A Compact Planar Rogowski Coil Current Sensor
for Active Current Balancing of Parallel-Connected
Silicon Carbide MOSFETs
Yang Xue, Junjie Lu, Zhiqiang Wang, Leon M. Tolbert, Benjamin J. Blalock, Fred Wang
Center for Ultra-Wide-Area Resilient Electric Energy Transmission Networks (CURENT)
Department of Electrical Engineering and Computer Science
The University of Tennessee
Knoxville, TN 37996-2250, USA
yxue5@vols.utk.edu
Abstract- In this paper, a compact planar current sensor is
developed to be used in active current balancing applications for
parallel-connected Silicon Carbide (SiC) MOSFETs. The designed
Rogowski coil allows non-intrusive current measurement with low
profile, compact size, and high bandwidth. The sensor circuit
design extends both lower and higher cutoff frequency of the
sensor, and allows a continuous measurement of current
waveforms that contain a DC component. The simulated
bandwidth of the proposed current sensor is 2.66 Hz-100 MHz.
The measured switching waveforms in the experiment are
comparable to a 120 MHz commercial current probe.
I. INTRODUCTION
The relatively small die size and current capacity of wideband-gap (WBG) devices such as SiC MOSFETs make parallel
connection necessary in high power applications. However, the
mismatch of device parameters and external circuits can induce
current unbalance in the paralleled devices, and cause uneven
distribution of loss and temperature, affecting the performance
and reliability of the system [1]. The multiple root causes and
unpredictable nature of current unbalance call for automated
methods of current balancing. An active current balancing
(ACB) scheme has been proposed in [2-3]. It is able to sense
the unbalanced current and eliminate it in closed loop by
varying the gate delay to each device. However, this scheme is
limited to two devices in parallel, mainly due to the limitation
of current sensing, which only senses the current difference in
two paralleled devices. To overcome this limitation, we
propose to sense the current of each individual device, and
based on the sensed currents, a controller can adjust the gate
drive signals to eliminate the unbalance. The major challenge
of this new scheme is the design of the current sensor, which
needs to be compact and low-cost to have one for each power
switch. In addition, to measure the dynamic unbalance during
switching transitions accurately, a high bandwidth is required.
Among the available low-cost current sensing techniques, a
current transformer has a bulky core and is susceptible to
saturation; resistive shunt adds power loss and lacks galvanic
isolation; and Hall-effect sensor's bandwidth is not wide
enough for fast current transitions. A Rogowski coil is an air-
978-1-4799-5776-7/14/$31.00 ©2014 IEEE
core coil wrapped around the current carrying conductor. It
provides non-intrusive current measurement with good
bandwidth and linearity. It has been used in applications such
as motor control [4], power system relaying [5], and short
circuit protection [6]. PCB Rogowski coil has a low profile
design. Its bandwidth is usually higher than wire-wound coils
due to lower parasitic capacitance, and it has good accuracy
and repeatability due to the tight tolerance of PCB fabrication.
Many PCB Rogowski coils are designed for a single device
with screw terminal, and the current conductor goes through a
hole on the PCB, making it difficult to achieve the small size
required [7-9]. A novel Rogowski coil design was presented in
[10], in which the coil is embedded between two bus
conductors carrying opposite currents. However, the bandwidth
of this sensor is limited by the integrator design, and it lacks
DC sensing capability.
In this work, we propose a PCB Rogowski coil current
sensor featuring compact and planar structure, and bandwidth
extended toward both high and low frequency ends. Compared
to previous works, it achieves small size, wide bandwidth and
the ability to sense current waveforms that contain a DC
component, suitable for current balancing application of fastswitching WBG devices, as well as any other applications
where compact and fast current measurement is required.
II. BANDWIDTH REQUIREMENT OF CURRENT SENSING
IN ACB APPLICATIONS
In this work, the current sensor needs to sense the dynamic
unbalance current at the switching transitions. We mainly
focus on the current unbalance at turn-on transition, as turn-on
gate drive edge is usually slower than turn-off, making the
current unbalance due to threshold mismatch more significant.
In addition, the current overshoot during turn-on due to
discharging of drain capacitance increases the absolute
magnitude of current unbalance [2]. Being a majority-carrier
device, the SiC MOSFET turns on very fast, and the current
rise time tr is on the order of 10 ns, placing stringent bandwidth
requirement on the current sensor. However, it can be shown
that this requirement can be relaxed if we are only concerned
with the current unbalance (differential currents) in paralleled
4685
Power
Switch
2IL
IL+ΔI
Ld
RON
Ld
Ld
Ron
Ron
Current
Conductors
Via
IL−ΔI
IL
Coil
2ΔI
(a)
(b)
(a)
Relative Accuracy
Fig. 1. Equivalent circuits of power switches after turn-on (a) single device,
(b) two devices in parallel.
1.00
0.90
0.80
(b)
0.70
0
20
40
60
80
Fig. 3. PCB Rogowski coil design in (a) side view, (b) top view.
100
Sensor Bandwidth (MHz)
Relative Accuracy
(a)
Rogowski coil model
1.00
Lc
0.90
0.80
I
McdI/dt
Rc
Cc
Rd Vcoil
0.70
0
20
40
60
80
100
Sensor Bandwidth (MHz)
Fig. 4. Simplified circuit model of the coil.
(b)
Fig. 2. Relative sensing accuracy versus sensor bandwidth in (a) single device,
(b) two paralleled devices.
devices. The equivalent circuits of power switches just after
being fully turned on are shown in Fig. 1. In the single device
case (Fig. 1(a)), the overshoot current in the device has to
decay very fast because the load inductor acts as a constant
current and the capacitance at the drain is small. However, in
the paralleled case (Fig. 1(b)), the differential current 2ΔI
caused by dynamic unbalance will circulate in the loop formed
by the paralleled devices, and the drain inductances of the
devices prevent it from changing abruptly. The decay time
constant of ΔI is given by τ=Ld/Ron, where Ld is the package
and PCB inductance at drain, and Ron is the on-state resistance
of the power switch. The typical value of τ is on the order of
100 ns, about an order of magnitude larger than tr. This large
decay time constant slows down the change rate of ΔI and
relaxes the bandwidth requirement of current sensing. To
verify that, simulations were performed to measure the drain
current in the single device and the differential current in
paralleled devices, respectively. The relative sensing
accuracies as a function of current sensor bandwidth are
plotted in Fig. 2. It can be seen that to achieve a 95% accuracy
for a single device current measurement, 35 MHz sensing
bandwidth is required. However, only 17 MHz is required to
achieve the same accuracy in the measurement of current
unbalance in paralleled devices. It should be noted that
although two-device case is analyzed here, a similar conclusion
can be drawn for multiple devices in parallel.
III. DESIGN OF THE ROGOWSKI COIL
The Rogowski coil senses the rate of current change in a
nearby conductor through mutual inductance. The design of the
Rogowski coil in this work is based on [10], several
improvements have been adopted to further reduce its size and
facilitate a non-intrusive current measurement. The coil is
realized with traces on a double-layer PCB, sandwiched
between two conductors carrying balanced currents, shown in
Fig. 3. It has 10 turns, and a size of 8mm×8mm. Minimum
trace width is used to reduce the inter-winding capacitance and
increase bandwidth. Two soldering pads on the top and bottom
layer and a row of vias connect the power device to the
mainboard through the conductors. The current under
measurement flows from the device terminal through the top
4686
RF
a
R2
Mc
IV. CURRENT SENSOR CIRCUIT DESIGN
A1
Rd Vin
The Rogowski coil senses the di/dt in the current carrying
conductor, and an integrator circuit is needed to integrate the
output of the coil to produce the current measurement. The
PCB Rogowski coil has a very wide bandwidth, therefore the
bandwidth of the sensor system is usually limited by the
integrator. The inverting integrator topology used in [10] is not
suitable for high frequency applications because of the signal
coupling from input to output by the integrating capacitor at
high frequency. This causes undershoot in the step response,
and generates a right-half-plane zero in the integrator transfer
function, degrading the stability.
The non-inverting integrator [11] eliminates this capacitive
coupling by connecting the coil to the non-inverting input of
the amplifier, as in Fig. 5(a). It further improves the high
frequency performance by splitting up the integration task. The
passive integrator R1C1 processes the high frequency
components. The active integrator R2/C2/A1 processes the low
frequency components; and at high frequency, it acts as a unitgain buffer, achieving the widest possible bandwidth. It can be
shown that the transfer function of the integrator is:
Vout
C1
−
Passive
Integrator
Coil
b
C2
R1
+
I
because it achieves fast response without overshoot. Rd can be
sized according to (1) to yield a critical damping of ζ=1.
Active
Integrator
(a)
reset
R
R4 b a 6
a R3
A2
C3
R5
R7
b
C4
R8
(b)
(c)
Fig. 5. (a) Non-inverting integrator topology. (b) Passive LPF to extend the
lower cutoff frequency [11]. (c) The proposed active LPF together with the
reset scheme.
H i ( s) =
conductor to the vias, then back to circuitry on the mainboard
through the bottom conductor. Since the top and bottom pads
are aligned, and the device pins that are not measured bypass
directly through the PCB holes, the sensor does not change the
device footprint. Therefore, it can be transparently inserted
between the device and the mainboard without layout change.
The embedded design doubles the sensitivity by having two
balanced currents around the coil; it is insensitive to the
distance variation between the conductors and the PCB; and
the conductors serve as shielding for the coil.
The Rogowski coil can be modeled as a lumped circuit
shown in Fig. 4. The current in the conductor is coupled to the
coil through the mutual inductance Mc, shown as the voltage
source. The coil has a self-inductance of Lc, and a winding
resistance Rc. The winding resistance can usually be neglected
because it is very small. The parasitic capacitance can be
modeled as the Cc. A damping resistor Rd is added externally to
improve the coil’s frequency response. It can be shown that the
coil has a 2nd-order transfer function and the natural frequency
ωn and the damping factor ζ of the system can be derived:
ωn = 1 Lc Cc
ζ = 2 Rd ⋅ Lc / Cc .
(1)
The natural frequency limits the maximum operating
frequency of the coil, and the damping factor affects the step
response of the coil. Usually, critical damping is preferred
Vout
1+τ2s
=
,
Vin τ 2 s(1 + τ 1 s)
(2)
where τ1 = R1 C1, and τ2 = R2 C2. By selecting R1 C1 = R2 C2 = τi,
the desired integrator response can be obtained and the current
sensor's sensitivity is given by:
S = Vout I = M c τ i .
(3)
The ideal integrator has infinite gain at DC. In a practical
design, the DC gain has to be limited to avoid excessive output
error due to the amplifier's offset. In Fig. 5(a), RF serves this
purpose [10], and the output error is given by Verror = RF / R2 ×
Vos, where Vos is the offset voltage of the amplifier. However,
this scheme degrades the low frequency response of the sensor,
since it is given by f-3dB,low = 1 / (2 π RF C2). This limitation can
be especially severe in this work because the relatively low Mc
of the PCB Rogowski coil compared to wire-wound ones
requires small τi and therefore small C2 to achieve comparable
sensitivity.
A passive low pass filter (LPF) shown in Fig. 5(b) can be
used to extend the lower cutoff frequency of the sensor [11],
but the value of R3 + R4 is limited because it causes output error
similar to RF. As a result, the filter capacitor C3 has to be very
large to achieve good low frequency response (the actual value
will be given in the next section), increasing the sensor size.
The proposed scheme in Fig. 5(c) uses a voltage buffer to
decouple the two constraints of Verror and f-3dB,low. R7 can be
large to reduce the size of C4 without increasing the output
error. The additional amplifier A2 does not significantly add to
the system's cost, since it operates at very low frequency and a
4687
V(vout)
-20dB
-40dB
-60dB
-80dB
1Hz
Fig. 6. Fabricated PCB Rogowski coil.
100Hz
10KHz
1MHz
100MHz
(a)
Magnitude (dB)
100
undamped
50
24V
V(vout)*14.3-0.4
V(n010)
damped
14V
0
4V
Phase (deg)
90
0
-6V
0μ s
6
8
40μ s
60μ s
80μ s
100μ s
(b)
Fig. 8. Simulation results of the sensor with experimentally extracted coil
parameters: (a) ac response, (b) transient response.
-90
10
10
Frequency (Rad/Sec)
20μ s
10
10
Fig. 7. Impedance Bode plots of the Rogowski coil.
V(vout)
-20dB
low-cost opamp can be used. When the sensor is used to
measure the current in the power switch, which is unipolar and
contains a DC component, the integrator has to be reset
occasionally to establish the correct DC level at the output,
because the Rogowski coil does not sense DC components.
This also helps to prevent the output error from accumulating.
The reset switch implemented with the MOSFET in Fig. 5(c)
turns on to reset the integrator when the device current is
known to be zero (off-state). The reset control signal can be
easily generated by the controller or derived from the PWM
signal. Because of the good low frequency performance of the
integrator, the reset can be executed once every tens of
milliseconds, minimizing the interruption of continuous current
monitoring. Compared to the reset scheme in [4] where the
switch is placed across the integrating capacitor C2, the
proposed technique significantly reduces the errors caused by
switch charge injection and parasitic capacitances, because C4
is much larger than C2.
-40dB
-60dB
-80dB
100Hz
1MHz
100MHz
(a)
V(vout)*14.3-0.4
V(n007)
18V
8V
-2V
-12V
0μ s
V. COIL CHARACTERIZATION AND COMPONENT SELECTION
The fabricated PCB Rogowski coil is shown in Fig. 6. To
determine the component values in the integrator, the coil
parameters in Fig. 4 are extracted experimentally using an
impedance analyzer with the conductors attached: Lc=156.0
nH, Cc=3.271 pF, Rc=501.4 mΩ. The impedance Bode plot of
the Rogowski coil is shown in Fig. 7, it can be seen that the
coil has a self-resonance frequency of more than 220 MHz,
10KHz
20μ s
40μ s
60μ s
80μ s
100μ s
(b)
Fig. 9. Simulation results without the proposed active LPF circuit:
(a) ac response, (b) transient response.
indicating good high frequency performance. The damping
resistor Rd can be determined to be 437 Ω according to (1) with
4688
15
400
200
5
Probe
Current Sensor
Drain Voltage 0
Fig. 10. Assembled current sensor compared to a U.S. quarter.
0
0
VDS (V)
ID (A)
10
5
10
Time (μsec)
15
(a)
15
400
Fig. 11. Experimental setup of a DPT for current sensor.
200
5
0
0
2
ζ=1. The Bode plot after adding Rd in Fig. 7 shows a largely
damped resonance peak with negligible bandwidth reduction.
The mutual inductance Mc is extracted using a network
analyzer: Mc = 10.69 nH. By properly choosing R1R2 and C1C2,
a current sensor sensitivity of S = 0.0715A/V is achieved.
Amplifier A1 and A2 are chosen to be single-package dualamplifier to save layout area. The typical output error due to
amplifier offset is Verror =14.7 mV. R7, R8 and C4 are chosen to
obtain a low pass corner f-3dB,low = 2.6 Hz, and their values are
reasonable for surface mount components. To achieve the same
Verror, however, the passive LPF circuit in Fig. 5(b) [11] needs
to have R3 + R4 ≤ 100 kΩ. Also, C3 has to be as large as 4700
μF to achieve the same f-3dB,low.
2.1
2.2
Time (μsec)
2.3
10
400
5
200
0
0
12
12.1
12.2
Time (μsec)
VDS (V)
ID (A)
(b)
VI. SIMULATION RESULTS
The current sensor system is simulated using the coil
parameters extracted as in Section V. The -3dB bandwidth of
the current sensor is 2.66 Hz – 100 MHz, shown in Fig. 8(a).
The frequency at which the phase error is 45° is 30 MHz. The
transient response when measuring the power switch current in
a boost converter is shown in Fig. 8(b), compared to the real
current. As a comparison, instead of the proposed active LPF
shown in Fig. 5(c), RF is used to achieve the same Verror, and
the required RF is 100 kHz. The resulting sensor bandwidth is
7.11 kHz – 100 MHz (Fig. 9(a)). The lower cut-off frequency
is significantly increased, causing severe droop error in the
transient response (Fig. 9(b)).
VDS (V)
ID (A)
10
12.3
(c)
Fig. 12. The comparison of current measured by the proposed current sensor
(red trace) and a 120 MHz commercial current probe (blue trace) in the DPT
test at (a) on state, (b) turn-on transition, (c) turn off transition.
VII. EXPERIMENTAL RESULTS
The picture of the assembled current sensor is shown in Fig.
10. Its performance is demonstrated in a double pulse test
(DPT) setup, shown in Fig. 11. The device whose current is
measured is a first generation SiC MOSFET (Cree
CMF20120D). It is mounted on the current sensor daughter
4689
board and the sensor board is then connected to the DPT
mainboard. Since the current sensor does not change the
footprint of the device, no layout change is needed to insert the
sensor between the device and mainboard. The DC bus is 400
V and the load current is about 8 A. The gate resistors are 10 Ω
for turn-on and 4.7 Ω for turn-off. The proposed current
sensor is compared to a 120 MHz commercial current probe
and the results are plotted in Fig. 12. It can be seen that the
current measured by the proposed current sensor (red trace)
agrees well with the current probe (blue trace) in both on-state
and switching transitions, demonstrating good performance at
both low and high ends of the frequency band. The sensor
exhibits a propagation delay of about 7 ns, caused by the coil
and the integrator circuit. This delay can be easily calibrated
out at the beginning of measurement.
VIII. CONCLUSIONS
Active current balancing of paralleled WBG devices requires
current sensors with small size and high bandwidth. We
showed that when measuring the unbalance currents in
paralleled devices at turn-on transition, the time constant in the
paralleled loop slows down the change rate of unbalance
current and relaxes the bandwidth requirement of current
sensing. Then we proposed a current sensor based on PCB
Rogowski coil. The planar and compact design of the coil
allows nonintrusive insertion of current measurement. The
integrator design extends both low and high ends of the sensor
frequency response. The proposed reset scheme enables the
measurement of device switching currents with a DC
component. The model of the fabricated Rogowski coil was
extracted in experiment, and simulations based on the model
parameters show a sensing bandwidth of 2.66 Hz – 100 MHz.
The performance is further verified by the experimental results,
which demonstrate that the current measured by the sensor
agrees well with that measured by a 120 MHz commercial
current probe.
ACKNOWLEDGEMENT
Oak Ridge National Laboratory under the U.S. Department of
Energy’s Vehicle Technologies Program. This work made use
of Engineering Research Center Shared Facilities supported by
the Engineering Research Center Program of the National
Science Foundation and DOE under NSF Award Number
EEC-1041877 and the CURENT Industry Partnership
Program.
REFERENCES
[1] G. Wang, J. Mookken, J. Rice, M. Schupbach, “Dynamic and static
behavior of packaged silicon carbide MOSFETs in paralleled
applications,” IEEE Applied Power Electronics Conference and Exposition
(APEC), Mar. 16-20, 2014, pp.1478-1483.
[2] Y. Xue, J. Lu, Z. Wang, L. M. Tolbert, B. J. Blalock, F. Wang, “Active
current balancing for parallel-connected Silicon Carbide MOSFETs,”
IEEE Energy Conversion Congress and Exposition (ECCE), Denver,
Colorado, Sept. 15-19, 2013, pp.1563-1569.
[3] Y. Xue, J. Lu, Z. Wang, L. M. Tolbert, B. J. Blalock, F. Wang, “Active
compensation of current unbalance in paralleled silicon carbide
MOSFETs,” IEEE Applied Power Electronics Conference and Exposition
(APEC), Mar. 16-20, 2014, pp.1471-1477.
[4] A. Radun, “An alternative low-cost current-sensing scheme for highcurrent power electronics circuits,” IEEE Transactions on Industrial
Electronics, vol. 42, no. 1, pp. 78–84, Feb. 1995.
[5] L. A. Kojovic, et al., “Practical aspects of Rogowski coil applications to
relaying,” IEEE PSRC Special Report, Sept. 2010.
[6] D. Gerber, T. Guillod, R. Leutwyler, J. Biela, “Gate unit with improved
short-circuit detection and turn-off capability for 4.5-kV press-pack IGBTs
operated at 4-kA pulse current,” IEEE Transactions on Plasma Science,
vol. 41, no. 10, pp. 2641–2648, Oct. 2013.
[7] A. Ahmed, L. Coulbeck, A. Castellazzi, C. M. Johnson, “Design and test of
a PCB Rogowski coil for very high dI/dt detection,” IEEE International
Power Electronics and Motion Control Conference (EPE-PEMC), Novi
Sad, Serbia, Sept. 4-6, 2012, pp.1-4.
[8] T. Guillod, D. Gerber, J. Biela, A. Muesing, “Design of a PCB Rogowski
coil based on the PEEC Method,” IEEE Integrated Power Electronics
Systems (CIPS), Nuremberg, Germany, March 6-8, 2012, pp. 1-6.
[9] Q. Chen, H. Li, M. Zhang, Y. Liu, “Design and characteristics of two
Rogowski coils based on printed circuit board,” IEEE Transactions on
Instrumentation and Measurement, vol. 55, no. 3, pp. 939-943, June 2006.
[10] L. Zhao, J. D. van Wyk, W. G. Odendaal, “Planar embedded pick-up coil
sensor for power electronic modules,” IEEE Applied Power Electronics
Conference and Exposition (APEC), 2004, pp. 945-951.
[11] W. F. Ray, R. M. Davis, “High frequency improvements in wide
bandwidth Rogowski current transducers,” IEEE European Conference on
Power Electronics and Application (EPE), Sept. 1999, pp. 1-9.
This work was partially funded by the II-VI Foundation and
4690