Abstract:
A capacitive encoder includes a signal-balanced shield electrode configuration that does not require electrical ground connection or active sensing and control in order to maintain the shield electrode(s) at a sufficiently constant voltage during capacitive position measurements. The shield electrode configuration is positioned in a capacitive coupling gap between transmitter electrodes and receiver electrodes during operation. The shield electrode configuration is patterned in a manner that complements the layout of the transmitter electrodes, such that the shield electrode configuration inherently floats at a nominally constant electrical potential when coupled to the signals present on the transmitter electrodes. The resulting capacitive encoder is thus more economical to build, convenient to install, and reliable during operation than capacitive encoders which use an electrical connection, compensation drive circuitry, or grounding in order to control the potential of a shield member that operates at a potential that is not inherently constant.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates generally to displacement sensing capacitive encoders, and more particularly to capacitive encoders including a scale having signal-balanced shield electrode configuration that does not require an electrical connection or grounding of the shield electrode, in order to provide low cost, reliable, and high accuracy displacement sensing.  
       BACKGROUND OF THE INVENTION  
       [0002]     Numerous capacitance-type measuring devices for making linear and angular displacement or position measurements have been developed wherein two members that are fixed relative to each other include respective capacitive electrodes that are capacitively coupled between the two support members and a third member is relatively movable between the two members to alter their capacitive coupling. The third member alters their capacitive coupling in a manner corresponding to the position of the third member relative to the first two members. The capacitive coupling affects one or more signals used to determine the position of the third member relative to the first two members. In a number of such measuring devices, the capacitive coupling, that is, the capacitance, is sensed by applying a plurality of temporally phase-shifted periodic signals to a plurality of capacitive transmitter electrodes on one of the first two members and measuring the relative phase shift of the one or more “summed” signals present on one or more capacitive receiver electrodes on the other one of the first two members, the relative phase shift of the one or more “summed” signals resulting from the effect of the third member on the capacitive coupling between the electrodes first two members. Such capacitance-type measuring devices have a broad range of applications including motion control systems, measuring devices, and the like.  
         [0003]     In a number of such capacitance-type measuring devices the third member includes one or more conductive electrodes that are effectively grounded to act as a “shield electrode” which affects or blocks the capacitive coupling between the first two members. For example, in U.S. Pat. No. 3,517,282, to Miller; U.S. Pat. No. 3,702,957, to Wolfendale; U.S. Pat. No. 3,732,553, to Hardway; U.S. Pat. No. 3,784,897, to Norrie; and U.S. Pat. No. 5,537,109, to Dowd, each of which is incorporated herein by reference for all of its relevant teachings, the third member includes one or more shield electrodes that are grounded to circuit or earth ground by electrical connection through a wire and/or wiper. Alternatively, U.S. Pat. No. 4,449,179, to Meyer, which is incorporated herein by reference for all of its relevant teachings, discloses grounding a “belt” shield electrode to earth ground (called “mass potential”) by electrical connection, or by suitable capacitive coupling to an earth ground member.  
         [0004]     In a further alternative, U.S. Pat. No. 3,668,672, to Parnell, which is incorporated herein by reference for all of its relevant teachings, discloses connecting a shield electrode to a receiver electrode through an amplifier in such a way that the shield electrode is maintained at the same signal level as the receiving electrode. U.S. Pat. No. 6,492,911, to Netzer, incorporated herein by reference in its entirety, provides an overview that further discusses numerous configurations for such capacitance-type measuring devices and their disadvantages, including some of the configurations included in the foregoing incorporated references. The &#39;911 patent further discloses and claims a configuration that capacitively senses a signal on an electrode on the third member and, after amplification, feeds back a capacitively coupled signal of the opposite polarity to the shield electrode in order to actively control its voltage or potential.  
       SUMMARY OF THE INVENTION  
       [0005]     It should be appreciated that the electrical connections and or capacitive coupling provided by the embodiments indicated above may be inconvenient, unreliable, or “insufficient” to effectively and fully ground the shield electrode in a variety of desirable capacitance-type measuring device configurations and applications. Furthermore, the amplifier circuitry indicated above that feeds back a capacitively coupled signal of the opposite polarity to the shield electrode in order to actively control its voltage or potential introduces additional complexity and cost and may also be inconvenient, unreliable, or “insufficient” to effectively and fully control the voltage or potential of the shield electrode in a variety of desirable capacitance-type measuring device configurations and applications. Thus, a capacitance-type measuring device that can overcome the foregoing problems and disadvantages, individually or in combination, is desirable.  
         [0006]     The present invention is directed to providing a capacitive encoder that overcomes the foregoing and other disadvantages. The capacitive encoder includes two members that are fixed relative to each other and that include respective capacitive electrodes that are capacitively coupled between the two members. A third member includes a shield electrode that is relatively movable between the two members to alter their capacitive coupling in a manner corresponding to the position of the third member relative to the first two members. The capacitive coupling affects one or more signals used to determine the position of the third member relative to the first two members. In general, to provide a relatively simple device that provides reliable and accurate operation, it is desirable that the shield electrode has a constant or standard voltage, at least at the time of measuring the one or more signals used to determine the position. Furthermore, it is desirable to avoid reliance on inconvenient and/or unreliable electrical connections and/or complex active circuits in order to maintain the shield electrode at a constant or standard voltage. Thus, more specifically, the present invention is directed to a capacitive encoder including a signal-balanced shield electrode configuration that does not require electrical ground connection or active sensing and control of its shield electrode(s) voltage in order to maintain the shield electrode(s) at a sufficiently constant voltage or potential to achieve a desired level of accuracy during capacitive displacement or position measurements.  
         [0007]     Alternatively, rather than replacing or eliminating the previously outlined electrical ground connection or active sensing and control of a shield electrode(s) voltage, the present invention can be used to maintain the shield electrode(s) at an approximately constant voltage or potential during capacitive displacement or position measurements in combination with such electrical ground connection or active sensing and control configurations and methods, in order to provide an additional measure of signal stability reliability, and/or to relatively reduce the complexity and/or operational requirements of the electrical ground connection or active sensing and control elements. In either case, the present invention provides a number of desirable features, including relatively reduced cost, increased reliability, and high accuracy displacement sensing.  
         [0008]     A capacitive encoder including a signal-balanced shield electrode configuration is disclosed. In accordance with one aspect of the invention, the signal-balanced shield electrode is patterned in a manner that complements the layout of the transmitter electrodes of the capacitive encoder, such that the signal-balanced shield electrode inherently or passively floats at a nominally constant electrical potential or voltage when coupled to the signals present on the transmitter electrodes. The resulting capacitive encoder is thus more economical to build, convenient to install, and reliable during operation than capacitive encoders which use an electrical connection, compensation drive circuitry, or grounding in order to control the voltage or potential of a shield member that operates at a voltage or potential that is not inherently constant.  
         [0009]     In accordance with a further aspect of the invention, the signal-balanced shield electrode modulates the capacitive coupling between a plurality of capacitive encoder transmitter electrodes and at least one capacitive encoder receiver electrode(s), the modulation being a function of the displacement or position of the shield electrode along a measuring axis relative to the transmitter and receiver electrodes.  
         [0010]     In accordance with a further aspect of the invention, at least one signal arising from a receiver electrode depends on the modulated capacitive coupling.  
         [0011]     In accordance with a separate aspect of the invention, the signal-balancing shield electrode floats electrically.  
         [0012]     In accordance with a further aspect of the invention, the signal-balancing shield electrode is configured and/or mounted in a manner that relatively reduces its capacitive coupling to an external member that is mechanically coupled to move the signal-balancing shield electrode.  
         [0013]     In accordance with a separate aspect of the invention, at least two respective signals arising from at least two receiver electrodes are provided for input to a differential signal processing circuit, the least two respective signals depending on the modulated capacitive coupling.  
         [0014]     In accordance with a separate aspect of the invention, at least two respective signals arising from at least two receiver electrodes provide quadrature signals.  
         [0015]     In accordance with a separate aspect of the invention, the signal-balanced shield electrode modulates the capacitive coupling between a plurality of capacitive encoder transmitter electrodes and at least one capacitive encoder receiver electrode(s) such that the modulation includes an approximately sinusoidal component as a function of the displacement or position of the shield electrode along a measuring axis relative to the transmitter and receiver electrodes.  
         [0016]     In accordance with a separate aspect of the invention, the signal-balanced shield electrode includes a configuration that is periodic along a measuring axis direction according to a shield electrode spatial wavelength or pitch.  
         [0017]     In accordance with a further aspect of the invention, at least one respective receiver electrode has a dimension along the measuring axis direction that corresponds to an integer number of the shield electrode spatial wavelength or pitch.  
         [0018]     In accordance with a further aspect of the invention, the signal-balanced shield electrode configuration that is periodic along a measuring axis direction includes at least one electrode boundary that meanders in a periodic fashion along the measuring axis direction.  
         [0019]     In accordance with a further aspect of the invention, the at least one electrode boundary that meanders in a periodic fashion along the measuring axis direction creates an overlapping shield area for at least one receiver electrode, the overlapping shield area periodically spatially modulated along the measuring axis direction based on the periodic meander of the at least one boundary.  
         [0020]     In accordance with a further aspect of the invention, a plurality of transmitter electrodes at least approximately span the width of the entire shield electrode along a direction perpendicular to the measuring axis direction, regardless of the periodic meander of the at least one boundary, such that the overlapping shield area for each of the plurality of transmitter electrodes is constant, regardless of the periodic meander and regardless of the relative position of the transmitter electrodes and the shield electrode along the measuring axis direction.  
         [0021]     In accordance with a separate aspect of the invention, a plurality of respective transmitter electrodes are operable to provide a plurality of respective transmitter signals, the plurality of respective transmitter electrodes form a group that is repeated along the measuring axis direction according to the shield electrode spatial wavelength or pitch.  
         [0022]     In accordance with a separate aspect of the invention, the measuring axis direction follows a path that is one of straight, circular, and cylindrical.  
         [0023]     In accordance with a separate aspect of the invention, the capacitive encoder includes at least two respective signal-balanced shield electrodes patterned in a manner that complements the layout of respective transmitter electrodes of the capacitive encoder, such that each signal-balanced shield electrode inherently or passively floats at a nominally constant electrical potential or voltage when coupled to the signals present on the transmitter electrodes and each respective signal-balanced shield electrode includes a configuration that is periodic along a measuring axis direction according to a unique respective shield electrode spatial wavelength or pitch such that the capacitive encoder is usable to determine an absolute position over at least a first range of positions based on at least two respective signals modulated according to at least two unique respective shield electrode spatial wavelengths or pitches.  
         [0024]     In various exemplary embodiments, at least one pair of transmitter electrodes provides at least one pair of changing input voltage signals having equal and opposite magnitudes. In various exemplary embodiments, each such signal pair is a pair of sinusoidal AC voltages having 180 degrees temporal phase difference. In various exemplary embodiments, the signal-balanced shield electrode is configured such that it overlaps each electrode of such electrode pairs so as to provide the same net capacitive coupling area to each electrode, regardless of the relative position of the shield electrode and the pair of electrodes along the measuring axis direction. Thus, in such embodiments, the shield electrode is always equally capacitively coupled to input voltage signals having equal and opposite magnitudes, and accordingly it inherently or passively floats at a nominally constant DC voltage determined by the transmitter signals. The DC voltage determined by the transmitter signals may be “zero volts” electrical potential or a DC voltage that is the same as the circuit ground potential in various exemplary embodiments. Thus, the shield electrode is effectively maintained at a constant DC potential, without the use of a ground connection (although, as previously discussed, a redundant active or passive ground connection is also within the scope of this invention.)  
         [0025]     Hence, the invention overcomes the disadvantages of prior art capacitive displacement sensing devices that use electrically connected, externally coupled, or actively controlled shield electrodes, in order to provide either rotary or linear measurements with sensing systems that are more convenient, economical, reliable and compact. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0026]     The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same become better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein:  
         [0027]      FIG. 1  is an exploded isometric view of a first exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in a capacitive encoder according to this invention;  
         [0028]      FIG. 2  is a plan view of a receiver electrode configuration usable in a second exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0029]      FIG. 3  is a plan view of a shield electrode configuration usable in the second exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0030]      FIG. 4  is a plan view of a transmitter electrode configuration usable in the second exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0031]      FIG. 5  is a plan view showing the alignment of the receiver electrode configuration of  FIG. 2 , the shield electrode configuration of  FIG. 3 , and the transmitter electrode configuration of  FIG. 4 , for the second exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0032]      FIG. 6  is an exploded view of a third exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in a capacitive encoder according to this invention;  
         [0033]      FIG. 7  is a plan view showing the alignment of the receiver electrode configuration, the shield electrode configuration and the transmitter electrode configuration of  FIG. 6 , for the third exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0034]      FIG. 8  is an exploded isometric view of a fourth exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in a rotary capacitive encoder according to this invention;  
         [0035]      FIG. 9  is a plan view showing the alignment of the shield electrode configuration and the transmitter electrode configuration of  FIG. 8 , for the fourth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0036]      FIG. 10  is a plan view of a receiver electrode configuration usable in a fifth exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in an absolute rotary capacitive encoder according to this invention;  
         [0037]      FIG. 11  is a plan view of a transmitter electrode configuration usable in the fifth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0038]      FIG. 12  is a plan view of a shield electrode configuration usable in the fifth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0039]      FIG. 13  is a plan view showing the alignment of the receiver electrode configuration of  FIG. 10 , the shield electrode configuration of  FIG. 11 , and the central electrodes of the transmitter electrode configuration of  FIG. 12 , for the fifth exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in an absolute rotary capacitive encoder according to this invention;  
         [0040]      FIG. 14  is an exploded isometric view of a sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention that is usable in a rotary capacitive encoder according to this invention;  
         [0041]      FIG. 15  is a plan view showing the receiver electrode configuration of  FIG. 14 , for the sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0042]      FIG. 16  is a plan view showing the shield electrode configuration of  FIG. 14 , and its alignment with the receiver electrode configuration of  FIG. 15 , for the sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0043]      FIG. 17  is a plan view showing the transmitter electrode configuration of  FIG. 14 , for the sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0044]      FIG. 18  is a plan view showing the alignment of the transmitter electrode configuration of  FIG. 17 , the shield electrode configuration of  FIG. 16 , and areas where the transmitter electrode configuration is capacitively coupled to the receiver electrode configuration of  FIG. 15 , for the sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention;  
         [0045]      FIG. 19  is a side cross-sectional view through an exemplary rotary capacitive encoder assembly according to this invention, including the elements shown in  
         [0046]      FIGS. 14-18  for the sixth exemplary embodiment of a signal-balanced electrode configuration according to this invention; and  
         [0047]      FIG. 20  is an exploded view of one exemplary cylindrical rotary capacitive encoder assembly according to this invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0048]      FIG. 1  shows a generic first exemplary embodiment of a signal-balanced electrode configuration  100  according to this invention that is usable in a capacitive encoder according to this invention. As shown in  FIG. 1 , the first exemplary embodiment of a signal-balanced electrode configuration  100  includes a transmitter electrode configuration  120  carried on a transmitter electrode member  139 , a shield electrode configuration  140  carried on a shield electrode member  159 , and a receiver electrode configuration  160  carried on a receiver electrode member  179 . The shield electrode member  159  acts as the scale for displacement measurement, and various shield electrode configurations, shield electrode members and/or shield electrodes may also be referred to as scales herein. In various embodiments, the shield electrode configuration  140  should be understood to comprise a segment of an arbitrarily longer shield electrode configuration  140 .  
         [0049]     Also shown in  FIG. 1  are a measuring axis/direction  80  and an X-Y-Z orthogonal coordinate axes, for convenience of description. In general, in the following discussions, the X-axis is aligned with the measuring axis/direction  80 , the Z-axis is perpendicular to the measuring axis/direction  80  and generally normal to the surfaces of the various electrodes described herein, and the Y-axis is perpendicular to the measuring axis/direction  80  and to the direction normal to the surfaces of the various electrodes described herein. At various locations along the measuring axis/direction  80 , the Y-axis is generally parallel to the surfaces of the various electrodes described herein. For convenience of description, it is useful to define respective alignment/centerlines  121 ,  141  and  161  for the transmitter electrode configuration  120 , the shield electrode configuration  140  and the receiver electrode configuration  160 , respectively, as described in greater detail below. For convenience of description, it is also useful to define respective first and second capacitive coupling zones  84  and  85  extending along the measuring axis/direction  80  and having respective widths extending along the Y-axis on opposite sides of the alignment/centerlines  121 ,  141  and  161  as shown in  FIG. 1 .  
         [0050]     In the exemplary embodiment shown in  FIG. 1 , the shield electrode configuration  140  includes a shield electrode  142  that meanders to form a periodic pattern extending along the measuring axis/direction  80 . The periodic pattern has a wavelength or pitch P, which is also indicated by the dimension  146  in  FIG. 1 , along the measuring axis/direction  80 . The shield electrode  142  has a first shield electrode border  143  and a second shield electrode border  145  that are separated along the Y-axis direction by a constant effective shield electrode width  156 . The shield electrode  142  also has a shield electrode span width  157  along the Y-axis direction that encompasses the extents of the shield electrode and is conveniently made constant along the measuring axis/direction  80  as shown in  FIG. 1 . For convenience of description, it is useful to define respective first and second shield electrode portions  142 A and  142 B that extend along the measuring axis/direction  80  and define first and second shield electrode coupling tracks  154  and  155 , which fall within the first and second capacitive coupling zones  84  and  85 , respectively. In the exemplary embodiment shown in  FIG. 1 , first and second shield electrode portions  142 A and  142 B conveniently have approximately equal areas and approximately equal respective portion span widths, which are each one half of the shield electrode span width  157 , along the Y-axis direction in the respective first and second shield electrode coupling tracks  154  and  155 .  
         [0051]     In the exemplary embodiment shown in  FIG. 1 , the transmitter electrode configuration  120  includes a first transmitter electrode  122  having first transmitter electrode connection  122 C and a second transmitter electrode  123  having second transmitter electrode connection  123 C. The first and second transmitter electrodes  122  and  123  are separated by an insulating gap along the Y-axis direction.  
         [0052]     The first and second transmitter electrodes  122  and  123  have respective lengths  126  and  127  that are equal to each other and equal to 2P in the exemplary embodiment shown in  FIG. 1 . In general, the lengths of the transmitter electrodes are also made equal to or greater than a receiver electrode group length  177  of the receiver electrode configuration  160  along the measuring axis/direction  80 , as described further below. More generally, in various exemplary embodiments, the lengths of the transmitter electrodes are equal to each other and to an integer number times the wavelength P. It should be appreciated that when the lengths of the transmitter electrodes are made equal to each other and to an integer number times the wavelength P, and when there is an approximately constant operating gap along the Z-axis direction between transmitter electrode configuration  120  and the shield electrode configuration  140 , the previously described meandering shield electrode  142  will capacitively couple approximately equally to the first and second transmitter electrodes  122  and  123 , regardless of its relative position along the measuring axis/direction  80 , providing one aspect of a signal-balanced electrode configuration according to the principles of this invention.  
         [0053]     For convenience of description, it is useful to define a first transmitter electrode coupling track  134  and a second transmitter electrode coupling track  135 , which fall within the first and second capacitive coupling zones  84  and  85 , respectively. In the exemplary embodiment shown in  FIG. 1 , the first transmitter electrode  122  and the second transmitter electrode  123  conveniently have approximately equal areas and approximately equal span widths along the Y-axis direction in the respective first and second transmitter electrode coupling tracks  134  and  135 .  
         [0054]     In the exemplary embodiment shown in  FIG. 1 , the first and second transmitter electrodes  122  and  123  also have equal areas outside the first and second transmitter electrode coupling tracks  134  and  135 , which tends to help balance various common mode errors that may arise in the measurement signals provided using the signal-balanced electrode configuration  100 . However, in various other embodiments, provided that the shield electrode  142  will capacitively couple approximately equally to the first and second transmitter electrodes  122  and  123 , regardless of its relative position along the measuring axis/direction  80 , it is not strictly necessary that the first and second transmitter electrodes  122  and  123  also have equal areas.  
         [0055]     In general, a combined transmitter electrode span width  137  is advantageously made approximately the equal to the shield electrode span width  157 , which tends to provide a compact transducer while also providing a maximum measurement signal amplitude for the embodiment shown in  FIG. 1 . In practice, it is also advantageous in various exemplary embodiments to provide a combined transmitter electrode span width  137  that is slightly greater than the shield electrode span width  157  and less than the width of the receiver electrodes  162  and  163  along the Y-axis, such that minor variations in the alignment of the various electrode members does not alter the overlapping capacitive coupling area between either of the first or second transmitter electrodes  122  or  123  and the various other transducer electrodes, in order to reduce potential signal error contributions due to the minor misalignments.  
         [0056]     As shown in  FIG. 1 , the receiver electrode configuration  160  includes a first receiver electrode  162  having a first receiver electrode connection  162 C and a second receiver electrode  163  having a second receiver electrode connection  163 C. For convenience of description, it is useful to define a respective first portion  162 A and second portion  162 B of the receiver electrode  162  and a respective first portion  163 A and second portion  163 B of the receiver electrode  163 .  
         [0057]     For convenience of description, it is useful to define first and second receiver electrode coupling tracks  174  and  175  which fall within the first and second capacitive coupling zones  84  and  85 , respectively. In the exemplary embodiment shown in  FIG. 1 , the first portion  162 A and second portion  162 B conveniently have approximately equal areas and approximately equal respective span widths along the Y-axis direction in the respective first and second receiver electrode coupling tracks  174  and  175 . Similarly, the first portion  163 A and second portion  163 B conveniently have approximately equal areas and approximately equal span widths along the Y-axis direction in the respective first and second receiver electrode coupling tracks  174  and  175 . In various exemplary embodiments, the first and second receiver electrodes  162  and  163  each have a width along the Y-axis that exceeds the shield electrode span width  157 , in order to encompass the extents of the shield electrode along the Y-axis when the receiver electrode configuration  160  and shield electrode configuration  140  are operably aligned.  
         [0058]     The first portions  162 A and  163 A and the second portions  162 B and  163 B of the first and second receiver electrodes  162  and  163  all have equal lengths  172  and  173  along the measuring axis/direction  80  (the X-axis direction). In the exemplary embodiment shown in  FIG. 1 , the lengths  172  and  173  are approximately one half of the wavelength P. The first and second receiver electrodes  162  and  163  are also offset from each other along the measuring axis/direction  80  by the offset dimension  166 , which is three-quarters of the wavelength P in the exemplary embodiment shown in  FIG. 1 , which leads to the production of quadrature signals on the first and second receiver electrodes  162  and  163 , as described further below. A receiver electrode group length  177  along the X-axis direction is defined by the combined extents of the receiver electrodes  162  and  163  along the X-axis direction.  
         [0059]     In operation, the transmitter electrode member  139 , the shield electrode member  159 , and the receiver electrode member  179  are arranged such that the alignment/centerlines  121 ,  141  and  161  are generally aligned as indicated by the dashed arrows  91 - 94  in  FIG. 1 , and the transmitter electrode configuration  120  and the receiver electrode configuration  160  are positioned along the measuring axis/direction  80  such that they are centered relative to each other (or as otherwise appropriate according to their mutual design in various specific embodiments.) The transmitter electrode member  139  and the receiver electrode member  179  are arranged in a fixed relationship with an operable and uniform capacitive gap between them along the Z-axis, the capacitive gap being somewhat greater than the thickness of the shield electrode member  159  along the Z-axis such that the shield electrode member  159  may be moved along the measuring axis/direction  80  in the capacitive gap.  
         [0060]     It should be appreciated that during operation, in order for the shield electrode  142  to capacitively couple approximately equally to the first and second transmitter electrodes  122  and  123  regardless of its relative position along the measuring axis/direction  80  according to one aspect of this invention, and to provide the best practical accuracy, the shield electrode member  159  should be guided along the measuring axis/direction  80  such that the shield electrode  142  is maintained with the most uniform gap and alignment that is practical and/or economical relative to the transmitter electrodes  122  and  123 .  
         [0061]     It should be appreciated that when the operable capacitive gap between the transmitter electrode member  139  and the receiver electrode member  179  is relatively larger, the measurement signals provided using the signal-balanced electrode configuration  100  will exhibit relatively reduced errors due to minor variation in the alignment and guiding of the shield electrode member  159  in that gap. However, the magnitude of the measurement signals will also be relatively reduced at larger gaps. Conversely, when the operable capacitive gap is relatively smaller, the measurement signals provided using the signal-balanced electrode configuration  100  will exhibit relatively larger errors due to minor variation in the alignment and guiding of the shield electrode member  159  in that gap. However, the magnitude of the measurement signals will also be relatively increased at smaller gaps. The operable gap that establishes the best tradeoff between these effects can be established by analysis and/or confirmed experiment for any particular transducer including a signal-balanced electrode configuration according to this invention.  
         [0062]     As previously mentioned, when there is an approximately uniform operating gap along the Z-axis direction between the transmitter electrode configuration  120  and the shield electrode configuration  140 , the previously described shield electrode configuration  140  will capacitively couple approximately equally to the first and second transmitter electrodes  122  and  123 , regardless of their relative position along the measuring axis/direction  80 , providing one aspect a signal-balanced electrode configuration according to the principles of this invention. Thus, in operation, when respective changing voltage signals of equal amplitude and opposite polarity are connected through the first and second transmitter electrodes connections  122 C and  123 C and provided on the first and second transmitter electrodes  122  and  123 , their respective contributions to the response voltage arising on the shield electrode will likewise be of equal amplitude and opposite polarity. Accordingly, the signals thus balance each other to provide no net change in the voltage of the electrically floating shield electrode  142 , according to the principles of this invention. In various exemplary embodiments, the shield electrode  142  will thus be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments.  
         [0063]     It should be appreciated that according to the principles and configurations disclosed herein, when a shield electrode maintains no net change in its voltage, at least at each time that the transducer provides a displacement measurement signal, then the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0064]     Regarding another aspect of operation of the signal-balanced electrode configuration  100 , when there is an approximately uniform operating gap along the Z-axis direction between the previously described transmitter electrode configuration  120  and receiver electrode configuration  160 , in the hypothetical absence of the shield electrode  142  each of the first and second transmitter electrodes  122  and  123  will capacitively couple approximately equally to the first and second receiver electrodes  162  and  163 . Thus, when respective voltage signals of equal and opposite polarity are provided on the first and second transmitter electrodes  122  and  123 , their respective contributions to the voltage arising on either of the respective first and second transmitter electrodes  162  and  163  will likewise be of equal and opposite polarity, thus balancing each other to provide no net change in the respective signals provided by the respective first and second receiver electrodes  162  and  163 . In various exemplary embodiments, the signals from the first and second receiver electrodes  162  and  163  would thus be constant at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, in the hypothetical absence of the shield electrode  142 . This tends to reduce or eliminate certain signal errors that may otherwise arise in the measurement signals provided using various signal-balanced electrode configurations according to this invention.  
         [0065]     Regarding another aspect of operation of the signal-balanced electrode configuration  100 , as shown in  FIG. 1  the respective dashed phantom outlines  182  and  183  represent the projection of the areas of first and second receiver electrodes  162  and  163 , respectively, onto the shield electrode element  159 . The shaded portions of the dashed phantom outlines  182  and  183  represent the areas where the shield electrode  142  effectively screens or blocks the first and second receiver electrodes  162  and  163  from capacitively coupling to the first and second transmitter electrode elements  122  and  123 .  
         [0066]     Accordingly, the dashed phantom outlines  174 A- 174 C represent the remaining areas where the first transmitter electrode  122  capacitively couples to the first and second receiver electrodes  162  and  163 , and the dashed phantom outlines  175 A and  175 B represent the remaining areas where the second transmitter electrode  123  capacitively couples to the first and second receiver electrodes  162  and  163 . For the relative position of the shield electrode member shown in  FIG. 1 , it can be seen that the corresponding capacitively coupled areas  174 A and  175 A on the first receiver electrode  162  are approximately equal, thus when respective voltage signals of equal and opposite polarity are provided on the first and second transmitter electrodes  122  and  123  in operation, the capacitive coupling to the capacitively coupled areas  174 A and  175 B will provide approximately equal and opposite signal contributions to the first receiver electrode  162 , corresponding to an output signal of approximately zero volts at the first receiver electrode connection  162 C. In contrast, for the relative position of the shield electrode member shown in  FIG. 1 , it can be seen that the corresponding capacitively coupled area  175 BA is approximately 3 times the area of the capacitively coupled area [ 174 B+ 174 C] on the second receiver electrode  163 . Thus, when respective voltage signals of equal and opposite polarity are provided on the first and second transmitter electrodes  122  and  123  in operation, the capacitive coupling to the capacitively coupled areas [ 174 B+ 174 C] and  175 B will provide an output signal at the second receiver electrode connection  163 C that has a significant voltage magnitude and a polarity corresponding to the signal polarity provided on the more strongly coupled second transmitter electrode  123 .  
         [0067]     It should be appreciated that as the shield electrode member  159  is displaced to the left, for example, along the measuring axis/direction  80 , the “unscreened” or “unblocked” capacitive coupling from each of the first and second transmitter electrodes  122  and  123  to the second receiver electrode  163  will vary to give rise to a changing voltage output signal at the second receiver electrode connection  163 C that has a signal amplitude and polarity that varies as a function of the displacement. In one exemplary embodiment, by using one of the transmitter input signals as a reference signal, the peak amplitude and polarity receiver electrode output signals at a particular time or phase relative to the reference signal may be captured and/or measured by known circuit techniques to provide a position-dependent voltage signal that varies in between a positive and negative value. The position-dependent signal will be periodic with displacement, in correspondence with the wavelength P of the periodically meandering shield electrode  142 . Due to the ¾*P offset of the first receiver electrode  162  to the right of the second receiver electrode  163 , the position-dependent signal similarly derived from the first receiver electrode connection  162 C will follow the spatially periodic position-dependent signal of the second receiver electrode connection  163 C with a displacement lag of ¼*p, as the shield electrode member  159  is displaced to the left. Such a relationship between the signals is known as a “quadrature” relationship, as generally known to one of ordinary skill in the art. It should be appreciated that in embodiments where the meandering pattern of the shield electrode  142  is made sinusoidal, the two position-dependent signals will provide sinusoidal quadrature signals, which are advantageous for position interpolation within a given period P of the shield electrode, according to known techniques.  
         [0068]     The exemplary embodiment of the signal-balanced electrode configuration  100  shown in  FIG. 1  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  100  shown in  FIG. 1  may be conveniently and reliably operated with an electrically floating shield electrode  142 , if desired. The specific embodiment of the signal-balanced electrode configuration  100  shown in  FIG. 1  provides two periodic signals having a conventional quadrature relationship on the first and second receiver electrodes  122  and  123  as the shield electrode member  159  is displaced relative to the transmitter and receiver electrode members  139  and  179  along the measuring axis/direction  80 . Any one of a variety of known methods and circuits may be used for providing suitable transmitter signals and processing the resulting quadrature signals to determine desired relative displacement values for such a configuration.  
         [0069]     It should be appreciated that, provided that a shield electrode  142  will capacitively couple approximately equally to first and second transmitter electrodes  122  and  123  regardless of its relative position along the measuring axis/direction  80 , numerous alternative electrode configurations including either minor or substantial electrode variations are possible. As one simple example, the first and second receiver electrodes  162  and  163  may be repeated at integer wavelength spacings along the measuring axis/direction  80 , and the lengths of the first and second transmitter electrodes  122  and  123  increased accordingly, to provide increased signal strength. Furthermore, in addition to a planar/linear configuration, the components shown in  FIG. 1  may alternatively be understood to represent parts of a cylindrical encoder, where the measuring axis/direction  80  is a cylindrical or circular measuring axis/direction and the shield electrode configuration  140  represents a segment of an element that continues to form a partial or complete cylindrical configuration along the measuring axis/direction  80 . In such a case the X-axis is everywhere along a tangential direction, the Y-axis is parallel to the cylinder axis, and the Z-axis is everywhere in the radial direction. Thus, it will be understood that the configuration disclosed above is illustrative only, and not limiting.  
         [0070]      FIG. 2  shows a plan view of a receiver electrode configuration  260  usable in a second exemplary embodiment of a signal-balanced electrode configuration  200 , which is described further in  FIGS. 3-5 .  FIG. 2  shows the previously described X-axis, Y-axis, and measuring axis/direction  80 . For convenience of description, it is useful to define an alignment/centerline  261  for the electrode layout of the receiver electrode configuration  260 , as shown in  FIG. 2 . The receiver electrode configuration  260  is carried on a receiver electrode member  279  and includes first receiver electrode portions  262 A and  262 B that are electrically connected together by a first receiver electrode connection  262 C and a second receiver electrode  263  that has a second receiver electrode connection  263 C. The first receiver electrode portions  262 A and  262 B are separated from the second receiver electrode  263  along the Y-axis by the nominally equal gaps  269 A and  269 B, respectively, and have respective span widths  276 A and  276 B along the Y-axis direction that are conveniently made equal in the embodiment shown in  FIG. 2 . For convenience of description, it is useful to define first and second portions  263 A and  263 B of the second receiver electrode  263  that lie on opposite sides of the alignment/centerline  261  and have respective span widths along the Y-axis direction  278 A and  278 B that are equal. For convenience of description, it is useful to define first and second receiver electrode coupling tracks  274  and  275 , respectively, which lie symmetrically on opposite sides of the alignment/centerline  261  and fall within first and second capacitive coupling zone portions  284  and  285 , respectively (described further below.) The first receiver electrode coupling track  274  includes subtracks  274 ′ and  274 ″, which include the first receiver electrode portion  262 A and the first portion  263 A of the second receiver electrode  263 , respectively. The second receiver electrode coupling track  275  includes subtracks  275 ′ and  275 ″, which include the first receiver electrode portion  262 B and the second portion  263 B of the second receiver electrode  263 , respectively. The first receiver electrode portions  262 A and  262 B and the second receiver electrode  263  each have the same dimension along the X-axis direction, the electrode group length  277 , which is 4 times a wavelength P′ (described below) for the embodiment shown in  FIG. 2 .  
         [0071]      FIG. 3  is a plan view of a left end segment of a shield electrode configuration  240  usable in the second exemplary embodiment of a signal-balanced electrode configuration  200 , which is described further in  FIGS. 4-5 . In the exemplary embodiment shown in  FIG. 3 , the shield electrode configuration  240  is carried on the shield electrode member  259  and includes a shield electrode  242 . The shield electrode  242  has a first half  242 A and a second half  242 B that periodically merge at the regions  243  to electrically connect along an alignment/centerline  241 . The first and second halves  242 A and  242 B each meander in a periodic fashion along the measuring axis/direction  80  to form a periodic sinusoidal pattern extending along the measuring axis/direction  80 . The periodic pattern has a wavelength or pitch P′, which is also indicated by the dimension  246  in  FIG. 3 , along the measuring axis/direction  80 . The shield electrode first half  242 A has a first shield electrode border  243  and a second shield electrode border  245  that are separated along the Y-axis direction by a constant effective shield electrode half-width  256 . The shield electrode second half  242 B similarly has a first shield electrode border  243 ′ and a second shield electrode border  245 ′ that are separated along the Y-axis direction by the same constant effective shield electrode half-width  256 . It should be appreciated that the second shield electrode borders  245  and  245 ′ are “interrupted” by the previously described electrode-merging connections at each of the regions  243 . The shield electrode  242  also has a shield electrode span width  257  along the Y-axis direction that encompasses the extents of the shield electrode and is conveniently made constant along the measuring axis/direction  80  as shown in  FIG. 3 .  
         [0072]     In operation, the alignment/centerline  241  of the shield electrode configuration  240  is aligned with the alignment/centerline  261  of the receiver electrode configuration  260  such that the various portions of the shield electrode first half  242 A are aligned with the first receiver electrode coupling track  274 , the subtracks  274 ′ and  274 ″ and the gap  269 A and various portions of the shield electrode second half  242 B are aligned with the second receiver electrode coupling track  275 , the subtracks  275 ′ and  275 ″, and the gap  269 B, all approximately as shown in  FIG. 3 . Thus, it should be appreciated that the various Y-axis dimensions of the shield electrode configuration  240  are dimensioned relative to the various Y-axis dimensions of the receiver electrode configuration  260  such that the alignment/centerline  241  can be slightly misaligned along the Y-axis relative to the alignment/centerline  261  and the various capacitive coupling areas between the shield electrode configuration  240  and the receiver electrode configuration  260  will tend to be relatively unchanged by the slight misalignment. For larger misalignments, it should be appreciated that, relative to nominal alignment, capacitive coupling area lost or gained in the subtracks  274 ′ and  274 ″ due to a given lateral misalignment will tend to be oppositely and compensatingly gained or lost in the subtracks  275 ′ and  275 ″ for that same misalignment, due to the symmetrical configurations of the shield electrode configuration  240  and the receiver electrode configuration  260 . Furthermore, the effects of “roll” misalignment about an axis parallel to the measuring axis will also tend to affect the signals output on the receiver electrode connections  215 C and  216 C by similar amounts. Thus, the signal-balanced electrode configuration  200 , which is described further in  FIGS. 4-5 , provides a particularly robust design with respect to preserving measurement accuracy despite various alignment errors during assembly and operation.  
         [0073]      FIG. 4  is a plan view of a transmitter electrode configuration  220  usable in the second exemplary embodiment of a signal-balanced electrode configuration  200 , which is described further in  FIG. 5 . In the exemplary embodiment shown in  FIG. 4 , the transmitter electrode configuration  220  is carried on transmitter electrode member  239 , which may be a printed circuit board for example, carrying four transmitter electrode groups  210 A- 210 D. The first transmitter electrode group  210 A has first, second, third and fourth transmitter electrodes  222 A- 225 A, the second transmitter electrode group  210 B has first, second, third and fourth transmitter electrodes  222 B- 225 B, and so on, as shown in  FIG. 4 . The four transmitter electrode groups  210 A- 210 D have similar overall dimensions and are repeated periodically along the measuring axis/direction  80  according to transmitter electrode group pitch  216  which is equal to the wavelength P′. An overall transmitter electrode group length  227  is thus 4 times the wavelength P′ for the embodiment shown in  FIG. 4 . A surrounding circuit ground plane electrode  215  having a circuit ground plane electrode connection  215 C includes portions located adjacent to the end transmitter electrodes  222 A and  225 D, in order to make their operational capacitive coupling more similar to that of the interior transmitter electrodes, which are surrounded by neighboring transmitter electrodes on both sides along the measuring axis/direction  80 .  
         [0074]     Within each of the transmitter electrode groups  210 “X”, as exemplified by the transmitter electrode group  210 A in  FIG. 4 , each of the transmitter electrodes  222 X- 225 X have the same X-axis dimensions, and conveniently have the same Y-axis dimension (although the same Y-axis dimension is not a requirement in various other exemplary embodiments.) Each of the transmitter electrodes  222 X- 225 X are fabricated on a first side of an insulating substrate, such as a printed circuit board substrate. They are separated by similar insulating gaps  229  along the measuring axis/direction  80 , which are advantageously as narrow as practical in various exemplary embodiments. Thus, the transmitter electrodes  222 X- 225 X are of equal sizes and are uniformly distributed within the transmitter electrode group pitch  216  along the measuring axis/direction  80 .  
         [0075]     The first transmitter electrodes  222 A- 222 D are all electrically interconnected in conventional fashion by conductive through holes  222 H and wiring traces  222 W located on a second side of the insulating substrate, for example as shown in  FIG. 4 . The electrically interconnected first transmitter electrodes  222 A- 222 D are provided with a first transmitter electrode connection  222 K. Each of the sets of second transmitter electrodes  223 A- 223 D, third transmitter electrodes  224 A- 224 D and forth transmitter electrodes  225 A- 225 D are similarly interconnected and each is similarly provided with respective second, third and fourth transmitter electrode connections  223 K,  224 K and  225 K.  
         [0076]     Also shown in  FIG. 4  is an alignment/centerline  221  for the transmitter electrode configuration  240 , and the relative location of the capacitive coupling tracks  274  and  275  and their respective subtracks  274 ′ and  274 ″, and  275 ′ and  275 ″, for a nominally aligned transmitter electrode configuration  240 . It should be appreciated that the transmitter electrode configuration  220  is provided with a transmitter electrode span width  237  along the Y-axis that encompasses the shield electrode  242  and all of the receiver electrodes  262 A,  262 B and  263  and provides additional width margins  238 A and  238 B such that it will encompass the shield electrode  242  and all of the receiver electrodes  262 A,  262 B and  263  regardless of any expected misalignment along the Y-axis, in order that such misalignments will not affect the capacitive coupling from the transmitter electrodes to any of the other electrodes of the signal-balanced electrode configuration  200 , and especially will not affect the capacitive coupling from the transmitter electrodes to the shield electrode  242 .  
         [0077]      FIG. 5  is a plan view showing the operational alignment of the receiver electrode configuration  260  of  FIG. 2 , the shield electrode configuration  240  of  FIG. 3 , and the transmitter electrode configuration  220  of  FIG. 4 , for the second exemplary embodiment of a signal-balanced electrode configuration  200  according to this invention.  
         [0078]     In operation, the transmitter electrode member  239 , the shield electrode member  259 , and the receiver electrode member  279  are arranged such that the alignment/centerlines  221 ,  241  and  261  are nominally aligned along the Z-axis (the direction normal to the X-Y plane), and the transmitter electrode configuration  220  and the receiver electrode configuration  260  are positioned along the measuring axis/direction  80  such that the receiver electrode group length  277  coincides with the overall transmitter electrode group length  227 . For the configuration shown in  FIG. 5 , the receiver electrode member  279  is positioned to the far side of the arrangement along the Z-axis, with the operational receiver electrodes facing up, the transmitter electrode member  239  is positioned to the near side of the arrangement, with the operational transmitter electrodes facing down, and the shield electrode member  259  is positioned between them. The transmitter electrode member  239  and the receiver electrode member  279  are arranged in a fixed relationship with an operable and uniform capacitive gap between them along the Z-axis, the capacitive gap being somewhat greater than the thickness of the shield electrode member  159  along the Z-axis such that the shield electrode member  159  may be moved along the measuring axis/direction  80  in the capacitive gap.  
         [0079]     It should be appreciated that during operation, in order for the shield electrode  242  to capacitively couple approximately equally to the various transmitter electrodes  222 X- 225 X of the transmitter electrode configuration  220 , regardless of its relative position along the measuring axis/direction  80  according to one aspect of this invention, and to provide the best practical accuracy, the shield electrode member  259  should be guided along the measuring axis/direction  80  such that the shield electrode  242  is maintained with the most uniform gap and alignment that is practical and/or economical relative to the transmitter electrode configuration  220 . It should be appreciated that the operable capacitive gap between the transmitter electrode member  239  and the receiver electrode member  279  that establishes the best tradeoff between signal strength and measurement errors due to various potential misalignments can be established by analysis and/or confirmed experiment for the signal-balanced electrode configuration  200 , as previously discussed with reference for  FIG. 1 .  
         [0080]     Similarly to the signal-balanced electrode configuration  100 , for the configuration of the signal-balanced electrode configuration  200  shown in  FIG. 5 , when there is an approximately uniform operating gap along the Z-axis direction between the transmitter electrode configuration  220  and the shield electrode configuration  240 , the shield electrode configuration  240  will capacitively couple approximately equally to each of the transmitter electrodes regardless of their relative position along the measuring axis/direction  80 , providing one aspect of a signal-balanced electrode configuration according to the principles of this invention. In operation, a sinusoidal AC voltage signal having 0 degrees of temporal phase shift is applied to the interconnected electrodes  222 X through the respective first electrode connection  222 K. Similarly, respective similar sinusoidal AC voltage signals having 90, 180, and 270 degrees of temporal phase shift are applied to the interconnected electrodes  223 X,  224 X and  225 X, respectively, through the respective second, third and fourth transmitter electrode connections  223 K,  224 K and  225 K. For such a configuration of transmitter signals, it should be appreciated that the 0 and 180 degree pair of transmitter signals and the 90 and 270 degree pair of transmitter signals each provide signals of equal magnitude and opposite polarity and because they are equally capacitively coupled to the shield electrode  242 , their respective contributions to the response voltage arising on the shield electrode  242  will likewise be of equal and opposite polarity. Accordingly, the signals thus balance each other to provide no net change in the voltage of the electrically floating shield electrode  242 , according to the principles of this invention. In various exemplary embodiments, the shield electrode  242  will thus be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments. As previously discussed, according to the principles and configurations disclosed herein, when a shield electrode maintains no net change in its voltage, at least at each time that the transducer provides a displacement measurement signal, then the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0081]     Regarding another aspect of operation of the signal-balanced electrode configuration  200 , when there is an approximately uniform operating gap along the Z-axis direction between the previously described transmitter electrode configuration  220  and receiver electrode configuration  260 , in the hypothetical absence of the shield electrode  242 , each of the transmitter electrodes of the transmitter electrode groups  210 A- 210 D will capacitively couple approximately equally to the receiver electrodes  262 A,  262 B and  263 . Thus, when two pairs of similar sinusoidal AC voltage signals of equal and opposite polarity are provided on the four transmitter electrodes in each of the transmitter electrode groups  210 A- 210 D, their respective contributions to the voltage arising on the receiver electrodes  262 A,  262 B and  263  will be equal, thus balancing each other to provide no net change in the respective signals provided by the receiver electrodes  262 A,  262 B and  263 . In various exemplary embodiments, the signals from the first and second receiver electrode connections  262 C and  263 C would thus be constant at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, in the hypothetical absence of the shield electrode  242 . This tends to reduce or eliminate certain signal errors that may otherwise arise in the measurement signals provided using various signal-balanced electrode configurations according to this invention.  
         [0082]     Another aspect of operation of the signal-balanced electrode configuration  200 , is explained with reference to the capacitive coupling between the transmitter electrodes of the transmitter electrode groups  210 A- 210 D and the receiver electrode  262 A, and the second receiver electrode portion  263 A, along the capacitive coupling tracks  274 ′ and  274 ″, respectively. As shown in  FIG. 5 , the capacitive coupling area between the transmitter electrodes of the transmitter electrode groups  210 A- 210 D and the receiver electrode  262 A along the capacitive coupling track  274 ′ that is not effectively screened by the shield electrode portion  242 A varies sinusoidally along the measuring axis/direction  80 . Accordingly, at any position relative to the shield electrode  242  along the measuring axis/direction  80 , the signal contributions on the receiver electrode  262 A include those arising from the 0 degree AC signal on the transmitter electrodes  222 X times the portion of the sinusoidal capacitive coupling area corresponding to the transmitter electrodes  222 X, and similarly those arising from the respective 90, 180, and 270 degree AC signals on the transmitter electrodes  223 X,  224 X and  225 X, respectively, times their respective portions of the sinusoidal capacitive coupling areas corresponding to the transmitter electrodes  223 X,  224 X and  225 X, respectively. These signal contributions are effectively summed on the receiver electrode  262 A, to give rise to a net sinusoidal AC voltage signal on the receiver electrode  262 A.  
         [0083]     It should be appreciated that this net sinusoidal AC voltage signal on the receiver electrode  262 A will have a net temporal phase determined by the relative strength or magnitude of the various “unscreened” capacitive coupling areas of the various transmitter electrodes  222 X- 225 X. The net temporal phase of the net sinusoidal AC voltage signal is thus determined by the relative position of the shield electrode  242  along the measuring axis/direction  80 , and the net temporal phase of the net sinusoidal AC voltage signal is thus indicative of the relative position. It should be appreciated that due to the periodic sinusoidal variation of the shape of the capacitive coupling area along the capacitive coupling track  274 ′, the net temporal phase of the net sinusoidal AC voltage signal will vary as an approximately linear function of the relative position of the shield electrode  242  along the measuring axis/direction  80 .  
         [0084]     It should be appreciated that the capacitive coupling between the transmitter electrodes of the transmitter electrode groups  210 A- 210 D and the second receiver electrode portion  263 A along the capacitive coupling track  274 ″ is similar to the previous description regarding the capacitive coupling track  274 ′, except that due to the configuration of the shield electrode portion  242 A the capacitive coupling along the capacitive coupling track  274 ″ that is not effectively screened by the shield electrode portion  242 A has a spatial phase shift of 180 degrees, that is, one half of the wavelength P′ along the measuring axis/direction  80 , relative to that provided along the capacitive coupling track  274 ′. Thus, the net temporal phase of a net sinusoidal AC voltage signal arising on the second receiver electrode portion  263 A will vary as an approximately linear function of the relative position of the shield electrode  242  along the measuring axis/direction  80 , and the net temporal phase of that net sinusoidal AC voltage signal will be shifted 180 degrees of temporal phase shift relative to the net temporal phase of the signal arising on the receiver electrode  262 A.  
         [0085]     As will be apparent to one of ordinary skill in the art, due to the symmetry of the electrode configurations of the signal-balanced electrode configuration  200 , along the capacitive coupling track  275 ″ the signal arising on the second receiver electrode portion  263 B at any relative position of the shield electrode  242  will nominally be identical to that arising on the second receiver electrode portion  263 A and the sum of these signals will be available at the second receiver electrode connection  263 C. Similarly, along the capacitive coupling track  275 ′ the signal arising on the first receiver electrode portion  262 B at any relative position of the shield electrode  242  will nominally be identical to that arising on the first receiver electrode portion  262 A and the sum of these signals will be available at the first receiver electrode connection  262 C.  
         [0086]     As previously outlined, for various misalignments along the Y-axis misalignments it should be appreciated that, relative to nominal alignment, capacitive coupling area lost or gained in the subtracks  274 ′ and  274 ″ due to a given misalignment will tend to be oppositely and compensatingly gained or lost in the subtracks  275 ′ and  275 ″ for that same misalignment, due to the symmetrical configurations of the shield electrode configuration  240  and the receiver electrode configuration  260 . Thus, the signal at the first receiver electrode connection  262 C that is effectively the sum of the signal contributions for the capacitive coupling tracks  274 ′ and  274 ″ will tend to be stable despite reasonably expected misalignments along the Y-axis and the signal at the second receiver electrode connection  263 C that is effectively the sum of the signal contributions for the capacitive coupling tracks  275 ′ and  275 ″ will tend to be stable despite reasonably expected misalignments along the Y-axis.  
         [0087]     As described above, in operation, the signals output on the first and second receiver electrode connections  262 C and  263 C will have nominally equal and opposite signal magnitudes. In various exemplary embodiments, these signals are sampled and input to a differential amplifier configuration which provides a measurement signal that is the amplified difference between the two signals, thus doubling the position measurement signal and removing various common mode errors that may be included in the receiver electrode signals. The differential measurement signal will have a temporal phase shift relative to a reference phase of signals input to the transmitters, that indicates the position of the shield electrode  242  relative to the transmitter and receiver electrode configurations  220  and  260 , within a particular current wavelength P′.  
         [0088]     The exemplary embodiment of the signal-balanced electrode configuration  200  shown in  FIGS. 2-5  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  200  may be conveniently and reliably operated with an electrically floating shield electrode  242 , if desired. The specific embodiment of the signal-balanced electrode configuration  200  described above with reference to  FIGS. 2-5  provides a position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  259  is displaced relative to the transmitter and receiver electrode members  239  and  279  along the measuring axis/direction  80 . Any one of a variety of known methods and circuits may be used for providing suitable transmitter signals and processing the resulting output signals to determine desired relative displacement values for such a configuration. For example, one of ordinary skill in the art can readily adapt various circuits and signal processing techniques disclosed in U.S. Pat. No. 4,879,508, to Andermo, which is incorporated herein by reference in its entirety, to provide circuits and signal processing techniques that are suitable for the various embodiments disclosed herein.  
         [0089]     It should be appreciated that, provided that a shield electrode  242  will capacitively couple approximately equally to each of the transmitter electrodes  222 X- 225 X regardless of its relative position along the measuring axis/direction  80 , numerous alternative electrode configurations including either minor or substantial electrode variations are possible while preserving the previously described advantages and features of the signal-balanced electrode configuration  200 . As a first example, it should be appreciated that although the foregoing embodiment provides two receiver electrode signals that are suitable for differential signal processing, that it is possible to omit one or the other of these signals and their associated receiver electrode in various exemplary embodiments. The remaining receiver electrode and receiver electrode signal will still provide a sinusoidal AC voltage signal having a net temporal phase that will vary as an approximately linear function of the relative position of the shield electrode  242  along the measuring axis/direction  80  to provide an operable signal-balanced electrode configuration according to this invention. Only the certain common mode error rejection features will be lost. It should be appreciated that such a single-electrode receiver electrode configuration can be similarly adapted by one of ordinary skill in the art to provide an alternative embodiment for the dual-receiver electrode configurations described below with reference to the signal-balanced electrode configurations  300 - 600 .  
         [0090]     As a second example, in one alternative embodiment that is otherwise similar to the previously described signal-balanced electrode configuration  200 , a three-phase transmitter electrode configuration is used. In such an alternative embodiment, each of the transmitter electrode groups  210  includes 3 transmitter electrodes, instead of 4 transmitter electrodes, the 3 transmitter electrodes in each group distributed evenly over one period P′ of the signal-balanced electrode configuration. By analogy with the foregoing description, the three transmitter electrodes in each group are generically designated here as electrodes  222 ′X,  223 ′X and  224 ′X. In operation, a respective sinusoidal AC voltage signal having 0 degrees of temporal phase shift is applied to the interconnected electrodes  222 ′X. Respective similar sinusoidal AC voltage signals having 120 and 240 degrees of temporal phase shift are applied to the interconnected electrodes  223 ′X,  224 ′X, respectively. Such a configuration of transmitter signals, will also operate to provide a position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  259  is displaced relative to the transmitter and receiver electrode members  239  and  279  along the measuring axis/direction  80 , as previously described. Furthermore, for such a configuration of transmitter signals, it should be appreciated that because they are equally capacitively coupled to the shield electrode  242 , their respective contributions to the response voltage arising on the shield electrode  242  will sum to zero. Accordingly, such 3-phase signals thus balance each other to provide no net change in the voltage of the electrically floating shield electrode  242 , according to the principles of this invention. It should be appreciated that an analogous 3-phase configuration of transmitter electrodes can be similarly adapted by one of ordinary skill in the art to provide an alternative embodiment for various 4-phase transmitter electrode configurations described below with reference to the signal-balanced electrode configurations  300 - 600 .  
         [0091]     Furthermore, in addition to a planar/linear configuration, the components shown in  FIGS. 2-5  may alternatively be understood to represent parts of a cylindrical encoder, where the measuring axis/direction  80  is a cylindrical or circular measuring axis/direction and the shield electrode configuration  140  represents a segment of an element that continues to form a partial or complete cylindrical configuration along the measuring axis/direction  80 , as previously described with reference to the signal-balanced electrode configuration  100 .  
         [0092]     These and other alternative electrode configurations including either minor or substantial electrode variations are possible while preserving the previously described advantages and features of the signal-balanced electrode configuration  200 . Thus, it will be understood that the configuration of the signal-balanced electrode configuration  200  disclosed above is illustrative only, and not limiting.  
         [0093]      FIGS. 6 and 7  illustrate a third exemplary embodiment of a signal-balanced electrode configuration  300  according to this invention that is usable in a capacitive encoder according to this invention.  FIG. 6  is an exploded view of the third exemplary embodiment of a signal-balanced electrode configuration  300  according to this invention, and  FIG. 7  is a plan view showing the operational alignment of the receiver electrode configuration  360 , the shield electrode configuration  340 , and the transmitter electrode configuration  320 , for the third exemplary embodiment of a signal-balanced electrode configuration  300  according to this invention.  
         [0094]     The signal-balanced electrode configuration  300  has many elements and operating characteristics that are similar to those of the previously described signal-balanced electrode configuration  200 . Such similarities will be understood by one of ordinary skill in the art, thus, only significantly different elements and operating characteristics will be described in detail below. As shown in  FIG. 6 , the third exemplary embodiment of a signal-balanced electrode configuration  300  includes a transmitter electrode configuration  320  carried on a transmitter electrode member  339 , a shield electrode configuration  340  carried on a shield electrode member  359  (a representative segment of which is shown in  FIG. 6 ), and a receiver electrode configuration  360  carried on a receiver electrode member  379 .  
         [0095]     The receiver electrode configuration  360  includes first receiver electrode portions  362 A and  362 B that are electrically connected together by a first receiver electrode connection  362 C and a second receiver electrode  363  that has a second receiver electrode connection  363 C. The first receiver electrode portions  362 A and  362 B are separated from the second receiver electrode  363  along the Y-axis by the nominally equal gaps  369 A and  369 B, respectively, and have respective span widths along the Y-axis direction that are conveniently made equal in the embodiment shown in  FIG. 6 . For convenience of description, it is useful to define first and second portions  363 A and  363 B of the second receiver electrode  363  that lie on opposite sides of the alignment/centerline  361  and have respective span widths along the Y-axis direction that are equal. The first receiver electrode portions  362 A and  362 B and the second receiver electrode  363  each have the same dimension along the X-axis direction, the receiver electrode group length  377 , which is 2 times a wavelength P″ (described below) for the embodiment shown in  FIG. 6 . For convenience of description, it is useful to define receiver electrode coupling tracks  374 ′,  374 ″ and  375 , which extend along the measuring axis/direction  80  and are located along the Y-axis to coincide with the span of the various receiver electrodes, as shown in  FIG. 6 .  
         [0096]     In contrast to the previously described shield electrodes that meander in a periodic fashion along the measuring axis direction, the shield electrode configuration  340  shown in  FIG. 6  includes a shield electrode element having approximately rectangular portions  342  that alternate with approximately rectangular portions  342 ′ along the measuring axis/direction  80 , to form a periodic pattern having a wavelength or pitch P″, which is also indicated by the dimension  346  in  FIG. 6 . The portions  342 ′ have a span width  357  along the Y-axis direction that encompasses the extents of operably aligned electrodes of both the transmitter electrode configuration  320  and the receiver electrode configuration  360 , and is conveniently made constant along the measuring axis/direction  80  as shown in  FIG. 6 . In one exemplary embodiment of the shield electrode configuration  340 , the shield electrode member  359  is an insulating printed circuit board material and the portions  342 ′ are conventionally-fabricated conductive portions on the printed circuit board, while the portions  342  are the insulating printed circuit board material of the shield electrode member  359 . In an alternative embodiment, the portions  342 ′ are the insulating printed circuit board material and the portions  342  are conductive portions. In yet another embodiment, the shield electrode member  359  is conductive strip, tape, or bar, that is punched, machined, or etched through in the portions  342 ′, the remaining conductive material forming the portions  342 .  
         [0097]     It should be appreciated that in operation, similarly to the signal-balanced electrode configuration  200 , the alignment/centerline  341  of the shield electrode configuration  340  is aligned with the alignment/centerline  361  of the receiver electrode configuration  360 , and the Y-axis dimensions of the shield electrode configuration  240  are dimensioned relative to the various Y-axis dimensions of the receiver electrode configuration  360  such that the alignment/centerline  341  can be somewhat misaligned along the Y-axis relative to the alignment/centerline  361  and the various capacitive coupling areas between the shield electrode configuration  340  and the receiver electrode configuration  360  will tend to be relatively unchanged by the misalignment, as best seen in  FIG. 7 .  
         [0098]     It should be appreciated that despite substantial differences in electrode geometry, the transmitter electrode configuration  320 , shown in  FIGS. 6 and 7 , is electrically connected and operated in a manner very similar to the previously described transmitter electrode configuration  220 . The differences in geometry are due to the fact that for the signal-balanced electrode configuration  300  the transmitter electrode configuration  320  is arranged to provide a sinusoidal capacitive coupling variation vs. displacement, whereas this sinusoidal capacitive coupling variation was provided by the shield electrode configuration  240 , not the transmitter electrode configuration, in the signal-balanced electrode configuration  200 .  
         [0099]     As best seen in  FIG. 6 , the transmitter electrode configuration  320  includes a transmitter electrode member  359 , which may be a printed circuit board for example, carrying three transmitter electrode group regions A-C, nominally demarcated by the dashed reference lines  312 - 314  in  FIG. 6 . Corresponding to the capacitive coupling track  375  of the transmitter electrode configuration  320 , the first transmitter electrode group region A includes primarily, from left to right in  FIG. 6 , second, third, fourth and first transmitter electrodes  2 A,  3 A,  4 A and  1 A; the second transmitter electrode group region B has second, third, fourth and first transmitter electrodes  2 B,  3 B,  4 B and  1 B, and the third transmitter electrode group region C is similarly arranged, except that it is conveniently split into “left and right portions” that flank the transmitter electrode group regions A and B, as shown in  FIG. 6 . The three transmitter electrode group regions A-C have nominally equal net functional dimensions (ignoring the convenient split layout of the group region C) and are repeated periodically along the measuring axis/direction  80  according to a transmitter electrode group pitch  316  which is equal to the wavelength P″. An overall transmitter electrode group length  327  is thus 3 times the wavelength P″ for the embodiment shown in  FIGS. 6 and 7 .  
         [0100]     It should be appreciated that each of the transmitter electrodes arranged along the capacitive coupling track  375  have identical dimensions, and each individual electrode is shaped such that its width dimension along the Y-axis at each point along the measuring axis/direction  80  is a sinusoidal function of that position, going through one half of a sinusoidal cycle over the total electrode length of approximately P″/2 along the measuring axis/direction  80 . This corresponds to the characteristic “S” appearance of the transmitter electrodes n  FIGS. 6 and 7 .  
         [0101]     Regarding the transmitter electrodes arranged along the capacitive coupling tracks  374 ′ and  374 ″, respectively, it should be appreciated that these transmitter electrodes are arranged, sized and shaped in a manner that is completely analogous to the foregoing description for the transmitter electrodes arranged along the capacitive coupling track  375 , with one geometrical exception: The transmitter electrodes arranged along each of the capacitive coupling tracks  374 ′ and  374 ″, respectively, have a width dimension along the Y-axis at each point along the measuring axis/direction  80  that is nominally one-half of the corresponding width dimension of the transmitter electrodes arranged along the capacitive coupling track  375 .  
         [0102]     The functional electrical connection of the electrodes is shown schematically in  FIG. 6 . It should be appreciated that some electrical connections are schematically routed in series through various electrodes in  FIG. 6 , as indicated by connecting lines located in the zones indicated by the reference numbers  311 ′ and  311 ″. The reference numbers  0 - 3 , shown on each transmitter electrode in  FIGS. 6 and 7 , indicate which electrodes are connected to each of the similarly numbered transmitter signal sources T 0 -T 3  provided by a transducer electronic circuit  380 . In operation, a sinusoidal AC voltage signal having 0 degrees of temporal phase shift is applied to the interconnected electrodes numbered 0. Similarly, respective similar sinusoidal AC voltage signals having 90, 180, and 270 degrees of temporal phase shift are applied to the electrodes numbered 1, 2, and 3, respectively.  
         [0103]     As best seen in  FIG. 7 , it should be appreciated that opposite-phase transmitter electrodes, for example the “0” and “2” transmitter electrodes, are always aligned “side-by-side” with each other along the Y-axis direction, and extend over the same span along the measuring axis/direction  80 . Furthermore, each “0” transmitter electrode, for example, along the central capacitive coupling track  375  is always aligned with two opposite-phase “2” transmitter electrodes along the outer capacitive coupling tracks  374 ′ and  374 ″, respectively, which each having one half of the effective width and/or area of the central “0” transmitter electrode. This “balancing” arrangement holds true for each “number/type” of transmitter electrode at each location along the measuring axis direction. Furthermore, as previously mentioned, each transmitter electrode has a total span of P″/2 along the measuring axis/direction  80 , which matches the span of each of the portions  42  and  42 ′ of the shield electrode configuration  340 .  
         [0104]     For such a configuration of transmitter electrodes and signals, it should be appreciated that the net capacitive signal coupling to any of the individual portions  342  or  342 ′, whichever is a shield electrode portion in a given embodiment, or their sum, will always be balanced, according to the principles of this invention. For example, with reference to a shield electrode portion  342 ′ located between the dashed reference lines  318  and  319  in  FIG. 7 , it can be seen that along a vertical direction approximately through the center of that shield electrode portion  342 ′ the 0 and 180 degree pair of transmitter signals on the 0 and 2 transmitter electrodes, respectively, will each provide signals of equal magnitude and opposite polarity and because they are equally capacitively coupled to that shield electrode portion  342 ′, and their respective contributions to the response voltage arising on that shield electrode  342 ′ will likewise be of equal and opposite polarity. Along a vertical direction at the left edge of that shield electrode  342 ′, the 90 and 270 degree pair of transmitter signals on the capacitively coupled areas of the central “1” and outer “3” transmitter electrodes will similarly balance. Likewise, along a vertical direction at the right edge of that shield electrode  342 ′, opposite-phase signals on the capacitively coupled areas of the central “3” and outer “1” transmitter electrodes will similarly balance.  
         [0105]     Thus, similarly to the signal-balanced electrode configuration  200 , for such a configuration of transmitter electrodes and signals, the operative shield electrode(s) of the signal-balanced shield electrode configuration  340  will be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, at least at each time that the transducer provides a displacement measurement signal, and the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0106]     Also similarly to the signal-balanced electrode configuration  200 , in operation, when the sinusoidal AC voltage signals having 0, 90, 180, and 270 degrees of temporal phase shift are applied to the interconnected electrodes numbered 0, 1, 2, and 3, respectively, the capacitive coupling along the capacitive coupling track  375  that is not effectively screened by the shield electrode portion(s)  342 ′, for example, will give rise to a net sinusoidal AC voltage signal arising on the second receiver electrode portion  363  that will have a temporal phase that varies as an approximately linear function of the relative position of the shield electrode configuration  340  along the measuring axis/direction  80 . Similarly, the capacitive coupling along the capacitive coupling tracks  374 ′ and  374 ″ that is not effectively screened by the shield electrode portion(s)  342 ′, for example, will give rise to a net sinusoidal AC voltage signal arising on the electrically connected first receiver electrode portions  362 A and  362 B that has a temporal and spatial phase shift of 180 degrees, that is, one half of the wavelength P″ along the measuring axis/direction  80 , relative to that provided along the capacitive coupling track  375 .  
         [0107]     Thus, measurement signals of equal magnitude and opposite phase will generally be available at the second receiver electrode connection  263 C and the first receiver electrode connection  262 C, respectively. In various exemplary embodiments, these signals are input to the transducer electronic circuit  380  receiver electrode inputs R+ and R−, where they are sampled and input to a differential amplifier configuration which provides a measurement signal that is the amplified difference between the two signals, thus doubling the position measurement signal and removing various common mode errors that may be included in the receiver electrode signals. The differential measurement signal will have a temporal phase shift relative to a reference phase of signals input to the transmitters, that indicates the position of the shield electrode configuration  340  relative to the transmitter and receiver electrode configurations  320  and  360 , within a particular current wavelength P′.  
         [0108]     The exemplary embodiment of the signal-balanced electrode configuration  300  shown in  FIGS. 6 and 7  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  300  may be conveniently and reliably operated with an electrically floating shield electrode  242 , if desired. The specific embodiment of the signal-balanced electrode configuration  300  shown in  FIGS. 6 and 7  provides a position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  359  is displaced relative to the transmitter and receiver electrode members  339  and  379  along the measuring axis/direction  80 . However, it should be appreciated that other electrode configuration variations that provide non-linear position signals are also operable in various embodiments according to this invention, although such embodiments may provide less resolution and accuracy, they may have cost advantages or other benefits in various specific applications. In any case, any one of a variety of known methods and circuits may be used for providing suitable transmitter signals and processing the resulting output signals to determine desired relative displacement values for such configurations.  
         [0109]     In addition to a planar/linear configuration, the components shown in  FIGS. 6 and 7  may alternatively be understood to represent parts of a cylindrical encoder, where the measuring axis/direction  80  is a cylindrical or circular measuring axis/direction and the shield electrode configuration  140  represents a segment of an element that continues to form a partial or complete cylindrical configuration along the measuring axis/direction  80 , as previously described with reference to the signal-balanced electrode configuration  100 . Thus, it will be understood that the configuration of the signal-balanced electrode configuration  300  disclosed above is illustrative only, and not limiting.  
         [0110]      FIGS. 8 and 9  illustrate a fourth exemplary embodiment of a signal-balanced electrode configuration  400  according to this invention that is usable in a rotary or angular capacitive encoder according to this invention.  FIG. 8  is an exploded view of the fourth exemplary embodiment  400 , showing the receiver electrode configuration  460 , the shield electrode configuration  440 , and the transmitter electrode configuration  420 .  FIG. 9  is a plan view showing the operational alignment of the shield electrode configuration  440 , and the transmitter electrode configuration  420 , for the fourth exemplary embodiment of a signal-balanced electrode configuration  400  according to this invention.  
         [0111]     The signal-balanced electrode configuration  400  has many elements and operating characteristics that are similar to those of the previously described signal-balanced electrode configuration  200 , despite the fact that is a rotary configuration. Such similarities will be understood by one of ordinary skill in the art, thus, only significantly different elements and operating characteristics will be described in detail below. As shown in  FIG. 8 , the third exemplary embodiment of a signal-balanced electrode configuration  400  includes a transmitter electrode configuration  420  carried on a transmitter electrode member  439 , a shield electrode configuration  440  carried on a shield electrode member  459 , and a receiver electrode configuration  460  carried on a receiver electrode member  479 .  
         [0112]     The receiver electrode configuration  460  includes a circular receiver electrode member  479  that carries a circular first receiver electrode  462  and a circular second receiver electrode  463  that have schematically illustrated first and second receiver electrode connections  462 C and  463 C, respectively. For convenience of description, it is useful to define capacitive coupling tracks  474 ′ and  474 ″, which extend along the circular measuring direction  80  and are located along the radial Y′-direction to coincide with the span of the receiver electrodes  462  and  463 , respectively, as shown in  FIG. 8 . The first and second receiver electrodes  462  and  463  are separated along the radial Y′-direction by the circular gap  469 , and have respective spans widths along the radial Y′-direction such that they provide nominally equal capacitive coupling areas along the capacitive coupling tracks  474 ′,  474 ″, as will be described in greater detail below.  
         [0113]     The shield electrode configuration  440  is carried on, or integral with, a shield electrode member  459  and includes a circular shield electrode  442 . A mounting hub  458  may be provided and attached to, or integral with, the shield electrode member  459  in various exemplary embodiments. In any case the shield electrode member  459  and/or the mounting hub  458  is coupled to a rotating shaft that extends along a rotation axis  81  in various applications, such that the angular displacement of the rotating shaft is measured based on the angular displacement of the shield electrode configuration  440  relative to the remainder of the signal-balanced electrode configuration  400 . The shield electrode  442  has a first portion that forms a first circular track  442 A and a second portion that forms a second circular track  442 B, which approximately coincide with the capacitive coupling tracks  474 ′ and  474 ″, respectively, and capacitively couple to the first and second receiver electrodes  462  and  463 , respectively. Each of the first and second circular tracks  442 A and  442 B include a periodic pattern extending along the measuring axis/direction  80 ′ that produces an approximately sinusoidal or quasi-sinusoidal capacitive coupling, as described further below with reference to  FIG. 9 . Each periodic pattern has an angular wavelength or pitch P″′, which is also indicated by the dimension  446  in  FIGS. 8 and 9 . It should be appreciated that the design of the shield electrode configuration  440  is suitable for fabrication by etching or punching, or the like, from a single conductive sheet of material. Alternatively, it may be fabricated as a conductive pattern on a non-conductive printed circuit substrate (not shown).  
         [0114]     In various exemplary embodiments, the various radial Y′-direction dimensions of the shield electrode configuration  440  are dimensioned relative to the various radial Y′-direction dimensions of the receiver electrode configuration  460  such that the centers of shield electrode configuration  440  and receiver electrode configuration  460  can be slightly misaligned and the various capacitive coupling areas between the shield electrode configuration  440  and the receiver electrode configuration  460  will tend to be relatively unchanged by the slight misalignment. For example, as best seen in  FIG. 8 , the peak-to-peak radial dimension of the pattern in the first circular track  442 A is less than and nominally centered within the radial dimension of the first receiver electrode  462 . The radial dimensions of the second circular track  442 B and the second receiver electrode are similarly configured. In addition, the radial dimension of the transmitter electrodes of the transmitter electrode configuration  420  is sufficient to overlap all of the shield and receiver electrodes described electrodes despite similar misalignments. Thus, the signal-balanced electrode configuration  400 , provides a particularly robust design with respect to preserving measurement accuracy despite various alignment errors during assembly and operation. By way of contrast,  FIG. 9  shows an alternative embodiment of the shield electrode configuration  440  and the transmitter electrode configuration  420 , where the radial dimensions of various electrodes are approximately the same. Such embodiments will be less accurate if the alignment is not sufficiently precise. However, such effects may be tolerable, or overcome by precise alignment in various applications, and such embodiments are within the scope of this invention.  
         [0115]     The transmitter electrode configuration  420  should be understood to be essentially functionally and schematically similar to the previously described transmitter electrode configuration  220 , except for the fact that is arranged in a rotary configuration having an angular wavelength or pitch P″′ as described below. Such functional and schematic similarities will be understood by one of ordinary skill in the art, thus, only significantly different elements and operating characteristics will be described in detail below.  
         [0116]     In the exemplary embodiment shown in  FIGS. 8 and 9 , the transmitter electrode configuration  420  is carried on transmitter electrode member  459 , which may be an printed circuit board for example, carrying a plurality of transmitter electrode groups represented by the exemplary explicitly numbered transmitter electrode groups  410 A,  4101 B and  410 D, shown in  FIG. 8 . The first transmitter electrode group  410 A has first, second, third and fourth transmitter electrodes  422 A- 225 A, the second transmitter electrode group  4101 B has first, second, third and fourth transmitter electrodes  422 B- 225 B, and so on along the circular axis direction of the transmitter electrode configuration  420  for other similar transmitter electrode groups. Each of the transmitter electrode groups have similar overall dimensions and are repeated periodically along the measuring axis/direction  80 ′ according to a transmitter electrode group angular pitch  416  which is equal to the angular wavelength P″′.  
         [0117]     There are an integer number of angular wavelengths P″′ and, thus, an integer number of transmitter electrode groups  410  arranged around the circumference of the transmitter electrode configuration  420 . Each of the transmitter electrodes  422 X- 425 X have the same angular dimension along the measuring axis/direction  80 ′ and conveniently may have the same radial Y′-direction dimension. Each of the transmitter electrodes  422 X- 425 X may be fabricated on a printed circuit board with the “A” electrodes interconnected, the “B” electrodes interconnected, the “C” electrodes interconnected, and the “D” electrodes interconnected, approximately as previously described for the transmitter electrode configuration  220 .  
         [0118]      FIG. 9  shows the configuration and operational alignment of the shield electrode configuration  440  relative to the transmitter electrode configuration  420 , as viewed along the direction of the rotational axis  81 .  
         [0119]     It should be appreciated that in order for the shield electrode configuration  440  to have a balanced signal according to the principles of this invention, the electrode area overlapped by each transmitter electrode must be the same. Unlike the linear transducer configurations, if each of the electrode boundaries  443 ,  453  and  455  were a purely sinusoidal function, due to the radial tapering of the transmitter electrodes the electrode area overlapped by various transmitter electrodes would vary. Thus, it is necessary to adjust the various shield electrode boundaries based on their nominal radial location.  
         [0120]     One way of generating the required electrode boundaries is described as follows. It is convenient to define a “boundary generator” mid-line  445 . In one exemplary embodiment, where there are N angular wavelengths P″′ around the circumference of the shield electrode configuration  440 , the radial coordinate of the generator midline  445  as a function of the angle α, in radians, along the measuring axis/direction  80 ′, may be defined as follows: 
 
 M (α)= M   nom   +A   M   cos ( N α)  (EQ. 1) 
 
 where M nom  is the nominal radial “reference” location of the generator midline  445 . 
 
         [0121]     In general, an incremental amount of overlapping area dA along measuring axis direction may be defined as approximately: 
 
 dA=span   r   *r (α)* da   (EQ. 2) 
 
 where r is the nominal radial location of the increment of area, span r  is the length of the increment of area along the radial direction, and r*dα is the nominal dimension of the incremental area along the measuring axis direction at the nominal radial location. 
 
         [0122]     Thus, in order for the electrode area overlapped by each transmitter electrode to be the same between the reference radii  491  (r 1 ) and  494  (r 4 ), the shield electrode radial span at each angle coordinate a must be adjusted for the nominal radial location of the span between the reference radii  491  (r 1 ) and  494  (r 4 ). That is, dA=a constant, therefore:  
                     span   r     ⁡     (   α   )       =       K     r   ⁡     (   α   )         ⁢           ⁢   or       ,   when     ⁢          ⁢         r   ⁡     (   α   )       =     M   ⁡     (   α   )         ,     
     ⁢         span   r     ⁡     (   α   )       =     K     M   ⁡     (   α   )                     (     EQ   .           ⁢   3     )             
 
 According to this way of generating the shield electrode boundaries, along the radial coordinate direction the span r (α) is centered at the location M(α). The ends of the span define the required electrode boundaries. The relation of EQUATION 3 is exemplified by a relatively shorter radial span  447  at relatively larger nominal radial coordinate, and a relatively larger radial span  447 ′ at relatively smaller nominal radial coordinate, in  FIG. 9 . 
 
         [0123]     Equations 1-3 can be used to generate a wide variety of quasi-sinusoidal boundaries that provide a signal balanced shield electrode configuration along a circular measuring axis according to this invention. The constant K generally determines the radial spacing between the outer and inner electrode boundaries. In various exemplary embodiments, the constant K can be defined by an expression of the form 
 
 K≈C 1 *M   nom   +C 2  (EQ. 4) 
 
 where C1 and C2 are constants that provide a constant K that scales with the overall size of the shield electrode configuration. For example, for shield electrode configurations approximately as shown herein, C1≈2 and C2 is generally greater that zero, for example, approximately 1. However, this expression and these values are exemplary only, and not limiting. For any given embodiment, the constant K can be determined by analysis or trial and error, in order to provide the desired radial spacings. 
 
         [0124]     As shown in  FIG. 9 , the pattern of the shield electrode first circular track  442 A has a first shield electrode border  443  that meanders in a periodic fashion according to an approximately quasi-sinusoidal function having an angular wavelength P″′ along the measuring axis/direction  80 ′, between a maximum radial dimension r 4  corresponding to the reference line  494  and a minimum radial dimension r 3  corresponding to the reference line  493 .  
         [0125]     The pattern of the shield electrode second circular track  442 B has individual openings  451 , rather than continuous borders, in order that mechanical support for the first circular track  442 A is provided by the material between the openings. The shape of the windows may be understood by considering the actual portion of the window opening delineated by a dashed line and marked with reference number  452 , and a hypothetical portion of a hypothetical window opening delineated by a dashed line and marked with reference number  452 ′, which have very similar approximately mirror image shapes.  
         [0126]     It will be appreciated that if the hypothetical opening portion  452 ′ were included in the openings, instead of the actual opening portion  452 , the openings would have a border that follows a quasi-sinusoidal function of the angle α, having an angular wavelength P″′, entirely as described above with reference to EQUATIONS 1-3. However, such a border would completely sever the shield electrode member at the reference radius  491 . Thus, it should be appreciated that the actual opening portion  452 A is formed as the functional equivalent of the quasi-sinusoidal hypothetical opening portion  452 ′.  
         [0127]     This is accomplished as follows. Each opening  451  is bounded by four lines: a maximum radial dimension r 2  corresponding to the reference line  492 ; a minimum radial dimension r 1  corresponding to the reference line  491 ; a boundary line  453  generated according to EQUATIONS 1-3, and a boundary line  455  what is identical to the boundary line  453  but offset along the measuring axis/direction  80 ′ by one half of the period P″′.  
         [0128]     The foregoing method of generating a shield electrode provides a quasi-sinusoidal capactive coupling variation, that is, shielded area variation, between the various transmitter and receiver electrodes as a function of rotational displacement. A more ideal sinusoidal capactive coupling variation, that is, shielded area variation, between the various transmitter and receiver electrodes as a function of rotational displacement may be provided by shield electrode boundaries determined as follows. With reference to the previously described radial dimensions r 1  through r 4 , the radial coordinate of the first shield electrode border  443  may be defined by the expression:  
                 r   ′     ⁡     (   α   )       =         r   3   2     +       1   2     ⁢     (       r   4   2     -     r   3   2       )     *     (     1   +     cos   ⁢           ⁢   N   ⁢           ⁢   α       )                   (     EQ   .           ⁢   5     )             
 
 Similarly, the radial coordinate of the boundary line  453  may be defined by the expression:  
                 r   ′′     ⁡     (   α   )       =         r   1   2     +       1   2     ⁢     (       r   2   2     -     r   1   2       )     *     (     1   +     cos   ⁢           ⁢   N   ⁢           ⁢   α       )                   (     EQ   .           ⁢   6     )             
 
 Similar to the description above, opening  451  is the bounded by four lines: a maximum radial dimension r 2  corresponding to the reference line  492 ; a minimum radial dimension r 1  corresponding to the reference line  491 ; a boundary line  453  generated according to EQUATION 6, and a boundary line  455  what is identical to the boundary line  453  but offset along the measuring axis/direction  80 ′ by one half of the period P″′. The receiver electrodes  462  and  463  will provide signals having approximately equal amplitudes when the radial dimensions r 1  through r 4  are chosen such that the receiver electrodes  462  and  463  have equal areas. 
 
         [0129]     It should be appreciated that as a result of the patterning methods outlined above, for any angle α, the exemplary embodiment of the shield electrode configuration  440  shown in  FIGS. 8 and 9  provides a constant capacitive coupling area to each transmitter electrode at each location around its circumference, in order to provide a signal-balanced shield electrode configuration  440  according to this invention.  
         [0130]     In operation, the transmitter electrodes  422 X- 425 X maybe supplied with input signals through the connections  422 K- 425 K, in the same manner previously described for the signals input through the corresponding connections  222 K- 225 K of the signal-balanced electrode configuration  200 . Thus, similarly to the previously described signal-balanced electrode configuration  200 , for such a configuration of transmitter electrodes and signals, the operative shield electrode(s) of the signal-balanced shield electrode configuration  440  will be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, at least at each time that the transducer provides a displacement measurement signal, and the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0131]     The exemplary embodiment of the signal-balanced electrode configuration  400  shown in  FIGS. 8 and 9  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  400  may be conveniently and reliably operated with an electrically floating shield electrode  442 , if desired. The specific embodiments of the signal-balanced electrode configuration  400  described above and shown in  FIGS. 8 and 9  provide an angular position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  459  is rotationally displaced relative to the transmitter and receiver electrode members  439  and  479  along the measuring axis/direction  80 ′. However, it should be appreciated that other electrode configuration variations that provide non-linear position signals are also operable in various embodiments according to this invention, although such embodiments may provide less resolution and accuracy, they may have cost advantages or other benefits in various specific applications. In any case, any one of a variety of known methods and circuits may be used for providing suitable transmitter signals and processing the resulting output signals to determine desired relative displacement values for such configurations.  
         [0132]     It should be appreciated that according to the embodiment described above, the signals output on the receiver electrode connections  462 C and  463 C may be input to a differential signal processing circuit, to provide a position or displacement measurement as previously described herein. According to the shield electrode boundary determining method outlined above, because span r (α) is centered at the location M(α), it will be found that when the receiver electrode boundary radii are chosen to approximately correspond to the inner and outer peaks of the respective shield electrode boundaries, then the signals output on the receiver electrode connections  462 C and  463 C will be of equal magnitude and oppositite phase, which is advantageous for simplifying signal processing and removing certain common mode errors, in the same manner as previously described for the signals output on the receiver electrode connections  262 C and  263 C of the signal-balanced electrode configuration  200 .  
         [0133]      FIGS. 10-13  illustrate a fifth exemplary embodiment of a signal-balanced electrode configuration  500  according to this invention that is usable to provide absolute angular position measurement in a rotary or angular capacitive encoder according to this invention.  FIG. 10  is a plan view of a receiver electrode configuration  560 ,  FIG. 11  is a plan view of a transmitter electrode configuration  520 , and  FIG. 12  is a plan view of a shield electrode configuration  540 , all usable in the signal-balanced electrode configuration  500 .  FIG. 13  is a plan view showing the operation alignment of the receiver electrode configuration  560 , the shield electrode configuration  540 , and the central electrodes of the transmitter electrode configuration  520 . Certain transmitter electrodes and connections, and the like, are omitted in  FIG. 13 , to avoid visual clutter and provide greater clarity for certain aspects of the operation of the signal-balanced electrode configuration  500 .  
         [0134]     The signal-balanced electrode configuration  500  has many elements and operating characteristics that are similar to those of the previously described signal-balanced electrode configuration  400 . In general, correspondingly number elements are designed and operate similarly. For example, the element  562  corresponds to the previously described element  462 , and so on. Such similarities will be understood by one of ordinary skill in the art, thus, only significantly different elements and operating characteristics will be described in detail below.  
         [0135]     As shown in  FIG. 10 , the receiver electrode configuration  560  includes a circular receiver electrode member  579  that carries a circular first receiver electrode  562  and a circular second receiver electrode  563  that have schematically illustrated first and second receiver electrode connections  562 C and  563 C, respectively, all of which may be designed and operated in the same manner as previously described for the corresponding elements of the receiver electrode configuration  560 . For example, in one exemplary embodiment, the radial dimensions and locations of the receiver electrodes  562  and  563  can be identical to those previously described for the receiver electrode configuration  460 .  
         [0136]     In addition, the receiver electrode configuration  560  includes a circular third receiver electrode  564  having in inner border  564 ′ and an outer border  564 ″, and a circular fourth receiver electrode  565  having in inner border  565 ′ and an outer border  565 ″, that have schematically illustrated third and fourth receiver electrode connections  564 C and  565 C, respectively. For convenience of description, it is useful to define capacitive coupling tracks  575 ′ and  575 ″, which extend along the circular measuring axis/direction  80 ′ and are located along the radial Y′-direction to coincide with the span of the receiver electrodes  564  and  565 , respectively, as shown in  FIG. 10 . It is convenient to define the outer radius of the capacitive coupling track  575 ′, indicated by the dimension line  582 , as r 6  and the inner radius of the capacitive coupling track  575 ″, indicated by the dimension line  581 , as r 5 . The third and fourth receiver electrodes  564  and  565  are separated along the radial Y′-direction by the circular gap  569 , and have respective spans widths along the radial Y′-direction such that they provide nominally equal capacitive coupling areas along the capacitive coupling tracks  575 ′,  575 ″, as will be described in greater detail below.  
         [0137]     As shown in  FIG. 11 , the exemplary transmitter electrode configuration  520  is carried on a transmitter electrode member  539 , which may be an printed circuit board for example, carrying a plurality of transmitter electrode groups  510  represented by the exemplary generically numbered transmitter electrode group  510 X. Each of the transmitter electrode groups have similar overall dimensions and are repeated periodically along the measuring axis/direction  80 ′ according to a transmitter electrode group angular pitch  516  which is equal to the angular wavelength P″″. Each transmitter electrode group  510 X has first, second, third and fourth transmitter electrodes  522 X- 525 X. There are nominally an integer number of angular wavelengths P″″ and, thus, an integer number of transmitter electrode groups  510  arranged around the circumference of the transmitter electrode configuration  520 . However, in the exemplary embodiment shown in  FIG. 11 , one such transmitter electrode group  510  is omitted, to make room for the connections  526 K- 529 K to the central transmitter electrodes  526 - 529 , described in greater detail below.  
         [0138]     It should be understood that the plurality of transmitter electrode groups  510  may be designed and operated in the same manner as previously described for the transmitter electrode groups  410  of the transmitter electrode configuration  420 . For example, in one exemplary embodiment, the radial dimensions and locations of the transmitter electrodes of the transmitter electrode groups  510  can be identical to those previously described for the transmitter electrode configuration  420 . The interconnections between the various electrodes of the transmitter electrode groups  510  and their input signal connections  522 K- 525 K are schematically illustrated in  FIG. 11 .  
         [0139]     With regard to the central transmitter electrodes  526 - 529 , they are conveniently described as coinciding with quadrants of a circular capacitive coupling track that has an inner radius indicated by the dimension line  581 ′, which may be equal to the receiver electrode inner radius r 5  in various exemplary embodiments, and that has an outer radius indicated by the dimension line  582 ′, which may be equal to the receiver electrode outer radius r 6  in various exemplary embodiments. In operation, sinusoidal AC voltage signals having 0, 90, 180, and 270 degrees of temporal phase shift are applied to the central transmitter electrodes  526 - 529 , respectively, through the schematically-shown connections  526 K- 529 K, respectively. Accordingly, it should be appreciated that with such signals applied to the central transmitter electrodes  526 - 529 , the central transmitter electrodes  526 - 529  define a second angular wavelength Q corresponding to one rotation about the transmitter electrode configuration  520 , that is, Q=2π radians.  
         [0140]     As shown in  FIG. 12 , The shield electrode configuration  540  is carried on a shield electrode member  559  and includes a first shield electrode  542  that meanders in a periodic fashion along the circular measuring axis/direction  80 ′ and an approximately circular, but eccentrically located, second or central shield electrode  544 . The shield electrode member  559  is a nonconductive printed circuit substrate in various exemplary embodiments. The first shield electrode  542  has a first portion that forms a first circular track  542 A and a second portion that forms a second circular track  542 B, which approximately coincide with, and capacitively couple to, the first and second receiver electrodes  562  and  563 , respectively. Each of the first and second circular tracks  542 A and  542 B include a periodic pattern extending along the measuring axis/direction  80 ′ that produces an approximately sinusoidal capacitive coupling to the first and second receiver electrodes  562  and  563 , respectively. Each periodic pattern has an angular wavelength or pitch P″″, which is also indicated by the dimension  546  in  FIGS. 12 and 13 . The pattern of the shield electrode first circular track  542 A has a first shield electrode border  543  that meanders periodically along the measuring axis/direction  80 ′ according to a quasi-sinusoidal function having an angular wavelength P″″. In one exemplary embodiment, the radial location and quasi-sinusoidal path of the first shield electrode border  543  are identical to those of the previously described shield electrode border  443  of the shield electrode configuration  440 , and may be determined according to EQUATION 5, for example. The pattern of the shield electrode second circular track  542 B is not required to have individual openings like those of the shield electrode configuration  440  due to the mechanical support that the nonconductive substrate of the shield electrode member  559  provides for all shield electrode tracks. Rather, a second shield electrode border  543 ′, similar to the first shield electrode border  543 , also meanders periodically along the measuring axis/direction  80 ′ according to a quasi-sinusoidal function having an angular wavelength P″″, and in embodiments where the first shield electrode border  543  is determined as described above according to EQUATION 5, the second shield electrode border  543 ′ is determined according to EQUATION 6. In various other exemplary embodiments, the boundaries  543  and  543 ′ are each generated according to the teachings described above with reference to EQUATIONS 1-3.  
         [0141]     Similar to the shield electrode configuration  440 , as a result of the patterning described above, for any angle α, the exemplary embodiment of the first shield electrode  542  of the shield electrode configuration  540  shown in  FIG. 12  provides a constant capacitive coupling area to each transmitter electrode at each location around its circumference, in order to provide a signal-balanced first shield electrode  542  according to this invention.  
         [0142]     In operation, the transmitter electrodes  522 X- 525 X maybe supplied with input signals through the connections  522 K- 525 K, in the same manner previously described for the signals input through the corresponding connections  422 K- 425 K of the signal-balanced electrode configuration  400 . Thus, similarly to the previously described signal-balanced electrode configuration  400 , for such a configuration of transmitter electrodes and signals, the operative shield electrode(s) of the signal-balanced first shield electrode  542  will be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, at least at each time that the transducer provides a displacement measurement signal, and the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0143]     The exemplary embodiment of the signal-balanced first shield electrode  542  shown in  FIGS. 12 and 13  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  500  may be conveniently and reliably operated with an electrically floating first shield electrode  542 , if desired. The specific embodiment of the signal-balanced electrode configuration  500  described above and shown in  FIGS. 10-13  provides an angular position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  559  is rotationally displaced relative to the transmitter and receiver electrode members  539  and  579  along the measuring axis/direction  80 ′. However, it should be appreciated that other electrode configuration variations that provide non-linear position signals are also operable in various embodiments according to this invention, although such embodiments may provide less resolution and accuracy, they may have cost advantages or other benefits in various specific applications. In any case, any one of a variety of known methods and circuits may be used for providing suitable transmitter signals and processing the resulting output signals to determine desired relative displacement values for such configurations.  
         [0144]     It should be appreciated that according the embodiment described above, the signals output on the receiver electrode connections  562 C and  563 C may be input to a differential signal processing circuit, to provide a position or displacement measurement as previously described herein. According to the embodiment described above, when the receiver electrode boundary radii are chosen such that the receiver electrodes  562  and  563  have equal areas, then the signals output on the receiver electrode connections  562 C and  563 C will be of equal magnitude and oppositite phase, which is advantageous for simplifying signal processing and removing certain common mode errors, in the same manner as previously described for the signals output on the receiver electrode connections  262 C and  263 C of the signal-balanced electrode configuration  200 .  
         [0145]     With regard to the central shield electrode  544 , it appears as an approximately circular electrode, eccentrically located within the previously described circular capacitive coupling track that has an inner radius indicated by the dimension line  581 ′, and that has an outer radius indicated by the dimension line  582 ′, described with reference to  FIG. 10 . In various exemplary embodiments, the approximately circular central shield electrode  544  has inner and outer boundaries,  545 ′ and  545  respectively, determined according to the teachings previously described with reference to EQUATIONS 1-3 or, alternatively, with reference to EQUATIONS 5 and 6. Because there is only one period “Q” of the central shield electrode  544  around 2π radians (N=1), described further below, the resulting quasi-sinusoidal boundaries  545  and  545 ′ appear approximately as eccentric circles, with respectively different center locations.  
         [0146]     In various exemplary embodiments, better tolerance for various misalignments is provided if the maximum radial extent of the central shield electrode  544  indicated by the dimension line  582 ″, is slightly less than the radial dimensions  582 ′ and  582 , shown in  FIGS. 11 and 10 , respectively. Similarly, it is advantageous if the minimum radial extent of the central shield electrode  544  indicated by the dimension line  581 ″, is slightly greater than the radial dimensions  581 ′ and  581 , shown in  FIGS. 11 and 10 , respectively.  
         [0147]     In operation, sinusoidal AC voltage signals having 0, 90, 180, and 270 degrees of temporal phase shift are applied to the central transmitter electrodes  526 - 529 , respectively, through the schematically-shown connections  526 K- 529 K, respectively, as best shown in  FIG. 11 . Accordingly, it should be appreciated that with such signals applied to the central transmitter electrodes  526 - 529 , the central transmitter electrodes  526 - 529  define a second angular wavelength Q corresponding to one rotation about the transmitter electrode configuration  520 , that is, Q=2π radians.  
         [0148]     As best shown in  FIG. 13 , the central shield electrode  544  always fully overlaps each of the transmitter electrodes  526 - 529 . Thus, for such a configuration of transmitter electrodes and signals, the operative shield electrode(s) of the central shield electrode  544  with boundaries determined as previously outline, will be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, at least at each time that the transducer provides a displacement measurement signal, and the central shield electrode  544  will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0149]     Furthermore, similarly to the previously described multi-period first shield electrode  542 , the single-period central shield electrode  544  provides an angular position signal having a temporal phase shift that varies nearly linearly as the shield electrode member  559  is rotationally displaced relative to the transmitter and receiver electrode members  539  and  579  along the measuring axis/direction  80 ′. For example, is indicated by the high-density cross-hatching shown in  FIG. 13 , for the relative position shown in  FIG. 13 , the central shield electrode  544  is shielding strongly in the vicinity between the receiver electrode  564  and the transmitter electrodes  526  and  529 . Therefore, the signals from the transmitter electrodes  527  and  528  will predominate on the receiver electrode  564 , to produce a signal having a relative phase shift of approximately 135 degrees on the receiver electrode  564 . In an analogous manner, the signals for the transmitter electrodes  526  and  529  will predominate on the receiver electrode  565 , to produce a signal having a relative phase shift of approximately 315 degrees on the receiver electrode  565 .  
         [0150]     It should be appreciated that according to the embodiment described above, the signals output on the receiver electrode connections  562 C and  563 C may be input to a differential signal processing circuit, to provide a position or displacement measurement as previously described herein. In addition, if the boundaries of the central shield electrode  542  are determined as previously described, and the receiver electrode boundary radii are chosen such that the receiver electrodes  564  and  565  have equal areas, then the signals output on the receiver electrode connections  562 C and  563 C will be of equal magnitude and oppositite phase, which is advantageous for simplifying signal processing and removing certain common mode errors, in the same manner as previously described for the signals output on the receiver electrode connections  462 C and  463 C of the signal-balanced electrode configuration  400 .  
         [0151]     It should be appreciated that the angular position signal resulting from the operation of the capacitive coupling tracks corresponding to the receiver electrodes  461  and  463  provides a unique signal value at each angular position around one full rotation of the shield electrode member  559  relative to the transmitter and receiver electrode members  539  and  579 . This everywhere unique or “absolute” “coarse position signal can be analyzed or “interpolated” to identify an “absolute” angle that corresponds to a particular one of the finer resolution periods corresponding to the capacitive coupling tracks  542 A and  542 B, corresponding to the first shield electrode  542  and the receiver electrodes  562  and  563 . The nearly linear angular position signal resulting from the operation of the capacitive coupling tracks  542 A and  542 B can then be analyzed or “interpolated” to refine the absolute angle measurement provided the signal-balanced electrode configuration  500 . The signal-balanced electrode configuration  500  thus provides a high-resolution absolute angular measurement capability around a full rotation of the transducer.  
         [0152]      FIGS. 14-18  illustrate a sixth exemplary embodiment of a signal-balanced electrode configuration  600  according to this invention that is usable to provide absolute angular position measurement in a rotary or angular capacitive encoder according to this invention over one full rotation of 2π radians.  FIG. 14  is an exploded isometric view of the sixth exemplary embodiment of the signal-balanced electrode configuration  600 .  FIG. 15  is a plan view showing the receiver electrode configuration  660  of  FIG. 14 ,  FIG. 16  is a plan view showing the shield electrode configuration  640  of  FIG. 14  and its alignment with the receiver electrode tracks of  FIG. 15 ,  FIG. 17  is a plan view showing the transmitter electrode configuration  620  of  FIG. 14 , and  FIG. 18  is a plan view showing the alignment of the transmitter electrode configuration  620 , the shield electrode configuration  640 , and areas where the transmitter electrode configuration  620  is capacitively coupled to the receiver electrode configuration  660 , for the sixth exemplary embodiment of a signal-balanced electrode configuration  600 .  
         [0153]     The signal-balanced electrode configuration  600  has some elements and operating characteristics that are similar to those of the centrally located single-period portions of the previously described signal-balanced electrode configuration  500 . In general, correspondingly number elements are designed and operate similarly. Such similarities will be understood by one of ordinary skill in the art, thus, only significantly different elements and operating characteristics will be described in detail below.  
         [0154]     As shown in  FIG. 14 , the receiver electrode configuration  660  includes a circular receiver electrode member  679  (shown in transparent outline form) that has a central hole  678  and that carries a circular first receiver electrode  664  and a circular second receiver electrode  665  that have schematically illustrated first and second receiver electrode connections  664 C and  665 C, respectively. The first and second receiver electrodes  664  and  665  are separated by a circular gap  669  and may be designed and operated approximately as previously described for the corresponding elements  564  and  565  of the receiver electrode configuration  560 . As best seen in  FIG. 15 , the receiver electrode  664  has in inner border  664 ′ and an outer border  664 ″, and the receiver electrode  665  has in inner border  665 ′ and an outer border  665 ″, respectively. When the radial dimensions of the receiver electrodes  664  and  665  are dimensioned such that the receiver electrodes  664  and  665  have equal capacitive coupling areas and the transmitter and shield electrodes are designed as described below, the signals provided by the receiver electrodes  664  and  665  will have approximately equal amplitudes.  
         [0155]     As shown in  FIG. 14 , the exemplary transmitter electrode configuration  620  is carried on a transmitter electrode member  639  that has a central hole  638 , and which may be a printed circuit board, for example, that may include an area  637  for carrying circuitry for driving various transmitter electrode connections and receiving signals from the receiver electrode connections  664 C and  665 C in various exemplary embodiments. The transmitter electrode configuration  620  is described in greater detail below. The exemplary shield electrode configuration  640  includes a shield electrode member  659  and a mounting hub  658  that passes with clearance through the central holes  678  and  638  when the signal-balanced electrode configuration  600  is operationally aligned and assembled. A through hole  657  receives an external shaft that supports and rotates the shield electrode member  659  relative to the receiver and transmitter electrode members  679  and  639  during operation.  
         [0156]      FIG. 16  shows the shield electrode configuration  640  and its operational alignment relative to the position of the receiver electrodes  664  and  665 , which are shown in dashed outline. In various exemplary embodiments, the shield electrode configuration  640  is provided integrally with the conductive shield electrode member  659 , which may be punched or etched to provide the desired electrode shape, in various exemplary embodiments. The shield electrode configuration  640  includes an outer electrode portion  642  overlaps with the receiver electrode  664  and an inner electrode portion  644  that overlaps with the receiver electrode  665 . In one exemplary embodiment, a boundary  643  of the outer electrode portion  642  is determined according to the teachings previously described with reference to EQUATIONS 5, with r 3  approximately corresponding to the radial dimension of the inner border  664 ′ of the receiver electrode  664  and r 4  approximately corresponding to the radial dimension of the outer border  664 ″. Because there is only one period of the shield electrode boundary  643  around 2π radians (N=1), the resulting quasi-sinusoidal boundary  643  appears approximately as an eccentric circle. In various exemplary embodiments, better tolerance for various misalignments is provided if the maximum radial extent of the border  643  is slightly less than the radial dimension of the outer border  664 ″.  
         [0157]     The inner electrode portion  644  is circular about the center of rotation and nominally coincides with the receiver electrode  644 , as shown in  FIG. 16 . The inner electrode portion  644  includes open window areas  644 A and  644 B, that similarly nominally coincide with the receiver electrode  644 , but may be slightly wider (or narrower) along the radial direction so as to minimize signal variations due to minor radial misalignments.  
         [0158]      FIG. 17  shows the transmitter electrode configuration  620  in greater detail. The transmitter electrode configuration  620  includes transmitter electrodes  626 - 629 . Each transmitter electrode  626 - 629  includes outer portions  626 ′- 629 ′ that are conveniently described as coinciding with quadrants of a circular capacitive coupling track that corresponds to the receiver electrode  664 . In addition, each transmitter electrode  626 - 629  includes inner portions  626 ″- 629 ″ that have the same total area as the outer portions  626 ′- 629 ′ and are interlaced approximately as shown in  FIG. 17 , to lie with a shared circular capacitive coupling track that is slightly narrower than, and nominally centered within, the radial boundaries of the receiver electrode  665 . The inner portions  626 ″- 629 ″ are separated from each other by a small insulating gap at the electrode borders shown in  FIG. 17 . In various exemplary embodiments, the boundaries of each of the respective inner portions  626 ″- 629 ″ are determined by analysis or trial and error design such that the incremental area dA′ as a function of angle along an inner portion is a sinusoidal function over a range of 180 degrees around the center of rotation, approximately as shown in  FIG. 17 . The respective inner portions  626 ″- 629 ″ are thus identical, except that the maximum value of dA′ for each respective inner portion occurs at an angular coordinate that corresponds to the angular midpoint of the corresponding electrically-connected outer portion.  
         [0159]     According to the foregoing description, as one of the open window areas  644 A or  644 B that are aligned with the inner portions  626 ″- 629 ″ rotate along the direction of the measuring axis/direction  80 ′, the area of each of the inner portions  626 ″- 629 ″ that overlaps the open window area  644 A or  644 B will vary approximately sinusoidally due to the as a function of the angular location of the open window area  644 A or  644 B along the direction of the measuring axis/direction  80 ′. In addition, as the outer boundary  643  of the outer electrode portion  642  that is aligned with the transmitter electrode outer portions  626 ′- 629 ′ rotates along the direction of the measuring axis/direction  80 ′, the area of each of the outer portions  626 ′- 629 ′ that overlaps the shield electrode portion  642  will vary approximately sinusoidally due to the “eccentric” path of the outer boundary  643  that has one period around one rotation of the shield electrode member  659 .  
         [0160]     In operation, sinusoidal AC voltage signals having 0, 90, 180, and 270 degrees of temporal phase shift are applied to the transmitter electrodes  626 - 629 , respectively, through the schematically-shown connections  626 C- 629 C, respectively. Accordingly, it should be appreciated that with such signals applied to the transmitter electrodes  626 - 629 , the transmitter electrodes  626 - 629  define an angular wavelength Q corresponding to one rotation about the transmitter electrode configuration  620 , that is, Q=2π radians.  
         [0161]      FIG. 18  shows the alignment of the transmitter electrode configuration  620  and the shield electrode configuration  640 , and the areas where the transmitter electrode configuration  620  is shielded, and not shielded, by shield electrode configuration  640 . Similarly to the single-period central portions of the previously described signal-balanced electrode configuration  500 , the signal-balanced electrode configuration  600  provides an angular position signal having a temporal phase shift that varies nearly linearly as the shield electrode member  659  is rotationally displaced relative to the transmitter and receiver electrode members  639  and  679  along the measuring axis/direction  80 ′. As shown at the exemplary relative position shown in  FIG. 18 , when the outer electrode portion  626 ′ is essentially unshielded (the dark solid area in  FIG. 13 ) by the shield electrode, the outer electrode portions  627 ′ and  629 ′ are approximately one half shielded (the crosshatched area in  FIG. 13 ), and the outer electrode portion  628 ′ is essentially fully shielded. Therefore, the opposite phase signals from the transmitter electrode outer portions  627 ′ and  629 ′ will approximately balance and the signal from the unshielded transmitter electrode outer portion  626 ′ will predominate on the receiver electrode  664 , to produce a signal having a relative phase shift of approximately 0 degrees on the receiver electrode  664 .  
         [0162]     In an analogous manner, the inner electrode portion  626 ″ is essentially fully shielded by the shield electrode, the inner electrode portions  627 ″ and  629 ″ are approximately one half unshielded (the crosshatched area in  FIG. 13 ), and the inner electrode portion  628 ″ is fully unshielded (the horizontally crosshatched area in  FIG. 13 ). Therefore, the opposite phase signals from the transmitter electrode outer portions  627 ″ and  629 ″ will approximately balance and the signal from the unshielded transmitter electrode inner portion  628 ″ will predominate on the receiver electrode  665 , to produce a signal having a relative phase shift of approximately 180 degrees on the receiver electrode  665 .  
         [0163]     It should be appreciated that according to the embodiment described above, the signals output on the receiver electrode connections  662 C and  663 C may be input to a differential signal processing circuit, to provide a position or displacement measurement as previously described herein. In addition, the signals output on the receiver electrode connections  662 C and  663 C will be of equal magnitude and oppositite phase, which is advantageous for simplifying signal processing and removing certain common mode errors, in the same manner as previously described for the signals output on the receiver electrode connections  462 C and  463 C of the signal-balanced electrode configuration  400 .  
         [0164]     It should also be appreciated according to the foregoing description that the shield electrode configuration  640  couples equally to each of the transmitter electrodes  626 - 629 , regardless of its relative rotational position, in order to provide a signal-balanced shield electrode configuration  640  according to this invention. Thus, for such a configuration of transmitter electrodes and signals, the shield electrode of the signal-balanced shield electrode configuration  640  will be maintained at a DC voltage determined by the transmitter signals, which may be zero volts in various exemplary embodiments, at least at each time that the transducer provides a displacement measurement signal, and the shield electrode itself will not contribute to any erroneous voltage-related signal variations on the receiver electrodes. Accordingly, it will act as desired, that is, simply as a displacement-dependent screening or blocking element between the transmitter and receiver electrodes.  
         [0165]     The exemplary embodiment of the signal-balanced electrode configuration  600  shown in  FIGS. 14-18  is thus reliably operable according to the principles of this invention. The signal-balanced electrode configuration  600  may be conveniently and reliably operated with an electrically floating shield electrode, if desired. The specific embodiment of the signal-balanced electrode configuration  600  described above and shown in  FIGS. 14-18  provides an angular position signal having a temporal phase shift that varies approximately linearly as the shield electrode member  659  is rotationally displaced relative to the transmitter and receiver electrode members  639  and  679  along the measuring axis/direction  80 ′. However, it should be appreciated that other electrode configuration variations that provide non-linear position signals are also operable in various embodiments according to this invention, although such embodiments may provide less resolution and accuracy, they may have cost advantages or other benefits in various specific applications.  
         [0166]     It should be appreciated that the angular position signal resulting from the operation of the capacitive coupling tracks corresponding to the receiver electrodes  664  and  665  provides a unique signal value at each angular position around one full rotation of the shield electrode member  659  relative to the transmitter and receiver electrode members  639  and  679 . The signal-balanced electrode configuration  600  thus provides an “absolute” angular measurement capability around a full rotation of the transducer.  
         [0167]      FIG. 19  is a side cross-sectional view through an exemplary rotary capacitive encoder assembly  700  according to this invention, including the elements shown in  FIGS. 14-18  for the sixth exemplary embodiment of a signal-balanced electrode configuration  600  according to this invention. As shown in  FIG. 19 , the rotary capacitive encoder assembly  700  includes a housing  708  including an upper portion  708 A and a lower portion  708 B. The transmitter electrode member  639  is attached to the upper portion  708 A and the receiver electrode member  679  is attached to the lower portion  708 B. The upper and lower portions  708 A and  708 B are configured such that they provide a through hole, indicated by the through hole walls  702 , that provides an operating clearance for a non-conductive mounting hub  658 . Furthermore the upper and lower portions  708 A and  708 B are configured such that they provide an space  701 .  
         [0168]     The shield electrode configuration  640  including the outer and inner portions  642  and  644 , is located in the space  701 . In the exemplary embodiment shown in  FIG. 19 , the conductive electrode portion of the shield electrode configuration  640  is sandwiched between the an upper portion  658 A and a lower portion  658 B of the non-conductive mounting hub  658 . It should be appreciated that relative to a conductive mounting hub, the non-conductive mounting hub  658  tends to isolate or remove the conductive electrode portion of the shield electrode configuration  640  from any noise signals that might be present on a motor shaft or the like that is inserted through the mounting hub  658  to support and rotate the shield electrode configuration  640  in the space  701 . The crosshatched region  658 C indicates material that may optionally be omitted from the mounting hub  658  to provide an air gap that tends to further isolate or reduces the noise signals that might otherwise be coupled to the shield electrode configuration. Thus, the electrically floating signal-balanced shield electrode configuration  640  shown in the rotary capacitive encoder assembly  700  will tend to isolate the various previously outlined transmitter and receiver circuits from such noise signals that might be present on a motor shaft or the like that is inserted through the mounting hub  658 .  
         [0169]      FIG. 20  is an exploded view of one exemplary cylindrical rotary capacitive encoder assembly  800  according to this invention, including the elements of a generic cylindrical signal-balanced electrode configuration according to this invention. The elements of the generic cylindrical signal-balanced electrode configuration are substantially similar to similarly number elements of any of the previously described linear signal-balanced electrode configurations. For example, the set of generic elements  820 ,  840  and  860  may be curved forms of any of the sets of elements  120 ,  140 , and  160 , or  220 ,  240 , and  260 , or  320 ,  340 , and  360 , and so on. In general, the curved shield electrode configuration  840  will include an integer number of periods of the included shield electrode(s)  842 , or the like, around part or all of its circumference. The curved forms may be provided by fabricating the required electrode configurations, connections, and the like, on flexible printed circuit material, and curving the flexible printed circuits as desired.  
         [0170]     As shown in  FIG. 20 , the cylindrical rotary capacitive encoder assembly  800  includes a housing  808  including an outer wall portion  808 A and an inner wall portion  808 B. The transmitter electrode member  839  is attached to the inner wall portion  808 B and the receiver electrode member  879  is attached to the outer wall portion  808 A, in operational alignment, with their measuring axis directions aligned with measuring axis/direction  80 ″. Electrical connections to the various transmitter electrodes and receiver electrodes are provided through a multi-conductor wire  869  that passes through the housing  808 . The outer wall portion  808 A and inner wall portion  808 B are configured such that they provide a cylindrical space  801 . The inner wall portion  808 B includes a hole  802 , that provides an operating clearance for a lower hub portion  858 B of a non-conductive mounting hub  858 . One or more roller bearing assemblies  803  are provided along the hole  802 , for receiving the lower hub portion  858 B and operationally aligning the mounting hub  858  and the shield electrode member  859 . The cylindrical shield electrode member  859 , carrying the shield electrode  842  or the like is operationally aligned between the transmitter electrode member  839  and the receiver electrode member  879  in the cylindrical space  801 .  
         [0171]     In the exemplary embodiment shown in  FIG. 20 , the cylindrical shield electrode member  859  fits snugly over and is rigidly attached to the shoulder portion  858 C of the mounting hub  858 . It should be appreciated that relative to a conductive mounting hub, the non-conductive mounting hub  858  tends to isolate or remove the conductive electrode portion of the shield electrode configuration  840 , as well as the transmitter and receiver electrode configurations  820  and  860  from any noise signals that might be present on a motor shaft or the like that is inserted through the mounting hub  858  to rotate the shield electrode configuration  840  in the space  801 .  
         [0172]     While the various exemplary embodiments of the invention have been illustrated and described, it will be appreciated that the foregoing embodiments are illustrative only, and not limiting. Thus, various changes can be made therein without departing from the spirit and scope of the invention.