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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 3, JUNE 2007 753
High-Performance Low-Cost Rogowski Transducers
and Accompanying Circuitry
Ehsan Abdi-Jalebi, Member, IEEE, and Richard McMahon
Abstract—Rogowski transducers have become an increasingly
popular method of measuring current within prototyping appli-
cations and power electronics equipment due to their significant
advantages compared to an equivalent current transformer. This
paper presents a simple and practical construction technique of
high-performance low-cost Rogowski transducers and accompa-
nying circuitry. Experimental tests were carried out to show the
validity of the proposed construction technique.
Index Terms—Current measurement, experimental verifica-
tions, integrating circuit, practical construction, Rogowski coil,
simple construction.
I. INTRODUCTION
ROGOWSKI coil current transducers have contributed
greatly to the art of measuring electric currents in difficult
or unusual circumstances as well as for normal situations. They
possess many features which offer several advantages over iron-
cored current measuring devices [1], [2].
Over the past decade, interest in applications of Rogowski
transducers in research environments has grown. They have
been mainly used for prototyping applications. It is very cost
effective if the coil can be made of simple elements which are
cheap and easy to find in research laboratories. Furthermore, it
is desirable to know how to construct a Rogowski coil by a sim-
ple method to make suitable coils for particular applications.
Our particular interest has been to measure rotor-bar currents
in electrical machines [3]. In this application, the limited space
between the rotor bars and the need to measure large current
(3000 A peak-to-peak) led us to use the Rogowski coil. The
accompanying circuitry is battery powered and is installed on
the rotor shaft.
Comprehensive investigations on the design, characteristics,
and applications of Rogowski coils have been made in several
publications [4]–[7]. However, there is still a lack of a good
reference on how to simply and practically construct a high-
performance Rogowski coil. Currently, there are no specific
standards for Rogowski coils; however, a Rogowski transducer
may be referred to as “high performance” if its specifications
such as linearity and accuracy are within typical commercial
values [8].
This paper will present a step-by-step construction technique
of a reasonably high-performance low-cost Rogowski coil. This
practical technique uses basic components to make the coil, and
Manuscript received June 15, 2005; revised January 8, 2007.
The authors are with the Engineering Department, University of Cambridge,
CB3 0FA Cambridge, U.K. (e-mail: ea257@cam.ac.uk; ram1@cam.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2007.894801
instructions are given to increase the reliability, accuracy, and
robustness of the coil. The components are easily available in
research laboratories.
The Rogowski coil output voltage is proportional to the rate
of change of measured current. To obtain a voltage proportional
to measured current, the coil output voltage must be integrated.
Due to the small voltage produced by the Rogowski coil (typ-
ically 1 µV/Hz for 1 A current flowing in the conductor), the
design of a suitable integrating amplifier circuit is not a trivial
matter. Several publications have discussed the design of the
integrator using operational amplifiers (op-amps) [6], [9]. The
offset level and noise rejection of the integrator greatly depend
on the op-amp characteristics. This paper will present an in-
tegrating circuit using a recently introduced high-performance
op-amp. The integrator is accompanied by an active filter to
give extra noise rejection ability.
The authors then propose a simple calibration technique to
calibrate the current probe, including the Rogowski coil and the
integrating circuit. Experimental measurements were carried
out to show the performance of the constructed current probe.
The performance is close to that of commercially available
Rogowski transducers. The results prove that a valuable tech-
nique of simple and practical construction of Rogowski probes
has been achieved. This construction knowledge was gained
during two years of experiments in current measurements in
the authors’ laboratory.
II. ROGOWSKI COIL CONSTRUCTION
The Rogowski coil, which is also called air-cored coil,
has been in use since 1912. It is a toroidal winding placed
around the conductor being measured. The main advantages of
Rogowski coils are high measuring accuracy, wide measuring
and frequency ranges, flexible construction, galvanic isolation,
low noise, and potentially low cost.
The voltage output from the coil is proportional to the rate
of change of the measured current. Assuming nand Aare the
turns per meter and cross-sectional area of the coil, respectively,
and iis the measured current, the voltage output of the coil is
given in (1). The µ0nA term is called coil sensitivity
νcoil =−µ0nA di
dt.(1)
Achieving ideal properties in a practical coil demands con-
siderable care in its design and construction. In order to main-
tain the coil performance, it is vital that the cross-sectional area
and the turn density remain essentially constant along the length
even when the coil is bent.
0018-9456/$25.00 © 2007 IEEE
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754 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 3, JUNE 2007
A. Core Selection
The core of the Rogowski coil can be made of any non-
magnetic material. The plastic sheath of an electric cable is
suggested for use as a former (core); however, the diameter
and flexibility of the former have to be considered. A coil with
a bigger diameter has a greater sensitivity, but it limits the
possible locations in which the coil can be used. The flexibility
of the core should be such that it is easily bent around the
conductor being measured while maintaining its uniformity.
B. Winding
Winding is a very important part of the Rogowski coil
construction. It greatly affects the sensitivity, accuracy, and
reliability of the transducer. To increase the accuracy of the
measurement, the winding order should be kept uniform along
the length of the coil. This requires patience from the coil maker
during the winding procedure.
It is possible to improve the sensitivity of the coil in several
ways, but many tradeoffs exist. Decreasing the size of the wire
allows more turns per unit length, but small gauge wire is
fragile and reduces the robustness of the coil. Increasing the
average turns by means of additional winding layers produces
greater output but results in increased overall diameter which
may limit the possible locations where the sensor can be used.
This method also increases interwinding capacitance and limits
the bandwidth. Single-layer coils are more convenient from
several viewpoints, which include ease of winding, better flex-
ibility, and relatively smaller inductance, which gives a better
bandwidth [10].
C. End Wires
To eliminate the interference from nearby conductors carry-
ing high currents, the end winding needs to be returned to its
start along the central axis of the coil (i.e., in the middle of
the former) [10]. However, although multiple layers make the
coil less flexible, if the coil has an even number of winding
layers, and the even layers are wound in the opposite direction
of the odd layers, there is no need for the return path through
the middle of the former.
To increase the reliability of the Rogowski transducer, special
care needs to be taken while taking out the end wires. Since the
winding wire is very thin, it is important to append thicker wires
to both ends of the coil. Figs. 1 and 2 show how to take out the
end wires ready to be connected to the connector.
To bend both ends of the Rogowski coil together, a thin wire
latched in the middle of the former can be used. Fig. 3 shows
the technique.
D. Heat Shrink Sleeving Protection
To protect the coil from mechanical hazards, heat shrink
sleeving is used. The coil is inserted into the heat shrink tube
which is heated using a hot air gun. To remove any extra error
due to the induced voltage in the attached leads, it is better to
keep the leads very close together. Again, heat shrink sleeving
Fig. 1. Appending (soldering) thicker wires to both ends of the Rogowski coil.
Fig. 2. Protecting the soldered joints by hiding them in the middle of the
former.
Fig. 3. Bending: A thin wire latched in middle of the former at both ends.
can be used. Fig. 4 shows the implementation of this technique
in Rogowski coil construction. Insulating tape can also be used
in both cases.
III. INTEGRATING AMPLIFIER CIRCUIT
As described before, the integrator is necessary since the
Rogowski coil provides a voltage proportional to the rate of
change of the measured current. In addition, the circuit needs
to amplify the signal as the Rogowski coil terminal voltage is
very small, particularly at low-frequency measurements (i.e.,
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ABDI-JALEBI AND McMAHON: ROGOWSKI TRANSDUCERS AND ACCOMPANYING CIRCUITRY 755
Fig. 4. Heat shrink sleeving for the Rogowski coil and attached leads.
typically several µV/A for a 50-Hz current). Fig. 5 shows
the integrating amplifier circuit designed for a low-frequency
current measurement probe (i.e., f<150 Hz). The integrator
is accompanied by an active filter to increase the noise rejection
capability.
Since the integrator gain increases as frequency decreases,
thereby amplifying the low-frequency random noise and zero-
frequency offset drift, it is necessary to reduce the integrator
gain for frequencies below which measurement accuracy is
not affected. A large resistor R2is put across C1to provide
dc feedback for stable biasing. The effect is to roll off the
integrator action at very low frequencies f<1/R2C1[11]. The
transfer function for the integrator shown in Fig. 5 is given by
the following:
Vint
Vin
=R2
R1(1 + jωR2C1).(2)
The integrator design, i.e., choosing values for R1,R2, and
C1is a tradeoff between gain, integrating pole position, and the
Rogowski coil loading. R1is in series with the coil, and hence,
it should be large enough to limit the loading effect, particularly
at high frequencies where the coil impedance is large. The
amplification gain is approximately 1/R1C1, and this is an
important parameter since the output voltage of the Rogowski
coil is small (typically 1 µV/AHz). On the other hand, when
measuring the maximum current, the integrator output should
not exceed the op-amp voltage rating. The integrating pole is
placed at f=1/2πR2C1. The accuracy of the integration is
greatly affected by the position of the integrating pole.
The values shown in Fig. 5 are chosen to meet the limi-
tations for our particular application. The measurement setup
is designed to measure the rotor-bar current with the range of
10 to 3000 A peak-to-peak and over a frequency range of 1 to
100 Hz.
The signal was then band limited to minimize noise using a
1 kHz low-pass two-pole Butterworth voltage-controlled
voltage-source active filter. The Butterworth filter produces the
flattest passband response at the expense of steepness in the
transition region from passband to stopband. It starts out nearly
flat at zero frequency and bends over near the cutoff frequency
fc[11]. The transfer function for the active filter is given by (3),
shown at the bottom of the page.
For the Butterworth filter, R3=R4=R5=R,R6=(k−
1)R5, and C2=C3=C, and hence, the cutoff frequency fcis
1/2πRC, and the transfer function is given by the following:
Vout
Vint
=k
1−(RCω)2+jωRC(3 −k).(4)
In applications where the accompanying circuitry cannot be
placed close to the Rogowski coil, i.e., the output lead of
the coil is long, a differential amplifier can be used before
the integrating circuitry to eliminate common-mode electrical
interference [11].
Fig. 6 shows the pole-zero location of the proposed design.
The integrating pole is placed at 0.08 Hz, and the active filter
poles are placed at 1 kHz. Fig. 7 shows the Bode plots of the
integrator and filter transfer function. High-frequency effects
of the Rogowski coil are not significant at the frequencies of
interest. This design gives a bandwidth of 1Hz <f<150 Hz
with a magnitude error of less than 0.3% and a phase error of
less than 4.5◦. At 50 Hz, the magnitude error is less than 0.01%,
and the phase error is less than 0.1◦.
The op-amp must be carefully chosen to have a low-input
offset voltage to allow operation at high gain at low frequencies.
It must also have low noise and sufficient bandwidth to ensure
accurate integration over the frequency range of interest. The
analog devices AD8552, a dual op-amp, which has a suitable
combination of precision, low noise, and low offset with a high
gain bandwidth product and high slew rate, is used for both the
integrating amplifier and active filter.
Since the maximum output voltage Voutmax of AD8552 is
3 V, the maximum current the sensor can measure Imax can be
obtained from the following:
Imax =Voutmax
SR×Ai×Af
(5)
where SRis the Rogowski coil sensitivity, and Aiand Afare
the integrator and the active filter gains, respectively. For the
circuit shown in Fig. 5, Aiis 1000, and Afis 1.6. For a typical
Rogowski coil with a sensitivity of 1 µV/Hz, the maximum
peak-to-peak measurable current is 1875 A.
Knowledge of the signal-to-noise ratio (SNR) is important
because it is directly related to the accuracy of the measure-
ment. Typically, it is measured in decibels. If the rms values of
the signal and noise are Sand N, respectively, then the SNR in
decibels is given by the following:
SNR = 20 log S
N.(6)
Vout
Vint
=R5+R6
R5−R3R4R5C2C3ω2+jω(R4R5C3+R3R5C3−R3R6C2)(3)
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756 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 3, JUNE 2007
Fig. 5. Integrating amplifier and active filter circuit diagram.
Fig. 6. Pole-zero location of the accompanying circuitry.
Fig. 7. Bode plots of the integrator and filter transfer function.
The SNR of the proposed accompanying circuitry is high due
to low voltage noise of AD8552 (1 µV p-p). For a sinusoidal
input voltage of 10 mV at 50 Hz, the SNR is 50 dB. The noise
level was measured by shorting the inputs of the electronic
circuitry.
Fig. 8. Simulation results: The output of the circuit shown in Fig. 5 when
a sinusoidal input of 10 mV, 50 Hz superimposed with a white noise
applied.
In order to show the effectiveness of the high SNR of the
designed circuit, a 10 mV, 50 Hz sinusoidal signal (which
corresponds to the output voltage of a 1 µV/AHz Rogowski
coil measuring 200 A, 50 Hz current) with a white noise
(with a power spectral density of 10−10 W/Hz) superim-
posed was applied to the circuit, and the output is shown
in Fig. 8.
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ABDI-JALEBI AND McMAHON: ROGOWSKI TRANSDUCERS AND ACCOMPANYING CIRCUITRY 757
Fig. 9. Multiturn wire used for calibration.
TAB L E I
PROTOTYP E ROGOWSKI COILS DESIGN SPECIFICATIONS
IV. CALIBRATION
Since the Rogowski current probe (including the Rogowski
coil and the integrating amplifying circuit) has linear charac-
teristics [12], it can be calibrated at 50 Hz using relatively
low magnitude currents. To achieve a higher current level, the
Rogowski transducer was attached around a multiturn wire,
as shown in Fig. 9. The calibration will be valid for any
measurement application as long as the cross-sectional area and
the turns density remain constant along the coil length.
V. E XPERIMENTAL RESULTS FOR
PERFORMANCE ANALYSIS
A high-performance Rogowski coil has less sensitivity to the
relative position of the conductor passing through the coil. It
also needs to be insensitive to other current carrying conductors
outside the coil.
Two Rogowski coils were made for performance analysis.
The design parameters are shown in Table I. Table II shows
the specifications of two Rogowski probes composed of the
prototype Rogowski coils attached to the electronic circuit.
Coil #1 has bigger cross-sectional area and higher sensitivity
and is designed to measure 50 Hz currents. Coil #2 has smaller
dimensions and less sensitivity and was particularly constructed
for rotor bar current measurements [3]. Since the coils are
designed for different applications, no direct comparison is
possible. Figs. 10 and 11 show the constructed coils and ac-
companying circuitry.
TAB L E II
PROTOTYP E ROGOWSKI CURRENT PROBES SPECIFICATIONS
Fig. 10. Rogowski coil #1 with accompanying circuitry.
Fig. 11. Rogowski coils #2 for rotor bar current measurements.
TABLE III
PERFORMANCE COMPARISON OF PROTOTYPE AND
COMMERCIAL ROGOWSKI COILS:TEST ERRORS
Three different tests, including off-center, edge, and pancake
tests, were carried out [9]. The results are compared to the
ones for commercial Rogowski coils [8], [10] and are shown
in Table III.
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758 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 3, JUNE 2007
Fig. 12. The 5 A current measurement using Rogowski probe #1.
Fig. 13. The 500 A current measurement using Rogowski probe #1.
A. Off-Center Rotational Test
The multiturn wire shown in Fig. 9 was used for this test.
Since the diameter of the multiturn wire is less than the diameter
of the coil, the coil is hanging off-center on the wire. The coil
was then rotated in eight 45◦angular positions around the wire,
and readings were taken. The maximum error for each coil is
shown in Table III.
B. Edge Test
In this test, the Rogowski coil was placed flat beside a
multiturn wire where the axis of the coil was parallel to the
axis of the multiturn wire. The main purpose of this test was to
evaluate the effect of the compensation turn. There should be no
output voltage at the coil terminals because the current carrying
conductor is not passing through the coil window. The edge test
errors are shown in Table III.
C. Pancake Test
In this test, the Rogowski coil was placed flat onto a multiturn
wire and similar to the edge test, the axis of the coil was
parallel to the axis of the multiturn wire. The coil output
voltage should be zero as no current is passing through the coil
window. Any coil output voltage is the result of a combination
of nonuniform coil turns and nonuniform cross-sectional area.
These two effects cannot be separated in this test. The errors are
shown in Table III.
Figs. 12 and 13 show the actual and measured currents using
coil #1. The measured current is the output of the integrating
Fig. 14. Rotor bar current for BDFM induction mode at 580 r/min measured
using Rogowski coil #2.
amplifier circuit. The difference between the measured and
actual current wave shapes is due to the effect of the low-
pass filter. The filter removes high-frequency harmonics and
smoothes the wave shape.
Rogowski coil #2 was used for rotor bar current measure-
ments of the Brushless Doubly Fed Machine (BDFM). The
BDFM shows economic promise as an improved replacement
for the induction machine as a variable speed motor and gen-
erator [13]. Bluetooth wireless technology was used for data
transmission from the moving rotor to a computer for logging
and analysis [3]. Fig. 14 shows a rotor bar current for the BDFM
induction mode measured at 580 r/min.
VI. CONCLUSION
A simple and cost-effective technique to construct high-
performance Rogowski transducers was presented. All ele-
ments required for the coil construction exist in most research
environments. An example design of the accompanying cir-
cuitry for low-frequency measurements was proposed. The
characteristics of the current probe, including the Rogowski
coil and the integrating amplifier circuit were presented. Ex-
perimental results from constructed probes have shown close
agreements with commercially available Rogowski probes.
REFERENCES
[1] D. A. Ward, “Measurement of current using Rogowski coils,” in Proc.
IEE Colloq. Instrum. Elect. Supply Ind., Jun. 1993, vol. 1, pp. 1–3.
[2] D. E. Shepard and D. W. Yauch, “An overview of Rogowski coil cur-
rent sensing technology,” LEM High Current Systems, 2000. Technical
Bulletins.
[3] E. Abdi-Jalebi, P. C. Roberts, and R. A. McMahon, “Real time rotor
bar current measurements using a Rogowski coil transmitted using wire-
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pp. 1–9.
[4] A. Rautiainen, P. Helisto, T. Mansten, and H. Seppa, “50 Hz current mea-
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[5] D. A. Ward and J. L. T. Exon, “Using Rogowski coils for transient current
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[8] M. J. V. Wimshurst, “Standards and Compliance,” in Proc. IEE Seminar
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ABDI-JALEBI AND McMAHON: ROGOWSKI TRANSDUCERS AND ACCOMPANYING CIRCUITRY 759
[9] C. Oates, “The design and use of Rogowski coils,” in Proc. IEE Colloq.
Meas. Tech. Power Electron., Dec. 1991, vol. 5, pp. 1–5.
[10] J. D. Ramboz, “Machinable Rogowski coil, design, and calibration,” IEEE
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[12] J. D. Ramboz, D. E. Destefan, and R. S. Stant, “The verification of
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Mar. 1997.
Ehsan Abdi-Jalebi (M’05) received the B.Sc. de-
gree in electrical engineering from Sharif University
of Technology, Tehran, Iran, in 2002 and the M.Phil.
and Ph.D. degrees from University of Cambridge,
Cambridge, U.K., in 2003 and 2006, respectively.
His main research interests include electrical
machines and drives, renewable power generation,
power electronics, electrical measurements and in-
strumentation, and digital wireless technologies.
He is currently with the Engineering Department,
University of Cambridge.
Dr. Abdi-Jalebi’s research has received several outstanding awards, including
the Scientific Instrument Makers Award in 2004, the Innovation in Engineering
Award in 2005, and the Best Young Professional Paper Award in 2006.
Richard McMahon received the B.A. (in electri-
cal sciences) and Ph.D. degrees from Cambridge
University, Cambridge, U.K., in 1976 and 1980,
respectively.
Following postdoctoral work on semiconductor
device processing, he was appointed University
Lecturer in electrical engineering in Engineering
Department, Cambridge University, in 1989 and be-
came a Senior Lecturer in 2000. His research inter-
ests include electrical drives, power electronics, and
semiconductor materials.
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