Abstract:
A current sensor coil design for reducing or eliminating long undulations of magnetic sensitivity. Such reduction or elimination improves isolation of the current sensor such that proximate currents and accompanying effects do not affect the accuracy of the current sensor determination of a current being measured. Several designs, which may be incorporated separately or in combination, include modifying the specifications of the quarter waveplate, cutting the fiber of the sensor coil to a proper length, choosing a proper perimeter length of the sensor coil or head, and using a particular length of fiber adjusted to work in conjunction with a multi-wavelength or broadband light source.

Description:
BACKGROUND 
     The invention pertains to current sensors and particularly to fiber optic current sensors. More particularly, the invention pertains to fiber optic current sensors having improved isolation. 
     Fiber optic current sensors operate on the principle that the magnetic field produced by an electrical current affects certain properties of the light contained in an optical fiber wound around the current carrying conductor. Through the Faraday effect, those properties affected can be either the polarization state of the light (polarimetric type sensor) or the velocity of the light (interferometric type sensor). Through Ampere&#39;s law, 
     
       
         φH·dl=I,  (1) 
       
     
     it is evident that for the current sensor to make an accurate determination of the current, I, the light in the fiber should be uniformly and linearly sensitive to the magnetic field, H, and the sensitive region should comprise as perfectly a closed path as possible. In this case, the sensor substantially measures φH·dl, thereby giving an indication of I as an output, provided that the sensor is well isolated against currents flowing outside the sensing loop. In addition, the sensor should return the correct value of I regardless of the actual location of the current flowing through the sensing coil. 
     A number of applications for current sensing exist which require the sensor to exhibit an extremely good isolation from external currents as well as extremely uniform response to currents that pass through the sensing coil at different physical locations. For example, a ground fault interrupter for large currents may have a difference current measurement system  11  with a sensor coil or head  14  that encloses both the outgoing  12  and return  13  currents (FIG.  5 ). Hundreds of amperes of current may flow through the wires, while a difference between the two currents  12  and  13  of a few milliamperes should be quickly recognized. Such a system may exist in the vicinity of many other conductors carrying hundreds of amperes of current. The isolation of sensor head  14  to external currents should therefore be better than ten parts-per-million, and sensor system  11  should respond uniformly to the outgoing and return currents to within ten parts-per-million. 
     A second example of how a fiber optic current sensor may advantageously benefit from good isolation/uniformity performance is the construction of a fiber optic current sensor  15  assisted current transformer  16  (FIG.  7 ). In this device, fiber optic current sensor  15  is operated using a secondary current  19  from current supply  49  to null the output (i.e., close the loop). A current  18  to be measured passes through a sensing coil or head  17 , while an equal and opposite loop closing current  19  passes through the sensing coil  16 , possibly through multiple turns. Loop closing current  19  includes the secondary of this fiber optic current sensor  15  assisted current transformer. The accuracy of this device depends on current sensor  15  exhibiting uniform response to currents passing therethrough for all the different physical locations of current  18 . 
     A third example of a fiber optic current sensor requiring superior isolation is the displacement current based voltage sensor  20  (FIG.  6 ). In this device, an AC voltage  21  is measured by integrating (by integrator  36  via electro-optics module  37 ) the output of a current sensor head  22  that responds to displacement current. Typically, sensor  20  might measure a few milliamperes of displacement current. The power line, which carries voltage  21  to be measured, may also carry a real current, which might typically be a few thousand amperes. Thus, to obtain a true measure of the voltage, it is necessary for the current sensor head  22  to be well isolated from the real current flowing through the power line. The isolation requirement for this application may easily exceed one part-per-million. 
     A problem with Faraday effect based optical current sensors, both polarimetric  23  (FIG. 2) and interferometric  24 ,  25  (FIGS.  3  and  4 ), is that the sensitivity of the light to the local magnetic field depends on the exact polarization state of the light at that point. It is very difficult to maintain a strictly uniform state of polarization of the light throughout a sensing path of the sensing head or coil, as stresses within the glass induce local birefringences that alter the polarization state of the light. Thus, a method of desensitizing the sensor head to these imperfections is needed in order to achieve the overall intended isolation and uniformity requirements. 
     SUMMARY OF THE INVENTION 
     It has been discovered that maintaining an unaltered polarization state of the light throughout the sensing loop(s) is not a practical necessity to achieve superior isolation and uniformity performance of the sensor. Rather, a sufficient requirement on the sensor head or coil for achieving good isolation and uniformity is that it not exhibit long period undulations in sensitivity. Undulations having long periods reduce isolation of the sensor head so as to be sensitive to other currents not intended to be measured. Accordingly, set forth here are design approaches for fiber optic current sensors that reduce long period undulations in the sensitivity of the sensing head coil. Remaining rapid undulations contribute negligibly to uniformity and isolation errors. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 shows the geometry of an electrical current, its associated magnetic field, and an optical current sensor coil. 
     FIG. 2 shows a polarimetric fiber optic current sensor. 
     FIG. 3 shows a Sagnac loop type fiber optic current sensor. 
     FIG. 4 shows an in-line interferometric type fiber optic current sensor. 
     FIG. 5 shows a fiber optic current sensor for measuring small differences between two large currents. 
     FIG. 6 shows a displacement current-based voltage sensor. 
     FIG. 7 shows a fiber optic current sensor assisted current transformer. 
     FIG. 8 shows a depiction of an optical fiber having a periodic structure used for making a fiber optic current sensing coil. 
     FIG. 9 shows the sensitivity of a fiber optic current sensing coil as a function of distance along the sensing fiber. 
     FIG. 10 shows the direction dependent sensitivity along the sensing coil for a Sagnac loop type fiber optic current sensor having an optimal length of sensing fiber. 
     FIG. 11 shows the direction dependent sensitivity of the sensing coil for an in-line interferometric type fiber current sensor having an optimal length of sensing fiber. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     For a complex plane Z, vector notation is z=ix+jy and scalar notation is z=x+iy). Vector quantities are typed in boldface. As shown in FIG. 1, a current  26 , I, flows perpendicular into the complex plane Z in the k direction at coordinate position z 0 . The magnetic field  27 , H, at position z associated with flowing current  26  is given by,                    H   =       I     2      π                         k   ×     (     z   -     z   0       )                z   -     z   0            2                     =       I     2      π               z   -     z   0            2              {       -     i        (     y   -     y   0       )         +     j        (     x   -     x   0       )         }                     (   2   )                                
     A fiber current sensor head  28  measures 
     
       
         I sensed =φS(z)H·dz,  (3) 
       
     
     where S(z) is the relative sensitivity of sensor head  28  at position z. Ideally, S(z)=1 for all z, i.e., sensor head  28  uniformly responds to magnetic field  27  all along its sensing path. Substituting equation (1) into equation (2) one finds that                I   sensed     =       I     2      π            ∮         S        (   z   )                z   -     z   0            2            {         -     (     y   -     y     0   )         )               x       +       (     x   -     x   0       )               y     .                         (   4   )                                
     Using the relations                        x   -     x   0       =       1   2          (     z   -     z   0     +     z   *     -     z   0                    *)     ;     dx   =       1   2          (     dz   +   dz                *)                   and           (   5   )                         y   -     y   0       =       1     2      i            (     z   -     z   0     +     z   *     -     z   0                    *)     ;     dy   =       1   2          (     dz   +   dz                *)     ,           (   6   )                                
     equation (4) is found to be                I   sensed     =       Re        [       I     2      π                 i            ∮         Re        [     S        (   z   )       ]         z   -     z   0                 z           ]       -       I     2      π                 i              Im        [     ∮         Im        [     S        (   z   )       ]         z   -     z   0                 z         ]       .                 (   7   )                                
     For all real problems, Im[S(z)] must vanish along the path of integration, since the sensitivity must ultimately be a real valued function along the sensing fiber (though it need not be real valued elsewhere). Consequently, the second integral in equation (7) is zero, and Re[S(z)] can be replaced by S(z) in the first integral. Thus, one has the general result that for real sensor heads,                I   sensed     =       Re        [       I     2      π                 i            ∮         Re        [     S        (   z   )       ]         z   -     z   0                 z           ]       .             (   8   )                                
     From equation (8), one can see that current  26  at position z 0  creates a single pole at that point. This corresponds to the physical pole in magnetic field  27  associated with the assumed infinitely thin current flow. For the ideal case that S(z)=1, equation (8) is solved using the residue theorem to yield I sensed =I when the path of integration encloses current  26  (i.e., the path integral encloses the pole at z 0 ), and I sensed =0 when the path of integration does not enclose current  26 . 
     For mathematical simplicity, one now makes the assumption that fiber sensor head  28  lies on the unit circle in the complex plane. Thus, sensor head  28  encloses current  26  carrying wire if |z 0 |&lt;1, and sensor head  28  does not enclose current  26  if |z 0 |&gt;1. The results that follow from this assumption apply exactly to the case of a fiber current sensor with a circular sensing head; however, the principles derived apply also to the case of a “non-circular” sensing head. For example, one could have a square or oval winding as part of sensor head  28 . The isolation and uniformity imperfections derived apply to all types of optical current sensors that operate by integrating the magnetic field. 
     Particular implementations of fiber optic current sensors include a polarimetric current sensor  23  in FIG. 2, a Sagnac loop current sensor  24  in FIG. 3, and an in-line interferometric current sensor  25  in FIG.  4 . 
     In sensor  23 , source  35  outputs light that goes through polarizer  38 , the optical fiber coil of sensor head  28 , and analyzer  39 . Magnetic field  27  of current  26  affects the polarization of the light. This change is noted by detector  40 . The output of detector  40  goes to electronics and signal processor  41 . 
     In sensor  24 , source  35  outputs light through coupler  42  and polarizer  38 . The light is split by coupler  43  into counterpropagating beams for sensor head  28 . The light beams go through quarter waveplates, for conversion to circular polarization and vice versa upon their return to coupler  43 . A bias modulation signal from electronics  41  applied to the light by modulator  44 . The returning beams go through coupler  43  and polarizer  38  to detector  40 . Magnetic field  27  of current  26  affects a phase relationship which is noted at detector  40 . The electrical output of detector  40  goes to electronics and signal processor  41 . 
     In sensor  25 , source  35  outputs light through coupler  42 , polarizer  38  and 45-degree splice  45  to modulator  46 . The output light of modulator  46  goes through fiber delay line  47  and quarter waveplate  33  to an optical fiber coil of sensor head  28 . The light is reflected back by mirror  48  back through the fiber coil of sensor head  28 , quarter waveplate polarization converter  33  and delay line  47  to modulator  46 . The light going back from modulator  46  goes through splice  45 , polarizer  38  and coupler  42  to detector  40 . Magnetic field  27  of current  26  affects the phase relationship of the entering light and returning light of sensor head  28 , which is noted at detector  40 . The electrical output from detector  40  goes to electronics and processor  41 . 
     This technology is related to the in-line optical fiber current sensor as disclosed in U.S. Pat. No. 5,644,397 issued Jul. 1, 1997, to inventor James N. Blake and entitled “Fiber Optic Interferometric Circuit and Magnetic Field Sensor”, which is incorporated herein by reference. Optical fiber sensors are also disclosed in U.S. Pat. No. 5,696,858 issued Dec. 9, 1997, to inventor James N. Blake and entitled, “Fiber Optics Apparatus and Method for Accurate Current Sensing”, which is incorporated herein by reference. 
     The Fourier components of the sensitivity function S(θ) in polar coordinates on the unit circle are e inθ  or e −inθ  where n is an integer. The corresponding Fourier component representations in the complex Z plane are z n  and z −n . 
     The sensitivity function of a ring fiber sensor head  28  can be represented in polar coordinates as                S        (   θ   )       =       S   0     +       ∑     n   =   1              a   n                                n                 θ           +       b   n                 -                      n                 θ                   (   9   )                                
     or generalized in the Z plane as                S        (   z   )       =       S   0     +       ∑     n   =   1              a   n          z   n         +       b   n            z     -   n       .                 (   10   )                                
     In these equations, one restricts the choices of a n  and b n  to satisfy the condition that S(z) is real valued on the unit circle of sensor head  28 . Substituting equation (10) into equation (8) and solving the integral using the residue theorem yields the general relationship between the sensed current and the real current. The results are                  I   sensed     =         I        [       S   0     +     Re        (       ∑     n   =   1              a   n          z   0   n         )         ]                     for                        z   0            &lt;   1                     and           (   11   )                 I   sensed     =         -     IRe        (       ∑     n   =   1              b   n          z   0     -   n           )                       for                        z   0            &gt;   1.             (   12   )                                
     Equation (11) represents the scale factor, or uniformity error associated with the current  26  being offset from the middle of fiber sensing coil  28 , and equation (12) represents the isolation of the sensor to currents  26  passing outside sensing coil  28 . 
     A particularly important example to solve is that where the sensitivity function is given by S(θ)=1+εcos(nθ). As will be shown later, for the case that a sensing fiber  30  of sensor head  28  comprises a periodic structure, a long period undulation in the sensitivity of the fiber to magnetic fields exists. These long undulations ultimately limit the uniformity and isolation performance of the sensor. 
     The radius of sensing fiber coil  28  is taken to be R, and the current  26  carrying wire is taken to be located at the point (r, φ) in polar coordinates. By solving equations (9) through (12), one finds the uniformity error due to a non-centered current to be given by                      I   sensed     I     -   1     =         ɛ   2            (     r   R     )     n                     cos        (     n                 φ     )                     R     &gt;   r       ,           (   13   )                                
     while the isolation to currents outside sensing fiber loop  28  is given by                  I   sensed     I     =           -   ɛ     2            (     R   r     )     n                     cos        (     n                 φ     )                     r     &gt;     R   .               (   14   )                                
     From these results one sees that higher order variations in the sensitivity of fiber sensor head  28  (corresponding to high values of n) contribute negligibly small uniformity errors for nearly centered currents and negligibly small isolation errors for nearby current carrying wires any reasonable distance from the fiber sensor. However, long period undulations in the sensitivity (corresponding to low values of n) give rise to significant errors and should be avoided in the optical design of the sensor head. 
     Both the Sagnac loop  24  and in-line interferometric  25  type current sensors operate on the principle that at circularly polarized light waves propagate with different velocities in the presence of a magnetic field  27 . Thus, for these types of sensor implementations, one desires to launch and maintain circularly polarized light waves in the sensing fiber. One method for maintaining circularly polarized light waves in an optical fiber is to construct a fiber  30  using a periodic structure  31  (illustrated in FIG. 8) with appropriate properties. 
     Sensing fiber  30  having a periodic structure  31  with lengths L may be modeled using a Jones matrix          (         A       B               -   B     *           A   *           )                               
     to represent each period of the periodic structure. The associated eigenvalues, λ ± , for this matrix are given by 
     
       
         λ ± =e ±jarccos[Re(A)]   (15) 
       
     
     and the associated eigenvectors, v ± , are given by                v   ±     =       (         B               λ   ±     -   A           )     .             (   16   )                                
     Appropriate periodic structures for maintaining circular polarization are those for which v ±  approximate right- and left-handed circular polarization states. 
     When light is launched into such a fiber  30 , the polarization state of the light will evolve with both rapid undulations (spatial harmonics of the period of the periodic structure) and a slow undulation (having a period much longer than the period of the periodic structure). FIG. 9 illustrates the fiber sensitivity having a long period undulation  32 . As shown above, the rapid undulations contribute negligibly to uniformity and isolation errors. Thus, the slow period  32  poses the biggest concern. For this fiber  30 , the slow period of polarization state evolution, ξ, is given by              ξ   =     L          π       cos     -   1            [     Re        (   A   )       ]         .               (   17   )                                
     Here L is the length  31  of each period of the periodic structure. 
     For the case that sensing fiber  30  with a periodic structure comprises a bent-spun birefringent fiber, the long spatial period that exists has been found to be 
     
       
         ξ≈4L B   2 /L rev .  (18) 
       
     
     Here L B  is the intrinsic polarization beat length of the fiber in its unspun state, and L rev  is the distance over which the fiber is twisted by one revolution. L rev  is the length  31  of each period in the periodic structure of fiber  30 . The long spatial period, ξ, is independent of the bend radius as long as fiber  30  is not bent too severely. For a highly bent spun fiber, ξ becomes shorter. The amplitude of this low frequency deviation of the polarization away from circular polarization increases with increasing bend birefringence (due to tighter bending). As a numerical example, a fiber  30  having an unspun beat length of L B =3 centimeters (cm), and a spin rate of L rev =5 millimeters (mm) will exhibit a periodic variation in sensitivity to magnetic fields with a period of approximately 72 cm. 
     As the light propagates down the fiber, the light oscillates in and out of the pure circular polarization state. For minimizing the power that leaves the desired circular state of polarization, it is important to optimize the ratio of the spin rate to the intrinsic polarization beat length of the fiber. If the spin rate is too fast, the intrinsic birefringence of the fiber is too well averaged and the fiber becomes very sensitive to bend induced birefringence. If the spin rate is too slow, the intrinsic birefringence is not well averaged, and the fiber does not hold a circular state of polarization for this reason. Numerical modeling of the characteristics of a bent spun birefringent fiber yields the result that for practical bend radii (2 to 10 cm) the optimum ratio of the spin rate to the intrinsic beat length is between 4 and 6. Minimum degradation of the circular polarization holding capability is achieved when the ratio is between 3 and 8. By choosing a fiber with a spin rate in this range, the circular polarization state of the fiber can be maintained for a long length of fiber allowing for the sensitivity of the sensor to be greatly increased. 
     Eigen vectors, v ± , represent those polarization states that repeat after each period  32  along the distance l  34  of the periodic structure  31  of fiber  30 . By launching the interfering waves into the exact eigen vector polarization states of the sensing fiber, slow period  32  of the polarization state evolution is nulled. Substantially matching the launched polarization state to the eigen vectors of the periodic structure of the sensing fiber constitutes a first method of overcoming slow or long undulations  32 . For the in-line  25  and Sagnac  24  type current sensors which use spun-birefringent sensing fiber  30 , one may change a (nominal) quarter waveplate  33  slightly such that the light that is launched into the sensing fiber is of that polarization state that maintains itself upon propagation along the sensing fiber. That is, for a quarter waveplate  33  having a length of 3 cm and angle of 45 degrees, a slightly changed quarter waveplate  33  would be at 2.8 cm and 42 degrees, to avoid long undulation. For the bent-spun fiber, this “eigen polarization state” is equal to that state which repeats itself after propagating a distance corresponding to one complete revolution of fiber twist. 
     A second method for overcoming this slow undulation  32  in the fiber sensitivity to magnetic fields  27  is to cut the overall length of the sensing fiber  30  to a proper length l  34 . For a double-pass device using a reflective termination  48  such as a in-line type  25  sensor head  28 , this proper length is Mξ/4, where M is an odd integer. For the Sagnac loop type sensor  24 , a proper length  31  is Mξ/2, where M is an odd integer. These length  31  choices cause the low-order variation of the magnetic field sensitivity as seen by the light traveling in one direction to be cancelled by the light traveling in the opposite direction. FIGS. 10 and 11 show the direction dependent local sensitivities of the sensing fiber  30  to magnetic field for the Sagnac and in-line sensors, respectively. 
     FIG. 10 shows the magnetic field sensitivity versus distance  34  (l) along fiber  30  of sensing coil  28  for Sagnac loop interferometric type fiber optic current sensor  24 , having an optimal fiber  30  length, L total . L total  is equal to Mξ/2 where M is an odd integer and ξ is the length of long period undulation  32 . Curve  50  shows the sensitivity in the first direction of fiber  30  of coil  28 . Curve  51  shows the sensitivity in the second direction of fiber  30 . The effects of these sensitivities cancel each other. 
     FIG. 11 shows the magnetic field sensitivity versus distance  34  (l), along fiber  30  of sensing coil  28  for in-line interferometric type fiber optic current sensor  25 , having an optimal fiber  30  length, L total . L total  is equal to Mξ/4, where M is an odd integer and ξ is the length of long period undulation  32 . Curve  52  shows the sensitivity in the first direction of fiber  30  in sensing head  28 . Curve  53  shows the sensitivity in the second direction of fiber  30 . The effects of these sensitivities cancel each other. 
     A third method for canceling this slowly varying sensitivity is to form a sensing coil  28  using multiple turns of sensing fiber  30  having a properly chosen perimeter length P. The perimeter of sensing coil  28  should be chosen to be such a length that the slow variations in sensitivity are averaged out over the whole sensing coil. Mathematically, this idea is developed as follows. 
     The local sensitivity of the sensing fiber to magnetic field along the length l  34  of fiber  30 , S(l) is written as (excluding high spatial frequency variations),                  S        (   l   )       =       S   0     +       S   1        Cos                   (         2      π                 l     ξ     +   ψ     )           ,           (   19   )                                
     where S 0  is the constant part or characteristic of the sensitivity, ξ is the long period of undulation in the polarization state of the light and ψ is a phase offset. S 0  should not be confused with S 1 , S 2 , etc., which represent imperfections of coil  28 . When a multi-turn optical fiber sensing coil  28  is used, one desires that the sum of the local sensitivities at each point at length l along the fiber length  34  in the sensing coil  28  accumulate to a constant. Thus, one requires that                      ∑     n   =   1       N   -   1            cos                   (         2      π                 l     +   nP     ξ     )         +   ψ     =   0     ,     for                 all                 l     ,           (   20   )                                
     where P is a perimeter length around the sensing coil and not the length of the sensing fiber, N is the total number of turns of fiber comprising sensing coil  28 , and n is the index of summation for all fibers at that point of nP. l is a distance along the length of the fiber. S n  represents the imperfections of coil  28 . Ideally, S n  should be zero. Besides S 0 , only S 1  and S 2  are of most concern. S 3 , S 4  and so forth are generally insignificant. The varying sensitivity around a perimeter of sensing coil  28  may be stated as                  S   o     +       ∑     n   =   1     ∞            S   n        cos                   (         2      n                 π                   z   ′       P     +     ϕ   n       )           ,           (   21   )                                
     where z′ is a distance along the perimeter P of sensing coil  28 , and ψ n &#39;s are constants. S 1  and S 2  are typically less than S 0 ·10 −3 . 
     The requirement of equation (20) can be simplified to yield,                    sin                   (       π                 NP     ξ     )         sin        (       π                 P     ξ     )         =   0     ,              or           (   22   )                 P   =       m                 ξ     N       ,           (   23   )                                
     where m=odd integer, excluding m=kN, k=any integer. Thus, by choosing the perimeter of sensor coil  28  to substantially meet the requirement imposed by equation (23), the overall sensitivity variation having a period ξ is canceled over the entire sensing coil. 
     A fourth method for overcoming the deleterious effects on isolation and uniformity performance of a slow undulation  32  in the magnetic field  27  sensitivity is to use a long length l  34  of sensing fiber  30  in combination with a multi-wavelength, or broad band light source  35 . The periods of slow undulations  32  in the sensing fiber  30  are typically wavelength dependent. For the bent-spun fiber  30 , the period of slow undulation  32  is proportional to wavelength squared. By employing a light source  35  with multiple wavelengths, the corresponding multiple periods of god sensitivity will eventually cause the sensitivity to average to a constant after a long distance  34  (l) of sensing fiber  30 . For fiber sensor coil  28  lengths greater than the slow undulation period  32  divided by the fractional bandwidth of light source  35 , significant averaging of the slow undulation will occur. Mathematically, this condition is expressed as                  L   total     &gt;     ξλ   Δλ       ,           (   24   )                                
     where L total  is the total length  34  of sensing fiber  30 , λ is the mean source  28  wavelength, and Δλ is the wavelength spread of the source. Typically, L total  would need to exceed several tens of meters for this technique to yield significant results. 
     These four methods for overcoming the deleterious effects on isolation and uniformity performance of a slow undulation  32  in the fiber  30  sensitivity to magnetic field  27  are complementary. They may be implemented either separately, or in any combination. 
     Though the invention has been described with respect to a specific preferred embodiment, many variations and modifications will become apparent to those skilled in the art upon reading the present application. It is therefore the intention that the appended claims be interpreted as broadly as possible in view of the prior art to include all such variations and modifications.