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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.
4 Chapter 1. Introduction
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.
6 Chapter 1. Introduction
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
8 Chapter 1. Introduction
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
1.2. Hall-Effect Current Sensors 9
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
.
10 Chapter 1. Introduction
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
1.2. Hall-Effect Current Sensors 11
+
-
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-
12 Chapter 1. Introduction
+
-
+
-
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
1.2. Hall-Effect Current Sensors 13
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
14 Chapter 1. Introduction
+
-
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
16 Chapter 1. Introduction
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
18 Chapter 1. Introduction
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.
20 Chapter 1. Introduction
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
24 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors
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
26 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors
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)
28 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors
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
2.3. Compensator Design 29
(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
30 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors
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
2.3. Compensator Design 31
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)||.
32 Chapter 2. Compensator Design for Closed Loop Hall-Effect Current Sensors
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
36 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
+
+
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
38 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
40 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
3.3. Step Current Generation 41
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.
42 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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)
3.3. Step Current Generation 43
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)
44 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
3.3. Step Current Generation 45
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
46 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
(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).
48 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
50 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
52 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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.
3.5. H-bridge Hardware Design 53
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
54 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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.
3.5. H-bridge Hardware Design 55
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].
56 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
58 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
3.6. Experimental Results 59
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
60 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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.
3.6. Experimental Results 61
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
62 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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.
3.6. Experimental Results 63
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
64 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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,
3.6. Experimental Results 65
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
66 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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.
68 Chapter 3. Power Electronic Converter for Characterization of Hall-Effect Current Sensors
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
74 Chapter 4. Laboratory Current Sensor
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
4.4. Design Example: PI Compensator 75
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)
76 Chapter 4. Laboratory Current Sensor
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
4.4. Design Example: PI Compensator 77
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.
78 Chapter 4. Laboratory Current Sensor
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
80 Chapter 4. Laboratory Current Sensor
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,
82 Chapter 4. Laboratory Current Sensor
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.
84 Chapter 4. Laboratory Current Sensor
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.
96 Appendix B. Design of the Laboratory Current Sensor
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.
98 Appendix B. Design of the Laboratory Current Sensor
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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