- Email: [email protected]
Faraday current sensors and the significance of subtended angles
Sensors and Actuators A 63 (1997) 119–123
Faraday current sensors and the significance of subtended angles N.E. Fisher, D.A. Jackson U, G.A. Woolsey 1 Applied Optics Group, Physics Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NR, UK Received 8 October 1996; revised 2 April 1997; accepted 2 April 1997
Abstract A series of experiments, involving measurements of Faraday rotation for light beams in linear and closed-loop optical current sensors, confirms that the degree of Faraday rotation of the polarization azimuth of a linearly polarized light beam, travelling in the vicinity of a current-carrying wire, is a linear function of the angle subtended at the wire by the beam. The experiments have been used to demonstrate the magnitudes of the errors that occur for different path geometries in a triangular closed-loop bulk-glass current sensor. The results of this work should enable geometrical design criteria for bulk-glass current sensors to be more readily established in future. q 1997 Elsevier Science S.A. Keywords: Bulk-glass current sensors; Faraday current sensors; Optical current sensors; Subtended angles
1. Introduction Optical current sensors are being developed for use in the power distribution industry, because of their immunity to high voltages and electromagnetic interference [1,2]. Other potential advantages of optical sensing, compared to conventional current monitors, include freedom from saturation effects, potential for the manufacture of compact and lowcost systems, and capability of providing remote, high-speed monitoring. Optical current sensors make use of the Faraday magneto-optic effect, in which the polarization azimuth of a linearly polarized light beam, propagating within a dielectric medium, is rotated in the presence of a magnetic field. The amount of rotation fF is given by
|
fFsV HPdl
(1)
L
where H is the component of the magnetic field intensity along the light path, V is the Verdet constant of the dielectric material, and the integral is taken over the length L where interaction takes place between the magnetic field and the light beam. The Verdet constant is characteristic of the dielectric material, is a function of temperature and wavelength, and is always positive. For optical glasses, V is of order of magnitude 10y6–10y5 rad Ay1.
Optical current sensors have been based on solid glass and optical-fibre sensing elements: for the latter case, the fibre is wound as a coil around the current-carrying conductor. Silica has a relatively small Verdet constant, 4.7=10y6 rad Ay1, and so a large number of turns allows the sensitivity of the system to be increased. A major advantage of the all-fibre system is that the complete sensor, including input and output links, can be fabricated from a single continuous length of fibre, thus making the system optically simple. Unfortunately, such an all-fibre current sensor exhibits a high degree of bendinduced linear and circular birefringence, and this results in reduced sensitivity and the introduction of temperature effects. Because of the birefringent problems encountered with all-fibre sensing, research into bulk-glass systems is still being pursued despite the more complex optics required. Several configurations have been used, and these have been reviewed by Ning and Jackson [3]. An important advantage of a bulk-glass system over an all-fibre system is that a glass with a large Verdet constant can be chosen: glasses are available with Verdet constants that are an order of magnitude higher than that of fused silica. The concept of a bulk-glass sensor can be demonstrated using a glass rod, around which the current-carrying wire is wrapped to form a solenoid. Under these conditions, the rotation of the polarization azimuth fF of the linearly polarized light passing along the axis of a rod of length L is given by
U
Corresponding author. Phone: q44 167 732 427. Fax: q44 167 733 413. E-mail: D.A. [email protected] 1 On leave from the Department of Physics, University of New England, Armidale, NSW 2351, Australia.
VNLNCIC fFs [(R2qL2)1/2yR] L
(2)
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 7 ) 0 1 5 8 4 - 7
Journal: SNA (Sensors and Actuators A)
Article: 1665
120
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
where V is the Verdet constant of the glass rod, NL is the number of times the light passes along the rod, NC is the number of turns of the solenoid, IC is the current in the wire and R is the radius of the solenoid. Of course, in practical situations, it is usually necessary to measure the current flowing in a straight current-carrying wire. This could be done simply by placing an appropriate glass rod normal to the wire, and measuring the resultant rotation fF for a polarized beam transmitted along the axis of the rod. To do this requires accurate data on the length of the glass rod, the relative positions of the light beam and wire, and the removal of all other magnetic fields from the vicinity of the glass rod. These requirements are disposed of by arranging for the light beam to traverse through a closed loop around the wire. Under these conditions, Eq. (1) can be written as
fFsV¢HPdl
(3)
and, using Ampe`re’s law, ¢BPdlsmI
(4)
where B is the magnetic induction, m is the magnetic permeability of the glass medium and I is the current in the wire, fF becomes
fFsVI
2. The role of subtended angle In Section 1, we saw how, for a closed optical path, the Faraday-effect relation may be reduced to a simpler and more practically useful form through the application of Ampe`re’s law. As demonstrated by Rogers [5], a similar reduction can be carried out for an optical path of any shape, with
fFs
VIa 2p
(6)
where a is the angle subtended at the conductor by the optical path. For a path in the form of a closed loop of exactly 2p, this reduces to Eq. (5). Eq. (6) has the following practical consequences when a current-carrying wire is placed normal to the plane containing an optical path: (i) each section of the optical path adjacent to the wire contributes to fF according to the angle subtended at the wire by the path; (ii) for a closed optical loop of exactly 2p, fF is independent of the location of the wire when it is within the loop; (iii) if the wire is placed outside a closed optical loop of exactly 2p, it makes no net contribution to fF; (iv) if the loop in a bulk-glass sensor is either incomplete or includes any additional optical paths within the glass, the total angle subtended at a wire within the loop is no longer 2p, and the measured net fF will depend on the position of the wire within the loop.
(5)
Several methods have been devised to provide a closed optical loop within a bulk-glass sensing element. These include arrangements which are square shaped, triangular shaped and ring shaped [3]. All have been demonstrated successfully, but each will require further refinement before they are likely to be accepted commercially. Their existing limitations are associated with the need to: (i) manufacture the bulk-glass units with very high tolerances in their optical geometries, so that the light reflections that produce the closed loop do not modify the polarization of the light beam, (ii) eliminate the effects of vibration: a method has recently been implemented to do this for a bulk-optic sensor that uses fibre links [4], and (iii) ensure that the total angle subtended at the currentcarrying wire by the optical path is indeed a perfect closed path. If these conditions are not satisfied, the amount of Faraday rotation, and hence the current measured by the sensor, may depend on the location of the wire within the loop, and any current-carrying conductors which are outside the loop may contribute to the net Faraday rotation. This paper focuses on condition (iii), by showing how the effect of an imperfect closed path can be quantified, and by demonstrating the effect for a triangular-shaped bulk-glass sensor.
3. Experimental results and discussion A series of experiments has been carried out to verify Eq. (6) and to demonstrate its consequences. Measurements of the rotation fF of the polarization azimuth were made for light within two bulk-glass systems, using the arrangements shown in Fig. 1. A Sharp LT023 780 nm laser diode was pigtailed to a length of single-mode optical fibre (Fibercore Hi-Bi 750; NA, 0.6; beat length, 2 mm; and cut-off wavelength, 750 nm), with the output polarization state of the laser light launched along one of the eigenaxes of the fibre. In this way, the polarization-maintaining property of the fibre was utilized. The polarized light from the fibre entered the bulkglass system through a GRIN lens and a polarizer. One of the two systems was a triangular closed-loop sensor as used by previous workers [6], manufactured from Schott SF-6 glass. The other was a glass rod of length 100 mm and square cross section of side 10 mm, with the light travelling along the axis. The rod was of Pilkington DEDF flint glass. The light leaving the bulk-glass system was detected after passing through an analyser, with the angle between the axis of the analyser and the axis of the input polarizer fixed at 458. Under these conditions, the detector signal has d.c. and peak a.c. components, Id.c. and Ia.c., which are related by Ia.c. sy2fF sin vt Id.c.
Journal: SNA (Sensors and Actuators A)
(7)
Article: 1665
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
121
Fig. 2. Polarization rotation per unit current (fF/I), for a straight wire near a glass rod, as a function of the angle a at the wire subtended by the rod.
3.2. Experiment b
Fig. 1. (a) Triangular current sensor: (b) Glass-rod current sensor.
where v is the frequency of the a.c. current, and so from measurements of these two components, fF may be determined. 3.1. Experiment a A vertical current-carrying wire was placed at different positions adjacent to the horizontal rod sensor. The wire of diameter 10 mm was placed with its length normal to the rod, so that it extended 25 cm above and below the horizontal rod. The wire was moved to different positions in the horizontal plane and the amount of polarization rotation per unit current (fF/I) measured for different angles subtended by the rod at the wire. Since the wire was of finite length, the values of fF were corrected to allow for reductions in B at the rod below the infinite-wire value of (mI/2pr). The correction factor varied from 1.05 for the largest angle used, to 3.24 for the smallest. Fig. 2 is a graph of corrected (fF/I) as a function of subtended angle a, for currents in the range 120 to 250 A, and a range of wire positions up to a perpendicular distance of 150 mm from the glass rod. A least-squares fit of the data together with Eq. (6), provides a value for the Verdet constant of the rod of 1.39"0.03=10y5 rad Ay1. In order to verify the value of the Verdet constant deduced from these data, a 100-turn solenoid was wound over the length of the rod, and the rotation of polarization measured as a function of current in the solenoid, for light of wavelength 780 nm. Using the solenoid data, Eq. (2) gives a value of 1.38"0.03=10y5 rad Ay1. The linear form of Fig. 2, and the agreement between the values of Verdet constant derived from the glass-rod data and the solenoid data, provide confirmation of Eq. (6) describing the relationship between Faraday rotation and subtended angle.
The geometry of the triangular bulk-glass current sensor is such that it is difficult to launch the light into the sensor so that the optical path is an exact closed loop. A small degree of overlap of the input and output arms invariably occurs. According to Eq. (6), this will result in a contribution to fF which will vary with the position of the current-carrying wire within the loop. This effect was investigated by examining the dependence of fF on wire position for the minimum degree of input/output path overlap, and for the maximum degree of overlap with the two paths moved as close as possible to the inner glass/air interface. The two overlap situations are drawn in Fig. 3 together with the chosen wire positions. For positions B, C, D and E, the wire was placed as close to the sensor edge as possible without touching it. For the minimum overlap position, the values of fF at the five positions were measured to have values within 0.3% of each other, and this is within the experimental uncertainty of
Fig. 3. Triangular sensor, positions of current-carrying wire, and light path for (a) minimum overlap within the sensor; (b) maximum overlap within the sensor.
Journal: SNA (Sensors and Actuators A)
Article: 1665
122
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
Table 1 Predicted and measured percentage increases in fF for different wire positions within the triangular current sensor, when maximum overlap of the input and output beams occurs
Table 2 Predicted and measured percentage increases in fF for different wire positions within the triangular current sensor, when the glass rod intercepts the output beam
Position
Subtended angle (rad)
Predicted % increase
Measured % increase
Position
Subtended angle (rad)
Predicted % increase
Measured % increase
A B C D E
0.192 0.175 0.175 0.157 0.245
3.1 2.8 2.8 2.5 3.9
3.2 4.6 4.3 2.8 5.2
A B C D E
0.148 0.070 0.227 0.131 0.166
2.4 1.1 3.6 2.1 2.6
3.2 0.2 3.6 2.5 3.2
the measurements. At minimum overlap, the optical path length outside the triangular closed loop is about 2 mm. This corresponds to an additional angle subtended at the wire for position E, where the maximum effect is to be expected, of only 9=10y3 rad, and this would add to fF by less than 0.2%. This result indicates that the wire position within the loop is not critical for this particular sensor, when the overlap of the input and output paths is kept to a minimum. When the conducting wire was moved outside the sensor, within the experimental uncertainty, no effect was observed for currents up to 200 A. The experiment was repeated for the maximum overlap position where each of the input and output paths has a length of 25 mm outside the closed loop. This corresponds to an additional angle for each wire position, varying from a minimum of 0.157 rad for position D to a maximum of 0.245 rad for position E, with the subtended angles for positions A, B and C, being closely the same at around 0.18 rad. Table 1 compares the measured percentage changes in fF for each wire position, with respect to the minimum overlap value for that position, and the percentage changes predicted from Eq. (6). All of the measurements show an increase in fF as predicted, and the measured values give very acceptable agreement with the predictions, considering that the optical system has to be completely realigned on going from minimum to maximum overlap. The results of this experiment clearly show that it is important to maintain the angle subtended at the current-carrying wire, within the loop of a Faraday-effect current sensor, as closely as possible to 2p. Any deviation from this value will modify the rotation of the polarization azimuth and hence introduce errors into the current measurement. The level of this modification can be predicted from the geometry of the system and Eq. (6). 3.3. Experiment c This experiment was designed to allow examination of the angular effect for a closed-path arrangement, in a manner which would require less realignment of the system optics than for Experiment b. It is essentially a combination of Experiments a and b, with measurements being made on the triangular current sensor, both with and without the 100 mm long glass rod being interposed along the output beam of the
triangular sensor. The arrangement of Fig. 1(a) was used with a long enough gap between the output face of the sensor and the analyser to accommodate the rod. The triangular sensor was aligned for minimum input/output beam overlap. Once again, measurements of fF were made for wire positions A, B, C, D and E. Table 2 lists the angles subtended by the rod at the wire for each position, and the percentage increases in fF that these should produce, as calculated using Eq. (6). It is interesting to note that the predicted effect on fF of the 100 mm long glass rod for most wire positions is somewhat less than that of the additional path of 50 mm produced at maximum cross-over in Experiment b, since, of course, it is the subtended angle that is significant and not simply the extra path length. When measurements of fF were made at a current of 120 A with the rod in position, the values obtained showed an increase over the values obtained without the rod in position. The measured percentage increases are listed in Table 2. Again, all show reasonable agreement with the predicted values and fall within the experimental uncertainties.
4. Conclusions Optical current sensors rely on the Faraday rotation of the polarization azimuth of a linearly polarized light beam, travelling in the vicinity of a current-carrying wire. Most practical sensors are designed to have an optical path which forms a closed loop around the current being measured so that the position of the current-carrying wire within the loop is irrelevant, and current sources external to the loop have no effect. When the angle subtended at the wire by the path is not exactly 2p, errors in current measurement can occur, but these can be readily predicted using the linear relation between degree of Faraday rotation and subtended angle. A series of experiments involving measurements of Faraday rotation for light beams in linear and closed-loop sensors has been carried out. The results of these measurements show clearly the linear dependence of the amount of rotation on the angle subtended at the current by the optical path. The experiments and the simple subtended-angle analysis have also been used to demonstrate the magnitudes of the errors that occur for different path geometries in a triangular closed-loop bulk-glass current sensor.
Journal: SNA (Sensors and Actuators A)
Article: 1665
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
Clearly, it is important to design current sensors with absolute minimum overlap. A small degree of overlap causes little error in the measured current when only the current being measured is taken into account. This is because the error will simply be the ratio of the angle subtended at the wire by the path beyond the closed loop relative to 2p. On the other hand, a nearby external current-carrying wire has the potential to introduce substantial error. For example, an optical path of 1 mm beyond the closed loop of a sensor can produce an additional angle of up to 0.01 rad for an external conductor at a distance of say, 100 mm. This represents an increase in angle over 2p of less than 0.2%; but if the external conductor is carrying a current of say, 10 times that being measured by the sensor, an error of nearly 2% will be introduced. In order for the error in the latter situation to be reduced to less than say, 0.2%, the external conductor would need to be more than 0.8 m from the sensor. Using the subtended-angle approach, such predictions can readily be made for any optical current sensor, and we believe that the results of this work will enable geometrical design criteria for bulk-glass current sensors to be more readily established in future.
References [1] A.M. Smith, Optical fibre for current measurement applications, Opt. Laser Tech., 12 (1980) 25–29. [2] A.J. Rogers, Optical-fibre current measurement, Int. J. Opt., 3 (1989) 391–407. [3] Y.N. Ning and D.A. Jackson, Review of optical current sensors using bulk-glass sensing elements, Sensors and Actuators A, 39 (1993) 219– 224. [4] N.E. Fisher and D.A. Jackson, A common-mode optical noise-rejection scheme for an extrinsic Faraday current sensor, Meas. Sci. Technol., 7 (1996) 1–5. [5] A.J. Rogers, Optical technique for measurement of current at high voltage, Proc. IEE, 120 (1973) 261–267. [6] B.C.B. Chu, Y.N. Ning and D.A. Jackson, Faraday current sensor that uses a triangular-shaped bulk-optic sensing element, Opt. Lett., 17 (1992) 1167–1169.
Biographies Norman Fisher studied physics at Queen Mary and Westfield College (University of London). He also obtained his Ph.D. there in solid-state physics in 1990. His research inter-
123
ests have included charge transport in polydiacetylenes, the interaction of microwaves with dielectric targets, strain sensing utilizing the Raman properties of polymer crystals, and Faraday current sensing. He is currently a research fellow with the Applied Optics Group at the University of Kent at Canterbury, where he is investigating the feasibility of using in-fibre Bragg gratings for medical applications. David Jackson was born in London. He studied physics at the University of Southampton and then undertook research leading to a Ph.D. in nuclear physics at Birkbeck College, University of London. In 1965 he joined the physics laboratory at the University of Kent at Canterbury, where his main research interests were in the study of microscopic and macroscopic motion by laser light scattering. In 1976 and 1979 he spent sabbatical years at the Naval Research Laboratory, Washington, DC, USA. During the second sabbatical year he was responsible for the introduction of the first servo-controlled all-fibre Mach–Zehnder interferometer. His current research activities include intrinsic and extrinsic monomode optic sensors and high-speed optical signal processing based upon fibre-optic topologies and secure high-bandwidth optical communications systems. He was awarded the Callendar Medal in 1987 by the Institute of Measurement and Control, and has authored or co-authored over 250 journal and 200 conference papers and publications. He is currently professor of applied optics and head of the Applied Optics Group at the University of Kent at Canterbury. Gerry Woolsey completed his B.Sc. and Ph.D. degrees in the Department of Physics at the Queen’s University of Belfast. In 1968, he joined the Department of Physics at the University of New England in Armidale, NSW, Australia, where he is now associate professor of physics. In 1980, he was visiting research fellow at the University of California, Santa Barbara, under the auspices of the US/Australia Scientific Cooperative Science Program, and for 1985, was Royal Society Guest Research Fellow in the Department of Electronic and Electrical Engineering at the University of Strathclyde. His research interests are in the areas of electrical discharges in gases, and the optical sensing of these discharges. He has published widely in these areas, and, in 1993, was awarded the degree of D.Sc. by the University of New England for his contributions to research on electrical discharges.
Journal: SNA (Sensors and Actuators A)
Article: 1665
Faraday current sensors and the significance of subtended angles N.E. Fisher, D.A. Jackson U, G.A. Woolsey 1 Applied Optics Group, Physics Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NR, UK Received 8 October 1996; revised 2 April 1997; accepted 2 April 1997
Abstract A series of experiments, involving measurements of Faraday rotation for light beams in linear and closed-loop optical current sensors, confirms that the degree of Faraday rotation of the polarization azimuth of a linearly polarized light beam, travelling in the vicinity of a current-carrying wire, is a linear function of the angle subtended at the wire by the beam. The experiments have been used to demonstrate the magnitudes of the errors that occur for different path geometries in a triangular closed-loop bulk-glass current sensor. The results of this work should enable geometrical design criteria for bulk-glass current sensors to be more readily established in future. q 1997 Elsevier Science S.A. Keywords: Bulk-glass current sensors; Faraday current sensors; Optical current sensors; Subtended angles
1. Introduction Optical current sensors are being developed for use in the power distribution industry, because of their immunity to high voltages and electromagnetic interference [1,2]. Other potential advantages of optical sensing, compared to conventional current monitors, include freedom from saturation effects, potential for the manufacture of compact and lowcost systems, and capability of providing remote, high-speed monitoring. Optical current sensors make use of the Faraday magneto-optic effect, in which the polarization azimuth of a linearly polarized light beam, propagating within a dielectric medium, is rotated in the presence of a magnetic field. The amount of rotation fF is given by
|
fFsV HPdl
(1)
L
where H is the component of the magnetic field intensity along the light path, V is the Verdet constant of the dielectric material, and the integral is taken over the length L where interaction takes place between the magnetic field and the light beam. The Verdet constant is characteristic of the dielectric material, is a function of temperature and wavelength, and is always positive. For optical glasses, V is of order of magnitude 10y6–10y5 rad Ay1.
Optical current sensors have been based on solid glass and optical-fibre sensing elements: for the latter case, the fibre is wound as a coil around the current-carrying conductor. Silica has a relatively small Verdet constant, 4.7=10y6 rad Ay1, and so a large number of turns allows the sensitivity of the system to be increased. A major advantage of the all-fibre system is that the complete sensor, including input and output links, can be fabricated from a single continuous length of fibre, thus making the system optically simple. Unfortunately, such an all-fibre current sensor exhibits a high degree of bendinduced linear and circular birefringence, and this results in reduced sensitivity and the introduction of temperature effects. Because of the birefringent problems encountered with all-fibre sensing, research into bulk-glass systems is still being pursued despite the more complex optics required. Several configurations have been used, and these have been reviewed by Ning and Jackson [3]. An important advantage of a bulk-glass system over an all-fibre system is that a glass with a large Verdet constant can be chosen: glasses are available with Verdet constants that are an order of magnitude higher than that of fused silica. The concept of a bulk-glass sensor can be demonstrated using a glass rod, around which the current-carrying wire is wrapped to form a solenoid. Under these conditions, the rotation of the polarization azimuth fF of the linearly polarized light passing along the axis of a rod of length L is given by
U
Corresponding author. Phone: q44 167 732 427. Fax: q44 167 733 413. E-mail: D.A. [email protected] 1 On leave from the Department of Physics, University of New England, Armidale, NSW 2351, Australia.
VNLNCIC fFs [(R2qL2)1/2yR] L
(2)
0924-4247/97/$17.00 q 1997 Elsevier Science S.A. All rights reserved PII S 0 9 2 4 - 4 2 4 7 ( 9 7 ) 0 1 5 8 4 - 7
Journal: SNA (Sensors and Actuators A)
Article: 1665
120
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
where V is the Verdet constant of the glass rod, NL is the number of times the light passes along the rod, NC is the number of turns of the solenoid, IC is the current in the wire and R is the radius of the solenoid. Of course, in practical situations, it is usually necessary to measure the current flowing in a straight current-carrying wire. This could be done simply by placing an appropriate glass rod normal to the wire, and measuring the resultant rotation fF for a polarized beam transmitted along the axis of the rod. To do this requires accurate data on the length of the glass rod, the relative positions of the light beam and wire, and the removal of all other magnetic fields from the vicinity of the glass rod. These requirements are disposed of by arranging for the light beam to traverse through a closed loop around the wire. Under these conditions, Eq. (1) can be written as
fFsV¢HPdl
(3)
and, using Ampe`re’s law, ¢BPdlsmI
(4)
where B is the magnetic induction, m is the magnetic permeability of the glass medium and I is the current in the wire, fF becomes
fFsVI
2. The role of subtended angle In Section 1, we saw how, for a closed optical path, the Faraday-effect relation may be reduced to a simpler and more practically useful form through the application of Ampe`re’s law. As demonstrated by Rogers [5], a similar reduction can be carried out for an optical path of any shape, with
fFs
VIa 2p
(6)
where a is the angle subtended at the conductor by the optical path. For a path in the form of a closed loop of exactly 2p, this reduces to Eq. (5). Eq. (6) has the following practical consequences when a current-carrying wire is placed normal to the plane containing an optical path: (i) each section of the optical path adjacent to the wire contributes to fF according to the angle subtended at the wire by the path; (ii) for a closed optical loop of exactly 2p, fF is independent of the location of the wire when it is within the loop; (iii) if the wire is placed outside a closed optical loop of exactly 2p, it makes no net contribution to fF; (iv) if the loop in a bulk-glass sensor is either incomplete or includes any additional optical paths within the glass, the total angle subtended at a wire within the loop is no longer 2p, and the measured net fF will depend on the position of the wire within the loop.
(5)
Several methods have been devised to provide a closed optical loop within a bulk-glass sensing element. These include arrangements which are square shaped, triangular shaped and ring shaped [3]. All have been demonstrated successfully, but each will require further refinement before they are likely to be accepted commercially. Their existing limitations are associated with the need to: (i) manufacture the bulk-glass units with very high tolerances in their optical geometries, so that the light reflections that produce the closed loop do not modify the polarization of the light beam, (ii) eliminate the effects of vibration: a method has recently been implemented to do this for a bulk-optic sensor that uses fibre links [4], and (iii) ensure that the total angle subtended at the currentcarrying wire by the optical path is indeed a perfect closed path. If these conditions are not satisfied, the amount of Faraday rotation, and hence the current measured by the sensor, may depend on the location of the wire within the loop, and any current-carrying conductors which are outside the loop may contribute to the net Faraday rotation. This paper focuses on condition (iii), by showing how the effect of an imperfect closed path can be quantified, and by demonstrating the effect for a triangular-shaped bulk-glass sensor.
3. Experimental results and discussion A series of experiments has been carried out to verify Eq. (6) and to demonstrate its consequences. Measurements of the rotation fF of the polarization azimuth were made for light within two bulk-glass systems, using the arrangements shown in Fig. 1. A Sharp LT023 780 nm laser diode was pigtailed to a length of single-mode optical fibre (Fibercore Hi-Bi 750; NA, 0.6; beat length, 2 mm; and cut-off wavelength, 750 nm), with the output polarization state of the laser light launched along one of the eigenaxes of the fibre. In this way, the polarization-maintaining property of the fibre was utilized. The polarized light from the fibre entered the bulkglass system through a GRIN lens and a polarizer. One of the two systems was a triangular closed-loop sensor as used by previous workers [6], manufactured from Schott SF-6 glass. The other was a glass rod of length 100 mm and square cross section of side 10 mm, with the light travelling along the axis. The rod was of Pilkington DEDF flint glass. The light leaving the bulk-glass system was detected after passing through an analyser, with the angle between the axis of the analyser and the axis of the input polarizer fixed at 458. Under these conditions, the detector signal has d.c. and peak a.c. components, Id.c. and Ia.c., which are related by Ia.c. sy2fF sin vt Id.c.
Journal: SNA (Sensors and Actuators A)
(7)
Article: 1665
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
121
Fig. 2. Polarization rotation per unit current (fF/I), for a straight wire near a glass rod, as a function of the angle a at the wire subtended by the rod.
3.2. Experiment b
Fig. 1. (a) Triangular current sensor: (b) Glass-rod current sensor.
where v is the frequency of the a.c. current, and so from measurements of these two components, fF may be determined. 3.1. Experiment a A vertical current-carrying wire was placed at different positions adjacent to the horizontal rod sensor. The wire of diameter 10 mm was placed with its length normal to the rod, so that it extended 25 cm above and below the horizontal rod. The wire was moved to different positions in the horizontal plane and the amount of polarization rotation per unit current (fF/I) measured for different angles subtended by the rod at the wire. Since the wire was of finite length, the values of fF were corrected to allow for reductions in B at the rod below the infinite-wire value of (mI/2pr). The correction factor varied from 1.05 for the largest angle used, to 3.24 for the smallest. Fig. 2 is a graph of corrected (fF/I) as a function of subtended angle a, for currents in the range 120 to 250 A, and a range of wire positions up to a perpendicular distance of 150 mm from the glass rod. A least-squares fit of the data together with Eq. (6), provides a value for the Verdet constant of the rod of 1.39"0.03=10y5 rad Ay1. In order to verify the value of the Verdet constant deduced from these data, a 100-turn solenoid was wound over the length of the rod, and the rotation of polarization measured as a function of current in the solenoid, for light of wavelength 780 nm. Using the solenoid data, Eq. (2) gives a value of 1.38"0.03=10y5 rad Ay1. The linear form of Fig. 2, and the agreement between the values of Verdet constant derived from the glass-rod data and the solenoid data, provide confirmation of Eq. (6) describing the relationship between Faraday rotation and subtended angle.
The geometry of the triangular bulk-glass current sensor is such that it is difficult to launch the light into the sensor so that the optical path is an exact closed loop. A small degree of overlap of the input and output arms invariably occurs. According to Eq. (6), this will result in a contribution to fF which will vary with the position of the current-carrying wire within the loop. This effect was investigated by examining the dependence of fF on wire position for the minimum degree of input/output path overlap, and for the maximum degree of overlap with the two paths moved as close as possible to the inner glass/air interface. The two overlap situations are drawn in Fig. 3 together with the chosen wire positions. For positions B, C, D and E, the wire was placed as close to the sensor edge as possible without touching it. For the minimum overlap position, the values of fF at the five positions were measured to have values within 0.3% of each other, and this is within the experimental uncertainty of
Fig. 3. Triangular sensor, positions of current-carrying wire, and light path for (a) minimum overlap within the sensor; (b) maximum overlap within the sensor.
Journal: SNA (Sensors and Actuators A)
Article: 1665
122
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
Table 1 Predicted and measured percentage increases in fF for different wire positions within the triangular current sensor, when maximum overlap of the input and output beams occurs
Table 2 Predicted and measured percentage increases in fF for different wire positions within the triangular current sensor, when the glass rod intercepts the output beam
Position
Subtended angle (rad)
Predicted % increase
Measured % increase
Position
Subtended angle (rad)
Predicted % increase
Measured % increase
A B C D E
0.192 0.175 0.175 0.157 0.245
3.1 2.8 2.8 2.5 3.9
3.2 4.6 4.3 2.8 5.2
A B C D E
0.148 0.070 0.227 0.131 0.166
2.4 1.1 3.6 2.1 2.6
3.2 0.2 3.6 2.5 3.2
the measurements. At minimum overlap, the optical path length outside the triangular closed loop is about 2 mm. This corresponds to an additional angle subtended at the wire for position E, where the maximum effect is to be expected, of only 9=10y3 rad, and this would add to fF by less than 0.2%. This result indicates that the wire position within the loop is not critical for this particular sensor, when the overlap of the input and output paths is kept to a minimum. When the conducting wire was moved outside the sensor, within the experimental uncertainty, no effect was observed for currents up to 200 A. The experiment was repeated for the maximum overlap position where each of the input and output paths has a length of 25 mm outside the closed loop. This corresponds to an additional angle for each wire position, varying from a minimum of 0.157 rad for position D to a maximum of 0.245 rad for position E, with the subtended angles for positions A, B and C, being closely the same at around 0.18 rad. Table 1 compares the measured percentage changes in fF for each wire position, with respect to the minimum overlap value for that position, and the percentage changes predicted from Eq. (6). All of the measurements show an increase in fF as predicted, and the measured values give very acceptable agreement with the predictions, considering that the optical system has to be completely realigned on going from minimum to maximum overlap. The results of this experiment clearly show that it is important to maintain the angle subtended at the current-carrying wire, within the loop of a Faraday-effect current sensor, as closely as possible to 2p. Any deviation from this value will modify the rotation of the polarization azimuth and hence introduce errors into the current measurement. The level of this modification can be predicted from the geometry of the system and Eq. (6). 3.3. Experiment c This experiment was designed to allow examination of the angular effect for a closed-path arrangement, in a manner which would require less realignment of the system optics than for Experiment b. It is essentially a combination of Experiments a and b, with measurements being made on the triangular current sensor, both with and without the 100 mm long glass rod being interposed along the output beam of the
triangular sensor. The arrangement of Fig. 1(a) was used with a long enough gap between the output face of the sensor and the analyser to accommodate the rod. The triangular sensor was aligned for minimum input/output beam overlap. Once again, measurements of fF were made for wire positions A, B, C, D and E. Table 2 lists the angles subtended by the rod at the wire for each position, and the percentage increases in fF that these should produce, as calculated using Eq. (6). It is interesting to note that the predicted effect on fF of the 100 mm long glass rod for most wire positions is somewhat less than that of the additional path of 50 mm produced at maximum cross-over in Experiment b, since, of course, it is the subtended angle that is significant and not simply the extra path length. When measurements of fF were made at a current of 120 A with the rod in position, the values obtained showed an increase over the values obtained without the rod in position. The measured percentage increases are listed in Table 2. Again, all show reasonable agreement with the predicted values and fall within the experimental uncertainties.
4. Conclusions Optical current sensors rely on the Faraday rotation of the polarization azimuth of a linearly polarized light beam, travelling in the vicinity of a current-carrying wire. Most practical sensors are designed to have an optical path which forms a closed loop around the current being measured so that the position of the current-carrying wire within the loop is irrelevant, and current sources external to the loop have no effect. When the angle subtended at the wire by the path is not exactly 2p, errors in current measurement can occur, but these can be readily predicted using the linear relation between degree of Faraday rotation and subtended angle. A series of experiments involving measurements of Faraday rotation for light beams in linear and closed-loop sensors has been carried out. The results of these measurements show clearly the linear dependence of the amount of rotation on the angle subtended at the current by the optical path. The experiments and the simple subtended-angle analysis have also been used to demonstrate the magnitudes of the errors that occur for different path geometries in a triangular closed-loop bulk-glass current sensor.
Journal: SNA (Sensors and Actuators A)
Article: 1665
N.E. Fisher et al. / Sensors and Actuators A 63 (1997) 119–123
Clearly, it is important to design current sensors with absolute minimum overlap. A small degree of overlap causes little error in the measured current when only the current being measured is taken into account. This is because the error will simply be the ratio of the angle subtended at the wire by the path beyond the closed loop relative to 2p. On the other hand, a nearby external current-carrying wire has the potential to introduce substantial error. For example, an optical path of 1 mm beyond the closed loop of a sensor can produce an additional angle of up to 0.01 rad for an external conductor at a distance of say, 100 mm. This represents an increase in angle over 2p of less than 0.2%; but if the external conductor is carrying a current of say, 10 times that being measured by the sensor, an error of nearly 2% will be introduced. In order for the error in the latter situation to be reduced to less than say, 0.2%, the external conductor would need to be more than 0.8 m from the sensor. Using the subtended-angle approach, such predictions can readily be made for any optical current sensor, and we believe that the results of this work will enable geometrical design criteria for bulk-glass current sensors to be more readily established in future.
References [1] A.M. Smith, Optical fibre for current measurement applications, Opt. Laser Tech., 12 (1980) 25–29. [2] A.J. Rogers, Optical-fibre current measurement, Int. J. Opt., 3 (1989) 391–407. [3] Y.N. Ning and D.A. Jackson, Review of optical current sensors using bulk-glass sensing elements, Sensors and Actuators A, 39 (1993) 219– 224. [4] N.E. Fisher and D.A. Jackson, A common-mode optical noise-rejection scheme for an extrinsic Faraday current sensor, Meas. Sci. Technol., 7 (1996) 1–5. [5] A.J. Rogers, Optical technique for measurement of current at high voltage, Proc. IEE, 120 (1973) 261–267. [6] B.C.B. Chu, Y.N. Ning and D.A. Jackson, Faraday current sensor that uses a triangular-shaped bulk-optic sensing element, Opt. Lett., 17 (1992) 1167–1169.
Biographies Norman Fisher studied physics at Queen Mary and Westfield College (University of London). He also obtained his Ph.D. there in solid-state physics in 1990. His research inter-
123
ests have included charge transport in polydiacetylenes, the interaction of microwaves with dielectric targets, strain sensing utilizing the Raman properties of polymer crystals, and Faraday current sensing. He is currently a research fellow with the Applied Optics Group at the University of Kent at Canterbury, where he is investigating the feasibility of using in-fibre Bragg gratings for medical applications. David Jackson was born in London. He studied physics at the University of Southampton and then undertook research leading to a Ph.D. in nuclear physics at Birkbeck College, University of London. In 1965 he joined the physics laboratory at the University of Kent at Canterbury, where his main research interests were in the study of microscopic and macroscopic motion by laser light scattering. In 1976 and 1979 he spent sabbatical years at the Naval Research Laboratory, Washington, DC, USA. During the second sabbatical year he was responsible for the introduction of the first servo-controlled all-fibre Mach–Zehnder interferometer. His current research activities include intrinsic and extrinsic monomode optic sensors and high-speed optical signal processing based upon fibre-optic topologies and secure high-bandwidth optical communications systems. He was awarded the Callendar Medal in 1987 by the Institute of Measurement and Control, and has authored or co-authored over 250 journal and 200 conference papers and publications. He is currently professor of applied optics and head of the Applied Optics Group at the University of Kent at Canterbury. Gerry Woolsey completed his B.Sc. and Ph.D. degrees in the Department of Physics at the Queen’s University of Belfast. In 1968, he joined the Department of Physics at the University of New England in Armidale, NSW, Australia, where he is now associate professor of physics. In 1980, he was visiting research fellow at the University of California, Santa Barbara, under the auspices of the US/Australia Scientific Cooperative Science Program, and for 1985, was Royal Society Guest Research Fellow in the Department of Electronic and Electrical Engineering at the University of Strathclyde. His research interests are in the areas of electrical discharges in gases, and the optical sensing of these discharges. He has published widely in these areas, and, in 1993, was awarded the degree of D.Sc. by the University of New England for his contributions to research on electrical discharges.
Journal: SNA (Sensors and Actuators A)
Article: 1665