110 and 120 may produce a flat response of sensor 100 across the entire range of frequencies of interest for sensor 100. In some respects, FIGS. 1B-E are provided to illustrate an example of a cross-over issue, which is herein referred to as “notching”, and which is manifested in the combination of signal paths 110 and 120 having a non-uniform frequency response. In the example of FIG. 1C, the non-uniformity in the combination of signals 118 and 127 (i.e., the non-uniformity in the frequency response of signal 141) is manifested by notch 155.

FIG. 1F is a diagram of sensor 100 when sensor 100 is arranged in accordance with the design of FIG. 1A. As illustrated, sensor 100 may include a substrate 160. The substrate 160 may be a silicon substrate and/or any other suitable type of substrate. Formed on the substrate may be the feedback coil 134, additional circuitry 147, and Hall elements 123. Feedback coil 134 may be implemented as a conductive trace defining one or more turns. The additional circuitry 147 may include all components of sensor 100 that are shown in FIG. 1A, except for feedback coil 134, sensing bridge 111, and Hall elements 123. In the example of FIG. 1F, feedback coil 134 is arranged to surround the sensing bridge 111, while Hall elements 123 are situated outside of feedback coil 134. Although, in the present example, feedback coil 134 is configured to surround sensing bridge 111, alternative implementations are possible in which feedback coil 134 is situated to the side of sensing bridge 111. Additionally or alternatively, in some implementations, feedback coil 134 may be situated in greater proximity to sensing bridge 111 than Hall elements 123. In some implementations, feedback coil 134 may be configured in such a way so as to cause the impact of the magnetic field generated by feedback coil 134 on Hall elements 123 to be minimized or ideally become nonexistent. FIG. 1F is provided to illustrate that in the example of FIG. 1A sensing bridge 111 is arranged in a closed-loop configuration while Hall elements 123 are arranged in an open-loop configuration. Under the nomenclature of the present disclosure, a sensing module (such as sensing bridge 111 or Hall elements 123) is arranged in a closed-loop configuration when the sensing module is subjected to a feedback magnetic field that is at least partially generated based on a signal that is output by the sensing module. Under the nomenclature of the present disclosure, a sensing module (such as sensing bridge 111 or Hall elements 123) is arranged in an open-loop configuration when the sensing module is not subjected to a feedback magnetic field that is at least partially generated based on a signal that is output by the sensing module.

FIG. 2A is a diagram of another implementation of magnetic field sensor 100, according to aspects of the disclosure. The implementation of sensor 100 that is shown in FIG. 2A is identical to the implementation of sensor 100 that is shown in FIG. 1A, but for: (i) sensor 100 including a second feedback path 230, and (ii) signal path 120 having an amplifier 224 added to it. As illustrated, amplifier 224 is configured to generate the signal 127 by amplifying the output of low-pass filter 126. Feedback path 230 may include a voltage-to-current (V/I) converter 231, a feedback coil driver 233, and a feedback coil 234. The V/I converter 231 may be configured to receive the signal 127 and generate a control signal 232 in response. The signal 232 is provided to feedback coil driver 233 where it is used by the feedback coil driver 233 to drive the feedback coil 234. Signal 232 may specify the level of electrical current that is required to be passed through the feedback coil 234 and/or the level of feedback magnetic field that is to be generated by the feedback coil.

In some implementations, feedback coil 134 may be positioned in greater proximity to sensing bridge 111 than Hall elements 123. Similarly, feedback coil 234 may be positioned in greater proximity to Hall elements 123 than sensing bridge 111. As a result of this arrangement, feedback coil 134 may be configured to adjust the sensitivity of sensing bridge 111 without significantly affecting the operation of Hall elements 123. Similarly, as a result of this arrangement, feedback coil 234 may be used to adjust the sensitivity of Hall elements 123 without significantly affecting the operation of sensing bridge 111. Accordingly, the respective sensitivities of the signal path 110 and the signal path 120 may be independently balanced, which in turn would result in greater accuracy of the design of FIG. 2A in comparison to the design of FIG. 1A. As a result of the feedback path 230 being provided in sensor 100, the stability of the sensitivity of signal path 120 is stabilized compared to the embodiment of FIG. 1A. On the other hand, in the design of FIG. 2A, the respective gains of signal paths 110 and 120 are required to be matched. This necessitates additional trimming to be performed on the gain of signal path 120 so that it matches the gain of signal path 110. The additional trimming may be performed by adjusting the current used to drive feedback coils 134 and 234 to correct for any mismatch that there might be between a first coupling coefficient that describes the magnetic coupling between feedback coil 134 and sensing bridge 111 and a second coupling coefficient that describes the magnetic coupling between feedback coil 234 and Hall elements 123. In the example of FIG. 2A, amplifier 224 is added in order to provide a high forward gain for feedback path 230.

In the example of FIG. 2A, the output of signal path 110 is described by equation 1, which is discussed above, the output of crossover 140 is described by equation 3, which is discussed above, and the output of signal path 120 is described by equation 4:

$\begin{matrix} S_{1 2 7} = \frac{B_{ext (LF)}}{K_{fbkHALL} * d_{HALL}} & (4) \end{matrix}$

- where S₁₂₇is the value of signal 127, B_ext(LF)is the magnitude of the low-frequency component of the external magnetic field that is being measured, K_fbkHALLis a coupling coefficient representing the transfer of energy between the feedback coil 234 and the Hall elements 123, and d_HALLis a scaling factor. FIG. 2B is a diagram of sensor 100 when sensor 100 is arranged in accordance with the design of FIG. 2A. The example of FIG. 2B is identical to the example of FIG. 1F, but for including additional circuitry 240, instead of additional circuitry 147, and also including the feedback coil 234. Additional circuitry 240 may include all components of sensor 100 that are shown in FIG. 2A, other than sensing bridge 111, feedback coil 134, Hall elements 123, and feedback coil 234. In the example of FIG. 2B, feedback coil 234 is implemented as a conductive trace that is formed on the substrate. Feedback coil 234 may include one or more turns, and it may be arranged to surround Hall elements 123. Although, in the example of FIG. 2B, feedback coil 234 is arranged to surround Hall elements 123, alternative implementations are possible in which feedback coil 234 is disposed to the side of Hall elements 123. Additionally or alternatively, in some instances, feedback coil 234 may be formed in greater proximity to Hall elements 123 than sensing bridge 111. In the example of FIG. 2B both of sensing bridge 111 and Hall elements 123 are arranged in a closed-loop configuration.

FIG. 3A is a diagram of another implementation of magnetic field sensor 100, according to aspects of the disclosure. The implementation of sensor 100 that is shown in FIG. 3A is identical to the implementation of sensor 100 that is shown in FIG. 2A, but for (i) sensor 100 including a signal path 310 instead of the signal path 110, and (ii) sensor 100 including summation circuits 312 and 314 instead of the crossover 140.

Signal path 310 may include the driver circuit 112, the sensing bridge 111, the control circuit 113, an amplifier 302, an LPF 304, and an amplifier 306. In operation, sensing bridge 111 may be configured to sense a magnetic field signal and generate a sensing signal 161 in response. The amplifier 302 may be configured to amplify the sensing signal 161 to produce an amplified signal 303. The LPF 304 may be configured to filter the signal 303 to produce a filtered signal 305. And the amplifier 306 may be configured to amplify the signal 305 to produce the signal 118. Summation circuit 314 may subtract signal 127 from signal 118 to produce a signal 313, which is representative of the offset of signal path 310. Summation circuit 312 may subtract signal 313 from signal 118 to produce the signal 141.

The operation of architecture shown in FIG. 3A may be described by equations 5-9 below:

$\begin{matrix} S_{1 1 8} = \frac{B_{ext} + B_{off}}{K_{fbkMR} * d_{MR}} & (5) \end{matrix}$

$\begin{matrix} S_{1 2 7} = \frac{B_{ext}}{K_{fbkHALL} * d_{hall}} & (6) \end{matrix}$

$\begin{matrix} K_{fbkMR} * d_{MR} = K_{fbkHall} * d_{hall} = K_{fb} * d & (7) \end{matrix}$

$\begin{matrix} V_{aux} = \frac{B_{ext} + B_off}{K_{fbkMR} * d_{MR}} - \frac{B_{ext}}{d_{hall} * K_{fbhall}} \underset{if (equation 7) is met}{\underset{︸}{=}} \frac{B_off}{K_{fbk} * d} & (8) \end{matrix}$

$\begin{matrix} S_{1 4 1} = S_{1 1 8} - V_{aux} = \frac{B_{ext} + B_{off}}{K_{fb} * d} - \frac{B_{off}}{K_{fb} * d} = B_{ext} / (d * K_{fb}) & (9) \end{matrix}$

where S₁₁₈is the value of signal 118, B_offis an offset, S₁₂₇is the value of signal 127, S₁₄₁is the value of signal 141, B_exis the magnitude of the external magnetic field that is being measured, K_fbkMRis a coupling coefficient representing the transfer of energy between the feedback coil 134 and the sensing bridge 111, KfbHall is a coupling coefficient representing the transfer of energy from feedback coil 234 and Hall elements 123, d_MRis a scaling factor, d_hallis a scaling factor, and d is a scaling factor.

In the example of FIG. 3A, no blocking capacitors are present in signal path 310. This is in contrast to signal path 110, which is shown in the examples of FIG. 1A and FIG. 2A. Because no blocking capacitors are present in signal path 310, an offset component B_offis present in signal 118. The offset component B_offis removed by summation circuits 312 and 314, which are used to combine signals 118 and 127 to produce the output signal 141. However, in order for the offset component to be successfully removed by summation circuits 312 and 314, equation 7 must hold true. In this regard, in the example of FIG. 3A, the components of sensor 100 are configured so that equation 7 would hold true. In some implementations, in order for equation 7 to hold true, signal paths 310 and 120 may be designed to have the same gain. Alternatively, in some implementations, the gains of signal paths 310 and 120 may be equalized by trimming the current used to drive feedback coils 134 and 234 to correct for any mismatch that there might be between a first coupling coefficient that describes the magnetic coupling between feedback coil 134 and sensing bridge 111 and a second coupling coefficient that describes the magnetic coupling between feedback coil 234 and Hall elements 123.

As noted above, in the example of FIG. 3A, the summation circuits 312 and 314 are used to replace the crossover 140 which is used in the examples of FIGS. 1A and 2A. One advantage of using the summation circuits 312 and 314 instead of the crossover 140 is that the summation circuits 312 and 314 are less expensive to design than the filter 143, which is part of crossover 140.

In another aspect, the design shown in FIG. 3A requires the gains of signal path 310 to be matched to the gain of signal path 120, or vice versa. The gain matching may be performed by selecting the appropriate gain values for each, or at least some, of amplifiers 302, 306, 125, and 224.

FIG. 3B is a diagram of sensor 100 when sensor 100 is arranged in accordance with the design of FIG. 3A. The example of FIG. 3B is identical to the example of FIG. 2B, but for including additional circuitry 340, instead of additional circuitry 240. Additional circuitry 340 may include all components of sensor 100 that are shown in FIG. 3A, other than sensing bridge 111, feedback coil 134, Hall elements 123, and feedback coil 234. In the example of FIG. 3B both of sensing bridge 111 and Hall elements 123 are arranged in a closed-loop configuration, and feedback coil 234 is arranged to surround Hall elements 123. In the example of FIG. 3B, feedback coil 134 may be arranged in such a way that the impact of the feedback magnetic field generated by feedback coil 134 on Hall elements 123 is negligible or ideally nonexistent. Similarly, feedback coil 234 may be arranged in such a way that the impact of the feedback magnetic field generated by feedback coil 234 on sensing bridge 111 is negligible or ideally nonexistent.

FIG. 4A is a diagram of another implementation of magnetic field sensor 100, according to aspects of the disclosure. The implementation of sensor 100 that is shown in FIG. 4A is identical to the implementation of sensor 100 that is shown in FIG. 3A, but for: (i) feedback path 230 being removed, (ii) signal path 120 including an extra trimming module 402 and an extra amplifier 406, and (iii) summation circuits 312 and 314 being replaced by a single summation circuit 412.

In the example of FIG. 4A, the trimming module 402 that is disposed between the LPF 126 and amplifier 224. Trimming module 402 may include any suitable type of circuit that is configured to remove any residual offset that remains after the chopping operation, which might be present in the output of LPF 126. In some implementations, an extra trimming module, such as the trimming module