Patent Publication Number: US-2011050214-A1

Title: System and method for measuring magnetic field strength using a mechanical resonator

Description:
RELATED APPLICATION 
     This application claims the benefit of prior U.S. provisional application No. 60/799,005 filed May 10, 2006. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to methods and systems for measuring magnetic field strength. 
     BACKGROUND OF THE INVENTION 
     Micromachining is becoming a mature technology and many of the micromachining projects are in the process of commercialization. As is the case for microelectronic technology, if fabrication, or at least prototyping, of a sensor is possible using a standard process, considerable savings can result in terms of overall cost and development time for a device. See for example M. N. Horenstein and P. R. Stone, Journal of Electrostatics, vol. 51-52, pp. 515-521, May 2001. 
     An example of the analytic modeling and Finite Element Simulations of a resonant micromachined magnetic field sensor is described in Bahreyni, Behraad; Shafai, Cyrus, “Analytic Modeling and FEM Simulation of a Resonant Micromachined Magnetic Field Sensor”, Canadian Conference of Electrical &amp; Computer Engineering, May, 2004 hereby incorporated by reference in its entirety. The resonant frequency of the sensor changes in response to the magnitude and direction of the present magnetic field. The output of the micromachined magnetic field sensor is input to a frequency measurement device such as a spectrum analyzer. An AC input voltage drives the arrangement, and the frequency of the AC voltage is swept across a range of interest. The overall frequency response is examined to determine the peak, and that corresponds to the resonant frequency. The resonant frequency, once determined, is used to determine the magnetic field using knowledge of the relationship between the resonant frequency and magnetic field. 
     SUMMARY OF THE INVENTION 
     According to one broad aspect, the invention provides an apparatus for measuring magnetic field comprising: a mechanical resonator having a resonator output and having an input for receiving a drive signal; signal conversion and amplification circuitry for converting the resonator output of the mechanical resonator into a voltage output; and a sense signal filtering circuit to isolate a sense signal from an interfering feedthrough signal. 
     In some embodiments, the sense signal filtering circuit comprises at least one of: a notch filter having a notch at the expected resonant frequency divided by two; one or more bandpass filters to isolate the sense signal from the interference signal; and one or more additional high-Q bandpass filters to remove beating components. 
     In some embodiments, the apparatus connected to form an oscillator loop with a feedback signal processing circuit that processes the sense signal to produce the drive signal; wherein the sense signal has a frequency shift representative of a magnetic field within which the apparatus is situated. 
     According to another broad aspect, the invention provides an apparatus for measuring magnetic field comprising: a mechanical resonator that undergoes mechanical motion and has an input for receiving a drive signal, the mechanical resonator having a resonant frequency that changes as a function of magnetic field; a motion detector that detects the mechanical motion of the mechanical resonator; and a sense signal filtering circuit for filtering a signal representative of the mechanical motion of the mechanical resonator to isolate a sense signal from interference due to the drive signal. 
     In some embodiments, the apparatus further comprises: signal conversion and amplification circuitry for converting an output of the motion detector into a voltage output as the signal representative of the mechanical motion of the mechanical resonator. 
     In some embodiments, the sense signal filtering circuit comprises at least one of: a notch filter having a notch at an expected resonant frequency divided by two; one or more bandpass filters to isolate the sense signal from the interference due to the drive signal; and one or more additional high-Q bandpass filters to remove beating components. 
     In some embodiments, the apparatus further comprises: a feedback signal processing circuit that processes the sense signal to produce the drive signal; wherein the sense signal has a frequency shift representative of a magnetic field within which the apparatus is situated. 
     In some embodiments, the feedback signal processing circuit comprises: a constant amplitude circuit to make the sense signal have substantially constant amplitude; a divide by 2 circuit; a phase adjustment circuit. 
     In some embodiments, the apparatus further comprises: an output processing circuit that processes the sense signal to produce an output representative of the magnetic field within which the apparatus is situated. 
     In some embodiments, the output processing circuit comprises: a frequency dependent phase shifting circuit that produces a phase shifted output; and a circuit that determines a phase shift introduced by the phase shifting circuit. 
     In some embodiments, the circuit that determines a phase shift introduced by the phase shifting circuit comprises: a phase detector. 
     In some embodiments, the apparatus further comprises a phase difference to voltage converter, that produces a voltage that represents a value for the magnetic field. 
     In some embodiments, the apparatus further comprises a downconverter circuit that downconverts a frequency of the sense signal. 
     In some embodiments, the phase shifting circuit comprises an all pass filter. 
     In some embodiments, the mechanical resonator comprises a resonant micromachined magnetic field sensor. 
     In some embodiments, the mechanical resonator is driven by means of electrostatic, optical, thermal, piezoelectric, piezoresistive. 
     In some embodiments, the motion detector comprises one of an electrostatic motion detector, optical motion detector, thermal motion detector, piezoelectric motion detector, and piezoresistive motion detector. 
     According to another broad aspect, the invention provides a method comprising: placing a mechanical resonator having a resonator output and having an input for receiving a drive signal in an area for which a magnetic field measurement is to be determined; converting and amplifying the resonator output into an electrical signal output; and filtering the electrical signal output to isolate a sense signal from an interfering feedthrough signal. 
     In some embodiments, the method further comprises: feeding a version of the sense signal back as the drive signal to form a closed loop. 
     In some embodiments, the method further comprises: performing feedback signal processing upon the sense signal to produce the drive signal. 
     In some embodiments, the method further comprises: processing the sense signal to produce an output representative of the magnetic field. 
     According to another broad aspect, the invention provides a resonator arrangement comprising: a mechanical resonator having a drive signal and a resonator output; a drive signal generation circuit that generates the drive signal for the mechanical resonator from the resonator output. 
     In some embodiments, the mechanical resonator is a MEMS resonator. 
     In some embodiments, the drive signal generation circuit comprises: signal conversion and amplification circuitry for converting the resonator output of the mechanical resonator into a voltage output; and a sense signal filtering circuit to isolate a sense signal from an interfering feedthrough signal. 
     In some embodiments, the sense signal filtering circuit comprises at least one of: a notch filter having a notch at the expected resonant frequency divided by two; one or more bandpass filters to isolate the sense signal from the interference signal; and one or more additional high-Q bandpass filters to remove beating components. 
     In some embodiments, the drive signal generation circuit comprises: a motion detector that detects the mechanical motion of the mechanical resonator; and a sense signal filtering circuit for filtering a signal representative of the mechanical motion of the mechanical resonator to isolate a sense signal from interference due to the drive signal. 
     In some embodiments, the resonator arrangement further comprises: signal conversion and amplification circuitry for converting an output of the motion detector into a voltage output as the signal representative of the mechanical motion of the mechanical resonator. 
     In some embodiments, the apparatus drive signal generation circuit further comprises: a feedback signal processing circuit that processes the sense signal to produce the drive signal. 
     In some embodiments, the feedback signal processing circuit comprises: a constant amplitude circuit to make the sense signal have substantially constant amplitude; a divide by 2 circuit; a phase adjustment circuit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the invention will now be described with reference to the attached drawings in which: 
         FIG. 1A  is a block diagram of an apparatus that can be used for measuring magnetic fields; 
         FIG. 1B  is a block diagram of an apparatus for measuring magnetic fields; 
         FIG. 2  is a circuit diagram used to drive a resonator according to an embodiment of the invention; 
         FIG. 3  is a block diagram of an example of an oscillator network according to an embodiment of the invention; 
         FIG. 4  is a block diagram of an example of the oscillator network of  FIG. 3  along with output processing components; and 
         FIG. 5  is a schematic of an example micromachined magnetic field sensor employed as a electrostatic resonator according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Various methods of employing a mechanical resonator using electrostatic, piezoelectric, piezoresistive, thermal, or other actuation mechanism as a magnetic field sensor will be described. Particular implementations employ micromachined magnetic field sensors described with reference to  FIG. 5  in detail below. However, more generally any mechanical structure that has a resonant frequency that varies as a function of an axial stress can be employed, for example due to an applied magnetic field. 
       FIG. 1A  is a block diagram of an apparatus that can be used for measuring magnetic fields. The system comprises a mechanical resonator  10  that has a resonant frequency that varies as a function of magnetic field in which the apparatus is located. The mechanical resonator  10  undergoes mechanical motion that is detected by a motion detector  12 . The mechanical resonator  10  receives a drive signal  18 . The motion detector produces a signal representative of the mechanical motion of the mechanical resonator. This is followed by an optional signal conversion and amplification circuit  14  that performs any necessary signal conversion from the form output by the motion detector  12  into a form suitable for electronic processing. This might for example simply consist of a current to voltage conversion and amplification. The output of the signal conversion and amplification circuit  14  is fed to a sense signal filtering circuit  16 . This output is also representative of the mechanical motion of the mechanical resonator. The sense signal filtering circuit  16  performs filtering on the signal to isolate a sense signal  20  from interference due to the drive signal  18 . The sense signal can be analyzed to determine the resonant frequency of the mechanical resonator assuming an appropriate drive signal, for example any AC drive signal that is swept across a range of frequencies. 
       FIG. 1B  is a block diagram of an apparatus for measuring magnetic fields. The system comprises a mechanical resonator  30  that has a resonant frequency that varies as a function of magnetic field in which the apparatus is located. The mechanical resonator  30  undergoes mechanical motion that is detected by a motion detector  32 . The mechanical resonator receives a drive signal  33 . The motion detector  32  produces a signal representative of the mechanical motion of the mechanical resonator  30 . This is followed by an optional signal conversion and amplification circuit  34  that performs any necessary signal conversion from the form output by the motion detector  32  into a form suitable for electronic processing. This might for example simply consist of a current to voltage conversion and amplification. The output of the signal conversion and amplification circuit  34  is fed to a sense signal filtering circuit  36 . This output is also representative of the mechanical motion of the mechanical resonator  30 . The sense signal filtering circuit  36  performs filtering on the signal to isolate a sense signal  37  from interference due to the drive signal  33 . In the closed loop configuration of  FIG. 1B , the sense signal  37  is representative of the resonant frequency of the mechanical resonator as described later. 
     The sense signal  37  output by the sense signal filtering circuit  36  is then fed through a feedback signal processing circuit  38  and back into the mechanical resonator  30  as the drive signal  33  to form an oscillator loop. The output of the sense signal filtering circuit  36  is representative of the resonant frequency of mechanical resonator, and this in turn is representative of the magnetic field. In some embodiments, additional circuitry is provided to convert that sense signal into a more representative form.  FIG. 1  shows an output processing circuit  40  that can be used to this effect. 
     In the description below, various detailed examples of the functionality that might be included in the various circuits of  FIGS. 1A and 1B  will be described. However, it is to be understood that the embodiments of  FIGS. 1A and 1B  are not to be limited to those specific examples. 
     The mechanical resonator is driven by means of an appropriate drive signal. Examples of the form this signal might take include electrostatic, optical, thermal, piezoelectric, piezoresistive, but others are possible. 
     The motion detector is any device capable of measuring the mechanical motion of the mechanical resonator. Examples include an electrostatic motion detector, optical motion detector, thermal motion detector, piezoelectric motion detector, and piezoresistive motion detector, but others are possible. The mechanical resonator may provide a suitable output on its own without a separate motion detector. The motion detector and mechanical resonator may be separate devices or an integrated device. 
     Driving the Resonator with No Bias 
     When driving an electrostatic or thermal resonator, a DC bias voltage can be used in order to bring down the level of the input AC voltages. An example of this is shown in  FIG. 2  where an electrostatic resonator  50  is shown with a bias voltage V G    52 , and an input AC voltage  54  having an input frequency ω a . In practice, there is also a very large feedthrough/interference signal at the drive signal frequency which makes accurate electrical measurements (amplitude or phase) of the sense signal very difficult. This is shown in  FIG. 2 , where an example of the spectrum of the output is shown. The spectrum includes a component  56  at ω a . This is the drive frequency (ω a ) given by the driving circuit  54 . There is a second component at frequency 2ω a  (twice the frequency of ω a ), and this represents the motion of resonator  50 , due to the drive frequency ω a . In the case of an electrostatically driven resonator embodiment of the sensor, the spike at frequency ω a  is the electrical drive signal  54  which acts as an interference signal to the measurement and can be removed by subsequent filtering circuitry, and the spike at frequency 2wa is the signal due to the speed of oscillatory motion of the resonator itself and is indeed a measure of the oscillatory motion of the resonator itself. 
     If V G  is set to 0V for the system shown in  FIG. 2 , the output current should theoretically have a single component representative of the motion of the resonator at the second harmonic of the drive signal for electrostatic and thermally actuated resonators because of the quadratic relationship between the drive voltage and electrostatic or thermal force. Interference and feedthrough signals may still pose problems in taking accurate measurements. However, since the output signal of the device is at twice the frequency of the interfering signals, it is possible to recover the sense signal with proper filtering of the output signal. If the non-linearities of the electronics are kept to a minimum, the signal at the second harmonic will be entirely from the resonator operation. 
     Using a Notch Filter 
     If bandpass or highpass filtering alone is to be employed to separate the sense signal from the interference signal, the small separation of the interference signal and the sense signal in the frequency domain and the needed amount of attenuation may require high order filters to extract the sensing signal. For example, if it is intended to attenuate the interference signal by a factor of about 5×10 3  or 74 dB, a highpass filter with a minimum of 12 poles may be needed. Designing and implementing such a filter is not a straightforward process, and requires careful attention to the practical limits of the devices, their tolerances, and matching of components between the cascaded stages. 
     Instead of relying on achievable attenuation from poles, in some embodiments the interference signal is dealt with by placing the zeros of the transfer function of a filter at the frequency of the interference. Such a filter is often referred to as a notch filter. The filter&#39;s quality factor may be set to maximize the attenuation of the interfering signals. One or more bandpass filters at the frequency of the second harmonic may be used in additional to the notch filter to attenuate the interfering signals further and amplify the main signal. In some implementations, both of the filters are realized with switched capacitor filters. 
     Removing Beating 
     The desired sense signal can be recovered by using a filter block consisting of a notch filter and bandpass filter as described above. However, beating between the output signal from the sensor and interfering signals from various sources (e.g., computer monitors and digital measurement equipment) may cause considerable variation in amplitude of the filter block output. Beating occurs when adding two sinusoidal signals whose frequencies are close to each other. In practice, neither the amplitude nor the frequency of the interfering signals is stable, which makes accurate measurements of the desired signal more difficult. 
     In some embodiments, additional high-Q bandpass filters are employed to shrink the bandwidth around the desired signal frequency and reject the signals outside of this band. However, tuning of these filters can be troublesome due to their narrow frequency response. In some embodiments, switched capacitor filters are used to greatly simplify the design flow, especially since the clock signal of the first filter block can be used for these high-Q filters, assuming it is also implemented with switched capacitor technology. 
     Dividing the Frequency by Two 
     The sense signal can be recovered using the setup described above. In some embodiments, to alleviate the need for a signal source, the resonator is used in an oscillator loop. The implementation of  FIG. 1B  takes this approach. The problem of the feedthrough signal in the oscillator design case can still be circumvented with the same circuitry described above. However, in some designs the electrostatic resonator has to be driven at half the resonant frequency of the device in this setup. Therefore, in such instances the frequency of the processed signal has to be divided by two. 
     Driving the Resonator with a Constant Amplitude 
     In some embodiments, since the magnetic field data is extracted from the frequency shifts of the signal from the sensor, the amplitude information is discarded. This can be done by processing the sinusoidal signal with an analog comparator to convert the sinusoidal wave into a square wave. Counting over a window produces a moving average representative of the sense frequency. Dividing the signal frequency by two can then be simply done with a T-flipflop. To minimize the spurious signals at the output of the oscillator, the output of the frequency divider is then converted back to sinusoidal, for example with a 4th order lowpass filter which attenuates the 3rd harmonic of the output of the frequency divider by about 40 dB. Using this configuration, the amplitude of the excitation signal is completely defined and set by the user and does not rely on the properties of the linear and nonlinear elements in the loop. A phase adjustment circuit between the lowpass filter and the resonator can also be used to assure excitation of the resonator at the correct frequency and phase. 
       FIG. 3  is a block diagram of an example of the oscillator network, this being a very specific example of the implementation of the mechanical resonator, motion detector, signal conversion and amplification circuit, sense signal filtering circuit and signal processing circuit of  FIG. 1B . This configuration improves the quality of the oscillator as a whole and greatly reduces phase-noise and jitter. This configuration includes all of the components discussed above, but not every implementation need include all of the components. 
     Shown is a mechanical resonator connected to a motion detector comprising a first amplifier element  102 , and a second amplifier element  104 . The output of the second amplifier element  104  is connected to the input of a notch filter  106  having frequency response F 1  which includes a notch at frequency f r /2, where f r /2 is a nominal resonant frequency of the mechanical resonator  100 . The notch frequency is set to match the frequency of the drive signal, thereby allowing an efficient elimination of most of the interference due to the drive signal. The output of the notch filter  106  is input to filters  108 , 110 , 112  connected together in sequence which are bandpass filters having frequency responses F 2 , F 3 , F 4  respectively that have passbands centred at the frequency f r  of the second harmonic. These are provided in addition to the notch filter  106  to attenuate the interfering signals further and amplify the main signal. In some implementations, both of the filters are realized with switched capacitor filters. In the example of  FIG. 3 , three bandpass filters ( 108 ,  110 , and  112 ) are provided to remove beating. Less or more such filters can be used as needed in a practical implementation. 
     The output of filter  112  is connected to the input of a lowpass filter  114  has frequency response F 5  which is a lowpass filter having a cutoff frequency of 60 kHz in the particular example illustrated. This filter  114  is used to provide extra filtering to remove high frequency noise from the signal and the filters  108 ,  110 , and  112  are used to remove the beating. 
     The output of the lowpass filter  114  is connected to an amplifier  116 . The output of amplifier  116  is connected to the input of a comparator  118 . The comparator output effectively produces a moving average of the twice the resonant frequency. Elements  116 , 118  function to remove the amplitude information from the sense signal, and give a digital indication of the resonator frequency. The output of the comparator  118  is divided by two with frequency divider circuit  120  to produce a drive signal near the resonant frequency of the mechanical resonator  100 . 
     To reduce the spurious signals at the output of the oscillator, the output of the frequency divider is then converted back to sinusoidal, for example with a lowpass filter  122  having frequency response F 2  which attenuates the 3rd harmonic of the output of the frequency divider by about 40 dB. Using this configuration, the amplitude of the excitation signal is completely defined and set by the user and does not rely on the properties of the linear and nonlinear elements in the loop. A phase adjustment circuit  124  is provided between the lowpass filter  122  and the resonator  100  to assure excitation of the resonator at the correct frequency and phase. Element P 1   124  may for example be implemented using an “all-pass filter”, which is used to adjust the phase of the signal coming from filter  122 , so that it is in phase with the motion of the resonator  100 . Element A 4   126  represents the gain for the all pass filter P 1 . This is shown as a separate block as this amplification can be inherent to the filter P 1 , and/or be from an additional amplifier. 
     Frequency Shift Measurement 
     Additional signal processing of the sense signal can be performed outside the loop to extract the magnetic field measurement. In some embodiments, this can be done by applying a frequency dependent phase-shift to the sense signal to convert the information embedded in the frequency of the signal to a phase difference between the sense signal and its delayed version. This can potentially improve the accuracy of measurements by converting small frequency shifts to relatively large phase differences. If the amplitude of the signal is controlled, the shifts in the resonant frequency of the structure are instantaneously converted to phase differences and can be measured. Therefore, sensitivity and bandwidth of measurements are both enhanced by using this technique. 
     The next step is to measure the phase difference in order to extract information about the amount of frequency shift. This can be done by using a phase detector which compares the relative phase of the signals at its inputs. As an example, the original signal and its phase-shifted (i.e., delayed) version can be converted to square waves by use of comparators. The phase difference between these square waves can then be measured with different digital phase detectors, such as an XOR gate. The output of the phase detector is then lowpass filtered to yield a DC voltage which is proportional to the phase difference between the input signals, and therefore, the amount of frequency shift in the original signal. 
     Use of Allpass Filters 
     To avoid the resulting complexities of using passive phase shift networks, in some embodiments an allpass (or delay) filter is used to implement the phase shift. Allpass filters do not modify the amplitude of the signal through them but will cause a predetermined phase shift at the designed frequency. This is done by properly choosing the location of poles and zeros of a given transfer functions. More specifically, the zeros and poles have the same frequency (to produce a flat amplitude response) but the zeros are placed in the right-half portion of the s-plane (to increase the phase difference between high and low frequencies). If allpass networks of orders larger than one are used, it is possible to independently control the frequency and phase performance (i.e., Q) of the circuit. 
     The phases of the delayed signal and the signal that was not delayed are compared with the phase detector block which produces an output proportional to the phase difference. This output is representative of the magnetic field measurement. 
     Down Conversion of Frequency 
     If the phase difference detection is to be done at the signal frequency, very high-Q allpass filters may be required. For example, if it is desired to have a 45° phase shift for a 1 Hz shift at the signal frequency of 40 kHz, a 2nd order allpass filter with a Q of about 6000 is needed, which is obviously difficult to realize. On the other hand, high-Q filters are generally prone to instability. Furthermore, tuning of high-Q filters is not easy because of their narrow bandwidth. To overcome these issues, in some embodiments a downconverter is used to bring down the frequency of the sense signal before feeding it to the delay circuitry. This reduction in signal frequency, which is essentially the same as removing the frequency offset that does not convey information, allows for performing sensitive phase difference measurements with relatively low-Q allpass filters. Additionally, if the difference between the downconverting signal and the sensor signal is kept constant, a stable and tuned circuit can be designed to produce the delay at the difference frequency, which greatly improves the versatility of the sensing electronics. 
     An example of a circuit including all of the output processing components described above is shown in  FIG. 4 , this circuit including the same components as described above with reference to  FIG. 3  plus additional components for realizing a specific implementation of the output processing circuit of  FIG. 1 . More generally, a particular implementation may include no output processing, or an arbitrary subset of the output processing components discussed above. 
     The output processing components include a lowpass filter  130  having frequency response F 7  that may be implemented having a cutoff frequency f r  that is the same as that of filters  108 , 110 , 112  for convenience, but other cutoff frequencies can be employed. The output of filter  130  is passed to downconverter  132  that is controlled by a reference voltage V ref  which serves to produce a sense signal at a lower frequency. The output of downconverter  132  is subject to further filtering in filters  134 , 136  having frequency responses F 8 , F 9  respectively to isolate the relevant component of the output of the downconverter  132 . Filter  134  is a lowpass filter having cutoff frequency f 0 . Filter  136  is a bandpass filter having passband centre frequency. The specific frequency f 0  value is not important, but the role of these filters is to eliminate high frequency noise after mixer  132 . A different filter(s) may alternatively be employed in place of filters  134 , 136 . The output of filter  136  is processed by two paths. The first path has a phase shifter  138  and a comparator  140 . The second path has a comparator  142 . The comparators convert the respective input signals to square waves. The outputs of the two comparators  140 , 142  are input to phase detector  144  which produces an output that is lowpass filtered with filter  146  having frequency response F 10 . In the illustrated example, this has a cutoff frequency of 10 Hz. 
     A schematic of an example micromachined magnetic field sensor that can be employed as the electrostatic resonator with the above-described system and method is illustrated in  FIG. 5 . This includes a resonator and motion detector. More generally, any mechanical resonator can be used as long as it can be put in a configuration where the magnetic force from the magnetic field can be transferred and applied to the resonator body. The sensor is composed of an electrostatic resonator, beam springs, and two crossbars. The shuttle of the sensor is kept under mechanical resonance during the sensor operation. When inside a magnetic field B, the current ISB, which flows through the crossbars (from pin  1  to pin  2  and then pin  3  to pin  4 ), causes exertion of an axial force on the beam springs according to Lorentz force equation. The axial force modifies the stiffness of the flexural beams, and consequently, the resonant frequency of the structure changes. Although a comb-drive actuator is shown in the Figure, lateral or vertical parallel plate electrostatic resonators can also be employed as the main resonating body of the sensor. The operation of the sensor involves simultaneous interaction of multiple physical domains with each other, including electrostatics, magnetostatics, elasticity, dynamics, and electro-thermo-mechanics. 
     Magnetic fields are measured by this sensor not by means of any magnetic material, but by using Lorentz force. Therefore, this sensor does not suffer from non-linearity or hysterisis effects, especially for high magnetic field measurements. 
     Lorentz force is the force upon a moving electric current (electrons) in the presence of a magnetic field. This force is proportional to the multiplication of the magnitude of the electric current and the magnitude of the magnetic field. Thus, when electrons move in a magnetic field, Lorentz force tends to push or pull upon the electrons, and so upon the wire carrying the electrons. 
     Hall effect magnetic field sensors also use Lorentz force to displace moving electrons within a semi-conducting material, and so create a differential voltage. The sensor of  FIG. 5 , however, does not require semi-conducting materials, and simply requires the use of an electrically conducting material, which for example can be either a metal or semiconductor. 
     Since no magnetic or semi-conducting materials are needed for the construction of the sensor, it can be fabricated in standard commercial micromachining processes, without needing any special post processing fabrication steps. This sensor can be readily designed and/or fabricated by many companies in the MEMS industry, such as Micralyne, MEMSCAP, or Analog Devices. Consequently, the fabrication cost of this sensor will be low. 
     In the illustrated example, a mechanical vibrator is first fabricated on a substrate. This can be a micromachined vibrator, commonly referred to as a MEMS (micro-electro-mechanical system), in order to make a small sub-millimetre sized device that can be easily packed on a silicon chip. In the illustrated example, the vibrator is comprised of a “comb actuator”. However, any mechanical structure capable of being driven into oscillation at a controlled frequency can be used (bridge, cantilever, membrane, etc.). The supporting micromachined crossbars are anchored to the substrate such that an electric current can be passed through them. In the presence of a magnetic field the Lorentz force on the crossbars will push/pull on the beam springs themselves, thereby causing a mechanical load on the microsprings, which changes the spring constant of the micro-springs. This will result in a change in the resonant frequency of oscillations of the mechanical vibrator. This change in frequency is used as the magnetic field sense mechanism. 
     The sensor is operated at its mechanical resonant frequency. At this frequency, the amplitude of oscillation is significantly higher than normal. This increases the measurement sensitivity. 
     The magnetic field is measured by monitoring the change in the mechanical resonant frequency of the mechanical vibrator, due to the change in the spring constant of the micro-springs caused by the Lorentz force. The amount of frequency shift is proportional to the magnetic field. The direction of frequency shift (increase or decrease in resonant frequency) is dependant on the direction of the magnetic field and the current in the crossbars. This is different from most of the conventional sensors, which produce a voltage or a current signal at their output. Consequently, the output signal of the designed sensor is more robust against noise and interference. 
     The embodiments have been described in their application to sensing magnetic field strength. More generally, the closed loop embodiments can be used as resonators that do not require externally generated drive signals. For example, the described MEMS resonator in conjunction with the circuit described makes a arrangement that features a MEMS resonator that does not need an external frequency generation system. For example, the embodiments of  FIGS. 1B and 3  provide can be used as such arrangements and may find applications other than sensing magnetic field strength. A specific example is a tuner circuit for a radio/cell phone. Instead of an external frequency generation system, spurious/environmental noise picked up by the circuit is filtered, and fed back to the mechanical resonator at the desired drive frequency. For such applications, there is no need for the output processing circuits of  FIGS. 1B and 4  since no magnetic field is being measured. In some embodiments, the mechanical resonator is a MEMs resonator. Specific examples of MEMs resonators have been described above, but more generally, any MEMs resonator can be employed for such embodiments. 
     A specific example of a resonator arrangement that does not require an external drive signal has been described. In another embodiment, a MEMs resonator is provided together with a drive signal generation circuit that generates a drive signal for the MEMs resonator from an output of the MEMs resonator. The elements  32 , 34 , 36 , 38  of  FIG. 1B  provide one example of a drive signal generation circuit. Elements  102 , 104 , 106 , 108 , 110 , 112 , 114 ,  116 , 118 , 120 , 122 , 124 , 126  of  FIG. 3  provide another example of a drive signal generation circuit. 
     Numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.