Flexible printed circuit Rogowski coil

Abstract

The invention discloses a flexible printed circuit Rogowski coil. The invention provides a flexible printed circuit Rogowski coil. The flexible printed circuit Rogowski coil may include a flexible printed circuit board, a first connector disposed proximal to a first end of the flexible printed circuit board, a second connector disposed proximal to the first end of the flexible printed circuit board, and a third connector disposed proximal to the second end of the flexible printed circuit board. A first portion of the air-core coil printed on a top side of the flexible printed circuit board as a first pattern and connected to the first connector, and a second portion of the air-core coil printed on a bottom side of the flexible printed circuit board as a second pattern and connected to the second connector, the second pattern corresponding to the first pattern.

Description

Technical Field

[0001] The present disclosure relates generally to circuit protection devices and devices for measuring current. More particularly, the present disclosure relates to flexible printed circuit Rogowski coils. Background Art

[0002] A Rogowski coil is an electrical device that can quantitatively and qualitatively measure alternating current (AC) or high-speed transient or pulse current by using both Ampere's law and Faraday's law. Figure 1 As seen, a known Rogowski coil 100 may include an air-core coil 102 for measuring current passing through a conductor 104. The air-core coil 102 may include a toroidal, spiral-shaped coil having N turns and a cross-sectional area A. As seen, the end of the wire forming the air-core coil 102 may be returned to the beginning of the wire through the center of the air-core coil 102, such that both terminals 106 of the air-core coil 102 are on one side of the air-core coil 102. This type of configuration allows the air-core coil 102 to span only the intended surface of the turns in the air-core coil 102, and nothing more, while also wrapping around the entire circumference of the conductor 104 being measured without physically interrupting the conductor 104.

[0003] The voltage generated at terminal 106 is governed by Faraday's law of induction as follows:

[0004]

[0005] Where k is a proportionality constant reflecting the construction of the air-core coil 102 and may depend on the physical dimensions A, N, and r of the air-core coil 102, where A is the cross-sectional area of ​​each turn in the air-core coil 102, N is the number of turns of the air-core coil 102, and r is the radius of the air-core coil 102. A signal processing circuit 108 connected to the terminal 106 measures the voltage v(t) across the terminal 106. The current i(t) through the conductor 104 is then derived from the voltage v(t) by integrating Equation 1. The integrator may be implemented using passive or active discrete components or by numerical integration in a computer.

[0006] Measuring the current i(t) in the conductor 104 using the Rogowski coil 100 has many advantages over other known methods for measuring current. First, because the air-core coil 102 is used without a magnetic core, there is no problem in saturating the core when there is an unexpected short circuit in the conductor circuit. Second, the frequency response of the air-core coil 102 is limited only by the size of the air-core coil 102 and the capabilities of the signal processing circuit 108. Next, the two terminals 106 on the same side of the air-core coil 102 provide non-intrusive installation. In particular, the air-core coil 102 can be flexibly wrapped around the conductor 104, including wires, isolated wires, busbars, etc., without blocking the conductor 104. In addition, the air-core coil 102 is naturally galvanically isolated from the conductor 104, and the internal impedance of the air-core coil 102 is very low, which increases the signal-to-noise ratio immunity. If the turns in the air core coil 102 are identical and evenly spaced, the voltage v(t) output is proportional to the derivative of the current i(t) through the conductor 104, thereby canceling all external electromagnetic fields not generated by the conductor 104. Finally, the positioning and orientation of the conductor 104 has a negligible effect on the measurement.

[0007] Despite its many advantages, the design and use of Rogowski coils known in the art is impractical due to several limitations on their practical implementation. First, Figure 1 Wiring the air-core coil 102 as shown is mechanically complex and expensive in mass production. In addition, it is difficult to achieve evenly spaced and identical turns in the air-core coil 102. Non-magnetic support cores can be used to assist in achieving evenly spaced and identical turns, but doing so reduces the flexibility of the air-core coil 102 while increasing its size and cost. However, without a support core, the wire must have a sufficiently large cross-sectional area to achieve a self-supporting construction, but such wires are typically expensive and inflexible, again reducing the flexibility of the air-core coil 102 while increasing the cost of the air-core coil 102.

[0008] In view of the above, there is a continuing, ongoing need for improved Rogowski coils. Summary of the invention

[0009] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter or as an aid in determining the scope of the claimed subject matter.

[0010] In some embodiments, a device according to the present disclosure may include a flexible printed circuit board, a first connector disposed proximate to a first end of the flexible printed circuit board, a second connector disposed proximate to the first end of the flexible printed circuit board, a first portion of a hollow coil printed as a first pattern on a top side of the flexible printed circuit board and connected to the first connector, and a second portion of the hollow coil printed as a second pattern on a bottom side of the flexible printed circuit board and connected to the second connector, the second pattern corresponding to the first pattern.

[0011] In some embodiments, the first portion of air-core coils may include a first plurality of coils, each coil in the first plurality of coils being separated from one another and electrically connected, and wherein the second portion of air-core coils includes a second plurality of coils, each coil in the second plurality of coils being separated from one another and electrically connected.

[0012] In some embodiments, the first plurality of coils and the second plurality of coils may be equal in number.

[0013] In some embodiments, the first plurality of coils may be vertically aligned with the second plurality of coils.

[0014] In some embodiments, the first portion of the air-core coil may be connected to the second portion of the air-core coil through respective through-holes located at respective centers of each coil in the first and second pluralities of coils.

[0015] In some embodiments, each coil in the first plurality of coils may be wound in a first direction, and each coil in the second plurality of coils may be wound in the first direction.

[0016] In some embodiments, each coil in the first plurality of coils and the second plurality of coils may include an equal number of turns.

[0017] In some embodiments, the electromotive force in each of the first plurality of coils and the second plurality of coils can be induced by a magnetic field generated by a conductor wrapped around the flexible printed circuit board, and the voltage v(t) measured across the first connector and the second connector can be the sum of the respective contributions of each of the first plurality of coils and the second plurality of coils.

[0018] In some embodiments, each coil in the first plurality of coils may be connected in series, and each coil in the second plurality of coils may be connected in series.

[0019] In some embodiments, the current i(t) flowing through the conductor can be measured by The integration is performed from the voltage v(t), where k is a proportionality constant that can depend on the physical dimensions A, N and r of each coil in the first plurality of coils and the second plurality of coils, where A is the corresponding cross-sectional area per turn, N is the number of turns, and r is the corresponding radius of each coil in the first plurality of coils and the second plurality of coils.

[0020] In some embodiments, the apparatus may include a plastic holder that supports the flexible printed circuit board such that each coil of the first plurality of coils and the second plurality of coils is perpendicular to a magnetic field generated by a conductor passing through a central hole of the plastic holder.

[0021] In some embodiments, a plurality of bending posts may protrude from a top surface of the plastic holder, and the flexible printed circuit board may be wrapped around the plurality of bending posts.

[0022] In some embodiments, a plurality of spacing holes may be distributed along the length of the flexible printed circuit board, and a plurality of spacing nodes may protrude from at least some of the plurality of bending posts, wherein each of the plurality of spacing holes may fit around a corresponding one of the plurality of spacing nodes to secure the flexible printed circuit board in place.

[0023] In some embodiments, a method according to the present disclosure may include printing a first portion of the hollow coil on the top side of the flexible printed circuit board as a first pattern, connecting the first portion of the hollow coil to a first connector disposed proximate the first end of the flexible printed circuit board, printing a second portion of the hollow coil on the bottom side of the flexible printed circuit board as a second pattern corresponding to the first pattern, connecting the second portion of the hollow coil to a second connector disposed proximate the first end of the flexible printed circuit board, and wrapping the flexible printed circuit board around a plurality of curved posts protruding from a top surface of a plastic holder so that the first portion of the hollow coil and the second portion of the hollow coil are perpendicular to a magnetic field generated by a conductor passing through a central hole of the plastic holder.

[0024] In some embodiments, the method may include physically separating a first plurality of coils in a first portion of air-core coils from one another, electrically connecting the first plurality of coils in series with one another, physically separating a second plurality of coils in a second portion of air-core coils from one another, and electrically connecting the second plurality of coils in series with one another.

[0025] In some embodiments, the method may include vertically aligning the first plurality of coils with the second plurality of coils.

[0026] In some embodiments, the method may include connecting the first portion of the air-core coil to the second portion of the air-core coil through a corresponding through hole located at a respective center of each coil in the first and second pluralities of coils.

[0027] In some embodiments, the method may include inducing an electromotive force in each of the first plurality of coils and the second plurality of coils by a magnetic field generated by a conductor, and measuring a voltage v(t) across the first connector and the second connector, wherein the voltage v(t) is the sum of the respective contributions of each of the first plurality of coils and the second plurality of coils.

[0028] In some embodiments, the current i(t) flowing through the conductor can be measured by The integration is performed from the voltage v(t), where k is a proportionality constant that may depend on the physical dimensions A, N, and r of each coil in the first plurality of coils and the second plurality of coils, where A is the respective cross-sectional area of ​​each turn in the first plurality of coils and the second plurality of coils, N is the number of turns of each coil in the first plurality of coils and the second plurality of coils, and r is the respective radius of each coil in the first plurality of coils and the second plurality of coils.

[0029] In some embodiments, the method may include fitting each of a plurality of spaced holes distributed along the length of the flexible printed circuit board around a corresponding one of a plurality of spaced nodes protruding from at least some of the plurality of bending posts to secure the flexible printed circuit board in place.

[0030] Other technical features may be easily apparent to those skilled in the art from the following drawings, descriptions and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a perspective view showing a Rogowski coil known in the art;

[0032] Figure 2A is a top view showing a flexible printed circuit Rogowski coil according to the disclosed embodiment;

[0033] Figure 2B is a bottom view showing a flexible printed circuit Rogowski coil according to a disclosed embodiment;

[0034] Figure 3A is a perspective view showing a plastic holder according to a disclosed embodiment;

[0035] Figure 3B is a perspective view showing a plastic holder with a flexible printed circuit Rogowski coil supported thereon according to a disclosed embodiment; and

[0036] Figure 4 is a flow chart illustrating a method according to the disclosed embodiments. DETAILED DESCRIPTION

[0037] Exemplary embodiments of flexible printed circuit Rogowski coils according to the present disclosure will now be described more fully below with reference to the accompanying drawings. However, the flexible printed circuit Rogowski coil can be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will convey certain exemplary aspects of the flexible printed Rogowski coil to those skilled in the art.

[0038] As disclosed herein, flexible printed circuit Rogowski coils may be used to quantitatively and qualitatively measure AC or high speed transient or pulse currents flowing through a conductor. Advantageously, the flexible printed circuit Rogowski coils disclosed herein may be suitable for mass production in a cost-effective manner compared to wired coil production.

[0039] Figure 2A is a top view of a flexible printed circuit (FPC) Rogowski coil 200 according to the disclosed embodiment, and Figure 2B is a bottom view of a flexible printed circuit Rogowski coil 200 according to the disclosed embodiments. As seen, in some embodiments, the flexible printed circuit Rogowski coil 200 may include flexible printed circuit boards 202a, 202b, a first portion of an air core coil 204a, a second portion of an air core coil 204b, a first connector 208a, 208b, a second connector 210a, 210b, a third connector 212a, 212b, and a plurality of spaced holes 214a, 214b. In some embodiments, the flexible printed circuit boards 202a, 202b may be double-sided, and in some embodiments, the flexible printed circuit boards 202a, 202b may be thin, for example, approximately 25 μm thick. Further, in some embodiments, the flexible printed circuit boards 202a, 202b may include a copper clad laminate. Advantageously, printing on the copper clad laminate may produce a distance between traces of the air core coils 204a, 204b as small as 100 μm.

[0040] In some embodiments, the first connector 208a, 208b can be disposed proximal to the first end of the flexible printed circuit board 202a, 202b, and the second connector 210a, 210b can be disposed proximal to the first end of the flexible printed circuit board 202a, 202b. That is, the first connector 208a, 208b and the second connector 210a, 210b can be disposed proximal to the same end of the flexible printed circuit board 202a, 202b. Advantageously, placing all of the connectors 208a, 208b, 210a, 210b, 212a, 212b proximal to the same end of the flexible printed circuit board 202a, 202b can facilitate non-invasive installation of the flexible printed circuit Rogowski coil 200.

[0041] In some embodiments, the first portion of the air-core coil 204a can be implemented (e.g., printed) as a first pattern on the top side of the flexible printed circuit board 202a and connected to the first connectors 208a, 208b. Similarly, in some embodiments, the second portion of the air-core coil 204b can be implemented (e.g., printed) as a second pattern on the bottom side of the flexible printed circuit board 202b and connected to the second connectors 210a, 210b.

[0042] In some embodiments, the first portion of the air-core coils 204a may include a first plurality of coils 206a, and each coil in the first plurality of coils 206a may be physically separated from and electrically connected to each other. Similarly, in some embodiments, the second portion of the air-core coils 204b may include a second plurality of coils 206b, and each coil in the second plurality of coils 206b may be physically separated from and electrically connected to each other. In some embodiments, each coil in the first plurality of coils 206a may be connected in series, and each coil in the second plurality of coils 206b may be connected in series.

[0043] In some embodiments, the second pattern of the second portion of the air-core coil 204b may correspond to the first pattern of the first portion of the air-core coil 204a. For example, in some embodiments, the first plurality of coils 206a and the second plurality of coils 206b may be equal in number. That is, in some embodiments, the first plurality of coils 206a may include M coils, and the second plurality of coils 206b may include M coils. In some embodiments, the first plurality of coils 206a may be vertically aligned with the second plurality of coils 206b. In addition, in some embodiments, each coil in the first plurality of coils 206a may be wound in a first direction, and each coil in the second plurality of coils 206b may be wound in the first direction. That is, the winding directions (first directions) of the first plurality of coils 206a and the second plurality of coils 206b may be the same. In some embodiments, each coil in the first plurality of coils 206a and the second plurality of coils 206b may include an equal number of turns. That is, in some embodiments, each coil in the first plurality of coils 206a may include N turns, and each coil in the second plurality of coils 206b may include N turns.

[0044] In some embodiments, a first portion of the air core coil 204a may be connected to a second portion of the air core coil 204b through respective through holes 216a, 216b located at respective centers of each coil in the first and second pluralities of coils.

[0045] In some embodiments, the plurality of spaced holes 214a, 214b may be distributed along the length of the flexible printed circuit board 202a, 202b. For example, in some embodiments, the plurality of spaced holes 214a, 214b may be interspersed with the plurality of coils 206a, 206b along the length of the flexible printed circuit board 202a, 202b.

[0046] According to the disclosed embodiments, the flexible printed circuit Rogowski coil 200 can be scalable and fully configurable. For example, the first pattern of the first portion of the air-core coil 204a and the second pattern of the second portion of the air-core coil 204b can be changed, for example, using a CAD tool as needed to achieve any desired parameters of the first plurality of coils 206a and the second plurality of coils 206b. In this regard, at least the following parameters can be configured: the thickness of the traces of the air-core coils 204a, 204b, the distance between the traces of the air-core coils 204a, 204b, the number of turns (N) of the first plurality of coils 206a and the second plurality of coils 206b, the number of coils (M) in the first plurality of coils 206a and the second plurality of coils 206b, the size of the first plurality of coils 206a and the second plurality of coils 206b, and the like.

[0047] Figure 3A 3 is a perspective view of a plastic retainer 300 according to a disclosed embodiment. As seen, in some embodiments, the plastic retainer 300 may include a flat disk 304a, a plurality of curved posts 306a protruding from a top surface of the flat disk 304a, for example in a vertical direction, and a central hole 312a. In some embodiments, a first plurality of curved posts 306a may form a first ring having a first radius around the central hole 312a, and a second plurality of curved posts 306a may form a second ring having a second radius greater than the first radius around the central hole 312a. In some embodiments, a plurality of spaced nodes 314a may protrude from an outwardly facing side of at least some of the plurality of curved posts 306a, for example, from each of the second plurality of curved posts 306a.

[0048] In some embodiments, the plastic retainer 300 can be formed from any low-cost plastic material, and in some embodiments, the plastic retainer 300 can be mass-produced using plastic extrusion machinery.

[0049] like Figure 3BAs seen in FIG. 1 , in some embodiments, the plastic holder 300 can support a flexible printed circuit Rogowski coil 302, such as the flexible printed circuit Rogowski coil 200, thereon. In some embodiments, the flexible printed circuit Rogowski coil 302 can be wrapped around a plurality of bending posts 306b for simple assembly. Advantageously, the plurality of bending posts 306b can ensure that the bending radius of the flexible printed circuit Rogowski coil 302 is above the minimum radius allowed by the material of the flexible printed circuit Rogowski coil 302. In addition, in some embodiments, each of the plurality of spacing holes (e.g., the plurality of spacing holes 214a, 214b) of the flexible printed circuit Rogowski coil 302 can be assembled around a corresponding one of the plurality of spacing nodes 314b to secure the flexible printed circuit Rogowski coil 302 in place. Advantageously, the plurality of spacing nodes 314b can ensure that the first plurality of coils and the second plurality of coils (e.g., the first plurality of coils 206a and the second plurality of coils 206b) of the flexible printed circuit Rogowski coil 302 are evenly and symmetrically distributed around the circumference of the plastic holder 300.

[0050] In some embodiments, the plastic holder 300 may support the flexible printed circuit Rogowski coil 302 in a configuration that ensures each coil in the first and second pluralities of coils is perpendicular to a magnetic field generated by a conductor passing through a central aperture 308 of the plastic holder 300 .

[0051] In some embodiments, the electromotive force in each of the first plurality of coils and the second plurality of coils may be induced by a magnetic field generated by a conductor passing through the central hole 308, and the voltage v(t) measured across the terminals 308, 310 (e.g., the first connectors 208a, 208b and the second connectors 210a, 210b) may be the sum of the respective contributions of each of the first plurality of coils and the second plurality of coils. In some embodiments, the direction of flow of the electromotive force may be equivalent to the winding direction of the first plurality of coils and the second plurality of coils.

[0052] In some embodiments, the current i(t) flowing through the conductor can be measured by The integration is derived from the voltage v(t), where k is a proportionality constant that can depend on the physical dimensions A, N, and r of each of the first and second pluralities of coils, where A is the respective cross-sectional area of ​​each turn in the first and second pluralities of coils, N is the number of turns of each of the first and second pluralities of coils, and r is the respective radius of each of the first and second pluralities of coils. Because the material of the flexible printed circuit Rogowski coil 302 is thin, the first and second pluralities of coils can be close enough together to effectively attenuate any electromagnetic interference that cuts through the first and second pluralities of coils.

[0053] Figure 4 4 is a flow chart of a method 400 according to the disclosed embodiments. As seen, in some embodiments, the method 400 may include printing a first portion of the air core coil 204a on the top side of the flexible printed circuit board 202a as a first pattern, and connecting the first portion of the air core coil 204a to a first connector 208a disposed proximate to the first end of the flexible printed circuit board 202a as in 404. The method 400 may also include printing a second portion of the air core coil 204b on the bottom side of the flexible printed circuit board 202b as a second pattern, and connecting the second portion of the air core coil 204b to a second connector 210b disposed proximate to the first end of the flexible printed circuit board 202b as in 408. In some embodiments, the second pattern may correspond to the first pattern.

[0054] In some embodiments, printing the first portion of the air-core coils 204a as a first pattern on the top side of the flexible printed circuit board 202a as in 402 may include physically separating the first plurality of coils 206a in the first portion of the air-core coils 204a from each other and electrically connecting the first plurality of coils 206a in series with each other. Similarly, in some embodiments, printing the second portion of the air-core coils 204b as a second pattern on the bottom side of the flexible printed circuit board 202b as in 406 may include physically separating the second plurality of coils 206b in the second portion of the air-core coils 204b from each other and electrically connecting the second plurality of coils 206b in series with each other. In some embodiments, the method 400 may include vertically aligning the first plurality of coils 206a with the second plurality of coils 206b, and in some embodiments, the method 400 may include connecting the first portion of the air-core coils 204a to the second portion of the air-core coils 204b through respective through holes 216a, 216b located at respective centers of each coil in the first plurality of coils 206a and the second plurality of coils 206b.

[0055] Next, the method 400 may include wrapping the flexible printed circuit board 202a, 202b around the plurality of curved posts 306a, 306b of the plastic holder 300 as in 410 such that the first portion of the air core coil 204a and the second portion of the air core coil 204b are perpendicular to the magnetic field generated by the conductor passing through the central hole 312a, 312b of the plastic holder 300. For example, in some embodiments, the method 400 may include fitting each of the plurality of spaced holes 214a, 214b distributed along the length of the flexible printed circuit board 202a, 202b around a corresponding one of the plurality of spaced nodes 314a, 314b protruding from at least some of the plurality of curved posts 306a, 306b to secure the flexible printed circuit board 202a, 202b in place.

[0056] In some embodiments, when current flows through the conductor, the method 400 may include inducing an electromotive force in each of the first plurality of coils 206a and the second plurality of coils 206b through a magnetic field generated by the conductor and measuring a voltage v(t) across the first connector 208a, 208b and the second connector 210a, 210b, wherein the voltage v(t) is the sum of the respective contributions of each of the first plurality of coils 206a and the second plurality of coils 206b.

[0057] In some embodiments, the current i(t) flowing through the conductor can be measured by The integration is derived from the voltage v(t), where k is a proportionality constant that may depend on the physical dimensions A, N, and r of each coil in the first plurality of coils 206a and the second plurality of coils 206b, where A is the respective cross-sectional area of ​​each turn in the first plurality of coils 206a and the second plurality of coils 206, N is the number of turns of each coil in the first plurality of coils 206a and the second plurality of coils 206b, and r is the respective radius of each coil in the first plurality of coils 206a and the second plurality of coils 206b.

[0058] As used herein, an element or step recited in the singular and beginning with the word "a" or "an" should be understood as not excluding plural elements or steps, unless such exclusion is explicitly stated. In addition, reference to "one embodiment" of the present disclosure is not intended to be interpreted as excluding the existence of other embodiments that also incorporate the described features.

[0059] Although the present disclosure refers to certain embodiments, many modifications, changes and variations of the described embodiments are possible without departing from the field and scope of the present disclosure as defined in the appended claims. Therefore, it is intended that the present disclosure is not limited to the described embodiments, but rather has the full scope defined by the language of the following claims and their equivalents.

Claims

1. A device comprising: Flexible printed circuit boards; A first connector disposed proximal to the first end of the flexible printed circuit board; a second connector disposed proximal to the first end of the flexible printed circuit board; a first portion of the air-core coil, which is printed as a first pattern on the top side of the flexible printed circuit board and connected to the first connector; as well as A second portion of the air-core coil is printed as a second pattern on the bottom side of the flexible printed circuit board and is connected to the second connector, the second pattern corresponding to the first pattern.

2. The device according to claim 1, wherein: The first portion of the air-core coils includes a first plurality of coils, each of which is separated from and electrically connected to one another, and wherein the second portion of the air-core coils includes a second plurality of coils, each of which is separated from and electrically connected to one another.

3. The device according to claim 2, wherein: The first plurality of coils are equal in number to the second plurality of coils.

4. The device according to claim 2 or 3, wherein: The first plurality of coils are vertically aligned with the second plurality of coils.

5. The device according to any one of claims 2 to 4, wherein: The first portion of the air-core coil is connected to the second portion of the air-core coil through a respective through hole located at a respective center of each coil of the first and second pluralities of coils.

6. The device according to any one of claims 2 to 5, wherein: Each coil of the first plurality of coils is wound in a first direction, and wherein each coil of the second plurality of coils is wound in the first direction.

7. The device according to any one of claims 2 to 6, wherein: Each coil of the first plurality of coils and the second plurality of coils includes an equal number of turns.

8. The device according to any one of claims 2 to 7, wherein: The electromotive force in each of the first plurality of coils and the second plurality of coils is induced by a magnetic field generated by a conductor around which the flexible printed circuit board is wrapped, and wherein the voltage v(t) measured across the first connector and the second connector is the sum of the respective contributions of each of the first plurality of coils and the second plurality of coils.

9. The device according to any one of claims 2 to 8, wherein: Each coil of the first plurality of coils is connected in series, and wherein each coil of the second plurality of coils is connected in series.

10. The device according to claim 8 or 9, wherein: The current i(t) flowing through the conductor is The integration is derived from the voltage v(t), where k is a proportionality constant that depends on the physical dimensions A, N, and r of each coil in the first plurality of coils and the second plurality of coils, where A is the corresponding cross-sectional area per turn, N is the number of turns, and r is the corresponding radius of each coil in the first plurality of coils and the second plurality of coils.

11. The device according to any one of claims 2 to 10, further comprising: a plastic holder that supports the flexible printed circuit board so that each of the first plurality of coils and the second plurality of coils is perpendicular to a magnetic field generated by a conductor passing through a central hole of the plastic holder, Preferably also includes: a plurality of curved posts protruding from a top surface of the plastic retainer, wherein the flexible printed circuit board is wound around the plurality of bending posts, More preferably, it also includes: a plurality of spaced apart holes distributed along the length of the flexible printed circuit board; and a plurality of spaced nodes protruding from at least some of the plurality of curved posts, Each of the plurality of spacing holes is assembled around a corresponding one of the plurality of spacing nodes to fix the flexible printed circuit board in place.

12. A method comprising: printing a first portion of the air-core coil as a first pattern on a top side of the flexible printed circuit board; connecting a first portion of the air-core coil to a first connector disposed proximate a first end of the flexible printed circuit board; printing a second portion of the air-core coil on a bottom side of the flexible printed circuit board as a second pattern, the second pattern corresponding to the first pattern; connecting a second portion of the air-core coil to a second connector disposed proximate the first end of the flexible printed circuit board; as well as The flexible printed circuit board is wrapped around a plurality of curved posts protruding from a top surface of a plastic holder so that a first portion of the air-core coil and a second portion of the air-core coil are perpendicular to a magnetic field generated by a conductor passing through a central hole of the plastic holder.

13. The method according to claim 12, further comprising: physically separating a first plurality of coils in the first portion of the air-core coils from each other; electrically connecting the first plurality of coils in series with one another; physically separating a second plurality of coils in the second portion of the air-core coils from each other; as well as The second plurality of coils are electrically connected in series with one another.

14. The method of claim 13, further comprising one or more of the following: - vertically aligning the first plurality of coils with the second plurality of coils; - connecting the first portion of the air-core coil to the second portion of the air-core coil through respective through holes located at respective centers of each coil of the first plurality of coils and the second plurality of coils; - inducing an electromotive force in each of the first plurality of coils and the second plurality of coils by a magnetic field generated by the conductor; as well as measuring a voltage v(t) across the first connector and the second connector, wherein the voltage v(t) is the sum of the respective contributions of each coil in the first plurality of coils and the second plurality of coils; - fitting each of a plurality of spaced holes distributed along the length of the flexible printed circuit board around a corresponding one of a plurality of spaced nodes protruding from at least some of the plurality of bending posts to secure the flexible printed circuit board in place.

15. The method according to claim 13 or 14, wherein: The current i(t) flowing through the conductor is The integration is derived from the voltage v(t), where k is a proportionality constant that depends on the physical dimensions A, N, and r of each coil in the first plurality of coils and the second plurality of coils, where A is the respective cross-sectional area of ​​each turn in the first plurality of coils and the second plurality of coils, N is the number of turns of each coil in the first plurality of coils and the second plurality of coils, and r is the respective radius of each coil in the first plurality of coils and the second plurality of coils.

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