Patent Publication Number: US-2022219969-A1

Title: Mems device with meandering electrodes

Description:
FIELD OF THE DISCLOSURE 
     The disclosure relates to microelectromechanical devices, and particularly to devices which comprise a mobile mass element which can move in relation to a surrounding fixed structure. The present disclosure further concerns electrodes which can be prepared on the mobile mass element and on the fixed structure to measure this movement. 
     BACKGROUND OF THE DISCLOSURE 
     Microelectromechanical (MEMS) devices often comprise a mobile mass element, which may be called a rotor. The rotor is typically suspended from a fixed structure with flexible suspenders which allow the rotor to move in relation to the fixed structure. The fixed structure may be called a stator. The movement of the rotor may be measured with a capacitive transducer which comprises a set of elongated electrode structures on the rotor interdigitated with a corresponding set of elongated electrode structures on the stator. 
       FIGS. 1 a    and  1   b  illustrate two ways of implementing a capacitive transducer with elongated electrodes. The figures illustrate a rotor  11  with a set of rotor electrodes  111 - 113  and a stator  12  with a set of stator electrodes  121 - 123 . The arrow next to the rotor  111  illustrate its direction of movement (the x-direction). In  FIG. 1 a    the rotor and stator electrodes extend in a direction (the y-direction) which is perpendicular to the direction in which the rotor  11  moves. The distance between each rotor/stator electrode increases or decreases in the x-direction as the rotor moves. In this measurement the capacitive response is sensitive to the displacement of the rotor, but the relationship between the response and the displacement is not linear. 
     In  FIG. 1 b    the rotor and stator electrodes extend in the direction (the x-direction) in which the rotor  11  moves.  FIG. 1 c    illustrates the position of a first rotor electrode  111  and a first stator electrode  121  when the rotor is in its rest position.  FIG. 1 d    illustrates the positions of the same electrodes when the rotor has moved a distance Δx to the left from its rest position. The capacitance between the two electrodes increases when their overlap in the x-direction increases. In this measurement the relationship between the capacitive response and the displacement is linear, but the capacitance increase obtained in  FIG. 1 d    is often quite small in relation to the capacitance measured in the rest position. The measurement signal is therefore not very sensitive. 
     BRIEF DESCRIPTION OF THE DISCLOSURE 
     An object of the present disclosure is to provide an apparatus which alleviates the above disadvantages. 
     The object of the disclosure is achieved by an arrangement which is characterized by what is stated in the independent claim. The preferred embodiments of the disclosure are disclosed in the dependent claims. 
     The disclosure is based on the idea of utilizing rotor and stator and stator electrodes with a meandering shape. With a suitable arrangement such electrodes can be used to measure a capacitive response which is highly sensitive to rotor displacement and also exhibits a linear dependence on that displacement. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following the disclosure will be described in greater detail by means of preferred embodiments with reference to the accompanying drawings, in which 
         FIGS. 1 a -1 b    illustrate capacitive transducers implemented with elongated electrodes. 
         FIGS. 1 c -1 d    illustrate how the capacitance changes when the rotor moves. 
         FIGS. 2 a -2 c    illustrate rotor and stator electrodes. 
         FIGS. 3 a -3 b    illustrate the change in main capacitance in a measurement where the meanders of the rotor and stator electrodes are partially aligned in the initial position. 
         FIGS. 3 c -3 d    illustrate the change in main capacitance in a measurement where the meanders of the rotor and stator electrodes are fully aligned in the initial position. 
         FIG. 3 e    illustrates stray capacitance components. 
         FIGS. 4 a -4 c    illustrate design options for a meandering electrode. 
         FIGS. 5 a -5 b    illustrate a device where a meandering rotor electrode is flanked by meandering stator electrodes on both sides. 
     
    
    
     DETAILED DESCRIPTION OF THE DISCLOSURE 
     This disclosure describes a microelectromechanical device comprising a mobile rotor and a fixed stator which lie in a device plane defined by a lateral axis and a transversal axis. The transversal axis is orthogonal to the lateral axis, and the device comprises at least one measurement region where an edge of the rotor and an edge of the stator are separated from each other by a rotor-stator gap. A rotor electrode extends from the edge of the rotor toward the stator in the rotor-stator gap. A first stator electrode extends from the edge of the stator toward the rotor in the rotor-stator gap. The rotor electrode and the first stator electrode are adjacent and substantially parallel to each other in the rotor-stator gap. 
     The rotor electrode is a meandering electrode which comprises two or more first lateral sections which lie on a first lateral baseline, and each first lateral section is separated from the adjacent first lateral section on the first lateral baseline by a first lateral gap. 
     The first stator electrode is a meandering electrode which comprises two or more second lateral sections which lie on a second lateral baseline, and each second lateral section is separated from the adjacent second lateral section on the second lateral baseline by a second lateral gap. At least one first lateral gap is adjacent to at least one second lateral gap and at least partially aligned with said at least one second lateral gap in the transversal direction. 
     The rotor and stator electrodes are folded beams with a serpentine shape. In other words, each of these meandering electrodes is a beam with a set of consecutive turns. The folds in the beam may for example comprise a plurality of mutually perpendicular sections—lateral sections which are connected to each other by transversal sections. Lateral sections which lie on a first lateral baseline are in this case connected by transversal sections to lateral sections which lie on a different lateral baseline. The connecting structure which joins two lateral sections on the first baseline to each other thereby contains two transversal sections with an additional lateral section between them. The mutually perpendicular sections of the folded beam thereby form a narrow meandering electrode with a rectangular pattern 
     However, the folds in the beam and the resulting turns of the meandering electrode do not necessarily have to be perpendicular. Instead of being connected to each other with a square- or rectangle-shaped folding, the lateral sections which lie on the same axis can alternatively be connected with a connecting structure with some other geometry, as described and illustrated in more detail below. 
     Although general measurement and design principles will be discussed below with reference to figures which illustrate just one or two elongated electrodes in each set of rotor and stator electrodes, the sets could be expanded to include any number of electrodes. Any principle which applies to an illustrated rotor—stator electrode pair will apply also to additional rotor—stator electrode pairs which are arranged adjacent to each other with the same geometry. 
       FIG. 2 a    illustrates a rotor  21  and a stator  22 . A rotor electrode  211  extends from the edge  219  of the rotor  21  toward the stator  22 , and a first stator electrode  221  extends from the edge  229  of the stator  22  toward the rotor  21 . The rotor and stator electrodes have a meandering shape. The lateral direction is the x-direction and the transversal direction is the y-direction. The edge  219  of the rotor is separated from the edge  229  of the stator by a rotor-stator gap  25 . 
     The rotor electrode  211  comprises first lateral sections  2111   a  and  2111   b  which lie on a first lateral baseline  291 . Two first lateral sections are illustrated, but many more could be used. Each pair of first lateral sections ( 2111   a+   2111   b ) is separated from each other on the first lateral baseline  291  by a first lateral gap  281 . Each first lateral section  2111   a  is connected to the following first lateral section  2111   b  by a first connecting structure  213  which extends away from the first lateral baseline  291 , leaving the first lateral gap  281  between the first lateral sections  2111   a  and  2111   b . These first connecting structures  213  could be of any shape and size which is suitable for separating the first lateral sections from each other by the desired first lateral gaps  281 . 
     The first stator electrode  221  comprises second lateral sections  2211   a  and  2211   b  which lie on a second lateral baseline  292 . Each pair of second lateral sections ( 2211   a+   2211   b ) is separated from each other on the second lateral baseline  292  by a second lateral gap  282 . Each second lateral section  2211   a  is connected to the following second lateral section  2211   b  by a second connecting structure  223  which extends away from the second lateral baseline  292 . The shapes of these second connecting structures  223  can also be freely selected, as long as they separate the second lateral sections from each other by the desired second lateral gaps  282 . 
       FIG. 2 a    illustrates a situation where the rotor  211  is in an initial position. In any embodiment of this disclosure, the initial position may for example be a rest position which the rotor assumes in an accelerometer when the accelerometer does not experience any acceleration in the direction of the x-axis. Alternatively, if the rotor and stator are used in a gyroscope, the rotor may for example be driven in linear primary oscillation in the direction of the y-axis. It may oscillate in the direction of the x-axis when the gyroscope undergoes rotation about a z-axis perpendicular to the xy-plane. In this case the initial position may be defined by the x-coordinate of the rotor when the gyroscope does not undergo any rotation about the z-axis. In either case, a capacitive measurement can be performed between the rotor and stator electrodes. The measured capacitance indicates the displacement of the rotor away from its initial position in the direction of the x-axis, i.e. the lateral direction. The words “left” and “right” refer in this disclosure to two opposing lateral directions which correspond to the left and right sides of the figures. 
       FIG. 2 a    illustrates an arrangement where the at least one first lateral gap  281  is partially aligned with the at least one second lateral gap  282  in the transversal direction when the rotor  21  is in its initial position. This means that there is a lateral offset between at least one side of the gaps (left or right side, or on both sides).  FIG. 2 a    shows an arrangement where the widths of the gaps  281  and  282  are equal, and each side of the second lateral gap  282  is offset from the corresponding side of the first lateral gap  281  by the same lateral offset distance O. 
     In any embodiment of this disclosure where lateral gaps are partially aligned, each pair of partially aligned lateral gaps may be arranged so that the lateral distance from the left side of the first lateral gap  281  to the left side of the second lateral gap  282  (a distance which corresponds to the offset distance O in  FIG. 2 a   ) is less than the lateral distance from the left side of the first lateral gap  281  to the right side of the second lateral gap  282  (a distance which is indicated as D in  FIG. 2 a   ). Alternatively or complementarily, the lateral distance (not illustrated in  FIG. 2 a   ) from the right side of the second lateral gap  282  to the right side of the first lateral gap  281  may be less than the lateral distance from the right side of the second lateral gap  282  to the left side of the first lateral gap  281  (indicated as D in  FIG. 2 a   ). However, the relationship between these distances could alternatively be the opposite (D could be less than O in  FIG. 2 a   ). 
     The first and second lateral gaps  281  and  282  do not necessarily need to have the same width when the gaps are partially aligned.  FIG. 2 b    illustrates an alternative arrangement where the widths differ from each other and where only the right side of the second lateral gap  282  is laterally offset from the right side of the first lateral gap  281 . The left sides of the two gaps are aligned with each other. 
     The at least one first lateral gap  281  may alternatively be fully aligned with the at least one second lateral gap  282  in the transversal direction when the rotor  21  is in its initial position. This option is illustrated in  FIG. 2 c   . In this case the first and second lateral gaps have the same lateral width and there is no lateral offset between the two gaps. Both the left and the rights sides of the gaps are aligned with each other. 
     The principles of the capacitive measurement will be described with reference to  FIGS. 3 a -3 c   , where reference numbers  31 ,  32 ,  311  and  321  correspond to reference numbers  21 ,  22 ,  211  and  221 , respectively, in  FIGS. 2 a   - 2   c.    
       FIG. 3 a    illustrates the rotor and stator electrodes  311  and  321  when the rotor is in the initial position. The meanders in the rotor electrode are offset from the corresponding meanders on the stator electrode by a lateral offset distance O. The main components of the capacitance between the rotor and stator electrodes in  FIG. 3 a    arise from the areas which are closest to each other. These components are illustrated by arrows, and their sum will be referred to as the main capacitance. Additional, but smaller, capacitive components arise in the areas which are not directly adjacent to each other. The sum of these components may be referred to as the stray capacitance. 
       FIG. 3 b    illustrates a situation where the rotor  31  has been displaced to the left from the initial position by a distance Δx. Due to the fact that the meanders of the rotor electrode  311  and those of the stator electrode  312  were offset from each other by an offset distance O in the initial position illustrated in  FIG. 3 a   , the main capacitance is larger in  FIG. 3 b    than in  FIG. 3 a   . The movement of the rotor  31  in the x-direction has brought the meanders almost into alignment with each other in the direction of the y-axis. The overlap between the lateral sections which lie closest to each other has therefore increased. 
     It is significant that every lateral section in the meander contributes an additional increase to the main capacitance. This can schematically be compared to the movement illustrated in  FIG. 1 d   , where the capacitance increase was illustrated with only two additional arrows compared to  FIG. 1 c   . In contrast, in  FIG. 3 b    each lateral section in the meandering electrode contributes to the increase in main capacitance with two additional arrows compared to  FIG. 3 a   . The original 12 arrows of the initial position in  FIG. 3 a    thereby become 20 arrows in  FIG. 3 b   . Electrodes with a meandering shape can therefore produce a capacitive response which is both linear and highly sensitive because the capacitive area will increase at each turn in the meander in  FIG. 3 b   , not merely at the tip of the electrode as in  FIG. 1   d.    
     The sensitivity can be increased by increasing the number of lateral sections in each electrode—i.e. by increasing the number of turns in the meander. However, some practical constraints have to be observed. In the arrangement illustrated in  FIGS. 3 a -3 b   , the meandering shapes and their offset have been designed so that the expected maximum displacement Δx max  (which is here assumed to be approximately equal to the Δx illustrated in  FIG. 3 b   ) is not greater than the offset distance O in  FIG. 3 a   . If this would not be the case, and if the rotor  31  would move to the left a distance which exceeds the offset distance, then the overlap between the adjacent meander turns (and thereby the main capacitance) would begin to decrease as a function of displacement when the rotor electrode  311  moves further past the stator electrode  321  than where it is illustrated in  FIG. 3 b   . The measured capacitance values would then not exhibit a linear dependence on displacement, and some capacitance values would correspond to multiple displacement values. The offset should therefore exceed the expected maximum displacement in the embodiments illustrated in  FIGS. 2 a  and 2 b   , and in  FIGS. 5 a  and 5 b    below. 
       FIGS. 3 c -3 d    illustrate the measurement which can be performed when the first and second lateral gaps are fully aligned in the initial position, as in  FIG. 2 c   .  FIG. 3 c    illustrates the initial position where the meander curves of the rotor and stator electrode are fully aligned with each other in the transversal direction (the y-direction). The main capacitance is at a maximum in the illustrated initial position (illustrated by 20 arrows).  FIG. 3 d    illustrates a situation where the rotor has moved away from the initial position to the right. The main capacitance has decreased so that only 12 arrows are left. A corresponding decrease in capacitance would be obtained if the rotor moved to the left. The movement of the rotor  31  may in this embodiment be restricted either to rightward movement or to leftward movement from the initial position, because these two movements cannot be distinguished from each other in the capacitive measurement. 
     In  FIG. 3 d    the expected maximum displacement Δx max  should be less than the widths of the first and second lateral sections and the widths of the first and second lateral gaps. If this would not be the case, the overlap between the adjacent meanders (and thereby the main capacitance) would not decrease as a linear function of displacement. 
       FIG. 3 e    illustrates the rotor in the same initial position as in  FIG. 3 a   . Reference numbers  313  and  323  correspond to reference numbers  213  and  223 , respectively, in  FIG. 2 a   . Reference number  3111  corresponds to reference numbers  2111   a  and  2111   b , and reference number  3211  corresponds to  2211   a  and  2211   b  in  FIGS. 2 a -2 c   . The arrows between the rotor electrode and the first stator electrode here illustrate the components which contribute to stray capacitance. These may include the capacitance between any first or second lateral section  3111 / 3211  and the opposing connecting section  313 / 323 , the capacitance between first and second lateral sections which are not adjacent to each other, and the capacitance between opposing connecting sections  313 / 323 . The magnitude of the stray capacitance will depend on the distance between the rotor and stator electrodes and on their geometry and dimensions. 
     The measured capacitance will always be a sum of the main capacitance and the stray capacitance, and the stray capacitance will not in general exhibit a completely linear dependence on displacement. However, the main capacitance can be much larger than the stray capacitance since the regions where the electrodes are closest to each other will contribute most to the capacitance between. The influence of the stray capacitance on the measured capacitance can also be minimized with suitable electrode design. 
       FIGS. 4 a -4 c    illustrate some options for electrode design. Reference numbers  41 ,  42 ,  411 ,  419 ,  421 ,  413 ,  423 ,  429 ,  481 ,  482 ,  491  and  492  correspond to reference numbers  21 ,  22 ,  211 ,  219 ,  221 ,  213 ,  223 ,  229 ,  281 ,  282 ,  291  and  292 , respectively, in  FIGS. 2 a -2 c   . Reference number  4111  corresponds to reference numbers  2111   a  and  2111   b , and reference number  4211  corresponds to  2211   a  and  2211   b  in  FIGS. 2 a   - 2   c.    
       FIG. 4 a    illustrates a rotor electrode with four first lateral sections  4111 , four second lateral sections  4211 , three first lateral gaps  481  and three second lateral gaps  482 . The figure illustrates the rotor in its initial position. Each first lateral gap  481  is in  FIG. 4 a    laterally offset from the adjacent second lateral gap  482  by the same lateral offset distance. However, the lateral offset distance does not necessarily have to be equal for each pair of first and second lateral gaps as long as the expected maximum displacement of the rotor is less than the smallest lateral offset in the direction of motion. 
     Each first lateral gap and each second lateral gap may have the same lateral width, as  FIG. 4 a    illustrates. Alternatively, the widths of some first or second lateral gaps may be different, as  FIG. 4 b    illustrates. Each first lateral section and each second lateral section may have the same lateral width, as  FIG. 4 b    illustrates. Alternatively, some first lateral sections may have widths which differ both from the widths of other first lateral sections and from the widths of some second lateral sections, as  FIG. 4 a    illustrates. 
     The rotor electrode may have a separate base section which is attached to the edge  419  of the rotor, and the first lateral sections  4111  and first connecting structures  413  may be connected in an alternating series to this base section. The first stator electrode could have a corresponding base section to which the second lateral sections  4211  and second connecting structures  423  are connected in an alternating series. The shapes and sizes of these base sections could differ from the shapes and sizes of the first and second lateral sections. Base sections have not been illustrated in  FIG. 4   a.    
     The number of first and second lateral gaps does not necessarily have to be equal, and each first lateral gap  481  does not necessarily have to be aligned with a corresponding second lateral gap  482 . This is illustrated in  FIG. 4 c   , where no second lateral gap on the first stator electrode is adjacent to first lateral gap  481   b  on the rotor electrode. The number of first lateral sections  4111   a - 4111   d  is four, but the number of second lateral sections  4111   a - 4111   c  is three. The capacitance between the rotor electrode  411  and the first stator electrode  421  will nevertheless increase when the rotor moves to the left and the overlap between the pairs  4111   a + 4211   a ,  4111   b + 4211   b  and  4111   c + 4211   c  increases. The extra first lateral section  4111   d  and the extra first lateral gap  481   b  will remain fully aligned with the long second lateral section  4211  as the rotor moves to the left, so they will not contribute to a change in capacitance.  FIG. 4 c    also illustrates a device where the lateral offsets O 1  and O 2  of two second lateral gaps  482   a  and  482   b  from the corresponding first lateral gaps  481   a  and  481   c  are not equal in the initial position. 
       FIG. 5 a    illustrates a device where the rotor electrode further comprises two or more third lateral sections  5112  which lie on a third lateral baseline  593 . Each third lateral section  5112  is separated from the adjacent third lateral section  5112  on the third lateral baseline  593  by a third lateral gap  583 . 
     A second stator electrode  522  extends from the edge of the stator  52  toward the rotor  51  in the rotor-stator gap. The rotor electrode  511  and the second stator electrode  522  are adjacent and substantially parallel to each other in the rotor-stator gap. 
     The second stator electrode  522  is a meandering electrode which comprises two or more fourth lateral sections  5221  which lie on a fourth lateral baseline  594 . Each fourth lateral section  5221  is separated from the adjacent fourth lateral section  5221  on the fourth lateral baseline  594  by a fourth lateral gap  584 . The second stator electrode is a folded beam with a serpentine shape. 
     The first lateral baseline  591  lies between the second lateral baseline  592  and the third lateral baseline  593 . The third lateral baseline  593  lies between the first lateral baseline  591  and the fourth lateral baseline  594 . 
     Each third lateral gap  583  is adjacent to one of the fourth lateral gaps  584 . Each third lateral gap  583  is at least partially aligned with said fourth lateral gap  584  in the transversal direction. The lateral widths of all third and fourth lateral gaps  583 / 584  are equal to the lateral widths of the first and second lateral gaps  581 / 582 . The widths of all of the two or more first, second, third and fourth second lateral sections  5111 / 5211 / 5112 / 5221  are also equal. 
     Each connecting structure on the rotor electrode in  FIG. 5 a    comprises two transversal sections such as  5131 , attached to the ends of the adjacent first lateral sections  5111 . Each connecting structure on the rotor electrode also comprises a third lateral section  5112  which extends between the two transversal sections  5131 . The connecting structures on the first stator electrode  521  could be the same as in  FIG. 2 a   , and similar connecting structures could be employed in the second stator electrode  522 . However,  FIG. 5 a    illustrates electrodes where the connecting structures on the first and second stator electrodes comprise two transversal sections (such as  5231  and  5232 ) joined together by additional lateral sections (such as  5212  and  5222 ). 
     The lateral widths of these additional lateral sections may be equal to the lateral widths of the first, second, third and fourth lateral sections. Furthermore, the transversal lengths of the transversal sections  5131 ,  5231  and  5232  may be equal to the lateral widths of all lateral sections. This yield the square-shaped meander shown in  FIG. 5 a   , where the gaps between all lateral sections have the same width. 
     As in  FIG. 2 a   , each first lateral gap  581  in  FIG. 5 a    is at least partially aligned with a second lateral gap  582  in the initial position. Furthermore, each third lateral gap  583  is at least partly aligned with a fourth lateral gap  584  in the initial position. Each of these alignments could be complete, as in  FIG. 2 c    or  3   c , or partial as in  FIG. 2 a   -or  2   c.    
     As before, in partial alignment each first lateral gap  581  in  FIG. 5 a    is laterally offset from the corresponding second lateral gap  582  by the same lateral offset distance O. Furthermore, each third lateral gap  583  may be laterally offset from the corresponding fourth lateral gap  584  by the same lateral offset distance O. In full alignment, each third lateral gap  583  is fully aligned with each fourth lateral gap  584  in the initial position, and each first lateral gap  581  is fully aligned with each second lateral gap  582 . 
     The part of the rotor/stator electrodes which is closest to the edge of the rotor/stator may be called a base section, as mentioned above.  FIG. 5 a    illustrates base sections  5113 ,  5213  and  5223  which are longer than the first ( 5111 ), second ( 5211 ), third ( 5111 ) and fourth ( 5221 ) lateral sections. 
       FIG. 5 b    illustrates an alternative configuration where lateral widths of the first ( 5111 ), second ( 5211 ), third ( 5111 ) and fourth ( 5221 ) lateral sections are all equal, but the transversal lengths of the transversal sections  5131 ,  5231  and  5232  are greater than the lateral widths of the lateral sections. This yields the rectangle-shaped meander illustrated in the figure. The embodiments illustrated in  FIGS. 5 a  and 5 b    could also be combined, for example so that the transversal sections on the rotor electrode are longer than the transversal sections on the stator electrode, or vice versa. 
     When the meander pattern of the first stator electrode  521  is aligned with the meander pattern of the second stator electrode  522  in the transversal direction as  FIGS. 5 a  and 5 b    illustrates, both sides  5111 / 5112  of the meandering rotor electrode will contribute to the main capacitance between the rotor and stator electrodes. Furthermore, with the square- or rectangular-shaped meanders illustrated in these figures, a portion of the stray capacitance (the portion which corresponds to the capacitance arrows which are parallel to the y-axis in  FIG. 3 e   ) will exhibit a linear dependence on displacement. The number of rotor and stator electrodes could be increased further, and the meander pattern of all additional rotor and stator electrodes may be fully aligned with the illustrated rotor and stator electrodes in the transversal direction. Small offsets in the additional rotor/stator electrode meanders (in relation to the illustrated meanders) are also possible. In any embodiment of this disclosure, the microelectromechanical device may comprise a set of meandering rotor electrodes which extend from the edge of the rotor toward the stator in the rotor-stator gap, and a corresponding set of meandering stator electrodes which extend from the edge of the stator toward the rotor in the rotor-stator gap. 
     The set of meandering rotor electrodes may be interdigitated with the set of meandering stator electrodes. The transversal distance from each rotor electrode to the two adjacent stator electrodes may be equal. In other words, the transversal distance between baselines  591  and  592  may be equal to the transversal distance between baselines  593  and  594  in  FIG. 5 a   , and baselines  595  and  596  may be separated by the same transversal distance from the baselines of the next rotor electrodes (which are not illustrated in the figure). 
     Alternatively, the rotor and stator electrodes may be organized pairwise so that a first transversal distance from each rotor electrode to the stator electrode on one side (for example to the electrode below, i.e. the distance between  591  and  592  in  FIG. 5 a   ) is L 1 , and a second transversal distance from the same rotor electrode to the stator electrode on the other side (above, i.e. the distance between  593  and  594 ) is L 2 . The distance L 1  may differ from L 2 , but each rotor electrode may be separated from the adjacent stator electrodes by the same first and second transversal distances L 1  and L 2 . 
     In all embodiments presented in this disclosure, meandering rotor and stator electrodes comprise lateral sections separated by lateral gaps. In some embodiments, the lateral sections of the rotor electrode are partially aligned with the lateral sections of the stator electrode in the initial position, and their degree of alignment increases when the rotor is displaced. The capacitance between the rotor and stator electrode then also increases as a function of displacement. In other embodiments, the lateral sections of the rotor electrode are fully aligned with the lateral sections of the stator electrode in the initial position, and their degree of alignment decreases when the rotor is displaced. The capacitance between the rotor and stator electrode then also decreases as a function of displacement.