Patent Description:
Micro-Electro-Mechanical Systems, or MEMS can be defined as miniaturized mechanical and electro-mechanical systems where at least some elements have a mechanical functionality. MEMS structures can be applied to quickly and accurately detect very small changes in physical properties. As an example, a microelectromechanical gyroscope can be applied to quickly and accurately detect very small angular displacements.

Motion can be considered to have six degrees of freedom: translations in three orthogonal directions and rotations around three orthogonal axes. The latter three may be measured by an angular rate sensor, also known as a gyroscope. MEMS gyroscopes use the Coriolis Effect to measure the angular rate. When a mass is moving in one direction and rotational angular velocity is applied, the mass experiences a force in orthogonal direction as a result of the Coriolis force. The resulting physical displacement caused by the Coriolis force may then be read from, for example, a capacitively, piezoelectrically or piezoresistively sensing structure.

In MEMS gyros the primary motion cannot be continuous rotation as in conventional ones due to lack of adequate bearings. Instead, mechanical oscillation may be used as the primary motion. When an oscillating gyroscope is subjected to an angular motion orthogonal to the direction of the primary motion, an undulating Coriolis force results. This creates a secondary oscillation orthogonal to the primary motion and to the axis of the angular motion, and at the frequency of the primary oscillation. The amplitude of this coupled oscillation can be used as the measure of the angular rate.

Gyroscopes are very complex inertial MEMS sensors. The basic challenge in gyroscope designs is that the Coriolis force is very small and therefore the generated signals tend to be minuscule compared to other electrical signals present in the gyroscope. Spurious resonances and susceptibility to vibration plague many MEMS gyro designs.

One challenge in gyroscope design is quadrature error motion. In an ideal gyroscope structure, the primary oscillation and the secondary oscillation are exactly orthogonal. However, in practical devices imperfections occur, causing direct coupling of the primary mode displacement of the seismic mass to the secondary mode of the gyroscope. This direct coupling is called the quadrature error. The phase difference between the angular motion signal and the quadrature signal is <NUM> degrees, which means that basically the quadrature error could be eliminated with phase sensitive demodulation. However, the quadrature signal can be very large in comparison with the angular motion signal, and may therefore cause unreasonable dynamic range requirements for the readout electronics or phase accuracy of the phase demodulation.

One known method to deal with this error source is electrostatic quadrature cancellation that removes the error signal at the sensor structure, before the quadrature signal is generated. For this, an electrostatic force, exactly in-phase with the primary oscillation and parallel to the secondary oscillation may be applied to the seismic mass.

Electrostatic quadrature suppression is a very effective and therefore widely used technique. It can also be easily combined for even higher performance with electronic quadrature cancellation and other processing methods in the integrated circuit side. However, advanced gyroscope structures may be complicated and the microfabrication tolerances may be poor compared to their dimensions, so voltages necessary to compensate the quadrature component in the drive motion may be very high. This tends to complicate electronics design and increases power consumption of the gyroscope device.

Document <CIT> discloses a solution where parametric amplification of the output of a MEMS gyroscope is achieved by modulating the sense capacitance, or an auxiliary capacitance having an applied DC voltage. Due to the orientation of the opposite capacitor pairs, a force modulated at twice the primary oscillation frequency is created.

Document <CIT> discloses a structure for attenuation or cancellation of quadrature error. An electrical circuit provides a voltage across comb finger capacitors to generate a position-dependent force, the position-dependent force having a component along an axis substantially orthogonal to the displacement axis, the magnitude of the position-dependent force varying in proportion to displacement along the displacement axis.

The object of the present invention is to enhance quadrature compensation in microelectromechanical sensing. The objects of the present invention are achieved with a microelectromechanical sensor device according to the characterizing portion of the independent claim <NUM>.

The claims define a microelectromechanical sensor device that comprises a seismic mass, a spring structure for suspending the seismic mass into a static support structure, wherein the spring structure defines for the seismic mass a drive direction, and a sense direction that is perpendicular to the drive direction, excitation means for driving the seismic mass into linear oscillation, the linear oscillation having a direction which has a primary component in the drive direction and a secondary component by quadrature error in the sense direction, and a capacitive transducer structure that includes a stator to be anchored to a static support structure, which stator includes a planar first stator surface, and a planar second stator surface, rotors mechanically connected to the seismic mass, which rotors include a planar first rotor surface positioned opposite the first stator surface, and a planar second rotor surface positioned opposite the second stator surface. The first rotor surface and the first stator surface form a first capacitor, and the second rotor surface and the second stator surface form a second capacitor. An electrical energy source is arranged to create a first electrostatic force between the first stator surface and the first rotor surface of the first capacitor, and a second electrostatic force between the second stator surface and the second rotor surface of the second capacitor, wherein the first electrostatic force is opposite to the second electrostatic force. The first capacitor and the second capacitor are arranged into a slanted orientation wherein a non-zero angle is formed between the drive direction and a tangent of the first stator surface such that the first electrostatic force becomes modulated in phase with the linear oscillation of the seismic mass, and a non-zero angle is formed between the drive direction and a tangent of the second stator surface, such that the second electrostatic force becomes modulated in phase with the linear oscillation of the seismic mass.

Due to the slanted orientation, also the distance between the stator and rotor surfaces changes during the linear oscillation of the seismic mass, introducing also gap modulation to the compensating force. This significantly increases effect of the compensating force.

Further advantages of the invention are discussed in more detail with the following embodiments.

In the following, the invention will be described in greater detail, in connection with preferred embodiments, with reference to the attached drawings, in which:.

Although the specification may refer to "an", "one", or "some" embodiment(s), this does not necessarily mean that each such reference is to the same embodiment(s), or that the feature only applies to a single embodiment. Single features of different embodiments may be combined to provide further embodiments.

In the following, features of the invention will be described with a simple example of a device architecture in which various embodiments of the invention may be implemented. Only elements relevant for illustrating the embodiments are described in detail. Various generic features of capacitive transducer structures or microelectromechanical devices that are generally known to a person skilled in the art may not be specifically described herein.

<FIG> illustrates basic elements of an exemplary resonator structure in which a capacitive transducer structure may be applied for quadrature compensation. The device may include a seismic mass <NUM>, a mass body that may be suspended to a static (non-oscillating) support structure to provide an inertial movement. In a gyroscope structure the static support may be provided by another body element of the gyroscope structure, for example, by an underlying handle wafer, or a covering cap wafer of a gyroscope die. It is noted, however, that divisions to a structure wafer, the handle wafer and the cap wafer are conceptual. For a person skilled in the art it is clear, for example, that the handle wafer and the structure wafer may be patterned separately or in combination from a layered silicon-insulator-silicon substrate.

The seismic mass <NUM> may be suspended to the static support through a spring structure <NUM>. The string structure refers here to any elastically directional element that is configured by the dimensions and/or properties of the spring structure to be flexible to displacements of the seismic mass in at least one direction, and very rigid to displacements of the seismic mass in any other directions. In a gyroscope structure, the spring structure is typically designed to allow displacements of the seismic mass in a drive direction D and in a sense direction S. The drive direction D refers here to a designed direction of linear oscillation of the seismic mass <NUM>, i.e. the direction of the linear oscillation of the seismic mass during ideal primary motion and in the absence of other forces acting on the seismic mass. The sense direction S refers here to a direction that is perpendicular to the drive direction, and therefore coincides with a detected Coriolis force resulting from angular motion of the resonator structure. <FIG> illustrates exemplary drive and sense directions in the exemplary simplified configuration. In practice, there are many ways to implement resonator structures, and arrange the sense and drive directions into them. Such solutions are widely documented and well known to a person skilled in the art of microelectromechanical devices.

The seismic mass <NUM> may be designed to be driven into linear oscillation in direction D, but because of the quadrature error, the direction of the actual motion of the seismic mass <NUM> is actually a result of a component in the drive direction D, and a secondary component Q generated by the quadrature error. This quadrature error may be eliminated by means of a capacitive transducer structure.

<FIG> illustrates an exemplary embodiment of a capacitive transducer structure according to the present invention. The disclosed configuration includes a seismic mass <NUM>, suspended to a static support through a spring structure (not shown), as described above. The spring structure defines for the seismic mass a drive direction D, and a sense direction S that is perpendicular to the drive direction D, as shown in <FIG>. The capacitive transducer structure includes rotors 21a and 21b. The term rotor refers here to an element that is mechanically connected to the seismic mass <NUM>, and thereby interactively coupled to move along its motion in relation to the static support structure.

The term transducer refers in general to a device that converts one form of energy to another. Electromechanical transducers are devices that convert mechanical energy to electrical energy, for example mechanical motion into variations of electric current or voltage, and vice versa. The term capacitive transducer is used herein to refer to an entity that includes a capacitor with variable capacitance. A combination of mechanical and electrical elements required to induce or apply the variable capacitance forms a capacitive transducer structure. In an apparatus, the capacitance of the capacitive transducer structure may be configured to change due to a change in the value of a selected input quantity. In quadrature compensation, the input quantity corresponds to spatial orientation of elements of the capacitive transducer structure, which spatial orientation changes in response to linear oscillation of a seismic mass of a gyroscope structure.

The capacitive transducer structure <NUM> includes stators 22a and 22b.

The term stator refers here to an element that is fixedly anchored to a static support structure. Depending on the configuration, the stator and the rotor may be anchored and suspended to a same static support structure or to different static support structures. As shown in <FIG>, the rotor includes a comb finger, an elongate element projecting out of the seismic mass <NUM>. The stator also includes an elongate element positioned such that an elongate stator surface <NUM> extends opposite an elongate rotor surface <NUM>.

The rotor 21b includes at least one planar rotor surface <NUM>, and the stator 22b includes at least one planar stator surface <NUM>. This means that at least part of the volume of the stator or rotor extends along a plane in two dimensions (length, width) and forms therein a planar surface. Within tolerances, the planar surface can thus be considered to contain all straight lines that connect any two points on it. It is, however, understood that a planar surface may include minor protrusions patterned on the rotor, or recesses patterned into it. It is noted that other forms of surfaces may applied within the scope, as well. For example, the surfaces may be curved or arched.

The rotors 21a, 21b and the stators 22a, 22b are configured to form pairs such that in a pair of a stator 21b and a rotor 22b, the stator surface <NUM> of the stator 22b and the rotor surface <NUM> of the rotor 21b are positioned opposite to each other. This means that the stator surface and the rotor surface are set over against the other across an intervening space. Advantageously, but not necessarily, the stator surface and the rotor surface are in initial state mutually aligned. The initial state refers here to the static state where the rotor is suspended to the static support structure but is not driven to move, or exposed to other external forces. In the example of <FIG>, the stator surfaces and rotor surfaces are planar, and the planar stator surfaces and the rotor surfaces in initial state are parallel to each other. In case of curved surfaces, initially the at least one curve of the stator surface is advantageously aligned with the at least one curve of the rotor. In the example of <FIG>, the rotor includes two comb fingers 21a, 21b, projecting in opposite sides from the seismic mass.

The stator includes also two stator comb fingers 22a, 22b and each of the rotor comb fingers 21a, 21b is arranged to oscillate opposite to a respective stator finger 22a, 22b. Either or both of the rotor comb fingers 21b includes an elongate rotor surface <NUM> on at least one side of the rotor comb finger such that the stator and rotor pairs in <FIG> are as follows: 21a and 22a, 21b and 22b.

The rotors 21a, 21b of <FIG> are mechanically connected to the seismic mass <NUM> such that each of the stator and rotor surface pairs forms a capacitor. The capacitive transducer structure includes also an electrical energy source (not shown) that is arranged to create an electrostatic force between the pairs of a stator surface and a rotor surface opposite it. Through the structural arrangement of the elements, the capacitance of the capacitor of the stator and rotor surface pair may be arranged to change when the rotor moves in relation to the stator because of the induced drive motion. This change of capacitance may also be arranged to modulate an electrostatic force between the stator surface and the rotor surface such that the electrostatic force opposes the quadrature error motion, and thereby reduces its effect as early as possible.

The seismic mass <NUM>, and thereby the rotors 21a, 21b may be excited to primary motion in a predetermined direction D. It is understood that various excitation structures capable of creating a driving input force in a specific direction may be applied within the scope. The excitation means may include a separate electrode that is configured to move with the seismic mass <NUM>, and interact electrically with further static electrode or electrodes (not shown), and as a result of this electrical interaction induce the seismic mass <NUM> to move. Alternatively, the seismic mass may itself be formed of conductive material, or include a deposited layer of conductive material that interacts with a further static electrode or electrodes. Also piezoelectrical excitation may be applied. Seismic mass excitation mechanisms are well known to a person skilled in the art, and will not be discussed in detail herein. The direction of the excited motion is mainly defined by the spring structure that supports the seismic mass <NUM>.

In linear oscillation, the seismic mass moves back and forth on an axis of oscillation about a point of equilibrium. The excitation means and the suspending springs are designed to drive the seismic mass <NUM> into linear oscillation in direction D, but, as discussed above, because of the quadrature error, the direction of the actual motion of the seismic mass <NUM> is actually a result of a primary component in the drive direction D, and a secondary component Q generated by the quadrature error. Since the quadrature error is caused by unintentional defects, its total magnitude and direction may vary from structure to structure. From the quadrature error elimination point of view, a varying component Q generated by the quadrature error in a direction perpendicular to the drive direction is most relevant. In <FIG>, the direction of the linear oscillation by the primary motion and the quadrature error is illustrated with the arrow D+Q. The quadrature error motion results into a deviation of the actual axis of oscillation from the intended axis of oscillation. In the configuration of <FIG>, the intended axis of oscillation is parallel to the drive direction D, but due to the quadrature error motion Q, the actual axis of oscillation would be parallel to the direction D+Q.

Let us assume that during the linear D+Q oscillation, the seismic mass <NUM>, and thereby also the rotor 21a displaces an amount X in the drive direction D and a small amount Y in the perpendicular sense direction S. This changes capacitances of the capacitors and creates a force for compensation against the quadrature error motion of the seismic mass. The total force acting on the seismic mass <NUM> in y-direction may be determined from the sum of forces: <MAT>.

Where Ci is a capacitor formed by a stator and rotor pair, and Vi is the voltage between them. This total force is negative in sign and includes the drive displacement X. Accordingly; the capacitive transducer structure creates a force against the displacement Y in the sense direction S in phase with the displacement X in the drive direction D.

In embodiments of the invention, the capacitive transducer structure is arranged into a slanted orientation where a non-zero angle α is formed between the drive direction and a tangent of the stator surface. In the example of <FIG>, the stator surfaces are planar and the tangent of a stator surface is thus aligned with it. It is noted that in order to visually highlight the orientation, the non-zero angle α is exaggerated in <FIG>. Typically a smaller angle is applied, as will be discussed later on. As shown in <FIG>, an angle α is formed between the drive direction D and the stator surface <NUM> of the stator 22b.

As discussed earlier, conventionally the varying overlap between opposing stator and rotor surfaces has been applied to create a force to compensate the quadrature error motion of the seismic mass. However, due to the slanted orientation, also the distance between the stator and rotor surfaces changes during the linear oscillation of the seismic mass, which introduces gap modulation to the compensating force. With typical dimensions of microelectromechanical gyroscope structures, the effect of this gap modulation has turned out to be very strong. For example, with the configuration of <FIG>, a slanted orientation with α= <NUM>° and gap width of <NUM>,<NUM>, a +<NUM>% increase in the compensating force was measured. The slanted orientation with α= <NUM>° and gap width of <NUM>,<NUM> provided a +<NUM>% increase to the compensating force.

Preferably the angle α of the slanted orientation is arranged to be larger than the angle of the expected quadrature deflection. The quadrature deflection angle in microelectromechanical gyroscope structures is typically less than <NUM>°, and optimal angles of the slanted orientation have proved to be in the range of α=<NUM>,<NUM>-<NUM>°.

<FIG> illustrates a configuration where compensating forces are created with two capacitors arranged in opposite pairs into lateral positions of the seismic mass. Lateral positions refer here to locations in the opposite extremes of the seismic mass along the primary motion of the seismic mass. Opposite pairs means here that the electrostatic force created between the stator surface <NUM> and the rotor surface <NUM> of the first pair of capacitor electrodes 21b and 22b is opposite to the electrostatic force created between the stator surface <NUM> and the rotor surface <NUM> of the second pair of capacitor electrodes 21a and 22a. In the configuration of <FIG> this is achieved by arranging the rotor surfaces <NUM>, <NUM> and the stator surfaces <NUM>, <NUM> in to be parallel; the stators 22a, 22b being positioned to opposite sides from the intended axis of oscillation. Accordingly, when the seismic mass <NUM> moves upwards in the shown orientation, the quadrature error motion would shift the seismic mass to the left, but the electrostatic force of the first pair of capacitor electrodes 21b and 22b reduces this deviation. Similarly, when the seismic mass <NUM> moves downwards in the shown orientation, the quadrature error motion would shift the seismic mass to the right, but the electrostatic force of the second pair of capacitor electrodes 21a and 22a reduces this deviation. The result of the quadrature error motion and the compensation by the capacitor pair shifts the actual axis of oscillation closer to the intended axis of oscillation.

The orientation of the opposite capacitor pairs is important; if the created electrostatic forces would not be opposite, but be in the same a force modulated at twice the primary oscillation frequency would be created. Such force would naturally not be applicable to compensate for quadrature error motion of linear oscillation.

In order to multiply the quadrature compensating force, the seismic mass may include a quadrature compensation comb that includes a plurality of capacitors, formed by opposing stator and rotor pairs. It is understood that while the electrostatic force is inversely proportional to the square of the distance between the charges, in practice a repulsive force cannot be effectively applied for quadrature compensation.

<FIG> illustrates a simplified structure of quadrature compensation comb that includes a number of compensating structures of <FIG> to compensate quadrature error in one direction Qcomp. It is noted that a rotor comb finger <NUM> is in practice exposed to opposite electrostatic forces by stator comb fingers <NUM> and <NUM>. However, because of the inverse proportionality to the square of the distance, the effect of the closer (opposite) stator comb finger <NUM> dominates. This compensation comb configuration is simple to bias but still allows tight comb structures and therefore efficient use of surface area for quadrature compensation. Advantageously, a gyroscope structure may include one comb for quadrature compensation in the positive sense direction and one comb structure for compensation in the negative sense direction. It is noted that the scope includes also configurations with only one capacitor per seismic mass. However, such structure may in practice be unbalanced and therefore not operate optimally.

<FIG> illustrates another type of a quadrature compensation comb structure. The structure includes a seismic mass <NUM> with a plurality of rotor comb fingers <NUM> projecting from the seismic mass <NUM>. The structure may include also a stator comb <NUM> with a plurality of stator comb fingers <NUM>. The stator surfaces of the stator comb fingers are arranged into opposite position in respect of the rotor surfaces of the rotor comb fingers <NUM>. The seismic mass may be configured to be excited to a linear oscillation in the drive direction D. The fingers of the quadrature compensation comb may be in a slanted orientation such that a non-zero angle α is again formed between the drive direction D and the stator surfaces of the stator comb fingers <NUM>. A stator surface providing the side of the angle α may, but does not necessarily be planar and extend to the whole length of its stator comb finger. The rotor surfaces of rotor comb fingers <NUM> may be correspondingly planar and be aligned with the stator surface. The other sides of the stator comb fingers and rotor comb fingers may be aligned with the drive direction D, thus forming a non-symmetric sawtooth-shaped compensation structure. The slanted orientation of the stator and rotor finger pairs provides the improved efficiency in quadrature compensation, as discussed above. The non-symmetric sawtooth-shaped compensation comb structure allows a tightened packing of the enhanced compensating finger pairs. A high performance is thus achieved with a reduced component size.

<FIG> illustrates a further structure where compensating forces may be created in both directions, and the slanted orientation of the stator and rotor finger pairs provides the improved efficiency to quadrature compensation in both directions. The capacitive transducer configuration may include at least two stators <NUM>, <NUM>, where a positive non-zero angle +α is formed between the drive direction D and a tangent of a stator surface of the first stator <NUM>, and a negative non-zero angle -α is formed between the drive direction D and a tangent of a stator surface of the second stator <NUM>. The first stator <NUM> may be positioned opposite a first rotor <NUM>, and the stator surface of the first stator <NUM> may be initially aligned to be parallel with the rotor surface of the first rotor <NUM>. Correspondingly, second stator <NUM> may be positioned opposite a second rotor <NUM>, and the stator surface of the second stator <NUM> may be initially aligned to be parallel with the rotor surface of the second rotor <NUM>. A compensating force may be thus effectively created in both sense directions.

As shown in <FIG>, also this configuration may be implemented with capacitors arranged in pairs into opposite lateral positions of the primary motion. A capacitor of the first stator <NUM> and the first rotor <NUM>, and a capacitor of a third stator <NUM> and a third rotor <NUM> may be applied to compensate a quadrature component in a negative sense direction and a capacitor of the second stator <NUM> and the second rotor <NUM>, and a capacitor of a fourth stator <NUM> and a fourth rotor <NUM> may be applied to compensate a quadrature component in a positive sense direction. Also this structure may be applied to form a quadrature compensation comb, where capacitors creating the electrostatic forces in opposite directions are arranged sequentially into parallel orientation along the sense direction S.

<FIG> illustrates a further embodiment that applies the element of the capacitive transducer structure of <FIG>, but the separate rotor comb fingers <NUM>, <NUM> and <NUM>, <NUM> have now been merged into tapering rotor comb fingers <NUM>, <NUM>. A tapering rotor comb finger <NUM> may include two rotor surfaces, one arranged opposite to a stator surface of a first stator <NUM>, and one opposite to a stator surface of a second stator <NUM>. A similar arrangement of opposite stator and rotor surfaces may be arranged into opposite lateral position of the seismic mass, in respect of the primary motion of the seismic mass. Also this structure may be applied to form a quadrature compensation comb, where capacitors creating the electrostatic forces in opposite directions are arranged sequentially into parallel orientation along the sense direction S. The configuration of <FIG> produces the same improved effect as the configuration of <FIG>, but requires less surface area.

Embodiments of the invention include a microelectromechanical sensor device that includes at least one capacitive transducer structure of <FIG>. <FIG> illustrates such embodiments with an exemplary gyroscope structure that includes at least one seismic mass <NUM>. The seismic mass <NUM> may be suspended with a spring structure <NUM>, <NUM> to a static support structure. The seismic mass <NUM> may be suspended to have two degrees of freedom, one in the drive direction D of the primary motion and one in the sense direction S that is opposite to the drive direction, as shown in <FIG>. The gyroscope structure may include an excitation comb <NUM> for driving the seismic mass <NUM> into the primary motion and a sense comb structure <NUM> for sensing the movement of the seismic mass because of a Coriolis force resulting from angular motion of the gyroscope structure. A capacitive transducer structure <NUM> may be applied to compensate a quadrature error in the positive sense direction, and a capacitive transducer structure <NUM> may be applied to compensate a quadrature error in the negative sense direction. As shown in <FIG>, the microelectromechanical sensor device may include two such gyroscope structures in axial symmetry on a plane.

<FIG> shows an enlarged extract of the gyroscope structure of <FIG>.

Claim 1:
A microelectromechanical sensor device that comprises:
a seismic mass (<NUM>);
a spring structure for suspending the seismic mass (<NUM>) into a static support structure, wherein the spring structure defines for the seismic mass a drive direction (D), and a sense direction (S) that is perpendicular to the drive direction (D);
excitation means for driving the seismic mass into linear oscillation, the linear oscillation having a direction which has a primary component in the drive direction and a secondary component by quadrature error in the sense direction;
a capacitive transducer structure that includes:
a stator (22a, 22b) to be anchored to a static support structure, which stator includes a planar first stator surface (<NUM>), and a planar second stator surface (<NUM>),
a first rotor (21b) and a second rotor (21a) mechanically connected to the seismic mass, wherein the first rotor (21b) includes a planar first rotor surface (<NUM>) positioned opposite the first stator surface (<NUM>), and the second rotor (21a) includes a planar second rotor surface (<NUM>) positioned opposite the second stator surface (<NUM>); wherein
the first rotor surface (<NUM>) and the first stator surface (<NUM>) are parallel and form a first capacitor, and the second rotor surface (<NUM>) and the second stator surface (<NUM>) are parallel and form a second capacitor;
an electrical energy source arranged to create a first electrostatic force between the first stator surface (<NUM>) and the first rotor surface (<NUM>) of the first capacitor, and a second electrostatic force between the second stator surface (<NUM>) and the second rotor surface (<NUM>) of the second capacitor,
characterized in that the first electrostatic force is opposite to the second electrostatic force; and in that
the first capacitor and the second capacitor are arranged into a slanted orientation wherein:
a non-zero angle (a) is formed between the drive direction and the first stator surface (<NUM>) such that the first electrostatic force becomes modulated in phase with the linear oscillation of the seismic mass;
the non-zero angle (a) is formed between the drive direction and the second stator surface (<NUM>), such that the second electrostatic force becomes modulated in phase with the linear oscillation of the seismic mass.