LINEAR INDUCTIVE POSITION SENSOR

Abstract

A position of a target is determined using a linear inductive position sensor that includes a target coil, an excitation coil, two sensors and a Vernier processor. The sensors each include two or more receive coils. The receive coils include multiple twisted loops. In the first sensor, the coils have a first period, with loops offset by first distance. In the second sensor, the coils have a second period, with loops offset by a second distance. The target coil width is a function of the first distance and the second distance. During operation, the coils output voltages in which third, fifth and/or seventh harmonics are cancelled. Based on the voltages, the sensors output respective first and second position signals, from which the Vernier processor calculates the target's position along an axis of the position sensor.

Claims

1. A linear inductive position sensor, comprising: an excitation coil extending along a given axis of a substrate forming a portion of the linear inductive position sensor; a target coil configured to move above the excitation coil and along the given axis of the substrate; a first sensor extending along the given axis of the substrate; wherein the first sensor comprises: a first receiver coil having a first period ; and a second receiver coil; and wherein a first ratio times the first period separates the first receiver coil from the second receiver coil along the given axis; wherein the excitation coil generates a first electromagnetic field while receiving an alternating signal from a power source; wherein the target coil is inductively coupled to the excitation coil by the first electromagnetic field; wherein, due to the inductive coupling of the target coil with the excitation coil, the target coil generates a second electromagnetic field; wherein the first receiver coil is first inductively coupled to the target coil by the second electromagnetic field; wherein the second receiver coil is second inductively coupled to the target coil by the second electromagnetic field; wherein a first receiver voltage Vr1 is generated in the first receiver coil due to the first inductive coupling; wherein Vr1 is dependent upon a current position of the target coil along the given axis; wherein a second receiver voltage Vr2 is generated in the second receiver coil due to the second inductive coupling; wherein Vr2 is dependent upon a current position of the target coil along the given axis; wherein Vr1 and Vr2 are utilized by a first processor to generate a first position signal X1; and wherein the first position signal X1 provides a scaled representation of a position of the target coil along the given axis of the substrate.

2. The linear inductive position sensor of claim 1, wherein the excitation coil extends in a multi loop configuration around a perimeter of the substrate.

3. The linear inductive position sensor of claim 2, wherein the first receiver coil and the second receiver coil are enclosed by the excitation coil.

4. The linear inductive position sensor of claim 1, wherein the first receiver coil includes a plurality of first receiver coil loops symmetrically extending from a first portion of the substrate, along the given axis of the substrate, to a second portion of the substrate and back to the first portion of the substrate; and wherein each loop of the plurality of first receiver coil loops is respectively offset from another loop of the plurality of first receiver coil loops by a first distance D1.

5. The linear inductive position sensor of claim 1, wherein the second receiver coil further comprises: a plurality of second receiver coil loops, corresponding in symmetry with a plurality of first receiver coil loops.

6. The linear inductive position sensor of claim 5, wherein even numbered harmonics generated in Vr1 and Vr2 are nullified.

7. The linear inductive position sensor of claim 6, wherein each loop of the plurality of first receiver coil loops occurs over a multiple of the first period ; and wherein each loop of the plurality of second receiver coil loops is offset by at least one of one-quarter and one-third of the first period .

8. The linear inductive position sensor of claim 7, wherein D1=(1/14)*.

9. The linear inductive position sensor of claim 7, wherein =6 mm.

10. The linear inductive position sensor of claim 1, wherein the first sensor further comprises: a third receiver coil further comprising: a plurality of third receiver coil loops, corresponding in symmetry with a plurality of first receiver coil loops and a plurality of second receiver coil loops; wherein each loop of the plurality of third receiver coil loops is respectively offset from a corresponding loop of the plurality of second receiver coil loops by one-third of the first period ; wherein the third receiver coil is third inductively coupled to the target coil by the second electromagnetic field; wherein a third receiver voltage Vr3 is generated in the third receiver coil due to the third inductive coupling; wherein Vr3 is dependent upon a current position of the target coil along the given axis; wherein Vr1, Vr2, and Vr3 are utilized by the first processor to generate the first position signal X1.

11. The linear inductive position sensor of claim 10, further comprising: a second sensor extending along the given axis of the substrate comprising; a second sensor first receiver coil; and a second sensor second receiver coil; wherein the second sensor first receiver coil is fourth inductively coupled to the target coil by the second electromagnetic field; wherein the second sensor second receiver coil is fifth inductively coupled to the target coil by the second electromagnetic field; wherein a second sensor first receiver coil voltage Vr1 is generated in the second sensor due to the fourth inductive coupling; wherein second sensor second receiver coil voltage Vr2 is generated in the second sensor due to the fifth inductive coupling; and wherein Vr1 and Vr2 are utilized by a second processor to generate a second position signal X2.

12. The linear inductive position sensor of claim 11, wherein Vr1 is dependent upon a current position of the target coil along the given axis; and wherein Vr2 is dependent upon the current position of the target coil along the given axis.

13. The linear inductive position sensor of claim 12, wherein the second sensor further comprises: a second sensor third receiver coil; wherein the second sensor first receiver coil is separated, along the given axis, from the second sensor second receiver coil by a first ratio times a second period 2; wherein the second sensor second receiver coil is separated, along the given axis, from the second sensor third receiver coil by the first ratio times the second period 2; wherein the second sensor first receiver coil extends a second period 2 along the given axis and further comprises: a second sensor first receiver coil first loop; and a second sensor first receiver coil second loop; and wherein a second distance (D2) separates the second sensor first receiver coil first loop from the second sensor first receiver coil second loop.

14. The linear inductive position sensor of claim 13, wherein the second sensor first receiver coil first loop symmetrically extends, in a twisted loop configuration, from a first portion of the substrate, along the given axis of the substrate, to a second portion of the substrate and back to the first portion of the substrate; wherein the second sensor first receiver coil second loop symmetrically extends in the twisted loop configuration; and wherein the second sensor second receiver coil further comprises: a second sensor second receiver coil first loop symmetrically extending in the twisted loop configuration; and a second sensor second receiver coil second loop symmetrically extending in the twisted loop configuration; wherein the second sensor second receiver coil first loop is offset from the second sensor second receiver coil loop by the second distance D2; wherein the second sensor third receiver coil further comprises: a second sensor third receiver coil first loop symmetrically extending in the twisted loop configuration; and a second sensor third receiver coil second loop symmetrically extending in the twisted loop configuration; wherein the second sensor third receiver coil first loop is offset from the second sensor third receiver coil loop by the second distance D2; wherein the second sensor first receiver coil first loop and second loop occur over a second period 2; wherein the second sensor second receiver coil first loop and second loop occur over the second period 2; and wherein the second sensor third receiver coil first loop and second loop occur over the second period 2.

15. The linear inductive position sensor of claim 13, wherein D2=(1/10)*2.

16. The linear inductive position sensor of claim 13, wherein third harmonic signals are cancelled.

17. The linear inductive position sensor of claim 13, wherein fifth harmonic signals are cancelled.

18. The linear inductive position sensor of claim 13, wherein a seventh harmonic signals are cancelled.

19. A linear inductive position sensor, comprising: an excitation coil extending along a given axis of a substrate forming a portion of the linear inductive position sensor; a target coil configured to move above the excitation coil and along the given axis of the substrate; wherein the target coil has a width of a third distance D3; wherein, when provided with an alternating current, the excitation coil inductively couples to the target coil; a Vernier processor; a first sensor comprising: a first processor coupled to the Vernier processor; a plurality of first sensor receiver coils, coupled to the first processor, each of the plurality of first sensor receiver coils further comprising: a plurality of first sensor twisted loops, symmetrically extending from a first portion of the substrate, along the given axis of the substrate, to a second portion of the substrate and back to the first portion of the substrate; and a plurality of first sensor second twisted loops, corresponding in symmetry with the plurality of first sensor twisted loops and respectively offset from a corresponding loop of the plurality of first sensor twisted loops by a first distance D1; and wherein each of the plurality of first sensor receiver coils are respectively offset from a preceding first sensor receiver coil by a first period ; wherein based upon voltages induced in the first sensor receiver coils, the first processor outputs a first position signal X1 to the Vernier processor; a second sensor comprising: a second processor coupled to the Vernier processor; a plurality of second sensor receiver coils, coupled to the second processor, each of the plurality of second sensor receiver coils further comprising: a plurality of second sensor first twisted loops, symmetrically extending from the first portion of the substrate, along the given axis of the substrate, to the second portion of the substrate and back to the first portion of the substrate; and a plurality of second sensor second twisted loops, corresponding in symmetry with the plurality of second sensor first twisted loops and respectively offset from a corresponding loop of the plurality of second sensor first twisted loops by a second distance D2; and wherein each of the plurality of second sensor receiver coils are respectively offset from a preceding second sensor receiver coil by a second period 2; wherein the third distance D3 is a function of a ratio of the first period and a ratio of the second period A2; wherein the target coil inductively couples with the first sensor receiving coils and the second sensor receiving coils; wherein based upon first voltages induced in the first sensor receiver coils, the first processor outputs a first position signal X1 to the Vernier processor; wherein based upon second voltages induced in the second sensor receiver coils, the second processor outputs a second position signal X2 to the Vernier processor; wherein the first processor cancels third and fifth harmonics in the first voltages; and wherein the second processor cancels third, fifth and seventh harmonics in the second voltages; and wherein using Vernier principles, the first position signal X1 and the second position signal X2 are utilized to generate a final position signal P that represents a location of the target coil along the given axis.

20. A method for determining a position of a target using a linear inductive position sensor comprising: receiving a first position signal X1 from a first sensor, the first sensor generating X1 based on a first plurality of first sensor voltage signals respectively induced in a plurality of first receiver coils by a target coil; receiving a second position signal X2 from a second sensor, the second sensor generating X2 based on a second plurality of second sensor voltage signals respectively induced in a plurality of second receiver coils by the target coil; and applying a Vernier calculation to the first position signal X1 and the second position signal X2 to determine a current position of the target coil; wherein the target coil is inductively coupled to an excitation coil extending along a given axis of the linear inductive position sensor; wherein the first sensor is configured to cancel third harmonics from the first plurality of first sensor voltages signals; wherein the second sensor is configured to cancel fifth harmonics from the second plurality of second sensor voltage signals; and wherein the target coil is sized to nullify seventh harmonics otherwise present in at least one of the first plurality of first sensor voltage signals and the second plurality of second sensor voltage signals.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The features, aspects, advantages, functions, modules, and components of the devices, systems and methods provided by the various implementations of the present disclosure are further disclosed herein regarding at least one of the following descriptions and accompanying drawing figures. In the appended figures, similar components or elements of the same type may have the same reference number, such as 108, with an additional alphabetic designator, such as 108a, 108n, or the like, wherein the alphabetic designator indicates that the components bearing the same reference number, e.g., 108, share common properties and/or characteristics. Further, various views of a component may be distinguished by a first reference label followed by a dash and a second reference label, wherein the second reference label is used for purposes of this description to designate a view of the component. When only the first reference label is used in the specification, the description is applicable to any of the similar components and/or views having the same first reference number irrespective of any additional alphabetic designators or second reference labels, if any.

[0027] FIG. 1 is a schematic representation of a conventional linear inductive position sensor.

[0028] FIG. 2 is a schematic representation of a conventional multiple target linear sensor arrangement.

[0029] FIG. 3A is a schematic representation of a linear position sensor configured in accordance with at least one implementation of the present disclosure.

[0030] FIG. 3B is a schematic representation of a linear position sensor having two receiver coils and as configured in accordance with at least one implementation of the present disclosure.

[0031] FIG. 3C is a schematic representation of a linear position sensor having three receiver coils and as configured in accordance with at least one implementation of the present disclosure.

[0032] FIG. 3D is an electrical schematic representation of the linear position sensor of FIG. 3C and as configured in accordance with at least one implementation of the present disclosure.

[0033] FIG. 3E is an enlarged view of a portion of the schematic representation of an implementation of a receiver coil having two loops for the linear position sensor of FIG. 3A and as configured in accordance with at least one implementation of the present disclosure.

[0034] FIG. 3F is an electrical schematic representation of the linear position sensor of FIG. 3E and as configured in accordance with at least one implementation of the present disclosure.

[0035] FIG. 4A is a schematic representation of a linear position sensor having two sensor circuits and as configured in accordance with at least one implementation of the present disclosure.

[0036] FIG. 4B is an electrical schematic representation of a linear position sensor having two sensor circuits and as configured in accordance with at least one implementation of the present disclosure.

[0037] FIG. 5 is a chart illustrating one application of the Vernier principle as applied to the linear inductive position sensor of FIG. 4 and in accordance with at least one implementation of the present disclosure.

[0038] FIG. 6 is a chart illustrating fundamental amplitudes as a function of a relative width of a target coil to the wavelength of the receiver coil as generated by the linear inductive position sensor of FIG. 4 and in accordance with at least one implementation of the present disclosure.

[0039] FIG. 7 is a chart illustrating relative signal strengths of harmonics generated by a single coil implementation of the linear inductive position sensor of FIGS. 3A-3B and in accordance with at least one implementation of the present disclosure.

[0040] FIG. 8 is a chart illustrating relative signal strengths of harmonics generated by a multiple, in series electrical arrangement, coil implementation of the linear inductive position sensor of FIG. 4 and in accordance with at least one implementation of the present disclosure.

DETAILED DESCRIPTION

[0041] The various implementations described herein are directed to devices, systems, and methods for inductively determining the position of an object using a linear inductive position sensor.

[0042] As shown in FIG. 3A and for at least one implementation of the present disclosure, a linear position sensor 300 includes an excitation coil 302, a first receiver coil 304(1) and a second receiver coil 304(2), and a target coil 306.

[0043] The excitation coil 302 may be configured on a PCB (not shown), where a top surface of the PCB forms a given axis along the length thereof such that linear position measurements of the target may be determined along all or a portion of the length of the given axis, such as the X axis. The PCB may provide a stator core for the excitation coil 302 and for the receiver coil(s) 304 and is used in generating electromagnetic fields when an AC signal is provided to the excitation coil 302. The target coil 306 may move along the given axis of the PCB, as separated therefrom by the before-mentioned air gap Z.

[0044] The excitation coil 302 may include a multi loop design. Any number of loops may be used for the excitation coil 302 with two loops being shown for purposes of illustration. The respective ends of the excitation coil 302 are coupled to a control circuit (not shown) which controls the providing of electrical currents to the excitation coil 302 from a power source (not shown). The control circuit may be coupled to and control one or more switches (not shown) which selectively couple the excitation coil 302 with a power source (not shown). The power source provides an AC signal, which results in the excitation coil 302 generating a first electromagnetic field (not shown). It is to be appreciated that control circuits, switches, and AC sources used with inductive position sensors are well known in the art and any such known or later arising components may be configured for use in an implementation of the present disclosure.

[0045] As shown in FIG. 3B, an implementation may utilize two receiver coils 304(1) and 304(2). The receiver coils 304 are printed over a distance corresponding to a period A for the receiver coil 304. The second receiver coil 304(2) may be shifted from the first receiver coil 304(1) by one-quarter of a period (/4) along the PCB and thereby form a sine-cosine pair with the first receiver coil 304(1). To cancel out even harmonics, the receiver coils 304(1) and 304(2) have a twisted loop configuration. Any desired length may be used for a receiver coil 304, such as 2 . . . n (where n is an integer). The receiver coils 304 are printed onto and through the PCB using known processes and in a symmetrical twisted loop design. Each receiver coil 304 may be formed such that a complete symmetrical loop occurs over a distance along the X axis of the PCB. For at least one implementation, =6 mm (six millimeters). Other distances for may be used for other implementations. By using symmetrical loops, even harmonics of a given sensor transfer function may be minimized.

[0046] As shown in FIG. 3C, an implementation may include three receiver coils 304(1), 304(2) and 304(3). When three receiver coils are utilized, the receiver coils may be shifted from another coil by one-third of a period (/3). The receiver coils 304 may include a twisted loop configuration and have a given length. The three receiver coils 304(1), 304(2) and 304(3) form a 3-phase system transfer function, where difference between any two phases negate third harmonics arising in a transfer function for a single given phase. It is to be appreciated that a twisted loop configuration minimizes the reception, by the receiver coil 304, of unintended electromagnetic fields and waves.

[0047] In FIG. 3D, the receiver coils 304(1), 304(2) and 304(3) may be offset by one-hundred and twenty degrees (120 deg.). Accordingly, a third harmonic received in each receiver coil 304 is offset by 3*120 deg. When each receiver coil 304 has the same phase and are configured with the same geometry, the third harmonics will have the same amplitude and, due to being offset by 3*120 deg., will cancel while the fundamental signal is not cancelled when measuring the voltage difference between two receiver coils. Accordingly, per FIG. 3C and an implementation where three receiver coils 304(1), 304(2) and 304(3) are utilized, a received voltage that is not influenced by third harmonic signals may be sensed by a control circuit.

[0048] In FIG. 3E, a portion of the linear position sensor 300 is shown, in an enlarged view, as indicated by section lines E-E in FIG. 3A. As shown with respect to, but not limited to, the first receiver coil 304(1), the first receiver coil 304(1) may include two or more receiver coil loops, such as a first receiver coil first loop 304(1)(L1) and a first receiver coil second loop 304(1)(L2). Any number of loops may be utilized and for an implementation. A loop of a given receiver coil 304 may be shifted a first distance D1 along the X-axis of the linear position sensor 300. For an implementation, D1=/14.

[0049] As shown in FIG. 3F, the multi loop implementation of FIG. 3E may be used with the multiple coil implementation of FIG. 3C such that a second receiver coil 304(2) may include a second receiver coil first loop 304(2)(L1) and a second receiver coil second loop 304(2)(L2) and a third receiver coil 304(3) may include a third receiver coil first loop 304(3)(L1) and a third receiver coil second loop 304(3)(L2). As per FIG. 3E, the second loop (L2) may be offset by a distance /14 form a corresponding first loop (L1) of a given receiver coil 304. It is to be appreciated that a receiver coil 304 when so configured per the implementation of FIG. 3F may result in a doubling of a fundamental signal and a cancellation of seventh harmonic signals.

[0050] The excitation coil 302 and receiver coils 304 may be printed, deposited, or otherwise formed on and in the PCB or other substrate using any known or desired compounds, such as copper, aluminum, gold, or others. In accordance with at least one implementation, the receiver coils 304 may be printed on the PCB with vias being used to connect different portions of the coils, as such different portions may be printed on different faces or layers of the PCB. The use of vias to connect PCB portions is well known in the art.

[0051] The target coil 306 may be fabricated on a target core (not shown) of any desired substance, such as a PCB or other substrate. The target coil 306 includes a conductive material that may be configured in a coil or any other conductive shape. The target coil 306 may be sized and configured to facilitate the detection of any desired range of linear movements of the target coil 306 across the given axis of the linear position sensor 300. For an implementation, the target coil 306 may include a twisted loop design. When a multi-layer PCB or similar material is used as a target core (not shown), the target coil 306 may include two or more twisted loops drawn between each of a top layer and a bottom layer of the target core. The target coil 306 generates a second electromagnetic field when the target coil 306 is inductively coupled to the excitation coil 302.

[0052] For at least one implementation, a transfer function defining a relationship between the excitation voltage Vx and the receive voltage Vr may be expressed mathematically as per Equation 1:

[00001]$\begin{array}{cc}{V}_r=\left(\frac{M_{\mathrm{xr}}}{L_x}-\frac{M_{xt}\left(Z\right)M_{\mathrm{tr}}(Z,2\left(x/\right)}{L_t{L}_x}\right)V_x& \mathrm{Equation}1\end{array}$

[0053] Where, Lx and Lt are constants and Mxr, which represents the direct coupling on the PCB between the excitation coil and the receiver coils, is also a constant. Further, Mxt is a function of the target to PCB air gap Z and Mtr is a function of both the air gap Z and the target position along the given axis formed by excitation coil 302 printed onto the PCB. For at least one implementation, Z=0.5 mm (one-half of a millimeter).

[0054] Further and as shown above, Mtr can be approximated as the product of two functions, F(z) and M(2x/), with the latter ideally being a pure sine or cosine. Since the receiver coil 304 is printed on the PCB with multiple loops shifted on the PCB by precise lengths, Mxr may be negligible and positions of the target coil 306 along the given axis can be determined using the arctangent of the ratio of the received signals.

[0055] As further shown in FIGS. 3D and 3F, a first processor 308 may be coupled to the receiver coils 304 and measure two values (for a two phase system, not shown) or three values (for a three phase system, as shown): Ca=Vr1Vr2; Cb=Vr2Vr3; and Cc=Vr3Vr1. It is to be appreciated, for a two-phase system, Vr1=A sin(2x/) and Vr2=A cos(2x/), with 2x/=atan(Vr1/Vr2). For a three-phase system, Vr1=A*sin(2x/), Vr2=A*sin(2(x/+1/3)) and Vr3=A*sin(2(x/+2/3)). The sine and cosine may be obtained using the commonly known alpha-beta transformation (which is also known as a Clarke transformation). Based on the values of Vr1, Vr2 and Vr3, a first position signal X1, calculated as an arctangent of the Ca, Cb and Cc values, is generated and output by the first processor 308.

[0056] As shown in FIGS. 4A and 4B and for another implementation of the present disclosure, a dual sensor linear position sensor 400 may include two sensors including a first sensor 402 and a second sensor 404. The first sensor 402 and the second sensor 404 may include a receiver coils with multi loop designs where each successive loop is shifted a given distance relative to the preceding loop, as described above with reference to FIGS. 3A-3F. In FIGS. 4A and 4B, the second sensor 404 is shown to include a three coil, multi-loop configuration. Herein, the coils and loops are identified by the designators 304 (coil #)(loop #), e.g., 304(1)(L1). The period of the coils 304 and 304 may respectively correspond to the first period and the second period 2. For at least one implementation, the first sensor 402 may have a first period =6 mm and the second sensor 404 may have a second period 2=6.3 mm.

[0057] By using a two sensor design, as shown in FIGS. 4A and 4B, each of the sensors 402 and 404 including multiple coils 304( ) and 304( ) The coils 304/304 further include multiple loops (L1), (L2) and (L3). For the first sensor 402, the loops for a given coil are offset by the first distance D1. For the second sensor 404, the loops for a given coil are offset by a second distance D2. Using such offsets between the loops (Ln), harmonics otherwise present in the Mtr transfer functions may be minimized, thereby facilitating generation of a high accuracy position signal P by the dual sensor linear position sensor 400. For at least one implementation, a high accuracy position signal P is a position that is determined to be within +/0.5 millimeters of an actual position of the target along the given axis. For an implementation, 2. For an implementation, D1=/14 and D2=2/10. For at least one implementation, the accuracy of the linear position sensor 300 is determinable based on the period of the sensor, as represented by the first period and the second period 2.

[0058] For at least one implementation, the target width (D3) of the target coil 306 may be determined based upon the first period and the second period 2. For an implementation, D3 satisfies both of the conditions in Equation Set 2.

[00002]$\begin{array}{cc}D3=\left(3/5\right)\mathrm{and}& \mathrm{Equation}\mathrm{Set}2\end{array}$$D3=2\left(4/7\right).$

[0059] Per Equation Set 2 and for at least one implementation, =6 mm (six millimeters), 2=6.3 mm (six-point three millimeters), and the width D3 of the target coil 306 equals three-point six millimeters (D3=3.6 mm). For at least one implementation, the dimensions , 2 and D3 may be determined based upon computer simulations to find an optimal value for each.

[0060] As shown in FIG. 4B, the first processor 308 generates and outputs the first position signal X1 and the second processor 408 likewise generates and outputs a second position signal X2. The first position signal X1 and the second position signal X2 are provided to a Vernier processor 410 which generates (as described below) and outputs a final position signal P. The final position signal P is provided to other control units used in conjunction with, and not otherwise described herein, a given implementation of the present disclosure.

[0061] As shown in FIG. 5, the Vernier principle may be used to determine the position of the target along the dual sensor linear position sensor 400 in view of the first period and the second period 2. In FIG. 5, the first position signal X1 and the second position signal X2 are depicted. As the target moves along the sensors, the positions X1 (for the first sensor 402) and X2 (for the second sensor 404) change, with X1 repeating three times for the first period and X2 repeating for times for the second period 2. Corresponding voltages are sensed as the target moves along the sensor, sine and cosinefunctions of the positionare calculated, and the arctangent thereof result in a given position signal (X1 or X2) scaled between zero (0) and one (1), as shown on the Y axis in FIG. 5. It is to be appreciated that per the Vernier principle, an accurate measurement of a given distance of an object from a reference point may be made by using two measurements, which form a unique pair for a given position of the target coil 306 along the given axis. Based upon the values of the position signals X1 and X2, the position of the target coil 306 on the given axis can be uniquely determined by the Vernier processor 410. For example, when X2=1.0 and X1=0.75, the target coil 306 is located at position A along the X axis of the dual sensor linear position sensor 400. Similarly, when X2=1.0 and X1=0.5, the target coil 306 is located at position B along the X axis of the linear position sensor 300. Similarly, when X2=0.9 and X1=0.15, the target coil 306 is located at position C along the X axis of the dual sensor linear position sensor 400. It is to be appreciated that the scale may be measured in any increments, with the range of 0 to 1 being depicted in FIG. 5 for illustrative purposes and across any given range such as 0 to 1.0 with the range corresponding to a gradation of a length of the given axis (such as the X axis) of the dual sensor linear position sensor 400. For an implementation, the control unit is configured to measure voltages received by each sensor and convert such voltages into a relative position.

[0062] As shown in FIG. 6, relationships between a fundamental amplitude A1, a fifth harmonic amplitude A5, and a seventh harmonic amplitude A7 are shown, as modeled for the linear inductive position sensor of FIG. 4, and as determined based on a relative target width DR ranging from zero (O) to two (2), where DR=D3/. As shown, A5 is null when D3=*(p/5), where p=0, 1, 2, etc., and A7 is null when D3=*(q/5), where q=0, 1, 2, etc. Accordingly, it is to be appreciated that for the linear position sensor of FIG. 4, D3 can be defined by Equation Set 3.

[00003]$\begin{array}{cc}D3=\left(p/5\right)=2\left(q/7\right);\mathrm{or}& \mathrm{Equation}\mathrm{Set}3\end{array}$$7p=5q2\left(\mathrm{when}p0,5,15,\mathrm{etc}.\mathrm{and}q0,7,14,\mathrm{etc}.\right)$

[0063] Using Equation Set 3, it can be seen that when p=3 and q=4, then 21=20 2. Accordingly, the Vernier has 21 periods for the first receiver coil 402 and 20 periods for the second receiver coil 404.

[0064] As shown in FIG. 7, since D3=(3/5)*, the fifth harmonic is canceled in the transfer function between the target coil 306 and the first receiver coil 302. As shown in FIG. 7, since D3=(4/7)*2, the seventh harmonic is canceled by the second receiver coil 404. Accordingly, by using the linear receiver coil implementation of FIGS. 3C, 3E, 4A and 4B, the seventh and fifth harmonics may be nullified in the first sensor 402 and in the second sensor 404. Further, when using a 3-phase system for the receiver coils each of the third, fifth and seventh harmonics and their respective multiples may be nullified as shown in FIG. 8. It is to be appreciated that such nullification of these harmonics facilitate closer placements (i.e., a smaller air gap Z) of the target coil 306 relative to the top surface of the PCB used for the excitation coil 302 and the receiver coils 304/304 and thereby greater sensitivity and accuracy of the dual sensor linear position sensor 400 to movements of the target coil 306.

[0065] In summary, the following harmonics are cancelled when a three-phase implementation of the present disclosure is utilized, with remaining harmonics (such as the 11.sup.th, 13.sup.th, 17.sup.th, 19.sup.th, etc.) having negligible influence, if any. [0066] Even Harmonics: [0067] Cancelled due to use of twisted loop geometry in the receiver coils; [0068] 3.sup.rd Harmonics (and multiples thereof): [0069] Cancelled due to measurement differences when a 3-phase system is utilized; [0070] 5.sup.th Harmonics: [0071] Cancelled in sensor 1 due to D3=(3/5)*; and [0072] Cancelled in sensor 2 due to spacing between coils in series=(1/10)*2; and [0073] 7.sup.th Harmonics: [0074] Cancelled in sensor 1 due to spacing between coils in series=(1/14)*; and [0075] Cancelled in sensor 2 due to D3=(4/7)*2.

[0076] In summary, the following harmonics are cancelled when a two-phase implementation of the present disclosure is utilized. [0077] Even Harmonics: [0078] Cancelled due to use of twisted loop geometry in the receiver coils; [0079] 3.sup.rd Harmonics (and multiples thereof): [0080] Cancelled in sensor 1 due to D3=(2/3)*; and [0081] Cancelled in sensor 2 due to spacing between coils in series=(1/6)*2; [0082] 5.sup.th Harmonics: [0083] Cancelled in sensor 1 due to spacing between coils in series=(1/10)*; and [0084] Cancelled in sensor 2 due to D3=(3/5)*2. [0085] 7.sup.th, 9.sup.th, 11.sup.th, 13.sup.th, 17.sup.th, 19.sup.th, etc. Harmonics: Not cancelled.

[0086] Further, it is to be appreciated that coupling may occur between leads used to connect the excitation coil and receiver coils to the control unit. Such coupling may be addressed by implementing one or more concepts disclosed in U.S. patent application Ser. No. 16/112,221, filed on Aug. 24, 2018, in the name of inventor Jacques Jean Bertin, entitled Devices, Systems and Methods for Determining and Compensating for Offset Errors Arising in Inductive Sensors, and which issued as U.S. Pat. No. 11,112,275 on Sep. 7, 2021the entire contents of which are incorporated herein by reference.

[0087] Although various implementations of the claimed invention have been described above with a certain degree of particularity, or with reference to one or more individual implementations, those skilled in the art could make alterations to the disclosed implementations without departing from the spirit or scope of the claimed invention. The use of the terms about, approximately or substantially means that a value of an element has a parameter that is expected to be close to a stated value or position. However, as is well known in the art, there may be minor variations that prevent the values from being exactly as stated. Accordingly, anticipated variances, such as 10% differences, are reasonable variances that a person having ordinary skill in the art would expect and know are acceptable relative to a stated or ideal goal for one or more implementations of the present disclosure. It is also to be appreciated that the terms top and bottom, left and right, up or down, first, second, before, after, and other similar terms are used for description and ease of reference purposes only and are not intended to be limiting to any orientation or configuration of any elements or sequences of operations for the various implementations of the present disclosure. Further, the terms and and or are not intended to be used in a limiting or expansive nature and cover any range of combinations of elements and operations of an implementation of the present disclosure. Other implementations are therefore contemplated. It is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative only of implementations and not limiting. Changes in detail or structure may be made without departing from the basic elements of the invention as defined in the following claims.