210A-B are situated above (or below) the conductor 430.

FIG. 4D shows region 460 of conductor 430 in greater detail. As illustrated, the through-hole 431 may have a width N1, through-hole 432 may have a width N2, leg 441 may have a width W_C1, leg 442 may have a width W_C2, and leg 443 may have a width W_C3. According to the present example, the width W_C1is equal to the width W_C2. However, alternative implementations are possible in which the widths W_C1and W_C2are different from each other. According to the present example, the width W_C3is greater than both of the widths W_C1and W_C2. However, alternative implementations are possible in which the width W_C3is different than at least one of the widths W_C1and W_C2. According to the present example, the width N2 of through-hole 432 is greater than the width N1 of through-hole 431. However, alternative implementations are possible in which the width N1 is greater than or equal to the width N1.

FIG. 4E shows an example of one possible set of dimensions for conductor 430, according to aspects of the disclosure. According to the example of FIG. 4E, the width W_C1of leg 441 may be equal to 2.16 mm; the width W_C2of leg 442 may be equal to 2.16 mm; the width W_C3of leg 443 may be equal to 4.02 mm; the width N1 of the through-hole 431 may be equal to 5.10 mm; the width N2 may of the through-hole 432 may be equal to 10.07 mm; the length L of conductor 430 may be equal to 7.6 mm; the width W of conductor 430 may be equal to 23.5 mm; and the thickness T of conductor 430 may be equal to 3 mm. In a preferred implementation, the widths W_C1, W_C2, W_C3, N1, and N2 may have a tolerance of +/−0.04 mm each, and the length L, the width W, and thickness T may each have a tolerance of +/−0.1 mm.

FIG. 4F is a perspective schematic view of system 470, according to aspects of the disclosure. FIG. 4F illustrates that the sensor 200 may be mounted on a PCB 471 that is disposed above or below the conductor 430. The PCB 471 may be the same or similar to the PCB 107, which is discussed above with respect to FIG. 1. Although not shown, PCB 471 may have a controller mounted thereon, one or more other current sensors, and/or any other suitable type of processing circuitry.

FIG. 4G is a cross-sectional planar view of the conductor 430, which is taken along an axis C-C (shown in FIG. 4F). FIG. 4G is provided to illustrate the principle of operation of conductor 430. Shown in FIG. 4G are magnetic field lines 491, 492, and 493. Line 491 corresponds to the magnetic field originating from leg 441. Line 492 corresponds to the magnetic field originating from leg 442. And line 493 corresponds to the magnetic field originating from leg 443.

Lines 491-493 illustrate that legs 441 and 442 contribute strongly (and equally) to the differential magnetic field sensed by the sensor 200, while leg 443 contributes very little (in comparison). The relative width of each one of legs 441, 442, and 443 determines the relative shift in the useful (to be sensed) magnetic field that it produces as frequency increases. At low frequency, conductor 430 is a current divider that is proportional to the relative cross-sectional areas of legs 441, 442, and 443. At higher frequency, the system is a current divider that is approximately proportional to relative cross-sectional surface areas of legs 441, 442, and 443. At high frequency, the system is a current divider that is approximately proportional to relative cross-sectional surface areas of legs 441, 442, and 443. At higher frequency, eddy currents affect the distribution of current density within each conductor, causing an increase in the relative current carried by conductors with smaller cross section. By varying the relative widths (and with this the relative surface areas) of legs 441, 442, and 443, one can vary the shift in the current density as frequency increases, and find an optimum where the shift is as small as possible, such that the sensitivity of the current sensor 200 minimally changes over frequency.

In one respect, the relative widths of legs 441, 442, and 443 may be described by first characteristic ratio R, which is defined by equation 3 below:

R
=

W

C
⁢
1

W

C
⁢
3

(
3
)

According to the present disclosure, it has been determined that values of R in the range of 0.45-0.6 yield gain error in the range of −2%-1.5%, for frequencies up to 1 KHz.

FIGS. 5A-D show an example of another implementation of the system 470, according to aspects of the disclosure. In the example of FIGS. 5A-D, notches 502 and 504 are formed on each side of region 460. The width of region 460 is still W, while end portions 501 and 503 of conductor 430 have widths W1 and W2, respectively. According to the present example the width W1 is the same as the width W2, however alternative implementations are possible in which they are different. Widths W1 and W2 are both greater than the width W. Although, in the present example, conductor 430 includes a notch on each side of the region 460, alternative implementations are possible in which a notch is provided in which a notch is provided only one side of the region 460. Apart from the conductor 430 being provided with one or more notches, the implementation of system 470 that is shown in FIGS. 5A-D is identical to the implementation shown in FIGS. 4B-G.

As noted above, the frequency response of conductor 430 may be tuned by varying the first characteristic ratio R between the width W_C1of leg 441 and the width W_C3of leg 443, as defined by equation 3 above. In this regard, several designs for conductor 430 are provided, which are herein enumerated as Designs 1-5. For each of Designs 1-5, the sum of the cross-sectional areas of the 3 legs 441-443 is 12 mm². The respective dimensions for each of Designs 1-5 are provided in table 800, which is shown in FIG. 8. Specifically, row 802 of table 800 shows the dimensions of Design 1; row 804 of table 800 shows the dimensions of Design 2; row 806 of table 800 shows the dimensions of Design 3; row 808 of table 800 shows the dimensions of Design 4; and row 810 of table 800 shows the dimensions of Design 5. As illustrated, the value of the first characteristic ratio R for Design 1 may be 0.53; the value of the first characteristic ratio R for Design 2 may be 0.54; the value of the first characteristic ratio R for Design 3 may be 0.56; the value of the first characteristic ratio R for Design 4 may be 0.58; and the value of the first characteristic ratio R for Design 2 may be 0.60.

FIG. 6 shows curves 602-610, which illustrate the respective gain error for each of Designs 1-5. Curve 602 represents the gain error for Design 1, and it shows that Design 1 may have a gain error of 1.1% at 2 kHz. Curve 604 represents the gain error for Design 2, and it shows that Design 2 may have a gain error of −0.2% at 2 kHz. Curve 606 represents the gain error for Design 3, and it shows that Design 3 may have a gain error of −1.0% at 2 kHz. Curve 608 represents the gain error for Design 4, and it shows that Design 4 may have a gain error of −1.8% at 2 kHz. Curve 610 represents the gain error for Design 5, and it shows that Design 5 may have a gain error of −2.3% at 2 kHz. Curves 602-610 were generated by simulating Designs 1-5 with the Ansys Maxwell™ electromechanical device analysis software.

FIG. 7 shows curves 622-630, which illustrate the respective phase error for each of Designs 1-5. Curve 622 represents the phase error for Design 1, and it shows that Design 1 may have a phase error of −0.6° at 2 kHz. Curve 624 represents the phase error for Design 2, and it shows that Design 2 may have a phase error of −0.9° at 2 kHz. Curve 626 represents the phase error for Design 3, and it shows that Design 3 may have a phase error of −1.0° at 2 kHz. Curve 628 represents the phase error for Design 4, and it shows that Design 4 may have a phase error of −1.2° at 2 kHz. Curve 630 represents the phase error for Design 5, and it shows that Design 5 may have a phase error of −1.3° at 2 kHz. Curves 622-630 were generated by simulating Designs 1-5 with the Ansys Maxwell™ electromagnetic simulation software.

FIGS. 6-8 show that a large change in the frequency response of conductor 430 may result from a small change in its dimensions and/or manufacturing tolerances. For instance, in the example of FIGS. 6-8, a shift from +1% to −1% gain error can result from a 40 μm change in the widths W_C1and W_C2and a 70 μm change in the width W_C3.

Additional several designs for conductor 430 are now described, which are enumerated as Designs 6-10. For each of designs 6-10, the sum of the cross-sectional area of legs 431-433 is 25 mm². The respective dimensions for each of Designs 6-10 are provided in table 1100, which is shown in FIG. 11. Specifically, row 1102 of table 1100 shows the dimensions of Design 6; row 1104 of table 1100 shows the dimensions of Design 7; row 1106 of table 1100 shows the dimensions of Design 8; row 1108 of table 1100 shows the dimensions of Design 9; and row 1110 of table 1100 shows the dimensions of Design 10. As illustrated, the value of the first characteristic ratio R for Design 6 may be 0.52; the value of the first characteristic ratio R for Design 7 may be 0.54; the value of the first characteristic ratio R for Design 8 may be 0.56; the value of the first characteristic ratio R for Design 9 may be 0.58; and the value of the first characteristic ratio R for Design 10 may be 0.60.

FIG. 9 shows curves 902-910, which illustrate the respective gain error for each of Designs 6-10. Curve 902 represents the gain error for Design 6, and it shows that Design 6 may have a gain error of −0.2% at 2 kHz. Curve 904 represents the gain error for Design 7, and it shows that Design 7 may have a gain error of −0.7% at 2 kHz. Curve 906 represents the gain error for Design 8, and it shows that Design 8 may have a gain error of −1.4% at 2 kHz. Curve 908 represents the gain error for Design 9, and it shows that Design 9 may have a gain error of −2.2% at 2 kHz. Curve 910 represents the gain error for Design 10, and it shows that Design 10 may have a gain error of −2.5% at 2 kHz. Curves 902-910 were generated by simulating Designs 6-10 with the Ansys Maxwell™ electromagnetic simulation software. The simulations modeled the magnetic fields generated when 600 A of electrical current flows through the conductor 430.

FIG. 10 shows curves 1022-1030, which illustrate the respective phase error for each of Designs 6-10. Curve 1022 represents the phase error for Design 6, and it shows that Design 6 may have a phase error of −1.7° at 2 kHz. Curve 1024 represents the phase error for Design 7, and it shows that Design 7 may have a phase error of −1.8° at 2 kHz. Curve 1026 represents the phase error for Design 8, and it shows that Design 8 may have a phase error of −2.0° at 2 kHz. Curve 1028 represents the phase error for Design 9, and it shows that Design 9 may have a phase error of −2.1° at 2 kHz. Curve 1030 represents the phase error for Design 10, and it shows that Design 10 may have a phase error of −2.2° at 2 kHz. Curves 1022-1030 were generated by simulating Designs 6-10 with the Ansys Maxwell™ electromagnetic simulation software. The simulations modeled the magnetic fields generated when 600 A of electrical current flows through the conductor 430.

FIGS. 9-11 illustrate that a large change in the frequency response of conductor 430 may result from a small change in its dimensions and/or manufacturing tolerances. For instance, in the example of FIGS. 9-11, a shift from +1% to −1% gain error can results from a 130 μm change in the widths W_C1and W_C2and a 270 μm change in the width W_C3.

FIG. 12 shows a graph 1200 which includes gain error curves 1202-1210, according to the present disclosure. Curve 1202 corresponds to a design of conductor 430 that has a first characteristic ratio R of 1.5; curve 1204 corresponds to a design of conductor 430 that has a first characteristic ratio R of 1.0; curve 1206 corresponds to a design of conductor 430 that has a first characteristic ratio R of 0.75; curve 1208 corresponds to a design of conductor 430 that has a first characteristic ratio R of 0.5; and curve 1210 corresponds to a design of conductor 430 that has a first characteristic ratio R of 0.25. FIG. 12 is provided for illustrative purposes only. In the example of FIG. 12 the value of the widths W