WO2012121821A2

WO2012121821A2 - Micromachined resonant magnetic field sensors

Info

Publication number: WO2012121821A2
Application number: PCT/US2012/023756
Authority: WO
Inventors: Joseph Seeger; Chiung C. LO; Baris Cagdaser; Derek Shaeffer
Original assignee: InvenSense Inc
Current assignee: InvenSense Inc
Priority date: 2011-01-11
Filing date: 2012-02-03
Publication date: 2012-09-13
Anticipated expiration: 2013-07-11
Also published as: US20120176128A1; US8860409B2; WO2012121821A3

Abstract

A micromachined magnetic field sensor comprising is disclosed. The micromachined magnetic field comprises a substrate; a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis. The micromachined magnetic field sensor also includes a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem.

Description

MICROMACHINED RESONANT MAGNETIC FIELD SENSORS

FIELD OF THE INVENTION

The present invention relates generally to sensors and more particularly to micromachined resonant magnetic field sensors.

RELATED APPLICATIONS

U.S. patent No. 6,892,575, entitled "X-Y Axis Dual-Mass Tuning Fork

Gyroscope with Vertically Integrated Electronics and Wafer-Scale Hermetic

Packaging," issued May 17, 2005,

U.S. patent No. 6,939,473, entitled "Method of Making an X-Y Axis Dual- Mass Tuning Fork Gyroscope with Vertically Integrated Electronics and Wafer-Scale Hermetic Packaging," issued September 6, 2005,

U.S. patent No. 7,104,129, entitled "Vertically Integrated MEMS Structure," issued September 12, 2006,

U.S. patent No. 7,247,246, entitled "Vertical Integration of a MEMS Structure with Electronics in a Hermetically Sealed Cavity," issued July 24, 2007.

U.S. patent No. 7,442,570, entitled "Method of Fabrication of Al /GE Bonding in a Wafer Packaging Environment and a Product Produced Therefrom," issued October 28, 2008,

U.S. patent application, Serial No. 12/184,231 , entitled "Method of

Fabrication of AI/GE Bonding in a Wafer Packaging Environment and a Product Produced Thereupon," filed on July 31 , 2008 and assigned to the assignee of the present invention,

U.S. patent application, Serial No. 2009019382, entitled "Dual Mode Sensing

For Vibratory Gyroscope, filed on August 6, 2009 and assigned to the assignee of the present invention; and U.S. Patent Application, entitled "Micromachined Resonant Magnetic Field Sensors," serial no. (IVS-145, 4977P), filed on even date herewith, and assigned to the assignee of the present invention, all of which are incorporated herein by reference in their entireties.

BACKGROUND OF THE INVENTION

Magnetic field sensors are widely deployed in consumer and industrial instruments for applications varying from position sensing, current sensing, data storage, and magnetic compassing. There are many methods to sense magnetic fields including Hall-effect, magneto-diode, magneto-transistor, magnetoresistive- effect, magnetic tunnel junction, magneto-optical, fluxgate, search coil, and Lorentz force.

The Lorentz force resonant sensor fabricated by means of MEMS technology is preferred due to its low-cost batch fabrication technology. Lorentz force-effect resonant sensors are manufactured in a process flow similar to the process of motion sensors, such as accelerometers and gyroscopes. In addition, because Lorentz force-effect does not require special magnetic materials, it is the most compatible sensing mechanism for an integrated platform of motion sensors;

magnetic field sensors, accelerometers, and gyroscopes.

However, to detect a magnetic field as weak as the earth magnetic field, the magnetic field sensor is desired to have high sensitivity and low offset. High sensitivity is generally achieved by exciting at the resonant frequency and being packaged in vacuum for high quality factor. However, if the drive frequency is off by Δί from the resonant frequency, the sensitivity decreases significantly which proportional to Δί. In prior art, a close-loop frequency control system is needed to adjust the driving frequency dynamically to prevent significant sensitivity variation and the complicated close-loop control system could consume as high as 1 milliwatt per axis. In addition, the offset is generally larger than the signal and the offset variation limits the minimum detectable signal level. Thus, the design to mitigate offset is critical. Accordingly, what is needed is a system and method to address the above-identified issues. The present invention addresses such a need.

BRIEF SUMMARY OF THE INVENTION

A micromachined magnetic field sensor is disclosed. The micromachined magnetic field comprises a substrate; a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis.

The micromachined magnetic field sensor also includes a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem.

In designing high sensitivity, high manufacturability, low cost, and low power consumption Lorentz force magnetic field sensors, the present invention addresses the need of:

1 . High-manufacturability, low power consumption, and low Brownian noise by establishing a open-loop dual-mode resonating devices;

2. High sensitivity and low cost fabrication by deploying electrostatic coupling spring with high bias voltage at the sensing subsystem;

3. Low offset by deploying: a) electrical shield structures comprising at least one electrical source connected to at least one electrode to reduce the electrostatic offset force along the second axis generated by parasitic capacitors around the drive subsystem;

b) the shield structure has a force-balanced characteristic with two shield structures sandwiching the drive subsystem along the second axis to cancel the electrostatic offset force generated by the shield structures.;

c) the voltage of the electrical source of the shield structures is equal to the voltage of the drive point of the drive subsystem to minimize the electrostatic offset force.

d) a mismatch-trimming actuator moving the micromachined magnetic sensor along the second axis in order to reduce the gap mismatch of the force- balanced electrostatic coupling springs.;

e) an AC ripple voltage detector where the detection connects a drive point to at least one anchor for detecting the ripple of the drive point.

4. Low power consumption by having electrostatic self-test actuator.

By harnessing these design strategies, a Lorentz force resonant sensor can be implemented in a way to allow for on-chip integration of magnetic field sensors with other motional sensors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an embodiment of a dual mode open-loop magnetometer system.

FIG. 2A and 2B are a model of a dual mass system (a) before coupled and (b) after coupled.

Figure 3 is the first transfer function of the dual mode open-loop

magnetometer system.

Figure 4 is the second transfer function of the dual mode open-loop magnetometer system. Figure 5 is the embodiment of a mechanical coupling spring.

Figure 6 is the embodiment of an electrostatic coupling spring.

Figure 7 is the embodiment of open-loop dual-mode Lorentz-force magnetic sensing device with signal processing circuitry.

Figure 8 is the embodiment of open-loop dual-mode Lorentz-force magnetic sensing device for sensing in-plane magnetic fields.

Figure 9 is an embodiment of open-loop dual-mode Lorentz-force magnetic sensing device for sensing out-of-plane magnetic fields.

Figure 10 is an embodiment of 3-axis magnetic sensing system with 3 open- loop dual-mode Lorentz-force magnetic sensing devices.

Figures 1 1 A-1 1 C are embodiments of a self-test actuator with a

magnetometer system (a) for a dual mode system; (b) an implementation with electrostatic comb self-test actuators; (c) for a single mode system.

Figures 1 1 D and 1 1 E are embodiments of a dual mode open loop system and a single mode open loop system, respectively that includes current carrying coils.

Figures 12A-12C are embodiments of a stiffness trimming block with a magnetometer system; (a) an embodiment for a dual mode system; (b) an implementation with electrostatic parallel plate actuators as the stiffness trimming block; (c) an embodiment for a single mode system.

Figures 13A and 13B are embodiments of a shield structure with (a) a dual mode open-loop magnetometer system; and (b) a single mode open-loop magnetometer system.

Figure 14A -14C are embodiments of a dual mode open-loop magnetometer system with a) a mismatch-trimming actuator (MTA), (b) an embodiment of MTA, and (c) an MTA embodiment with a single mode open-loop magnetometer system. Figure 15Aand 15B are embodiments of an AC voltage control system for a dual mode open-loop magnetometer system with (a) resistive type detection and (b) capacitive type detection.

Figure 16A and 16B are embodiments of self-test actuators, force-balanced shield structures, and mismatch trim actuators with open-loop dual-mode Lorentz- force magnetic sensing devices for detecting (a) in-plane and (b) out-of-plane magnetic fields.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates generally to sensors and more particularly to micromachined resonant magnetic field sensors. The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. The present invention is not intended to be limited to the implementations shown but is to be accorded the widest scope consistent with the principles and features described herein.

An embodiment of an open-loop Lorentz-force magnetic sensing device is shown in Figure 1 .

System

The dual mode open-loop system 2 comprises a drive subsystem 60, a sense subsystem 70 and a coupling spring 30, a position transducer 40, signal processing electronics 50, and drive electronics 80 for supplying a current flowing through a portion of the drive subsystem 60. The drive subsystem 60 comprises a plurality of beams, such that in the presence of a magnetic field, the drive

subsystem 60 is actuated through the Lorentz force proportional to the magnetic field. The coupling spring 30 couples the motion and the force of the drive subsystem 60 and the sense subsystem 70 resulting in at least two resonant modes: in-phase mode and anti-phase mode. The sense subsystem 70 comprising a plurality of beams and converts the actuation force from the coupling spring 30 into output motion. The position transducer 40 detects the output motion of the sense subsystem 70 and may be designed with mechanisms comprising parallel plate capacitive transducers, interdigitated comb capacitive transducers,

piezoresistive sensors, optical sensors, and piezoelectric sensors. The drive subsystem 60 and the sense subsystem 70 are mechanically anchored to a substrate 1 through plurality of beams, respectively.

Operation

FIG. 1 depicts the disclosed sensing method comprising flexibly-coupled drive and sense subsystems 60 and 70. An AC current generated by the drive electronics 80 passes through a plurality of beams 1 1 and 12 and establishes a current vector in the first axis at the drive point 10. A distributed Lorentz force is generated in the second axis in the presence of a magnetic field vector in the third axis, and the total force is

where the / is the magnitude of AC current, B is the magnitude of magnetic field density, and dl is the unit length of the portion of the plurality of beams 1 1 , 12 where AC current flows. The Lorentz force actuates the drive point 10 along the second axis proportional to the magnetic field density.

A coupling spring 30 couples the motion of the drive point 10 to the sense point 20 and the sense subsystem 70 resulting in motion at the sense subsystem 70 along the fourth axis proportional to the magnetic field density. The motion at the sense subsystem 70 is detected by a position transducer 40 and the electrical signals from the position transducer 40 are further processed by the signal processing unit 50.

FIG. 2A depicts the uncoupled mechanical model of a sense subsystem 1 70 characterized by a sense resonant mode having frequency s=V(k_s/m_s), and an uncoupled drive subsystem 1 60 characterized by a drive resonant mode having frequency _D=V(k_D/m_D). The sense subsystem 170 comprises mass m_s 140, a sense spring 1 20 with stiffness k_s-Ak, and the coupling spring 1 22 with stiffness Ak. The drive subsystem 160 comprises a mass m_D 130, a drive spring 1 1 0 with stiffness k_D-Ak, and the coupling spring 1 22 with stiffness Ak. The sense mass m_s 140 is suspended from the substrate 1 01 by the sense spring 1 20 while the drive mass m_D 130 is suspended from the substrate 1 01 by the drive spring 1 1 0.

Referring to FIG. 2B, the sense mass m_s 140 and the drive mass m_D 1 30 are flexibly coupled through the coupling spring 1 22 with stiffness Ak such that both stiffness k_s-Ak and stiffness k_D-Ak are greater than zero, i.e. k_s-Ak>0 and k_D-Ak>0. The sensing system from FIG. 2(b) yields a total of four transfer functions whose inputs are generalized forces F_s and F_D and outputs are motion of the particular mass, xs or x_D .

The relationship between the position of the sense mass m_s 140, x_s, and force acting on the drive mass 130, F_D, can be expressed as the following transfer function:

where oosi 220 and oos2 230 as shown in Figure 3 are modal frequencies assigned to two vibratory modes of the system from FIG. 2(b). Similarly, the relationship between the position of the drive mass 1 30, x_d, and force acting on the sense mass 140, Fs, can be expressed as a yet another transfer function:

Further, the relationship between the position of, and the force acting on either drive mass m_D 130 or sense mass m_s 140 can be expressed with the following transfer functions:

where CJO_s is the anti-resonance of the sense subsystem 170 and ω₀ is the anti- resonance of the drive subsystem 160.

Based on Equation (2) and (5), the force in drive subsystem results in the displacement of the drive subsystem which can be significantly smaller than the displacement of the sense subsystem for forcing frequency near _s.

The advantages of dual-mode Lorentz-force magnetic sensing device are two-fold: stable sensitivity and low Brownian noise. Both of these advantages are described herewith.

Stable Sensitivity

Shown in Figure 3, the first transfer functions 210 is the plot of Equation (2) which is from forces at the drive subsystem 160 of Figure 2B to the displacement of the sense subsystem 170. In addition, it is proportional to the sensitivity of the dual mode open-loop system 2B. Because of the existence of two subsystems, the transfer function 210 has at least two resonant peaks labeled as 220 and 230. Around the central frequency ω₀ 240 which are the root-mean-square of the frequencies of the two peaks 220 and 230, the gain of the transfer function 210 is stable even with small frequency perturbation. It is desired to achieve a stable gain by designing the frequency of the AC current from the drive electronics 80 of Figure 1 at the central frequency ω₀ 240. For an open-loop system, typically the frequency of the transfer function shifts because of manufacturing-related and temperature- related variations. The design of the dual mode system of Figure 2B operates around the central frequency ω₀ 240 stabilizes the gain and mitigates the effect of manufacturing-related and temperature-related variations.

Low Brownian Noise

The second transfer function 310 is the plot of Equation (4) which is from forces at the sense subsystem 170 of Figure 2A to the displacement of the sense subsystem 170 is shown in Figure 4. The transfer function has an anti-resonance at notch frequency WN 350 corresponding to the drive subsystem anti-resonance which can be designed to be close to the central frequency ω₀ 240. The total Brownian noise output is the sum in energy of the Brownian noise output from the drive subsystem 160 and that from the sense subsystem 170. The Brownian noise output is the product of the transfer function and the Brownian noise force. In general, the Brownian noise force at the sense subsystem 170 is larger than the Brownian noise force at the drive subsystem 160. By incorporating the anti- resonance of the transfer function 310, the Brownian noise output is minimized and the dual mode open-loop system 2 can achieve low Brownian noise.

The coupling spring 122 is important to the operation of a dual mode open- loop system. The frequency of two resonant peaks labeled as 220 and 230 of the transfer function 210 may be calculated as:

where k_s, k_D and Ak are the stiffness of the sense subsystem 170, the drive subsystem 160, and the coupling spring 122 and this stiffness define frequency separation between 220 and 230. Coupling stiffness Ak may be substantially large in order to separate peaks, yielding wider sensor bandwidth. On the other hand, coupling stiffness Ak may be substantially small to keep peaks close to achieve high transducer gain.

The coupling element 122 can be implemented as structural coupling springs or electrostatic coupling springs.

Structural Coupling Springs

An embodiment of a structural coupling spring 431 is shown in Figure 5. The spring 431 includes folded beams where the stiffness of the structural coupling spring 431 is defined by the structural width, length, height, and material properties. In some case, the sense point is preferred to be electrically isolated from the drive point 410 (Figure 1 ). For example, the sense point 420 (Figure 1 ) can be biased at high voltage to increase the transduction gain of the position transducer 40 (Figure 1 ) while the drive point 410 is biased at a low voltage that is limited by the drive electronics 80 (Figure 1 ). In this case, the material of the structural coupling spring 431 can be designed to be highly resistive or an additional dielectric layer can be inserted in the structural coupling spring 431 . However, a complicated process with at least one extra mask is required to establish low resistance structures for the drive subsystem 60 (Figure 1 ) and high resistance structures or structures with a dielectric layer for the coupling spring 431 . Electrostatic Coupling Springs 30

Electrostatic coupling springs can be designed for different mechanical movements, i.e., in-plane movement or out-of-plane movement.

In-plane electrostatic coupling springs:

An embodiment of electrostatic coupling spring 532 is shown in Figure 6. In the case of in-plane motion of the drive point 510 referenced to the sense point 520 along the second axis, the electrostatic coupling spring 532 includes electrostatic parallel plates with electrode gaps 532a and 532b, respectively. The in-plane coupling stiffness Ak can be modeled as

2s4

Ak °c —V^z (7)

8 where the ε, A, g, and V are the permittivity, electrode area, electrode gap, and bias voltage across the in-plane electrostatic coupling spring 532. The polarity of the in-plane coupling stiffness indicates that the in-plane electrostatic coupling spring is a negative spring and the total stiffness and the resonant frequency are reduced.

Out-of-plane electrostatic coupling springs:

The embodiment of the electrostatic coupling spring 532 shown in Figure 6 can be deployed for out-of-plane motion coupling. In the case of out-of-plane motion of the drive point 510 referenced to the sense point 520 along the third axis, the electrostatic coupling spring 532 acts as interdigitated combs. A typical device can be built with height ranging from 10 microns to 100 microns and a typical gap can vary from 1 micron to 5 microns. For a structural height of 30 microns and the gap of 2 microns, the out-of-plane coupling stiffness Ak can be modeled as

where the n, Lov, g, and V are the number of combs, comb overlap length, electrode gap, and bias voltage across the out-of-plane electrostatic coupling spring 532. The polarity of the out-of-plane coupling stiffness indicates that the out-of- plane electrostatic coupling spring is a positive spring and the total stiffness and resonant frequency are increased.

The advantages of electrostatic coupling springs are twofold. The first advantage is the high impedance at DC between the drive point 510 and the sense point 520. Thus, the sense point 520 can be biased at high voltage to increase the transduction gain of the position transducer 40 (Figure 1 ) without any complicated process mentioned in the section of the structural coupling spring 431 . The second advantage of the electrostatic coupling springs is that a weak stiffness is easily provided. As mentioned before, that coupling stiffness Ak may be substantially small to keep resonant peaks 220 and 230 of Figure 4 close to achieve high transducer gain. This could be problematic when utilizing a structural coupling spring 431 which may require a long and slender structure and may result in undesired low-frequency resonant modes. In the case of electrostatic coupling spring 532, a small stiffness can be achieve by reducing the electrode area for the in-plane electrostatic coupling spring 532 and shortening the comb overlap length for the out-of-plane electrostatic coupling spring 532.

Because of its stable gain and low noise floor, the circuitry requirement for the dual mode open-loop system is not complex and simple signal processing circuitry can be employed. Shown in Figure 7, a signal processing unit 651 in accordance with an embodiment comprising a charge-to-voltage converter 652, a de-modulator 653, and a low-pass filter 654 is coupled to the dual mode system 602. The charge-to-voltage converter 652 converts the output of the position transducer 640 into a voltage format. The de-modulator 653 down-converts the AC output signals of the charge-to-voltage converter 652 into a low frequency. The low- pass filter 654 reduces the high frequency noise and might served as an antialiasing filter prior digitization. In addition, the electrostatic coupling spring 632 is deployed with a high voltage bias 681 to the sense subsystem 670 resulting in high transduction gain of the position transducer 640 mentioned before. The examples noted here should not be interpreted to restrict the range of possible signal processing circuitry of the dual mode open-loop system. One of ordinary skill in the art readily recognizes a variety of types of signal processing circuitry can be utilized and that use would be within the spirit and scope of the present invention.

Embodiments for in-plane and out-of-plane dual mode open-loop systems are shown in Figures 8 and 9.

For an in-plane dual mode open-loop system 702, a drive point 710 and a sense point 720 are mechanically anchored to a substrate 701 through a plurality of beams 71 1 , 712 and 721 , 722, respectively.

In the drive subsystem 760, an AC current generated by the drive electronics 80 of the Figure 1 passes through a plurality of beams 71 1 , a drive point 710a, and a plurality of beams 712. In the presence of a magnetic field vector in X-axis, the Lorentz force generates a distributed actuation force in Z-axis along a drive beam 716 and the total force can be modeled as

where the /y is the current vector in Y-axis and B_x is the magnetic field vector in the X-axis.

The Lorentz force actuates the drive subsystem 760 and the drive point 710 and generates an out-of-plane displacement in Z-axis which is proportional to the magnetic field density. An out-of-plane electrostatic coupling spring 732 transfers the displacement of the drive point 710 to the sense point 720 via its mechanical stiffness and actuates the sense subsystem 770 into a rotational motion in Y-axis. The rotational motion of the sense subsystem 770 is detected by parallel plate capacitive transducers 740 located beneath the sense subsystem 770 as the position transducer 740 and the electrical signals from the position transducer 740 is further processed by the signal processing unit 50 shown in Figure 1 .

For an out-of-plane dual mode open-loop system 802, a drive subsystem 860 and a sense subsystem 870 are mechanically anchored to a substrate 801 through a plurality of beams 81 1 , 812 , 821 , and 822b, respectively.

In the drive subsystem 860, an AC current generated by the drive electronics 80 of the Figure 1 passes through a plurality of beams 81 1 , a drive point 810, and a plurality of beams 812. In the presence of a magnetic field vector in Z-axis, the Lorentz force generates a distributed actuation force in X-axis along a plurality of beams 81 1 and 812. The total force may be modeled as

where the /y is the current vector in Y-axis and B_z is the magnetic field vector in the Z-axis. The Lorentz force actuates the drive point 810 and generates an in-plane displacement in X-axis and the magnitude of the displacement is proportional to the magnetic field density. The motions of the drive subsystem 860 and the sense subsystem 870 are coupled through an in-plane electrostatic coupling spring 832.

The in-plane electrostatic coupling spring 832 transfers the displacement of the drive point 810 to a sense point 820 via its mechanical stiffness and actuates the sense subsystem 870 and the sense point 820. The motion of the sense subsystem 870 is detected by interdigitated comb capacitive transducers 840b as a position transducer and the electrical signals from the position transducer 840 is further processed by the signal processing unit 50 shown in Figure 1 . A multi-axis magnetic sensing system

A multi-axis magnetic sensing system 902 can be constructed from the disclosed open-loop dual mode Lorentz-force magnetic sensing devices and is shown in Figure 10. Magnetic field sensors 902a, 902b, and 902c are deployed for sensing x-axis, y-axis, and z-axis portion of the magnetic field vector, respectively.

The Z-axis micromachined magnetic field sensor 902c, wherein the Z-axis micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in a X-Y plane; and Lorentz force acting on the drive subsystem in the X- Y plane in response to a magnetic field along a Z axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein the sense subsystem moves in the X-Y plane; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem.

The X-axis micromachined magnetic field sensor 902a, wherein the X-axis micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in the X-Y plane; and Lorentz force acting on the drive subsystem along the Z-axis in response to a magnetic field along the X-axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein the sense subsystem moves partially along the Z-axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem. The Y-axis micromachined magnetic field sensor 902b, wherein the Y-axis micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in the X-Y plane; and Lorentz force acting on the drive subsystem along the Z-axis in response to a magnetic field along the Y axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein the sense subsystem moves partially along the Z-axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem. The method of establishing an open-loop dual mode Lorentz-force magnetic sensing device noted here should not be interpreted to restrict the range of possible multi -axis magnetic sensing systems. To form a multi-axis magnetic sensing system, the proposed open-loop dual mode Lorentz-force magnetic sensing device can be integrated with magnetic sensors consisting of Hall sensors, magnetoresistive sensors, magneto- diode sensors, magneto-transistors, fluxgates, magneto-impedance sensors, magneto-optical sensors, and MAGFETs.

Self-Test Function

A self-test function is important and is commonly implemented as a current- carrying coil to generate magnetic fields through the Ampere Law. However, it consumes significant power as high as several milli-watt. For example, 3-axis digital compass HMC5843 manufactured by Honeywell Corporation consumes 3 mA current to generate a 30uT magnetic field (comparable to the earth magnetic field).

Figure 1 1 A is an embodiment of the self-test function which includes a self- test actuator 1014 which connects to a drive subsystem 1060. In the self-test mode, the self-test actuator 1014 excites the drive subsystem 1060 and generates output via the first transfer function 210 of Figure 3. The self-test actuator 1014 can be designed with mechanisms comprising parallel plate capacitive transducers, interdigitated comb capacitive transducers, electro-thermal actuators, and piezoelectric actuators.

An embodiment of parallel plate capacitive transducers 1014a and 1014b as the self-test actuator 1014 is shown in Figure 1 1 B. In the self-test mode, the voltage of either capacitive transducers 1014a or 1014b biased at a self-test voltage which is different from the voltage of the drive subsystem 1060. The voltage difference results in an electrostatic force which actuates the dual mode open-loop system 1002. The method of establishing a self-test actuator 1014 for a magnetic sensing device noted here should not be interpreted to restrict the range of possible application. An embodiment of the self-test function with the self-test actuator 1014 for a single mode magnetic sensing device 1002 is shown in Figure 1 1 C.

In the case of the implementation of a parallel plate capacitive actuator as the self-test actuator 1014, the equivalent magnetic field density is

B Equivalent f ^ ST (H)

\ I ^■ dl where A_ST, gsT, V_D, V_ST, I, and L_D are the parallel plate area, parallel plate gap, the DC voltage of the drive subsystem 1060, a self-test voltage, current flow across the drive subsystem 1060 and the effective beam length of the drive subsystem 1060. With 30umx2.8um of the parallel plate area, 5um of the capacitive gap, biased at 1 voltage of the drive subsystem 1060, supplying 0.5 voltage of self-test voltage across the parallel plate creates a equivalent force of 30uT magnetic density when the drive subsystem 1060 is with 500um of the effective beam length of the drive subsystem 1060 and 1 mA of the driving AC current. The advantage of the proposed self-test function in turn of lowering power consumption is dramatic. Comparing with several milliwatts of the power

consumption for the prior art, the power consumption for voltage across the capacitor of the self-test actuator 1014 is negligible.

The examples noted here should not be interpreted to restrict the range of possible integration of the dual mode or single mode open-loop system with current- carrying coils to generate a magnetic field via the Ampere Law. Figures 1 1 D and 1 1 E are embodiments of a dual mode open loop system and a single mode open loop system respectively that includes current carrying coils 1014c. The current- carrying coils 1014c each generate a magnetic field along the third axis which interacts with the drive subsystem resulting in Lorentz force acting on the drive subsystem along the second axis.

To overcome process variation, frequency tuning is critical to ensure high signal to noise ratio. As before mentioned with reference to Figure 4, sensitivity is proportional to the first transfer function 210 and small frequency separation between two resonant peaks labeled as 220 and 230 leads to high sensitivity. In addition, the second transfer function 310 is related to the total Brownian noise. Ideally, by operating the dual mode open-loop system2 at the anti-resonance WN 350 of the transfer function 310, the Brownian noise output is minimized.

However, because of manufacturing variation resulting in changes in structure stiffness, the frequency separation two resonant peaks 220 and 230 could be widened leading to low sensitivity and the anti-resonance WN 350 of the transfer function 310 is pulled close to the one of the resonant peaks leading to high sensitivity variation. These outcomes degrades signal to noise ratio.

Stiffness Tuning Block

A stiffness tuning block 1 1 18 for a dual mode open-loop system 1 102 is proposed to address the effect of stiffness variation, shown in Figure 12A. Shown in Equation (6), the frequency separation between 220 and 230 is a function of the stiffness of a drive subsystem 1 1 60, a sense subsystem 1 1 70, and a coupling spring 1 1 30. Thus, the transfer function 21 0 and 31 0 and the resonant peaks 220 and 230 can be tuned by changing either the stiffness of the drive subsystem 1 1 60, or the sense subsystem 1 1 70, or the coupling spring 1 1 30. An embodiment of a stiffness tuning block 1 1 1 8 to tune the stiffness and frequency of the sense subsystem 1 1 70 for a dual mode open-loop system 1 102 is shown in Figure 1 2A. An example of electrostatic parallel plates 1 1 1 8a and 1 1 18b as the stiffness tuning block is shown in Figure 1 2B. The tuning stiffness Ak_T of the electrostatic parallel plates 1 1 18a and 1 1 1 8b can be modeled as Equation (7) where A, g, and V are the area of parallel plates 1 1 1 8a and 1 1 1 8b, electrode gap, and bias voltage across the parallel plates 1 1 18a and 1 1 1 8b. Thus, during calibration, the bias voltage across the parallel plates can be tuned and the tuning stiffness Akj from the stiffness tuning block changes the stiffness of the sense subsystem 1 1 70 and ensure the frequency separation and the anti-resonance ω_Ν 350 of the transfer function 31 0 matches the design values.

The application of the stiffness tuning block 1 1 1 8 is not limited to the embodiment shown in Figure 1 2A and 1 2B. Other tuning mechanism such as thermal actuators or piezoelectric actuators can be applied as an implementation of the stiffness tuning block 1 1 18. In addition, a similar frequency tuning block can be applied to change the stiffness of the drive subsystem 1 1 60 or the coupling spring 1 1 30. An example of the stiffness tuning block 1 1 18 for single mode magnetic field sensing system 1 1 02' is shown in Figure 1 2C.

Offset Cancellation

Resonant sensing systems are prevalent for their high sensitivity and the application ranges from magnetic field sensors, gyroscopes, accelerometers, chemical sensors, biosensors, pressure sensors, to force sensors. However, for resonant sensing systems with AC drive signals, the interactions between drive signals and the surrounding parasitic capacitors generates electrostatic offset forces and thus creates unwanted feedthrough outputs, or called offset. In general, the offset is larger than the signal generated by the field of interest. Thus, the offset variation may limit the minimum detectable signal level and the design to mitigate offset is critical.

For resonant magnetic field sensors, the first offset source is the electrostatic force from the shield structure. Shown in Figure 1 3A, a dual mode open-loop system 1 202 with shield structure comprising an electrical source 1 282, and at least one electrode, as 1 21 3 R and 1 21 3L, to reduce the electrostatic offset force along the second axis generated by parasitic capacitors around a drive subsystem 1 260. The equivalent offset from the electrostatic force generated by the shield electrodes is expressed

where H_SH, gsH, AV_D,SH, and AV_Ac are the height of the shield electrode, the gap of the shield electrode, and the DC voltage difference between the drive subsystem 1 260 and the electrical source 1 282 of the shield electrode, the AC voltage difference between the drive subsystem 1 260 and the electrical source 1 282 of the shield electrode. The label L or R of the height and the gap of the shield electrode indicates the left-side 1 21 3L or right-side of the shield 1 21 3 R, respectively.

Offset mitigation with shield structure with force-balanced characteristic

The force-balanced shield structure is implemented with two equal shield heights H_SH and gaps g_SH of the left-side shield 1 21 3L and right-side shield 1 21 3 R. Thus, the electrostatic forces generated by the left shield 1 21 3L is balanced by the force generated by the right-side shield 1 213R and the first term of Equation (1 1 ) is cancelled in the first order resulting in small offset.

Offset mitigation with voltage tuning of shield structure

However, due to manufacturing imperfection of mismatched shield height or shield gap, there is residue offset even with the design of the force-balanced shield structure. Additional cancellation can be achieved by tuning the voltage of the shield structure to null the DC voltage difference AV_D,SH between the drive subsystem 1 260 and the shield electrodes 1 21 3R and 1 21 3L. Thus, the second term of Equation (1 2) is cancelled resulting in small offset.

Offset mitigation with balanced AC voltage distribution

Additional cancellation can be achieved by designing the distribution of the

AC voltage of the drive subsystem 1 260. The effective beam length L_D of the drive subsystem 1 260 is the length of a plurality of beams 1 21 1 and 1 21 2. By having the same length of a plurality of beams 1 21 1 and 1 21 2 and applied same magnitude but opposite polarity of AC voltage distribution across the drive subsystem 1 260, the third term of equation (1 2) is cancelled resulting in small offset.

The examples noted here should not be interpreted to restrict the range of possible application of the offset mitigation technique with shield structure. An embodiment of the offset mitigation with shield structures for a single mode system

1 202 with shield structures 1 21 3R and 1 21 3L across a drive subsystem 1 260, as shown in Figure 1 3B.

A second offset source is the electrostatic force through the electrostatic coupling spring. The second offset source results from an AC electrostatic force generated by AC voltage across the electrostatic coupling spring element. The offset can be modeled as

where A_c, gc, AV_Ds, and AV_Ac,c are the area of the coupling spring, the gap of the coupling spring, the DC voltage difference between the drive subsystem 1 260 and the sense subsystem 1 270, the AC voltage difference at the coupling point between the drive subsystem 1 260 and the sense subsystem 1 270, and the label L or R of the area and the gap of the coupling spring 1230 indicates the two side of the coupling spring.

Offset mitigation with force-balanced coupling spring

Shown in Figure 6, a force-balanced coupling spring 532 for in-plane coupling is implemented with two equal coupling area and gaps of 532a and 532b. Thus, the electrostatic force generated by the left electrode 532a is balanced by the force generated by the right-side electrode 532b and the first term of Equation (1 3) is cancelled in the first order resulting in small offset. The same force-balance technique can be applied to the out-of-plane coupling spring 532.

Offset cancellation with mismatch-trimming actuator

However, due to manufacturing imperfection of mismatched gap, there is residue offset even with force-balanced coupling spring where the residue offset is proportional to the mismatch. Shown in Figure 14A, a mismatch-trimming actuator (MTA) 1 31 5 is implemented to move a sense subsystem 1 370 in order to reduce the gap mismatch. The MTA 1 31 5 can be designed with mechanisms comprising parallel plate capacitive transducers, interdigitated comb capacitive transducers, electro-thermal actuators, and piezoelectric actuators. An embodiment of parallel plate capacitive transducers as MTA 1 31 5 is shown in the Figure14B. The displacement of the electrostatic actuation can be expressed as

^MTA -^J rKv, -v_MTA,15a)² - (v_s -v_MTA,_5b)²] where A_MTA, QMAT, V_MTA, V_s and K_S, are the area of the MTA, the gap of the MTA, the applied voltage at MTA, the voltage of a sense point 1 320, and the stiffness of the sense subsystem 1 370. In a mismatch case that the gap 1 332b of the in-plane coupling spring 1 332 is larger than gap 1 332a, by applying the voltages of MTA 1 315a higher than MTA 1 31 5b and assuming Vs is larger than both voltages, the electrostatic actuation force of MTA 1 31 5b is larger than that of the MTA131 5a and moves the sense node 1 320 and the sense subsystem 1 370 toward the MTA 1 315b. Thus, the mismatch can be null. With the same concept, the MTA technique can be applied to out-of-plane coupling spring 1 332 with the implementation of such as out-of-plane parallel plate capacitive transducers.

Furthermore, a mismatch-trimming actuator (MTA) 1 31 5 can be applied to reduce the shield gap mismatch. Shown in Figure 1 3C, a mismatch-trimming actuator (MTA) 1 31 5 is implemented to move the drive subsystem 1 360 in order to reduce the shield gap mismatch. Thus, the first term of Equation 1 2 for offset caused by shield structure can be further reduced.

Offset cancellation with AC ripple detection

The ideal coupling location for the electrostatic coupling spring is at AC ground because the AC voltage difference AV_Ac,c is zero at the location. Therefore, the offset generated by electrostatic force across the electrostatic coupling spring is zero shown in Equation (1 3). However, due to manufacturing imperfection of resistance variation, there is ripple at the coupling point resulting in residue offset proportional to the magnitude of the ripple. Therefore, a structure to detect the ripple is proposed which can be connected to electronic circuits to null the ripple or to compensate for the ripple.

Shown in Figures 15A and 15B, the ripple detection at a drive point 1410 can be realized as the resistive type or capacitive type, respectively. Shown in Figure 15A, a resistive type detection 1417 connects the drive point 1410 to an anchor 1419 wherein the ripple of the drive point 1410 causes a current flow through the plurality of beams resulting in the voltage variation at an anchor 1419. Thus, the ripple of the drive point 1410 can be measured at the anchor 1419 by the ripple detection mechanism. Shown in Figure 15B, a capacitive type detection 1418 connects a drive point 1410 to an anchor 1419 wherein the ripple of the drive point 1410 causes a charge variation across the capacitor resulting in the current variation at the anchor 1419. Thus, the ripple of the drive point 1410 can be measured at the anchor 1419 by the ripple detection mechanism.

Examples of micromachined magnetic field sensors with the self test actuator, MTA, balanced shield, and resistive type ripple detection mechanism are shown in Figures 16A and 16B. Figure 16A shows an x-axis micromachined magnetic field sensor 1502. An AC current generated by a drive electronic passes through a plurality of beams 151 1 and 1512 and establishes a current vector in a Y- axis at a drive point 1510. A distributed Lorentz force is generated in a z-axis in the presence of a magnetic field in an x-axis. The sensor comprises an electrostatic actuator 1514 as a self test actuator to generate forces in the z-axis the same direction as the distributed Lorentz force, an electrostatic actuator 1515 as a MTA moving the sense subsystem along the z-axis, a balanced shield electrode 1513 located beneath a drive subsystem 1560 to null electrostatic offset torque about the y-axis, and a plurality of beams 1517 as a resistive type ripple detection mechanism and an anchor 1519 to sense the ripple voltage of the drive point 1510. A Z-axis micro machined magnetic field sensor 1602 is shown in Figure 16B. An AC current generated by a drive electronic passes through a plurality of beams 161 1 and 1612 and establishes a current vector in a Y-axis at a drive point 1610. A distributed Lorentz force is generated in an X-axis of a drive subsystem 1660 in the presence of a magnetic field in a Z-axis. The sensor comprises an electrostatic actuator 1614 as a self test actuator to generate forces in the x-axis the same direction as the distributed Lorentz force, an electrostatic actuator 1615 as a MTA moving the sense subsystem along the x-axis, balanced shield electrodes 1613 close to the drive subsystem 1660 to null electrostatic offset forces in the x-axis, and a plurality of beams 1617 as a resistive type ripple detection mechanism and an anchor 1619 to detect the ripple voltage of the drive point 1610.

The examples of the offset cancellation techniques in a magnetic field sensing system noted here should not be interpreted to restrict the range of possible application of the offset cancellation techniques. It is advantageous to implement the offset cancellation techniques to other resonant applications comprising gyroscopes, accelerometers, chemical sensors, biosensors, pressure sensors, to force sensors.

Advantages

A magnetic field sensor is utilized for MEMS gyroscopes and accelerometers without major process change. In addition, the sensor addresses the need of low- power, high-manufacturability, and high-sensitivity. The sensor includes the following features.

1 . A low cost and open-loop magnetic field resonant magnetic field sensor to achieve low power consumption in a system level circuit compared to a close loop frequency control resonant system.

2. Allows for use of a dual-mode resonating device to accommodate the process variation to achieve high manufacturability. 3. Incorporates an electrostatic coupling spring to deploy high bias voltage at the sensing node. The high bias voltage leads to high-sensitivity in the system.

4. Provides a low offset with several offset mitigation techniques to remove offset shift issues.

5. Includes a self-test function with electrostatic actuators to achieve low power consumption comparing to generating magnetic field directly with 3mA supply.

Integration with other motion sensors. By harnessing these design strategies, a Lorentz force-effect resonant sensor can be implemented in a way to allow for on- chip integration of magnetic field sensors with other motion sensors.

Although the present invention has been described in accordance with the embodiments shown, one of ordinary skill in the art will readily recognize that there could be variations to the embodiments and those variations would be within the spirit and scope of the present invention. Accordingly, many modifications may be made by one of ordinary skill in the art without departing from the spirit and scope of the appended claims.

Claims

CLAIMS What is claimed is:

1 . A micromachined magnetic field sensor comprising: a substrate;

a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis;

a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis;

a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem.

2. The micromachined magnetic field sensor of claim 1 , wherein the coupling spring comprises structural coupling springs.

3. The micromachined magnetic field sensor of claim 1 , wherein the coupling spring comprises electrostatic coupling springs.

4. The micromachined magnetic field sensor of claim 1 , wherein the third axis of the magnetic field is along a Z-axis which is normal to the plane of the substrate; the motion of the sense subsystem is along the fourth axis which is in a X-Y plane; and the electrostatic coupling spring causes motion of sense subsystem in the X-Y plane in response to magnetic field in the Z-axis.

5. The micromachined magnetic field sensor of claim 1 , wherein the third axis of the magnetic field is in a X-Y plane which is parallel to the plane of the substrate; the motion of the sense subsystem is along the fourth axis which is in a Z-axis; and the electrostatic coupling springs causes motion of sense subsystem in the Z-axis in response to the magnetic field in X-Y plane.

6. The micromachined magnetic field sensor of claim 1 , wherein the electrostatic coupling springs is utilized with any parallel plate capacitive

transducers, or interdigitated comb capacitive transducers

7. The micromachined magnetic field sensor of claim 1 , wherein the drive subsystem, the sense subsystem and the coupling spring form a mechanical system with at least two resonant modes, at least one drive subsystem anti- resonance and a least one sense subsystem anti-resonance.

8. The micromachined magnetic field sensor of claim 7, wherein the frequency of the electrical current along the first axis substantially matches the drive subsystem anti-resonance frequency; and the frequency of the electrical current along the first axis substantially matches the sense subsystem anti-resonance frequency.

9. The micromachined magnetic field sensor of claim 1 , wherein the position transducer comprises any of parallel plate capacitive transducers, interdigitated comb capacitive transducers, piezoresistive sensors, optical sensors, and piezoelectric sensors.

10. A micro machined resonant magnetic field sensor comprising:

a substrate;

a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis; and

a position transducer to detect the motion of the drive subsystem; and a self-test actuator causes force acting on the drive subsystem along the second axis.

1 1 . The micromachined resonant magnetic field sensor of claim 10, wherein the self-test actuator comprises electrostatic actuators.

12. The micromachined resonant magnetic field sensor of claim 10, wherein the self-test actuator comprises current-carrying coils to generate a magnetic field along the third axis which interacts with drive subsystem resulting in Lorentz force along the second axis acting on the drive subsystem.

13. A micromachined resonant magnetic field sensor comprising:

a substrate;

a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis a position transducer to detect the motion of the drive subsystem; a stiffness tuning block to change the stiffness of the drive subsystem in order to compensate manufacturing variation.

14. The micromachined resonant magnetic field sensor of claim 13, wherein the stiffness tuning block is utilized with mechanisms comprising

electrostatic transducers, electro-thermal actuators, and piezoelectric actuators.

15. A multi-axis magnetic field sensor system comprising:

at least one micromachined magnetic field sensor comprising: a substrate; a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis, a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem; and

at least one magnetic field sensor that responds to a magnetic field

perpendicular to the third axis.

16. The multi-axis magnetic field sensor of claim 15 wherein the at least one magnetic field sensor comprises any of or any combination of Hall sensors, magnetoresistive sensors, magneto-diode sensors, magneto-transistors, fluxgates, magneto-impedance sensors, magneto-optical sensors, and MAGFETs.

17. The multi-axis magnetic field sensor of claim 15 is further integrated with motion sensors including any of linear acceleration sensor, gyroscopes, pressure sensors, and acoustic sensors.

18. A multi-axis magnetic field sensor system comprising:

a substrate wherein a Z axis is normal to the plane of the substrate and an X- Y plane is parallel to the plane of the substrate.

a Z-axis micromachined magnetic field sensor, wherein the Z axis

micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in the X-Y plane; and Lorentz force acting on the drive subsystem in the X-Y plane in response to a magnetic field along the Z axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves in the X-Y plane; a coupling spring between the drive subsystem and the sense

subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem;

a X-axis micromachined magnetic field sensor, wherein the X-axis

micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in the X-Y plane; and Lorentz force acting on the drive subsystem along the Z-axis in response to a magnetic field along the X-axis; a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along the Z-axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem; and

a Y-axis micromachined magnetic field sensor, wherein the Y-axis

micromachined magnetic field sensor comprises a drive subsystem, the drive subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem in the X-Y plane; and Lorentz force acting on the drive subsystem along the Z-axis in response to a magnetic field along the Y axis; a sense subsystem comprising a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along the Z-axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of the sense subsystem in response to the magnetic field; and a position transducer to detect the motion of the sense subsystem.

19. A micromachined magnetic field sensor comprising: a substrate;

a sense subsystem, the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis; a coupling spring between the drive subsystem and the sense subsystem which causes motion of sense subsystem in response to the magnetic field;

a position transducer to detect the motion of the sense subsystem; and a self-test actuator causes force acting on the drive subsystem along the second axis.

20. A micromachined magnetic field sensor comprising: a substrate;

a drive subsystem, the drive subsystem comprises a plurality of beams, at least one anchor connected to the substrate; a mechanism for providing an electrical current through the drive subsystem along a first axis; and Lorentz force acting on the drive subsystem along a second axis in response to a magnetic field along a third axis;

a sense subsystem , the sense subsystem comprises a plurality of beams, and at least one anchor connected to the substrate; wherein a portion of the sense subsystem moves along a fourth axis;

a coupling spring between the drive subsystem and the sense subsystem which causes motion of sense subsystem in response to the magnetic field;

a position transducer to detect the motion of the sense subsystem; and a stiffness tuning block to change the stiffness of the sense subsystem in order to compensate manufacturing variation.