Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
Sensors & Transducers
© 2014 by IFSA Publishing, S. L.
http://www.sensorsportal.com
PCB Rogowski Coil for Electronic Current Transducer
Zhigang Di, Chunrong Jia, Jingxuan Zhang
College of Electrical Engineering, Hebei United University, Tangshan Hebei 063009, China
Tel.: 13730493008, fax: 0315-2592177
E-mail: dzg0512@126.com
Received: 11 May 2014 /Accepted: 27 May 2014 /Published: 31 May 2014
Abstract: The Electronic Current Transducer has been applied in power system for measurement and relay
protection. To improve the stability of transducer and increase the coefficient of mutual induction of Rogowski
coil, a novel Rogowski coil, namely PCB Rogowski coil was proposed. First, the relationship between
conureuration parameters and electromagnetic parameters were analyzed, and simulated their relationships.
Second, the influence of thermal expansion on relative error was analyzed. Third, the Rogowski coil
configuration parameters were optimized and the optimum parameters were proposed. At last, frequency
character of optimum Rogowski coil was simulated. The configuration parameters were h = 2 mm, b = 50 mm,
a = 30 mm, h’ = 0.08 mm, w = 0.8 mm, the mutual-inductance of optimum Rogowski coil is 0.163 × 10-5 H,
L = 1.31 × 10-4 H. The conclusion can be drawn from simulation result that the optimum PCB Rogowski coil
has enough mutual-inductance so as to adapt small current measurement, and it is easy to manufacture in large
quantities. Copyright © 2014 IFSA Publishing, S. L.
Keywords: Electronic current transducer, Small current measurement, Rogowski coil, Optimum design.
1. Introduction
In power system, current transducer is the most
equipment for electrical energy measurement and
relay protection, the precision and reliability
of current transducer have crucial relationship with
safe, reliable and economic working. With the
unceasing expansion of power system, the
transmission capability is increasing unceasingly,
voltage class is higher and higher. As a result, the
increasing strict claim is made for current transducer.
This moment, the traditional electromagnetism
current transducer exposed a series of defects, such
as complicated configuration, inherent magnetic
saturation, small dynamic state, and so on [1]. While
with the development of photoelectric technology,
electronic current transducer was invented, and it has
simple configuration, small volume, light weight and
so on [2]. So it is deemed to the ideal succedaneum
for electromagnetism current transducer. With the
206
development of science technology, electronic
current transducer is developing for accuracy
measurement, fiber transmission and digital output
directions. But the mutual-inductance of Rogowski
coil is very small because it has no iron core, and the
manufacture in quantity is difficult for traditional
Rogowski coil because enameled wire is brittle.
According to the above mentioned, a novel high
precise PCB Rogowski coil was designed in this
paper. The measurement range is 0 ~ 100 A, and it
has better linearity and very minor phase error, it can
meet the requirement of 0.2 level current transducer.
2. Principle of Electronic Current
Transducer
Electronic current transformer can adopt
traditional current transformer, Hall sensor,
Rogowski coil or optical equipment as sensing
http://www.sensorsportal.com/HTML/DIGEST/P_RP_0134.htm
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
component, utilizes fiber as transmission medium
between first converter and second converter, also
equipped with signal process system to magnify and
transmit, finally output the analog or digital voltage
signal [3, 4]. The development of fiber current
transformer is now toward to active type and passive
type. The active type has the virtues such as simple
configuration, steady operation, and so on. So this
task designed an active fiber current transformer, and
adopted Rogowski coil as sensor head, the framework of this transformer is shown in Fig. 1.
Fig. 1. Diagram of electronic current transformers.
The busbar current is sampled by Rogowski coil,
then the voltage signal will be achieved. This signal
will be disposed by high voltage signal process
circuit, so as to achieve the voltage signal which is
proportional to busbar current. First, this signal will
be converted to digital signal by ADC. Then, it will
be converted to optical signal by EOC, and be
transmitted to low voltage portion by fiber. The low
voltage portion receives the optical signal and
disposes it properly, then exports digital signal and
analog signal.
3. Design of Rogowski Coil
Rogowski coil was first proposed in 1912 [5], it is
a kind of sensor, which is made of copper wire and
nonmagnetic framework. It can be utilized to
measure current by electromagnetic induction.
Compared with traditional current transducers,
Rogowski coil has inapproachable merits as follows
[6]:
1). Good linearity.
2). High measurement precision, it can be up
to 0.1 %, normally is 1~3 %.
3). Wide measurement range, the same coil can
measure currents from several A to thousands A.
4). Wide frequency range, it can be 0.1~1 MHz,
especially it can be 200 MHz.
5). It can measure small current in restricted area
which can’t be measured by other technologies.
Because of the virtues above, the Rogowski coil
was utilized as sensor head of fiber current
transducer. Because the Rogowski coil has no iron
core, when it measure small currents which is smaller
than 1000 A, the output voltage is so weak that it is
very difficult to measure precisely because
of interference signals. So the manufacture
of Rogowski coil which is suit for small current
measurement is the acknowledged difficulty [7].
Traditional Rogowski coil is manufactured by
twining enameled wire on nonmagnetic framework,
so it is difficult to make enameled wire density and
cross-sectional area well distributed. As a result,
traditional Rogowski coil has poor repeatability and
big dispersion, then steady coefficient of mutual
inductance, uniform distribution parameters and antiinterference are unlikely [8]. So although all kinds
of traditional Rogowski coil were proposed, the high
accuracy and batch production are hard to realize, the
application and industrial development are limited
[9, 10]. In order to solve this problem, the novel PCB
Rogowski coil was proposed in this paper.
PCB Rogowski coil can realize digital wiring and
automation production, so as to overcome some
disadvantageous factors of traditional Rogowski coils
[11]. PCB Rogowski coil was first proposed by
Kojovic in 2001 and was licensed patent in USA [12],
the enameled wires were formed by wiring copper
foil which goes through PCB guide holes. From then
on, some kinds of PCB Rogowski coil emerged, they
were manufactured by copper foil going through
guide holes of Double-Sided Boards [13], so they
have simple wiring, easy to twine tightly, more
important, they can avoid the influence of disturbing
current that first conductor deviate from coil center.
But they still have bigger dispersion and poor antiinterference because coiling does not form real
symmetrical circular structure, and the plane
of single circular loop does not pass through coil axis.
PCB Rogowski coil can be fabricated very
accurate because of full automation, the error can be
1 mil. So PCB Rogowski coil not only overcome the
shortcomings of traditional Rogowski coil, but also is
superior to traditional Rogowski coil on sensitivity,
measurement accuracy and steady performance.
3.1. Principle of Rogowski Coil
The frame sketch map of Rogowski coil is shown
in Fig. 2.
In Fig. 2, Q is framework of coil, Ri is inside
radius, Ro is outside radius, h is the height of frame
sketch.
Supposed number of primary winding is N1,
secondary winding is N2, primary winding is inside
secondary winding, the current pass through is I(t),
then according to the Ampere law of magnetic circuit,
the induced voltage of secondary winding is
e (t ) = −
μ NN
dΦ
Ro di
= − 0 1 2 h ln
2π
dt
Ri dt
(1)
207
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
H( jω) =
=
Mjω
− L0C0ω + R0C0 jω +1
2
Mjω[R0C0ω + (1 − L0C0ω2 )]
(1 − L0C0ω2 )2 + (R0C0ω)2
(5)
According to the formula (5), the phase error is
θ = arctg
R0C0ω
1 − L0C0ω2
,
(6)
which L, R0, C0 is equivalent inductance, resistance
and capacitance of Rogowski coil.
Fig. 2. The frame sketch map of Rogowski coil.
3.2. The Structure of PCB Rogowski Coil
While e(t ) = − M
M=
di
, so
dt
μ 0 N1 N 2
Ro
h ln
2π
Ri
(2)
According to sinusoidal alternating current, the
output voltage root-mean-square value is
E = ωMI N
(3)
The equivalent circuit diagram of Rogowski coil
is shown in Fig. 3 [14].
When fabricate PCB Rogowski coil, first design
Protel picture utilizing drawing software, then utilize
advanced numerical control technique to process
according to picture parameters. So the shortcomings
of artificial wiring are avoided, and the PCB
Rogowski coil can meet practical requirement. The
structure of PCB Rogowski coil is shown in Fig. 4.
The design was utilized double sided PCB, two
circles represent inside and outside boundary of PCB
Rogowski coil, black full line represent top wire,
dotted line represent bottom wire, black dot represent
through hole via PCB, which connect top and bottom
wires. Top and bottom wires are distributed radiating
outward and uniformly-spaced centered-circle center.
The cross section of designed PCB Rogowski coil
is rectangle because of the limitation of PCB
production technology, shown as Fig. 5.
Fig. 3. The equivalent circuit diagram of Rogowski coil.
If the input is sinusoidal alternating current, the
transition function is
H ( jω) =
Mjω
L
R
− L0C0ω 2 + ( 0 + R0C0 ) jω + ( 0 + 1)
Rf
Rf
Fig. 4. The structure of designed PCB Rogowski coil.
(4)
For the given Rogowski coil, the output voltage
has differential relationship with input current, but
because of the influence of coil parameters, there is
certain phase error. So the output voltage has not
strict differential relationship with input current.
If the Rogowski coil is utilized to measure alternating
current, and secondary winding is open, namely
R f = ∞ , the transition function is
208
Fig. 5. Cross section of designed PCB Rogowski coil.
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
2). For the same “a”, “b” is bigger,
4. Analysis of Rogowski Coil
According to the principle of PCB Rogowski coil,
the electromagnetic parameters self-inductance L0
and internal resistance R0 can be computed as [15]
L0 =
R0 = ρ c
μ0 N 2 h b
ln ,
2π
a
4πa (b − a ) Lwire 16ha
+ 3 ,
ω 2h'
ω
b+a
b
ln − 1
2(b − a ) a
δ j decreases
is
to 0, for the same “a”,
δ j will increase with the increase of “b”.
(7)
4). After δ j decreases to 0, for the same “a”,
will decrease with the increase of “b”.
(8)
4.2. The Relationship of b and the Error
of Mutual Inductance
which μ0= 4π×10−7 H/m, ρc = 1.68×10−8Ω•m, N is
the number of windings, a and b is the inside and
outside radius, h is the height of PCB, h` is the
thickness of wire, w is the width of wire, lc is the
length of single side single winding, Lwire is the
whole length of wiring copper foil, Lwire=2lc*N.
The error of mutual-inductance is
δj =
quicker to 0.
3). Before
δj
δj
According to formula (9), taking “a” = 2, 4, 6 cm,
“b” = 6 ~ 20 cm, the relationship of “b” and δ j is
shown in Fig. 7.
(9)
4.1. The Relationship of “a” and the δ j
According to formula (9), taking “b” = 8, 10,
12 cm, “a” = 2~8 cm, the relationship of “a” and δ j
is shown in Fig. 6.
Fig. 7. Relationship of “b” vs.
δj.
The conclusion can be drawn from Fig. 7 that:
1). In a certain range, the δ j will decrease
with the increase of “b”, until
δ j = 0, then will
increase with the increase of “b”. But as we know,
“b” is limited, so δ j is limited.
2). For the same “b”, “a” is smaller,
quicker to 0.
3). Before
Fig. 6. Relationship of “a” vs.
δj.
The conclusion can be drawn from Fig. 6 that:
1). In a certain range, the δ j will decrease
with the increase of “a”, until
δj
= 0, then will
increase with the increase of “a”. But as we know,
a is smaller than b, so the error is limited.
δ j is
δ j decreases to 0, for the same “b”,
δ j will increase with the increase of “a”.
4). After
δ j = 0, for the same “b”, δ j will
decrease with the increase of “a”.
In summary, in the process of design PCB
Rogowski coil, lots of extrinsic factor should be
considered. As for inside and outside radius, on the
premise of big mutual-inductance, the sensitivity and
accuracy should be considered. As a result, the
suitable “a” and “b” has important signification
for PCB Rogowski coil design.
209
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
4.3. The Relationship Between Height and R0
For the copper wire, according to formula (8),
taking “a” = 30 mm, “b” = 80 mm, “h`” = 0.08 mm,
“w” = 0.2 mm, the relationship between “h” and R0 is
shown in Fig. 8.
From Fig. 8, the conclusion is that:
1). For the given “w”, the influence of “h” on R0
is very weak.
2). For the given other extrinsic factors, R0 is
proportionate to “h”.
of 0.2 ~ 1.9 mm, and this is very significance for the
accuracy and sensitivity of the system.
In conclusion, for the given “a” and “b”, “h” and
“w” are the main influencing parameters on R0.
Fig. 8 and Fig. 9 indicate that h has a few influences
on R0, but w has serious influence. So the research
on R0 can know about the property of PCB Rogowski
coil overall, and have practical guidance
on fabrication.
5. Optimization on PCB Rogowski Coil
Fig 8. The relationship between h and R0.
The accuracy and reliability of PCB Rogowski
coil must be ensured, so the optimization is very
important. Matlab software was utilized to optimize
PCB Rogowski coil, and the dynamic characters
were analyzed for different structure parameters
according to formula (5).
Taking “a” = 30 mm, “b” = 50 mm, sampling
resistor is 400 Ω, “h” and “N” were changed
respectively, the variety law of dynamic characters
under step response was researched. According
to formula (5), the transmission function has real
coefficient, and the roots of characteristic equation
were located in left half plane of the complex plane,
so the measurement system is steady. Taking
“h” = 1 mm, “N” = 600 ~ 1000, the step responses
for N = 600, 800, 1000 were shown in Fig. 10.
4.4. The Relationship Between w and R0
According to formula (8), taking “a” = 30 mm,
“b” = 80 mm, “h`” = 0.08 mm, “h” = 1 mm, the
relationship between “w” and R0 is shown in Fig. 9.
Fig. 10. The step response of different N.
Fig. 9. The relationship between w and R0.
From Fig. 9, for the given “a”, “b”, “h`”, “h”, the
conclusion can be drawn that:
1). R0 is affected by “w” heavily, and R0 will
decrease with “w” heavily in certain range.
2). If “w” exceeds 1.9 mm, R0 can’t change
with “w” anymore. In summary, considering big
mutual-inductance and R0, “w” must be in the range
210
From Fig. 10, the conclusion can be drawn that
N is bigger, the raise time of step response is longer,
response velocity is slower, the setting time
of system steady state is longer, and the system
sensitivity is lower too. But according to formula (2),
for the given “a” and “b”, the bigger “N” will have
bigger mutual-inductance, the width “w” must be
smaller, so R0 must increase. As a result, according
to mentioned above, “N” = 800 is optimum, and four
PCB Rogowski coil cascade together, for each coil,
“N” = 200.
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
Taking “N” = 800, “h” = 2, 3, 4 mm, the dynamic
characteristics were shown in Fig. 11.
Fig. 11. The dynamic characteristics of different h.
From Fig. 11, the conclusion can be drawn that
for bigger “h”, the raise time of induced voltage will
increase, and the setting time of system steady state
is longer, response velocity is slower too. While
according to formula (2), the bigger “h” will have
bigger mutual-inductance, namely has stronger
induced signal. In practice, it is very difficult
to fabricate PCB Rogowski coil for too big or too
small “h”, as a result, the height of PCB Rogowski
coil must be chosen properly. According
to mentioned above, “h” = 2 mm is optimum.
6. Numeral Simulation
Sum up, according to the optimization above,
the practical optimum single ring PCB Rogowski coil
has following structure parameters: “h” = 2 mm,
“a” = 30 mm, “b” = 50 mm, “h`” = 0.08 mm,
“w” = 0.8 mm, “N” = 800. In application, four
PCB Rogowski coils cascade as negative direction,
and the electronic parameters are: R0 = 8.5 Ω,
M = 1.63*10-6 H, L = 1.31*10-4 H, C0 = 345 pF.
To make the measurement circuit work at the best
damping mode and eliminate resonance oscillation,
taking Ra = 430 Ω. In order to research the
performance of PCB Rogowski coil which measure
current, according to the formula (4), Matlab
software was utilized to simulate the system, and the
frequency characteristics curve was shown in Fig. 12.
7. Method and Design of Electromagnetic
Shielding for PCB Rogowski Coil
The working environment of Rogowski coil is
very special, there is strong electric field and
magnetic field around it, so the accuracy must be
affected. As a result, method and design
of electromagnetic shielding for PCB Rogowski coil
is very important [16].
Fig. 12. Frequency characteristics curve of designed PCB
Rogowski coil.
7.1. Method and Design of Electric Field
Shielding
Rogowski coil is connected in high voltage power
system, the electric field of high voltage power
system will couple through distribution capacitance
of power line and Rogowski coil, then affect the
accuracy of Rogowski coil.
Assumed that u1 is the power line voltage, u2 is
the induced voltage of Rogowski coil, c1 is the
distribution capacitance between power line and
Rogowski coil, c2 is the distribution capacitance
between Rogowski coil and the ground, so
u2 =
c1u1
c1 + c2
(10)
According to the formula (10), the voltage
of Rogowski coil has relationship with their
distribution capacitance and ground capacitance.
Distribution capacitance among Rogowski coils are
difficult to adjust because Rogowski coils are bell
socketed in measured power line, so method and
design of electric field shielding must be adopted.
The essence of electric field shielding is to make
external power line terminate on shielding layer, the
inside implements can avoid the influence of power
line, so the shielding layer must be made of metal
conductor. For this reason, a copper foil was wrapped
on Rogowski coil to protect PCB Rogowski coil from
affecting of electric field. In the process of wrapping
copper foil, the head cannot connect with the end
to avoid producing loop current. And the
shielding field of Rogowski coil must connect
with shielding line of output voltage, they only have
one ground point.
211
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
7.2. Method and Design of Magnetism
Field Shielding
In complex working environment of Rogowski
coil, there are lots of stray magnetism fields, which
can produce voltage in Rogowski coil. The induced
voltage of measured current is necessary signal,
others are noises. In order to measure current
accurately, stray magnetism fields must be shielded.
Magnetism field shielding is more difficult than
electric field shielding because low frequency
magnetic field lines can penetrate metal layer and
affect Rogowski coil, as a result, only the low
resistance of high permeability material was utilized
to shunt magnetic field lines.
In this paper, the cast iron box was utilized, the
Rogowski coil was placed in box, so stray magnetism
field lines were shunt to cast iron box, and the
Rogowski coil was protected from stray magnetism
fields.
In the process of design, cast iron box can shunt
the magnetism field lines produced by measured
current, and can produce current in box, so as
to affect current measurement. So the following steps
were adopted.
1). Open a main air gap groove along crosssectional of box, which is shown in Fig. 13.
Fig. 13. The appearance of cast iron box.
Because the magnetoconductivity of cast iron is
bigger than air, air gap groove make iron box can’t
form loop, reluctance is very big, so the main
magnetic flux will flow into the Rogowski coil inside
the iron box.
2). Open a crack along interior side of iron box so
as to make main magnetic flux can flow into the
Rogowski coil. Without this crack, there will be
an induced current along iron box, so the main
magnetic flux can’t penetrate shielding box.
8. Conclusions
The influence of structure parameters (wire width,
PCB height, inside and outside radius) on electro-
212
magnetic parameters (mutual-inductance and internal
resistance) was researched. Then the frequency
performance and step response of different structure
parameters (N and h) was researched, and carried
on simulation analysis on research result. According
to the result above, the optimum structure parameters
were proposed. Finally the design of electromagnetic
shielding for PCB Rogowski coil was proposed.
From the research of this paper, the conclusion can
be drawn that the designed PCB Rogowski coil has
high sensitivity and accuracy, especially it has big
mutual inductance.
Acknowledgements
This research was supported in part by the Basic
Research Program of Hebei province No. 12212172
and 12212201. A project supported by scientific
research fund of Hebei provincial education
department
(ZD2013102);
Doctor
Scientific
Research Foundation of Hebei United University.
References
[1]. Shen Zhu, Luo Chengmu, Recent progress
in electronic current transformers, Automation
of Electric Power System, 25, 22, 2001, pp. 1-5.
[2]. Fiber Optic Sensors Working Group, Optical Current
Transducers for Power Systems: A Review, IEEE
Transon Power Delivery, 9, 4, 1994, pp. 1778-1788.
[3]. International Electrotechnical Commission, IEC
6004-7, Electronic Voltage Transformers.
[4]. International Electrotechnical Commission, IEC
6004-8, Electronic Current Transducers.
[5]. W. Rogowski, W. Steinhaus, Die Messung der
Magnetischen Spannung, Archtrotech, 1, 1, 1912,
pp. 141-150.
[6]. Ray W. F., The use of Rogowski coils for low
Amplitude
current
waveform
measurement,
in
Proceedings
of
the
IEE
Colloquium
on Measurement Techniques for Power Electronics,
University of Birmingham (UK), 1992, pp. 4-14.
[7]. Ljubomir Kojovic, Rogowski coils Suit Relay
Protection And Measurement, IEEE Computer
Applications in Power, July 1997, pp. 47-52.
[8]. Li Hongbin, Chen Qing, Zhang Mingming, et al.,
Rogowski coils with high accuracy based on printed
circuit boards, High Voltage Engineering, 30, 4, 2004,
pp. 54-55.
[9]. Chen Qing, Li Hongbin, Zhang Mingming, et al.,
Analysis and design of Rogowski coils with main
and assistant printed circuit boards, Automation
of Electric Power Systems, 28, 16, 2004, pp. 79-82.
[10]. Wang C. Y., Chen Y. P., Zhang G., etc., Design
of printed circuit board Rogowski coil for highly
accurate current measurement, in Proceedings of the
IEEE International Conference on Mechatronics and
Automation, 2007, pp. 3801-3806.
[11]. Zhang Y., Li H. B., The reliable design of PCB
Rogowski coil current transformer, in Proceedings
of the International Conference on Power System
Technology, 2006, pp. 1-4.
[12]. Kojovic L. A., Skendzic V., Williams S. E., etc.,
High precision Rogowski coil, USA, Patent 6313623,
2001-11-04.
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 206-213
[13]. Robles G., Argueso M., Sanz J., etc., Identification
of parameters in a Rogowski coil used for the
measurement of partial discharges, in Proceedings
of the IEEE Instrumentation and Measurement
Technology Conference, 2007, pp. 1-4.
[14]. Jin Yongtao, Liu Huijin, Xiong Lingling, Analysis on
the frequency characteristics of Rogowski coil and
also means to broaden the bandwidth of frequency
response, Electrical Measurement & Instrumentation,
40, 9, 2003, pp. 12-16.
[15]. K. Heumamn, Magnetic Potentiometer of High
Precision, IEEE Trans on IM, 15, 4, 1966,
pp. 245-250.
[16]. Qiao Hui, Research and realization of novel current
transducer based on Rogowski coil, Master Thesis,
WuHan University, 2004.
___________________
2014 Copyright ©, International Frequency Sensor Association (IFSA) Publishing, S. L. All rights reserved.
(http://www.sensorsportal.com)
213