Fig. 3.8. The analysis done in section 3.3 holds valid during the conduction interval of Dov

only. The second peak of vce1(t) is due to the didt

of iLs(t) in this interval, and depends upon

both ILs0 and Cov, as expressed in (3.9). This justification is validated by the experimental

observations shown in Fig. 3.21. In all the six cases the first peak is nearly same for a

constant 48A ILs0, and does not change with Cov. As expected, the second peak varies with

Cov according to (3.9). In Fig. 3.21 the second peak is shown to vary with ILs0 with constant

Cov.

Exact prediction of shape of iLs(t) requires detailed mathematical modelling of these

semiconductor devices based on the semiconductor physics and packaging techniques. This


Figure 3.21: Experimental waveforms of step current iLs(t) produced in the branch P1-P2

and IGBT voltage overshoot for different values of snubber capacitor Cov.

The peak value ILs0 is fixed at 48A for both falling and rising step current generation.

(a) - (c): falling step current iLs(t) and corresponding IG1 voltage vce1(t),

(d) - (f): rising step current iLs(t) and corresponding IG4 voltage vce4(t).

(a) Cov: 95nF, (b) Cov: 48nF, (c) Cov: 15nF, (d) Cov: 95nF, (e) Cov: 48nF, (f) Cov: 15nF.

iLs(t): 20A/div, vce1(t): 20V/div, vce4(t): 20V/div, time: 200ns/div.


Figure 3.22: Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t).

ILs0: 48A, Cov: 15nF, Rov: 50Ω. (a) falling step current, (b) rising step current.

iLs(t): 20A/div vCov(t): 20V/div time: 200ns.

type of analysis is beyond the scope of this research work. The main objective is to produce

step current with sufficiently small transition interval to validate the performance of Hall-

effect current sensors. But, small transition interval results in large voltage overshoot across

the IGBT. There is a trade-off between transition interval and voltage overshoot. Using the

hardware set-up a falling and a rising step current with peak 48A are produced with transition

time less than 200ns, shown in Fig. 3.21(c) and Fig. 3.21(f) respectively, which is sufficient to

emulate a step excitation for current sensors used in power electronic applications. During

the turn-off, the IGBT voltage shoots upto 85V only, which is well below the rating of

the IGBTs (600V). The experimental waveforms are shown for iLs(t) upto 48A, because

the current probe [82] is rated for 50A dc. As the IGBTs are rated for 600V, the voltage

overshoot can be allowed to go beyond 85V for higher value of the peak current ILs0, which is

again limited by the current rating of the power MOSFETs (80A). Moreover, there are three

MOSFET and IGBT legs in the hardware set-up. These legs may be operated in parallel

to achieve higher peak current ILs0 with suitable number of parallel diode Dov. In other

words, the hardware set-up can produce step currents having peak upto 240A, but presently,

it cannot be experimentally validated due to limitation of the measuring instruments in the

laboratory.

Fig. 3.23 shows the experimental waveforms of rising and falling step currents for 15nF

Cov and three different values of the peak current ILs0. As expressed in (3.8) and (3.13), the

fall time and the rise time do not vary with ILs0. The observed variations in the first and


Figure 3.23: Experimental waveforms of step current iLs(t) produced in the branch P1-P2

and IGBT voltage overshoot for different values of peak current ILs0.

The snubber capacitor Cov is fixed at 15nF for both falling and rising step current generation.

(a) - (c): falling step current iLs(t) and corresponding IG1 voltage vce1(t),

(d) - (f): rising step current iLs(t) and corresponding IG4 voltage vce4(t).

(a) ILs0: 10A, (b) ILs0: 25A, (c) ILs0: 48A, (d) ILs0: 10A, (e) ILs0: 25A, (f) ILs0: 48A.

Time scale: 200ns/div.

The fall time tf and the rise time tr are independent of ILs0.


the second peak of the voltage overshoot with ILs0 further validate the earlier discussion.

Figure 3.24: Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t).

ILs0: 48A, Cov: 15nF, Rov: 50Ω. (a) falling step current, (b) rising step current.

iLs(t): 20A/div vCov(t): 20V/div time: 200ns/div.

The capacitor voltage vCov(t) waveforms with 15nF Cov and 48A ILs0 are shown in

Fig. 3.24 for falling and rising step current. In both cases, vCov(t) is observed to rise sinu-

soidally from Vd as per the relation derived in (3.9). When the diode Dov stops conducting,

Cov starts getting discharged through the discharging resistor Rov. The ringing in vCov(t) is

observed due to lead inductance of Cov and Dov. Fig. 3.25 shows iLs(t) and vCov(t) wave-

forms during the discharge interval of mode-IV. In rising current case, iLs(t) starts getting

discharged through L0, D1 and M1. In both cases, vCov(t) gets down to the dc bus voltage

Vd within 2µs for 50Ω Rov with peak value of 88V. This discharge time is important, when

the IGBT leg will be switched periodically during sinusoidal current generation. It must be

smaller than the switching time period of the pulse width modulation strategy. If the legs

are switched at 10kHz, the discharge interval of 2µs is much smaller than 100µs. It allows

the IGBT leg with the designed over-voltage RCD snubber to be used in sinusoidal current

generation.

3.6.3 Sinusoidal Current

A method to generate sinusoidal current with adjustable magnitude and frequency is dis-

cussed in detail in section 3.4. The hybrid PWM strategy reduces the total switching loss

in the hardware. As the devices are hard-switched and the current levels are decided by

the shape of the output current, the switching loss can be further reduced by operating the


Figure 3.25: Experimental waveforms of step current iLs(t) and capacitor voltage vCov(t)

during discharge period of mode-IV. ILs0: 48A, Cov: 15nF, Rov: 50Ω.

(a) falling step current, (b) rising step current.

iLs(t): 20A/div vCov(t): 20V/div time: 10µs/div.

The capacitor Cov voltage shoots upto 88V, and gets discharged within 2µs.

circuit of Fig. 3.13 at low dc bus voltage Vd. Small Vd also facilitates the use of low voltage

DC bus electrolytic capacitors and power MOSFETs. It reduces the overall cost of the hard-

ware along with the loss in these devices. Low voltage power MOSFETs have smaller ON

resistance rds compared to that of higher voltage with the same current rating. It results

in smaller conduction loss in the MOSFET leg. The IGBT leg is used also in step current

generation, which requires relatively higher voltage rating to allow large voltage overshoot.

The voltage rating of the IGBT module [76] is 600V. The dc bus is fixed to 40V. A 100V

power MOSFET module [77] and 100V electrolytic capacitor [78] are used in the hardware

set-up. As the load is almost inductive, the dc bus capacitor bank needs to cater the reactive

power needed at the output stage. A bank of six parallel capacitors can deliver upto 150Arms

ripple current at 85C [78] ambient temperature.

The current rating of the MOSFET module is 80A, and the IGBTs are rated at 100A.

To operate these switches with safe margin the peak of the produced sinusoidal current i0(t)

is limited to 75A. If the three legs of the MOSFET module and IGBT modules are operated

in parallel, the peak current may be raised upto 200A safely. With higher current the load

inductor should be used in suitable parallel number, as they are rated at 70Arms. In the

following experiments only one leg of the MOSFET and the IGBT module are switched at

75A peak current.

A closed loop Hall-effect current sensor [79] is used as the sensor in the feedback path,


shown in Fig. 3.14. The sensor gain is fixed to 0.11V/A. Using the scheme described in the

section 3.4.2, a sinusoidal reference current i∗0(t) of 75A peak magnitude and frequency f0

from 1Hz to 1000Hz is generated in FPGA. Switching frequency fsw of the MOSFET leg is

fixed at 20kHz, while the IGBT leg is switched at the frequency f0 of the reference current

i∗0(t). At f0 = 1000Hz the ratio fswf0

becomes small. To avoid instability in this situation, the

gains Kp and Kr of the frequency adaptive PR current controller are selected based on the

guidelines reported in [65]. The system and controller parameters used in the experimental

set-up are enlisted in Table 3.2. Here, r0 is the dc winding resistance of the load inductor

L0.

Table 3.2: System and controller parameters shown in Fig. 3.14.

Vd L0 r0 Vp Hc ‖ I∗0 ‖ Kp Kr

40V 72µH 35mΩ 5V 0.11V/A 75A 0.6 2240s−1

While the fundamental frequency f0 varies from 1Hz to 1000Hz, the values of Kp and Kr

are fixed. In this frequency range the bandwidth of the closed loop system is 1.28kHz, and

phase margin is 68.5. The Bode magnitude plot of the open loop transfer function OL(s),

expressed in (3.16), is shown in Fig. 3.26 for f0 at 1Hz, 10Hz, 100Hz and 1000Hz. The PR

current controller is implemented in digital domain at sampling frequency of 40kHz.

With reference to Fig. 3.14 the error ierr(t) is defined as:

ierr(t) = i∗0(t)− i0(t) (3.17)

The experimental waveforms of output current i0(t) along with ierr(t) is shown in Fig.3.27 at

fundamental frequency of 1Hz and 1000Hz. There is little error at the fundamental frequency.

The error consists of switching ripples, and is more obvious at 1000Hz due to proximity to

the switching frequency (20kHz).

3.6.3.1 Current THD

The aim is to generate sinusoidal current at desired fundamental frequency without its

harmonic components. Due to PWM operation the switching components are unavoidable

in the output current. Total harmonics distortion (THD) of the produced sinusoidal current

represents the distortion of the current from its fundamental component. The THD of


1-50

0

50

100

150

200

Ma

gn

itud

e (

dB

)

Frequency (Hz)

0.01 0.1 10 100 1000 10000

Figure 3.26: Bode magnitude plot of the open loop transfer function at 1Hz, 10Hz, 100Hz

and 1000Hz resonant frequency of the PR current controller. In all four cases the bandwidth

is 1.28kHz, and the phase margin is 68.5.

experimentally obtained i0(t) should be low. Fig. 3.28 shows the THD in the output current

i0(t) based on the experimental data obtained in the range 1Hz to 1000Hz. In low frequency

range the THD hovers around 2%, and go upto 5.1% on the higher side.

3.6.3.2 Power consumption

To minimize the cost of heat-run test of current sensors the hardware set-up should draw

minimal active power from the mains power supply. It consumes 315W active power during

150A pk-pk sinusoidal current generation at 50Hz. The active power consumption goes upto

360W at 1kHz output current. The line-to-line voltage waveform of 415V 3-φ power supply

and the line current Ia(t) drawn by the hardware set-up are shown in Fig. 3.29. The peak

input current is 2.2A for 150A pk-pk sinusoidal current generation at 50Hz. Due to very low

power and current consumption from the mains, the current source can be used even in a

small laboratory or test premises.

3.7. Conclusion 67

Figure 3.27: Experimental waveforms of the controlled output current i0(t) and the error

ierr(t) at fundamental frequency of (a) 1Hz, (b) 10Hz, (c) 100Hz and (d) 1000Hz. The output

current i0(t) contains 20kHz switching components.

3.7 Conclusion

A power electronic converter based current source is designed to produce falling step current,

rising step current and sinusoidal current for performance validation of Hall-effect current

sensors used in power electronic applications. A novel circuit topology is proposed to generate

all these currents without any modification in the hardware set-up of the current source. The

configuration of the hardware set-up facilitates insertion and removal of the sensor under test.

The circuit resembles an H-bridge voltage source inverter consisting of a power MOSFET leg

and an IGBT leg. By modulating the switches in a particular fashion either of these three

currents can be produced in the designated section of the set-up.


10%

10 100 1000

1%

2%

3%

4%

5%

Figure 3.28: Experimentally observed THD of output current i0(t) in frequency range 1Hz -

1000Hz.

Using the proposed modulation strategy of the switches to produce step current, the rise

time and the fall time of the rising step current and the falling step current can be adjusted

by proper selection of capacitor of the RCD over-voltage clamp circuit. The peak value and

the fall/rise time of the step current can be controlled independently to produce current

with adjustable didt

. Zero reverse recovery SiC diode is used in the RCD snubber to remove

the dip near zero crossing of the step current. Experimental results related to production

of the step current with peak value 48A and fall/rise time less than 200ns are shown. The

experiments are performed for current upto 48A due to limitations of the measuring current

probe. The current source can be used to produce step current with higher peak value, again

constrained by the current rating of the switches.

For sinusoidal current generation a hybrid PWM technique is suggested to use to modu-

late the switches of the single phase VSI circuit to reduce total switching losses. A scheme is

proposed for on-line change of magnitude and frequency of the reference sinusoidal current.

The magnitude and the frequency of the sinusoidal current is changed on-line like a voltage

function generator. Due to limitation of the current rating of the MOSFETs used in the

hardware, the peak of the sinusoidal current is limited to 75A in the experiments. Exper-

imental results are shown for sinusoidal current with 75A peak and fundamental frequency

varying from 1Hz to 1000Hz. THD of the controlled output current hovers around 2% in low

3.7. Conclusion 69

Figure 3.29: Experimental waveforms of line-to-line voltage Vab(t) of 3-φ power supply and

the input line current Ia(t) drawn by the laboratory current source during 150A pk-pk

sinusoidal current generation at 50Hz. The hardware set-up draws 315W active power from

mains power supply.

frequency range, and goes upto 5.1% near 1000Hz. The hardware set-up consumes 315W

active power from mains power supply while producing sinusoidal current of peak 75A and

frequency 50Hz. Due to low power and current consumption from the mains power sup-

ply, the current source can be used even in a small laboratory or test premises to produce

continuous 75A peak sinusoidal current.

Chapter 4

Laboratory Current Sensor

4.1 Introduction

Closed loop Hall-effect current sensors used in power electronic applications require high

bandwidth and small transient errors. One of the objectives of this research work is to

develop a high performance closed loop current sensor in the laboratory, and to verify its

performance. In Chapter 2 an equivalent circuit model of the sensor was developed with the

assumptions acceptable for power electronic applications. It was shown that the compensator

had major impact on the undershoot reduction in the step response of the sensor. PI com-

pensator always results in zero steady error in dc measurement. Based on its step response

characteristics a novel procedure was devised to design the PI compensator to improve the

dynamic performance of the sensor.

In this chapter, a closed loop Hall-effect current sensor is built in the laboratory to

validate the analyses of Chapter 2. Based on the parameters of the laboratory current

sensor its model is simulated, and verified with the experimental results of its step response

obtained by using the current source developed in Chapter 3. The PI compensator is designed

for the sensor using the procedure devised earlier. Implementation issues of the compensator

using operational amplifiers are addressed. The steady state and the transient performance

of the sensor with final design is characterized with the laboratory current source at room

temperature.

4.2 Specifications

Biasing circuit of the Hall element, selection of the magnetic core, compensating coil winding

and various issues in designing the laboratory current sensor are discussed in Appendix B.

70

4.2. Specifications 71

+

-

+15V

1.2kΩ

1.2kΩ

-15V

1N4148

1N4148 +-

+

-2

13

8

LM301

+15V

2N2222A

2N2906A

1N4148

1N4148

-15VCC

SH-400

2

3

1

4

Figure 4.1: Overall schematic of the laboratory current sensor with PI compensator. The

single OpAmp based PI compensator is later replaced by two OpAmp based PI compensator

in the final design.

Fig. 4.1 shows the overall schematic of the laboratory current sensor with PI compensator.

A push-pull current booster amplifier stage is included at the output stage to overcome

the current source/sink limitation of the operational amplifier. The output voltage of the

Hall element contains differential voltage vH along with common mode voltage vCM [30].

The compensator Gc(s) should amplify only vH , and simultaneously reject vCM . A differ-

ential amplifier configuration is chosen to implement the compensator Gc(s) using LM301

operational amplifier.

Based on the design parameters discussed in Appendix B and datasheets of the Hall

element, the specifications of the laboratory current sensor are listed in Table 4.1. Kh is the

sensitivity of the Hall element SH-400 [35]. The system parameters RL and Km are used in

Chapter 2, and are calculated using (2.4) and (2.13).

Table 4.1: Specifications of the laboratory current sensor.

Kh r2 RB Lm RL Km

5.0 mV/mT 36Ω 100Ω 275mH 136Ω 42.1s−1

72 Chapter 4. Laboratory Current Sensor

4.3 Model Verification

Equivalent circuit model of closed loop Hall-effect current sensor derived in Chapter 2 is

simulated using the parameters of the sensor listed in Table 4.1. Its simulated step response

is verified with the experimental results. Three different sets of Kp and Ki, shown in Fig. 4.2,

Figure 4.2: Comparison of simulation and experimental results of step response of the lab-

oratory current sensor for three different values of the damping factor ζn and constant ωn.

The step excitation is 20A. (a)-(c): Vout(t) from the simulation model, (d)-(f): Vout(t) from

the experimental hardware.

(a), (d) ζn = 0.56, ωn = 592 rad/s; (b), (e) ζn = 1.80, ωn = 592 rad/s; (c), (f) ζn = 14.28,

ωn = 592 rad/s; vertical scale: 4A/div, time scale: 2ms/div.

are selected to validate the model and to show the variation in performance with gains of

the compensator. The damping factor ζn and the natural frequency ωn, used in the expres-

4.4. Design Example: PI Compensator 73

sion (2.24) of the step response, are calculated using (2.25) and (2.21). The results using

simulation model and corresponding experimental results obtained with the current sensor

are shown in Fig. 4.2. The results correspond to underdamped (ζn = 0.56), nearly critically

damped (ζn = 1.80) and overdamped (ζn = 14.28) sensor response. The experimental results

match closely with the simulation results, which validates the model developed in Chapter

2. Though PI compensator always ensures zero steady state error in dc measurement, the

undershoot and the settling time may become high with the trial and error approach to

design the compensator gains. In Fig. 4.2 it can be observed that increasing the value of

ζn reduces the initial undershoot, but the settling time is approximately 8 ms, which is not

desired. In the following section, the PI compensator for the laboratory current sensor will

be designed systematically using the procedure discussed in Chapter 2 to achieve minimal

undershoot with better settling time.

4.4 Design Example: PI Compensator

The approach to select the values of Kp and Ki that is outlined in section 2.3, has been

followed to design PI compensator for the laboratory current sensor with the parameters

shown in Table 4.1.

Eq. (2.25) is reproduced here:

ζn =KmKp + RL

Lm

2ωn

Keeping ζn = 1 and using the values of Km, RL and Lm from Table 4.1, the natural

frequency ωn turns out to be

ωn = 21.05Kp + 250.7 (4.1)

As discussed in section 2.3 a large value of ωn is desired for fast dynamic response, which can

be realised by choosing large Kp. The compensator gains Kp and KI are calculated using

(2.25) and (4.1) after proper selection of ωn.

The PI compensator is implemented using single operational amplifier as shown in Fig. 4.3.

The gains can be expressed in terms of the circuit elements as:

Kp =RF

RKi =

1

RCF

(4.2)

Ideally a very large value of Kp can be implemented assuming ideal behaviour of operational

amplifier, but finite gain-bandwidth product of the OpAmp reduces the bandwidth at high


gain. In turn, it limits Kp for a reasonable bandwidth of the OpAmp. With the selected Kp,

the value of ωn can be calculated using (4.1).

+

-2

13

8

LM301

+15V

+

-

2N2222A

2N2906A

1N4148

1N4148

4.7pF-15V

Figure 4.3: Circuit realization of PI compensator, Gc(s) using single operational amplifier

with current booster amplifier at the output stage. vH(s) is the output voltage of the Hall

element.

4.4.1 Realization of Gc(s) with Single Operational Amplifier

The Hall element produces output voltage at its two terminals with common mode and

differential mode components [30]. The differential component is proportional to magnetic

field, which needs to be passed through the compensator Gc(s). Realization of Gc(s) with

single operational amplifier limits the maximum gain attained along with reasonable band-

width and high common mode rejection ratio required. Kp = 392 is selected considering

these limitations. Various parameters are calculated based on this Kp and listed in Table

4.2.

Table 4.2: Parameters of PI compensator realized with single operational amplifier.

Kp Ki R RF CF

392 1714134 1.2 kΩ 470 kΩ 486 pF

ζn ωn tmin I2min

1.0 8495 117.7 µs 97.8%

A step rise of 20A in the primary coil should be measured as Vout = 1.0V across 100Ω


burden resistor. Fig. 4.4(a) and Fig. 4.4(b) show simulation and experimental result of step

response of the prototype current sensor with the designed PI compensator. Selection of large

value of Ki in this case increases ωn, which in turn reduces settling time. An undershoot

of 3.35% at 150µs is observed in the experiment, which is superior to that from Fig. 4.2.

The deviations from simulation results listed in Table 4.2 are due to tolerance in circuit

components and the assumptions of the current sensor analysis stated in section 2.3.

Channel - 1

Channel - 2

Figure 4.4: Comparison of simulation and experimental Vout(t) waveforms for large ωn with

a 20A step primary current. Ch-2 displays Ch-1 with 10x magnified vertical scale about the

steady state value

(a) response of the simulation model (b) experimental result.

Kp = 392, Ki = 1714134.

Ch-1: 500mV/div, Ch-2: 50mV/div, time scale: 200µs/div.

Experimental waveforms for 10Hz and 100Hz sinusoidal current excitations are shown in

Fig. 4.5. This indicates that a single OpAmp compensator is sufficient from a low frequency

perspective.

4.4.2 Realization of Gc(s) with Two Operational Amplifiers

Very high value of Kp and Ki can be attained, if PI compensator is realized as shown in

Fig. 4.6. External single pole compensation of the OpAmps are required to extract high gain

bandwidth product along with high common mode rejection ratio.

Expression of Gc(s) in Fig. 4.6 is given by:

Gc(s) =R2

R1

(R3

R1

+1

R1C1s

)(4.3)


Ch-2Ch-2

Ch-4 Ch-4

Figure 4.5: Experimental results: low frequency sinusoidal current measurement with the

laboratory current sensor using single OpAmp PI compensator: Kp = 392, Ki = 1714134.

Ch-2 (5A/div): reference current, Ch-4 (5A/div): current sensor output. time scale:(a)

25ms/div, (b) 2.5ms/div.

+

-2

13

8

LM301

4.7pF

+

-2

13

8

LM301

+15V

+

-

2N2222A

2N2906A

1N4148

1N4148R1

R1R1

R1

R2

R2

R3 C1

4.7pF-15V

Figure 4.6: Circuit realization of PI compensator, Gc(s) using two operational amplifiers

with class-B power amplifier at output stage.

Compensator parameters are listed in Table 4.3 with new value of Kp and respective com-

ponents value corresponding to the schematic in Fig. 4.6.

Fig. 4.7 shows the experimental waveforms obtained using two OpAmp high gain com-

pensator. The lower waveform is magnified view of the step response shown in channel-1

of the figure. Minimal undershoot is observed in this case as the calculated settling time

is ∼ 3 µs. The spike at the step jump is due to parasitic elements, which can be reduced

by improving winding strategy of the compensating coil and better packaging and layout of

circuit components. This concludes the design of the laboratory current sensor.

The small signal frequency response of the sensor is measured upto 1MHz with analog

network analyzer [81]. The observed data is plotted in Fig. 4.8. The -3dB small signal


Table 4.3: Parameters of PI compensator realized with two operational amplifiers.

Kp Ki R1 R2 R3 C1

15510 2.54x109 1.0 kΩ 470 kΩ 33 kΩ 185 pF

ζn ωn tmin I2min

1.0 326736 3.1 µs 99.94%

Figure 4.7: Experimental waveform of Vout(t), when PI compensator is realized with two

operational amplifiers for a 20A step primary current. Ch-2 displays Ch-1 with 10x magnified

vertical scale about the steady state value. Kp = 15510, Ki = 2.54x109.

Ch-1: 500mV/div, Ch-2: 50mV/div, time scale: 200µs/div.

bandwidth is found to be 265 kHz for the current sensor. The initial glitch observed around

10Hz is due to limitation of the network analyzer. Frequency range of the excitation source

in the analyzer is specified as 5Hz - 15MHz. The glitch is observed between 10Hz-20Hz,

which is close to the lower limit. The excitation signal is measured with digital storage

oscilloscope also, and found to be distorted sinusoid in the above low frequency range, which

may cause the observed glitch.


10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

-30 dB

-20 dB

-10 dB

-3 dB0 dB

10 dB

Figure 4.8: Small signal frequency response measurement of the laboratory current sensor.

||Vout(jω)i1(jω)

|| with gain normalized to one.

4.5 Performance Validation

Performance of this current sensor, having two OpAmp based PI compensator, is validated

using the power electronic converter based current source, developed in Chapter 3. The

current source can produce large signal sinusoidal and step current to characterize steady

state and transient performance of the laboratory current sensor. The current carrying

conductor used for excitation of the sensor is always positioned at the centre of the aperture

of the sensor. The effect of position of the primary conductor in the aperture is shown later

in this section. All experiments are performed at the room temperature.

4.5.1 Steady State

The steady state performance validation involves measurement of large signal frequency

response, accuracy and linearity of the sensor. The large signal response shows the capability

the sensor to measure rated current at grid frequency and its harmonics, with satisfactory

outcome. Accuracy and linearity of a current sensor are critical parameters in selection of

current sensors for high precision control system like speed/position control of servo motor

drive.

4.5. Performance Validation 79

Large signal frequency response

The large signal frequency response of the laboratory current sensor is measured with 75A

peak sinusoidal current and fundamental frequency from 1Hz to 1000Hz. Magnitude and

phase of the sensor’s response match closely with the excitation signal. Output of the sensor

with 75 A peak sinusoidal excitation at 100Hz is shown in Fig. 4.9.

Figure 4.9: Output of the laboratory current sensor with 75A peak sinusoidal excitation at

100Hz. Vertical scale: 37A/div, time: 5ms/div.

Accuracy

The accuracy is verified at 75A dc excitation, and the error is found to be less than 1%. As

reported in [22], typical accuracy error of a closed loop Hall-effect current sensor is better

than 1% at ambient temperature of 25C.

Linearity

The linearity of the sensor is verified in the range ±75A dc with incremental step of 5A.

The output is observed to be linear, and the linearity error is so small that it is below the

measurement range of the instruments available in the laboratory.

4.5.2 Step Response

Transient performance of the laboratory current sensor is verified with the rising step current

produced by the laboratory current source. Fig. 4.10(a) shows the step response measurement


of the laboratory current sensor with 40A step excitation. The reference step is measured

by the current probe having 100MHz bandwidth [82]. Output of the sensor reaches 90% of

its final value in 2µs. As per the definition, shown in Fig. 1.10, the response time of the

laboratory current sensor turns out to be 2µs. The settling time is observed to be 5µs.

Figure 4.10: Step response measurement of the laboratory current sensor with 40A step

excitation: (a) with energized Hall element (b) without energized Hall element.

Reference step current is produced by the laboratory hardware set-up.

Vertical scale: 10A/div, time: 1µs/div.

The response time in the step response is mainly governed by the current transformer

action of the sensor. Based on the expression of the step response given by (2.27) derived in

the section 2.3 the output of the sensor is expected to change instantaneously along with the

step excitation, but it takes some finite time to respond to the excitation. The expression

of the step response in section 2.3 is derived ignoring the high frequency behaviour of the

sensor, which is mainly decided by its current transformer structure. The leakage inductance,

mutual coupling with the primary conductor, parasitic winding capacitance, wiring layout at

the output stage and other factors delay the change in the secondary current i2, and hence

the output of the sensor. The Hall element plays no significant role in this step transition

interval. It can be experimentally verified by switching OFF the power supply of the biasing

circuit of the Hall element and its associated processing electronics. The output in absence of

energized Hall element is shown in Fig. 4.10(b). It can be seen that the response is identical

irrespective of the presence of the energized Hall element. Though the Hall element plays

no role in the aforementioned step transition, it has essential responsibility to maintain the

steady state dc value after the transition is completed. In absence of the energized Hall

element the output comes down to zero, as the current transformer cannot respond to a dc

4.5. Performance Validation 81

excitation. The response is shown in Fig. 4.11 for a longer duration, which is a typical step

response of a current transformer.

Figure 4.11: Step response of the laboratory current sensor after de-energizing the Hall

element circuit, captured for the duration of 20ms. The step excitation is 40A.

Vertical scale: 10A/div, time: 1µs/div.

In addition to maintain the steady state dc value the Hall element along with the compen-

sator Gc(s) also reduces the undershoot just after the transition edge in the step response,

shown in Fig. 2.5. This undershoot is significantly visible in the experimental waveforms

shown in Fig. 4.2. In section 4.4 it is shown that the careful design of Gc(s) reduces the

undershoot to 0.06%.

It may appear here that the Hall element and the compensator are solely responsible for

the reduction in the undershoot observed after the step transition edge. But, the current

transformer also partly plays role in this undershoot, as the magnetizing inductance Lm is

involved in the expression of this undershoot, shown in (2.29). Thus, the step response of a

closed loop Hall-effect current sensor is mainly divided into three consecutive time intervals:

• the step transition interval, the CT governs the transition characteristics,

• the interval, during which the undershoot occurs. Here both CT and the Hall-effect actions

play role, and

• the steady state interval, where the Hall element along with the compensator controls the

dc measurement error.

In order to design a high bandwidth closed loop current sensor with good accuracy, one

needs to design both the compensator and the CT parameters carefully. In this research work,


the main focus is to design the compensator, and to observe its effect on the performance

of the sensor. Its bandwidth and response time can be improved further by optimizing the

design of its current transformer parameters, namely air gap size, leakage and magnetizing

inductance and winding capacitance.

4.5.3 Performance Comparison with State-of-the-art Current Sen-

sor used in Power Electronics

The step response of the laboratory current sensor is compared with the state-of-the-art

current sensor [79] used in power electronic applications. The experimental results are shown

in Fig. 4.12. Response time and settling time of the laboratory current sensor is much less

than the state-of-the-art sensor.

Figure 4.12: Comparison of step response measurement with 87A step current generated

using the laboratory current source (a) response of the laboratory current sensor (b) response

of commercial current sensor [79].

Vertical scale : (a) 20A/div (b) 18A/div; Time scale: 5µs/div.

4.5.4 Positional Error

Hall-effect current sensor manufacturers always specify that the primary conductor carrying

the current to be sensed must be at the centre of the aperture of the magnetic core for the

best dynamic performance. This holds true for any gapped core current transformer also.

The magnetic flux created by the primary conductor interferes with the core flux through

the air gap. If the conductor is at the centre of a toroidal core, it results in minimum leakage

inductance. Large air gap leads to unwanted sensitivity to the position of the conductor.

4.6. Conclusion 83

Fringing of the field in the air gap also reduces the natural shielding of the toroid from

unwanted external field [9], [26], [27]. Fig. 4.13 shows the step response of the laboratory

current sensor for five positions (C, N, W, S, E) of the primary conductor with respect to the

air gap. Direction of the excitation current is out of the plane of the paper. The minimum

disturbance is observed, when the conductor is at the centre. Relatively more distortion is

observed, when the conductor is at the nearest and the furthest position from the air gap.

4.6 Conclusion

A prototype current sensor is built in laboratory to verify the analysis of Chapter 2. The

experimental waveforms match closely with the results obtained using the simulation model.

A PI compensator for the laboratory current sensor is designed using the procedure devised

in Chapter 2. The PI compensator is implemented using operational amplifier, but the finite

gain-bandwidth product of the OpAmp puts limitation on Kp, and in turn on ωn. This

is overcome by using two cascaded operational amplifiers with very high gain-bandwidth

product. The final design of PI compensator reduces the undershoot in the step response

to 0.06%. Steady state and transient performance of the laboratory current sensor with

two OpAmp based PI compensator are validated at the room temperature with the current

source developed in Chapter 3. The measured error in the accuracy is less than 1%. The

response time of the sensor is observed to be 2µs. Response time of the laboratory sensor is

found to be superior to a state-of-the-art current sensor used in power electronics. Distortion

due to position of the primary conductor with respect to the air gap of the toroidal core is

demonstrated. Small signal bandwidth of the sensor is measured with network analyzer, and

observed to be 265 kHz bandwidth, which is comparable to commercially available current

sensors.


N C S

E

W

Figure 4.13: Effect of position of the primary conductor with respect to the air gap on the

step resonse of the laboratory current sensor: (a) five different positions in the aperture of

the toroidal core; output of the sensor at the position (b) C (c) S (d) W (e) N and (f) E.

The step excitation is 40A, and the direction of the current is out of plane of the paper.

The inner diameter of the toroid is 30mm, and the conductor diameter is 3mm. Minimum

disturbance is observed at the centre.

Vertical scale : 20A/div ; Time scale: 1µs/div.

Chapter 5

Conclusion

An equivalent circuit model of closed loop Hall-effect current sensors is derived based on the

assumptions relevant from perspective of power electronic applications. The model is used

to derive analytical expression of step response of the sensor. The PI compensator always

results in zero steady state error in dc measurement. A tuning procedure is proposed to

determine the gains of PI compensator based on analytical expression of step response of

the sensor.

A power electronic converter is designed and fabricated in laboratory to validate the per-

formance of Hall-effect current sensors. A novel hardware topology is proposed, using which

the converter can produce step current of controlled magnitude upto 100A with controlled

rate of change to validate the transient performance of the sensors. The step transition time

is adjusted by proper selection of capacitor of the RCD snubber. The step transition time is

less than 200ns. Zero reverse recovery SiC diode is used in the RCD snubber to remove the

dip near zero crossing of the step current. The hardware set-up can also generate sinusoidal

current of controlled magnitude upto 75A peak and controlled frequency from 1Hz to 1000Hz

without any modification in the hardware configuration. The magnitude and the frequency

of the produced sinusoidal current can be varied on-line like a typical voltage function gen-

erator. Hybrid PWM technique is used to reduce losses in the converter while producing

sinusoidal current, which is advantageous during heat-run test of the sensors. The hardware

set-up consumes 315W active power from mains while producing sinusoidal current of peak

75A and frequency 50Hz. THD of the controlled sinusoidal current hovers around 2% in low

frequency range, and goes upto 5.1% near 1000Hz.

A prototype current sensor is built in laboratory to verify the proposed methodology for

compensator design of closed loop Hall-effect current sensors. The final design resulted in a

85

86 Chapter 5. Conclusion

current sensor with 265 kHz small signal bandwidth, which is comparable to commercially

available current sensors. Steady state and transient performance of the laboratory current

sensor are verified with the hardware set-up. Its response time is 2µs. The dynamic perfor-

mance of the laboratory current sensor is observed to be superior to state-of-the-art current

sensors.

5.1 Contributions of the work

Following are the main contributions of this research work:

1. A methodology is proposed for compensator design of closed loop Hall-effect current

sensors keeping step response characteristics of peak undershoot (and time of under-

shoot) and settling time as the design attributes.

2. A Power electronic converter is designed and fabricated in the laboratory for charac-

terisation of Hall-effect current sensors.

• A novel hardware topology is proposed to produce step current and sinusoidal

current without any modification in the hardware configuration.

• A novel switching scheme is proposed to produce falling and rising step current

of controlled peak value and rate of change.

• A scheme is suggested for on-line change in magnitude and frequency of the sinu-

soidal current with controlled magnitude and frequency.

• The hardware set-up consumes 315W active power from mains power supply while

producing continuous sinusoidal current at 75A peak and 50Hz frequency for heat-

run test.

5.2 Scope of Future Work

As discussed in Chapter 1, the bandwidth of closed loop Hall-effect current sensors can

be improved by careful design of its current transformer (CT) structure. High frequency

model of the sensor can be developed using high frequency behaviour of the CT [18]. This

model can be used to design the air gap length, compensating coil winding strategy, parasitic

capacitance and mutual coupling of the primary conductor with the magnetic core to get

5.2. Scope of Future Work 87

high bandwidth of the sensor. Mutual inductance of the gapped core current transformer

with respect to position of the primary conductor can be used to predict the change in

dynamic behaviour of the sensor [26], [27]. Earlier works on gapped toroidal transformers in

[19], [20] may be useful in analyzing the high frequency behaviour of the sensor.

Experimentally obtained minimum value of the step transition time of the step current

produced by the power electronic converter based current source is 170ns. It can be fur-

ther reduced significantly by using high speed wide band-gap power semiconductor devices,

commercially available these days. It will also reduce the overall losses in the system during

sinusoidal current generation. The set-up can also produce non-sinusoidal current wave-

form by combining fundamental and few of its harmonics, which can be used to characterize

Hall-effect current sensors under harmonic distortions [57].

Appendix A

Current Sensing Techniques

Similar to other physical quantities an electric current can be sensed by recording its after-

effect. It affects the conductor through which it flows as well as the conductors/semiconductors

in its vicinity. Current sensing techniques can be categorised based on the underlying phys-

ical principle, the device being used, polarity of the sensed current and nature of the output

signal. Electro-thermal, electromagnetic, Hall-effect, magneto-optic are few effects which are

generally used to measure current. Depending upon the nature of the sensed current the

device may be called unipolar/bipolar DC sensor, AC sensor or DC/AC sensor. If the output

circuit is isolated from the current carrying conductor, the device is called contactless sensor.

The output signal of most of the sensors are available externally to be used as voltage signal,

while in some sensors the output is used only for measurement purpose. The latter technique

is used in moving coil ammeter and current probes for oscilloscopes.

Based on the underlying fundamental physical principle, the current sensing techniques

can be basically classified into four categories [8]:

1. Ohm’s law of resistance

2. Faraday’s law of induction

3. Magnetic field sensors

4. Magneto-optic effect

A.1 Ohm’s Law of Resistance

The Ohm’s Law of resistance states that the voltage drop across a resistor is proportional

to the flowing current. This simple relation is used to sense both direct and alternating

88

A.2. Faraday’s Law of Induction 89

current with much lower cost compared to other techniques. The resistive voltage drop

can be observed across a resistor, a metallic segment (copper trace) or a semiconductor

(MOSFET).

A.1.1 Shunt Resistors

Shunts are differentiated from resistors by the fact that they are exclusively designed to mea-

sure current [11]. In most of integrated electronic devices thick film structure are used, which

can be integrated into surface mount devices (SMDs). Owing to low cost, high reliability

and compact size SMD shunt resistors are used in power converters, industrial applications,

mobile devices and consumer electronics. For large currents the shunt resistors become bulky

and dissipate considerable amount of heat, which makes packaging of the system difficult [8].

High performance coaxial shunts can be used to measure transient current pulses with high

magnitude. High frequency behaviour of the shunt resistor is critical in such applications.

If precision is not a critical consideration, the current can be measured through the voltage

drop across a current carrying copper trace [9].

A.1.2 Current Sensing MOSFETs

A MOSFET behaves like a resistor, when it is turned ON. Its internal drain-source resistance

rDS eliminates the need of external sense resistor. By measuring its drain-source voltage the

sensed current can be determined [10]. This method is cost-effective in low voltage high

current power converters. The precision of this method depends upon the accuracy of rDS.

These days there are MOSFETs, called senseFETs, custom-made for current sensing [21].

Instead of using rDS they employ current mirror to mimic the sensed current. This technique

is more accurate and efficient compared to the one using rDS.

A.2 Faraday’s Law of Induction

An electric current creates magnetic field around the current carrying conductor. Magnetic

flux created by this field can be tapped in an external conducting coil. The induced emf in

this coil will be proportional to the negative of the rate of change of magnetic flux through

it, which gives direct measure of the current to be sensed. Using this physical principle

only alternating current can be sensed, as it requires dynamic magnetic field to produce

90 Appendix A. Current Sensing Techniques

the voltage in the external coil. These sensors provide inherent galvanic isolation between

the circuit carrying the sensed current and the output signal. Current transformers (CTs),

Rogowski coils and coaxial current transformers make use of Faraday’s Law of induction for

current sensing.

A.2.1 Current Transformers

Due to simple operating principle and rugged structure current transformers are the most

widely used current sensors in industrial applications to measure ac current at grid frequency

as well as transient current. The secondary winding of a CT is loaded with a sense resistor.

The voltage drop across the resistor is directly proportional to the sensed current [18]. AC

current clamps are usually based on current transformer principles. High frequency behaviour

of CT becomes important when used in transient current measurement [17]. The rise time

of carefully designed CT can be made as low as few ns. Coaxial CT is a well known solution

for transient current sensing in large current power semiconductor devices [7].

A.2.2 Rogowski Coil

Performance of a CT is often limited by the characteristics of its core material (hysteresis,

nonlinearity, losses, saturation and remanent magnetization) [10]. The Rogowski coil is

a simple, inexpensive and accurate solution for current measurement. Its construction is

similar to a CT, but it uses air core or iron-less bobbins with hundreds or thousands of

secondary turns. The output voltage is proportional to the time derivative of the sensed

current. An integrator with infinite input impedance results in exact measure of the current

[8]. As the core never saturates, the output remains linear for large currents. These coils are

used to measure transient or pulsed current [15], [16].

A.3 Magnetic Field Sensors

The sensors, based on resistive principle, can be used to measure both dc and ac currents,

as the output is directly proportional to the sensed current. But they don’t provide galvanic

isolation. The contactless sensors, CTs and Rogowski coils, need time-changing magnetic

field, and cannot be used to measure dc. Magnetic field sensors respond to both static and

dynamic magnetic fields, and can be used to sense both dc and ac current with galvanic

A.3. Magnetic Field Sensors 91

isolation. Based on the type of magnetic sensors involved, these current sensors can be

further categorised into mainly three categories:

A.3.1 Hall-Effect

Hall-effect magnetic sensor produces output voltage in response to the magnetic field over

its designated surface. The output is proportional to the perpendicular component of the

magnetic field and the biasing current. It is a bipolar device, and can be used to sense

both static and alternating magnetic field [30]. This fact is utilized to build contactless

current sensors capable of measuring both dc and ac currents. It consists of a magnetic core

with an air gap. The Hall sensor is inserted in the gap. The current to be sensed is passed

through the aperture of the core, and produces magnetic field in the air gap. The Hall sensor

situated in the gap produces output voltage proportional to the field. This output voltage is

further amplified to bring it to measurable range. These sensors are commercially available

to measure current upto 10000A. Based on the configuration, the sensor may be called open

loop or closed loop Hall-effect current sensor. These sensors are discussed in [22], [23] as well

as in Chapter 1. Linear Hall ICs are used in PCB to sense track current upto ±100A with

galvanic isolation [24].

A.3.2 Fluxgate Principle

In fluxgate sensors the magnetic core is periodically saturated in both polarities by an ac

excitation coil. It causes the core permeability, and hence, its inductance to change. The

current to be measured produces flux in the core, which along with the flux produced by

the ac excitation coil changes the saturation level and inductance of the core. The variation

in the inductance is detected by processing electronics, which gives measure of the current.

Working principle of fluxgate magnetic sensors and current sensors is discussed in detail in

[30], [22]. These current sensors have excellent accuracy, much higher sensitivity and very

high resolution compared to Hall-effect sensors. But, the design of fluxgate current sensors

is relatively complex, and thus more expensive to produce [22].

A.3.3 Magnetoresistive Effect

Magnetoresistive effect is the change in electrical resistivity of a material, when an exter-

nal magnetic field is applied to it. The magnetoresistive (MR) sensors are based on this

92 Appendix A. Current Sensing Techniques

effect. MR sensors are also called magnetically controlled resistors. Normally the structure

of MR based current sensors consists of four MR sensors, placed in a Wheatstone bridge

configuration [8]. In the presence of magnetic field the values of the resistor changes, causing

imbalance in the bridge and producing an output voltage proportional to the magnetic field.

A known relation between the current to be measured and the produced output voltage is

used to determine the current. These are contactless sensors with high reliability due to

rugged construction. Anisotropic Magneto Resistance (AMR) and Giant Magneto Resis-

tance (GMR) are two popular MR effects used in MR current sensors. A typical application

is galvanically isolated current sensing in a PWM regulated brushless motors [9].

A.4 Magneto-Optic Effect

Magneto-optics assists measurements of magnetic fields by means of their interaction with

the light. If a linearly polarized light is passed through a medium placed in the magnetic

field and the direction of the field is parallel to that of light propagation, the plane of po-

larization of light rotates. This phenomenon is called Magneto-optic effect or Faraday effect

[30]. Magneto-optical current sensors have several advantages, which are useful in power dis-

tribution systems. They are ideally suited for high voltage high current applications due to

inherent electrical isolation and immunity to high electromagnetic interference levels [8], [9].

They are mostly employed in measuring large dc current (∼100kA) in HVDC transmission

systems.

A.5 Other Methods

Superconducting current sensors (SQUID), magnetically sensitive CMOS split-drain transis-

tors, magnetostrictive sensors and Lorentz force sensors are few examples of other current

sensing techniques used in practice but not widely used in industrial applications. More de-

tails about current sensors can be found in [8]-[14]. A comparative evaluation of performance

of these sensors is tabulated in [8], [10] and [11].

Appendix B

Design of the Laboratory Current

Sensor

B.1 Introduction

A closed loop Hall-effect current sensor is built in the laboratory for experimental verification

of the analysis of Chapter 2. Fig. B.1 shows the photograph of the current sensor . It is

designed to measure 300A rms current. It requires a dc power supply of +15V, 0V and -15V.

The output voltage is measured across the burden resistor. Various aspects in designing this

current sensor are discussed in the following sections.

Figure B.1: Photograph of 300A closed loop Hall-effect current sensor built in the laboratory.

93

94 Appendix B. Design of the Laboratory Current Sensor

+

-

+-

Figure B.2: (a) Working principle of a Hall element, (b) photograph of InSb Hall element

chip [30].

B.2 Hall Element

A Hall element senses the perpendicular component of the magnetic field B⊥ incident over

its designated surface, and produces voltage at the two output terminals, as depicted in

Fig. B.2(a), having differential component vH along with common mode component vCM .

The magnitude of differential voltage vH is proportional to the incident magnetic field, and

its polarity depends on the direction of B⊥. The common mode vCM is independent of the

magnetic field, and depends upon biasing condition. Its value may go upto ≈ 1V, while the

magnitude of vH is typically in the order of mV [30]. The working principle of Hall element

is briefly explained in Chapter 1. More details about Hall-effect semiconductor devices are

given in [29], [30], [33].

A Hall element can be biased either with constant current or constant voltage. GaAs

based Hall elements are used in open loop Hall-effect current sensors, while InSb thin film Hall

elements are suitable for closed loop current sensors. Output characteristic of a commercial

high sensitivity InSb thin film Hall element [35] are shown in Fig. B.3(a). Its output voltage

vH does not vary significantly with ambient temperature, when biased with constant voltage.

The offset voltage Vos is the value of vH produced in absence of any magnetic field over

the Hall element. Its variation with ambient temperature is shown in Fig. B.3(b) for InSb

Hall element. The constant voltage drive results in almost flat characteristic, which helps

the designer to implement a simple offset-nullification circuit for a wide ambient temperature

B.2. Hall Element 95

0

250

500

750

1000

-50 0 50 100 150

Icgconst

Vcgconst

AmbientgTemperatureg(°C)

VHg-gT

Out

putgV

olta

gegV

Hg(

mV

)

Icg=g5mA

Vcg=g1V

Bg=g50mT

0-50 50 100 150

AmbientgTemperatureg(°C)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Offs

etgV

olta

gegV

osg(

mV

)

Icgconst

Vcgconst

Icg=g5mA

Vcg=g1V

Bg=g0mT

Vosg-gT

Figure B.3: Output characteristics of SH-400 Hall sensor [35] with constant current drive

and constant voltage drive. Variation in (a) output voltage VH and (b) offset voltage Vos

with respect to ambient temperature. The constant voltage drive results in less variation in

VH and Vos compared to constant current drive.

range.

B.2.1 Biasing Circuit

A Hall element offers an input resistance Rin across its biasing terminals as shown in

Fig. B.4(a). The variation in Rin is shown in Fig. B.4(b) for SH-400 [35], and must be

accounted while designing the biasing circuit.

The constant voltage biasing circuit is shown in Fig. B.5(a) with relevant details. Fig. B.5(b)

shows the simulation results using LTspice IV [41] software. The biasing voltage Vc is almost

constant at 1.3V with R = 1.2kΩ for the given variation in Rin with ambient temperature.

B.2.2 Temperature Limitation

The bias voltage Vc puts limitation on the operating temperature of the Hall element, and

in turn on the current sensor. Input voltage derating curve of the Hall element SH-400 is

depicted in Fig. B.6. The biasing point of the Hall element must lie within the envelop for

safe operation. The constant voltage driving circuit, shown in Fig. B.5 (a), produces Vc =

1.3V, which limits the maximum operating temperature to 85C.


0-50 50 100 150

200

400

600

800

1000

1200

1400

0

Inpu

tSRes

ista

nceS

Rin

S(Ω

)

AmbientSTemperatureS(°C)

RinS-ST

BiasingSSource

Figure B.4: Input characteristics of SH-400 Hall sensor [35] (a) input resistance of a Hall

element, (b) variation in input resistance Rin with ambient temperature.

+15V

-15V

1N4148

1N4148

+

250Ω 300Ω 350Ω 400Ω 450Ω 500Ω 550Ω0V

0.5V

1.0V

1.5V

2.0VR = 1.2kΩ

R = 2.2kΩ

Figure B.5: Constant voltage drive circuit for SH-400 Hall element (a) the circuit used in the

laboratory current sensor (b) effect of variation in input resistance Rin on the bias voltage

Vc. The resistor R is chosen as 1.2kΩ to maintain Vc around 1.30V.

B.3 Magnetic Core

In closed loop current sensors the magnetic core is operated at nearly zero steady state flux.

A Nickel-Iron alloy has very small hysteresis loop, and maintains the linearity around zero

magnetic field excitation. The core geometry is given in Table B.1. It will be shown later

that the magnetizing inductance Lm of the toroidal core should be small to keep the insertion

impedance low. The core is cut just enough to accommodate the Hall element, as big air

gap reduces Lm.

B.4. Compensating Coil 97

-40 -20 0 20 40 60 80 100 1200

1.0

2.0

Ambient Temperature (°C)

Inpu

t Vol

tage

Vc

(V) Input Resistance

Rin : 240 to 550Ω

Input Voltage Derating Curve

Figure B.6: Input voltage derating curve of SH-400 [35] for constant voltage drive. The

input voltage Vc must stay within the curve envelop.

B.4 Compensating Coil

Table B.1: Magnetic core details

Material Tapewound Nickel Iron Alloy

Initial permeability @50gauss, 50Hz 80000

Saturation flux density @25C 600mT

Magnetic path length le 103.70mm

Cross sectional area Ac 13.5mm2

Air-gap length lg 1.10mm

Compensating coil Polyurethane Cu φ 0.187mm, single wire

The compensating coil is made of polyurethane copper wire of diameter 0.187mm, and

having total 2000 turns. The nominal current rating of the laboratory current sensor is 300A

rms. The wire is suitably chosen to carry the nominal current 300A2000

= 0.15A flowing through

it in steady state. The current flowing through this coil produces flux in the core in counter

direction to the flux sensed by the Hall element. As the Hall element is a bipolar device, the

sense of winding must be such that it counteracts the flux produced by the primary current.


Total winding resistance r2 of this coil is measured to be 36Ω.

B.5 Magnetizing Inductance Calculation

The inductance referred to the compensating coil side can be written as

Lm =n22µ0Ac

lg(B.1)

36.00

30.00

1.10

3.00

5.00

2.7

2.35

0.95

8.0

Figure B.7: Dimensions of (a) the toroidal core and (b) the Hall element SH-400 [35]. All

dimensions are in mm.

With 2000 turns on the secondary side and using the data given in Table B.1, Lm turns

out to be 61.7mH. Experimental value of Lm is observed to be 275mH. This difference in the

values cannot be accounted by the fringing effect alone. Various dimensions of the toroidal

core and the Hall elements are depicted in Fig. B.7. The Hall element is inserted in the air

gap as shown in Fig. B.8(a). It resides in the air gap of the magnetic core. Its internal cross

sectional view is shown in Fig. B.8(b). To calculate inductance the gap is assumed to be

filled with air only, while the Hall element is mainly composed of ferrite substrate. It causes

the resultant reluctance of the air gap to go down, and in turn increases Lm.

B.5. Magnetizing Inductance Calculation 99

A1

A2

SH-4002000 turns

Ferrite substrate

Ferrite chip

Electrodes

InSb thin film (d = 0.8μm)

Insulating layer

Insulating layer

Au wire

Figure B.8: (a) The Hall element SH-400 inserted in the air gap, (b) cross section of a high

sensitive InSb Hall element [34]. The ferrite substrate of SH-400 reduces the effective air gap

length.

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