CA2039847A1

CA2039847A1 - Digitizer with serpentine conductor grid having non-uniform repeat increment

Info

Publication number: CA2039847A1
Application number: CA002039847A
Authority: CA
Inventors: Robert M. Mcdermott
Original assignee: Summagraphics Corp
Current assignee: Summagraphics Corp
Priority date: 1990-04-06
Filing date: 1991-04-05
Publication date: 1991-10-07
Also published as: CN1026527C; EP0455985A1; US5051545A; JPH04227520A; CN1056575A; KR910018892A

Abstract

ABSTRACT OF THE DISCLOSURE
Disclosed herein are position determining apparatus and conductor structures or grids therefor. The conductor structure for each axis includes a number of conductors, at least one of which is run in a serpentine path with a non-uniform repeat in-crement. The repeat increment, which is the spacing between one run and the next of the same serpentine conductor, is constrained by a maximum repeat increment, or a minimum repeat increment, or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations thereof. In the preferred em-bodiments, there is at least a constraint on the maximum repeat increment to provide noise immunity. The conductors are arranged for each axis of the grid in a pattern such that signals obtained for that axis may be processed to provide binary numbers in a Gray-type code each unique to a small region of the active area in which the coil center is located. The small region for a given axis corresponds to the space between two immediately ad-jacent, active conductor portions for that axis, with a possible ambiguity of one space. Small regions in each axis define the coarse location of the coil center. Fine location within a region may be determined from the magnitudes of currents induced in selected runs by interpolation, or from the phase relationship of current induced in selected runs.

MD2/scg331.005

Description

t ' ~l 2 0 ~ 7 DIGITI~BR ~I~ BE~P~N~IN~ COND~C$0R GRID
EAVING NON-~NIPOR~ REPEA~ INCREME~T
BACKGROUND OF THE INVENTION
The invention disclosed herein relates to position determining devices, systems and methods, particularly to digitizer systems o~ the type including a tablet having a con-ductor structure which interacts with a movable element or pointer such as a stylus or cursor and the like to provide sig-nals, particularly for a computer, representing the position of the movable element relative to the tablet.
Digitizer systems having a conductor structure and a mov-able element may be of the electromagnetic type in which signals are electromagnetically coupled between electrical conductors in ~he conductor structur~ and an electrical conductor such as a coil in the movable element; of the capacitive or electrostatic type in which signals are capacitively coupled between electrical conductors in the conductor structure and an electrical conductor such an electrode in the movable element; of the optical type in which signals are optically coupled be~ween a light emitting or light receiving conductor structure and light receiving or light emitting structure in the movable element, respectively; of the sonic type in which signals are coupled by means of sound waves between a sound emitting or sound receiving conductor structure and sound receiving or sound emitting structure in the movable element, respectively; etc. The terms "conductor structure" and "conductor" as used herein are meant in a broad sense, and such a MD2/scg331.005 -1-t 2 ~ 7 conductor structure or conductor may receive or conduct signals of an electrical, magnetic, optical, sonic, etc., nature.
Similarly, "induced" is meant in a broad sense and means signals present in a conductor by virtue of some form of coupling.
Digitizinq systems provide signals, typically for use by computers, representing the location, e.g., coordinates, of the movable element relative to an active area of the conductor structure, the active area simply being that area at the tablet surface in which the digitizing system is active to provide such position-representing signals at a given accuracy, resolution, etc. Outside the active area, the digitizing system may not recognize or not process signals for conversion to position-representing signals, or may simply not be active to generate or receiva such signals, etc. Digitizing systems typically include a conductor structure for each coordinate axis. Description be-low with respect to the conductor structure of one axis of a coordinate system is generally applicable to the conductor struc-tures of the other axis.
Electromagnetic-type digitizer systems-are disclosed, for example, in U.S. Patent Nos. 3,873,770 or Ioannou; 3,944,082 of Kamm et al.; and 4,368,352 of Davis, all of which are assiyned to the assignee of this application.
An electrostatic digitizer system is disclosed, for exam-ple, in U.S. Patent No. 4,705,919 of Dhawan.
The conductor structure in those types of systems com-prise, for each coordinate axis, a number of conductors each of MD2/scg331.00S -2-2~3~7 which is switched to either couple signals received by the con-ductors from the movable element to common processing circuitry, or to energize the conductors so that signals thereon supplied from a common source may be coupled to the movable element.
Thus, a switch is requirad for each conductor of the conductor structure of each axis. Although the number of conductors that must be switched depends upon a number of factors including desired resolution and tablet size, it is not unusual for a tablet to employ four or more conductors per linear inch per axis, i.e., adjacent conductors are spaced 0.025 inch or less apart. Therefore, a tablet having an active area of only 12 in-ches by 12 inches may employ 48 or more conductors per axis re-quiring 48 or more switches per axis. Typically, the switche!s are embodied in a multiplexer, and six or more ~-input or three or more ~6-input multiplexers are employed per axis.
One way to reduce the overall number of switches or mul-tiplexer inputs required for each axis in digitizer systems of the above type while maintaining a given active area and a given conductor spacing, is to traverse-the active arèa for a particu-lar axis a number of times with the same conductor, i.e., run the conductor in a serpentine fashion such that active portions or "runs" of the conductor are run back and forth across the active area interconnected by connecting portions~outside the active area. Recent disclosures of serpentine pattern conductor struc-tures may be found, for exampler in U.S. Patent Nos. 4,734,546, MD2/scg331.005 -3--! 2 0 3 ~

issued March 29, 19~8, and 4,831,216, issued May 16, 1989, both of Landmeier; and 4,835,347 of Watson, issued May 30, 1989.
Digitizer systems employing serpentine pattern conductor structures are not, however, a recent development. See, for ex-ample, U.S. Patent Nos~ 3,466,646 of Lewin, issuecl September 9, 1969; 3,647,963 of Bailey, issued March 7, 1972, assigned to the assignee o~ this application; 3,705,956 of Dertouzos, issued De-cember 12, 1972; 3,819,857 of Inokuchi, issued June 25, 1974;
4,029,899 of Gordon issuad June 14, 1977; 4,378,465 of Green et al., issued March 29, 1983; and ~,552,991 of Hulls, issued Novem-ber 12, 1985.-Arranging the conductors in a serpentine pattern so thatspaces or regions between conductor runs (or the runs themselves) may be uniquely identified by unique binary numbers, e.g., in a Gray-type code, also is not a new development. See, for example, the '646 Lewin Patent (1969), the 'g56 Dertouzos Patent (1972) and the '857 Inokuchi Patent tl974).
One approach in digitizer systems employing serpentine-type grid conductor~ is to successively divide the active area into smaller and smaller regions. Thus, for example, one con-ductor divides the tablet in a given axis in half, another con-ductor in quarters, another in eights, etc. With three con ductors, a ta~let may be diviaed according to this approach into eights~ with four conductors into sixteenths, with five con ductors, into thirty-seconds. See, for example, the Inokuchi '857 Patent.

MD2/scg331.005 -4-2 ~ 3 ~
Using the above approach, the conductor that divides the active area in half, for a 12 inch tablet, separates the adjacent active portions or runs of that conductor by six inches. For a 24 inch tablet, the active portions of the conductor dividing the tablet in half are 12 inches apart. To opera~e with large spaces between conductor active portions while providing unambiguous signals induced in either the grid conductors or the movable ele-ment conductor, requires one or more of the following: high sig-nal levels; a large conductor in the movable element; or sensi-tive processing circuitry~
Another approach is to divide the tablet area into halves, quarters, etc., as above described, but using a plurality of runs of the same conduc~or in each sub-divided portion of the tablet, rather than only one conductor run per tablet half, tablet quarter, etc. See the Lewin '646 Patent cited above.
Since in this approach the individual runs of the same cond~ctor are not widely separated, the digitizer system does not require the higher signal levels, larger movable element conductor or sensi-tive processing circuitry of the approach discussed above.
However, with a given spacing between adjacent conductor runs of all conductors (said given spacing being referred to herein as "basic spacing"), using a number of runs of the same conductor in the same sub-divided tablet portion simply reduces the total num-ber of unique spaces tha$ can be identified with a given number of conductors.

MD2/scg331.005 -5-2~39~
Typically, grid conductor structures for electromagnetic digiti~er systems have four or more separate conductors or con-ductor active portions per inch of active area. ThereforP, a tablet having an active area of 12 inches along a particular axis requires at least 48 conductors or conductor active portions. A
tablet using serpentine conductor approaches described above then requires six serpentinely run conductors (26 = 64). Since digi-tal circuits typically are configured to handle data and ad-dresses in 4, 8, 16 or 32 bits, eight conductors and 8-bit multi-plexers would be used. Similarly, for larger tablets, more than eight conductors are needed, and a 16-bit multiplexer (or two 8-bit multiplexers) per axis would be used.
However, 8 or lS conductors arranged in particular con-ductor patterns as taught in the Lewin '64~ Patent results in a pattern having less than the maximum possible number of unique spaces that can be defined with a given basic~conductor run spac-ing and a given nu~ber of conductors. on the other hand, using a pattern as taught in the Inokuchi '857 Patent in a large tablet presents the ambiguity problem discussed above caused by large spaces between conductor runs of the conductor that divides the active area in half or in quarters, etc.
In the approach disclosed in the 1andmeier '546 Patent cited above, 16 conductors per axis are run in serpentine paths such that the tablet is uniquely divided only into quarters. A
coil in the movable element is uniquely locatable within a ta~let quarter from unique codes obtained from the signal phases on the MD2~scg331.005 -6-2~3~ 17 16 conductors. Signal processing then identifies two adjacent conductor active portions between which, or on one of which, the center of the coil is located. Further signal processing then locates the center of the coil as being between, or on one o~, the two adjacent conductor active portions. ~rhus, determining the location of a coil with respect to the grid is a three-step process per axis. See the Landmeier '216 and the Watson '347 for other approaches using serpentine grid conductor structures.
There is however a need for digitizer systems and digitizer conductor (grid) structures which employ a reduced num-ber of connections between the conductor structure and the signal processing circuitry, whose conductor patterns may be deter~ined relatively easily, which locate a movable element with respect to two conductors with simplified processing, and which perform, for example, with acceptable resolution and accuracy.
OBJECTS AND SUMMARY OF THE INVENTION
It is an object of the invention disclosed in this ap-plication to simplify and/or reduce the cost of position determining apparatus, particularly large area apparatus.
It is another object of the invention to improve and/or simplify conductor structures and/or signal processing circuitry for use in position determining apparatus.
It is another object of the invention to provide improved conductor structures which require a reduced number of switches or multiplexer inputs between the respective conductor structure MD2/scg331.005 -7-and signal processing or conductor energizing circuitry, for use in position determining apparatus.
It is another object of the invention to provide con-ductor structures and signal processing circuitry for large area position determining apparatus, e.g.,-apparatus having an active position determining area in one axis of up to ~8 inches or more.
It is another object of the invention to simplify methods for processing signals associated with such conductor structures to obtain signals representing the position of the movable ele-ment relative to the conductor structure.
~ t is another object of the invention to provide appara-tus and methods which simplify determination of the position of a movable element relative to a conductor structure of the appara-tus.
It is another object of the invention to provide a method for determining conductor patterns for such conductor structures.
A conductor structure or system (sometimes referred to hereafter as a l'grid") embodying the invention includes, for each axis, a number of conductors, at least one of which is run in a ~-serpentine path with a non-uniform repeat increment. A conductor run in such a serpentine path includes for a given axis spaced active portions or runs which are substantially parallel to each other running substantially parallel to the axis, and connecting portions interconnecting the active portions. The repeat incre-ment is simply the spacing between one run and the next of the same serpentine conductor, and may (but need not, depending on MD2~scg331.005 -8-f ~ 3 ~

factors such as noisa immunity and fine position determination accuracy) be constrained by a maximum repeat increment, or a min-imum repeat increment, or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations of a maximum repeat increment, a minimum repeat increment and a max-imum change in consecutive repeat increments.
The conductor structure may comprise at least first, sec-ond and third conductors each of which includes a plurality of active portions extending substantially in a first direction sub-stantially in or adjacent a common plane substantially parallel to each other. The repeat increments of at least one of the con-ductors are non-uniform. The conductors are electrically insu-lated or spaced from each other, for example, by extending in different, closely-spaced planes which are insulated in whole or part from each other, and/or by insulating crossover points of adjacent conductors, and/or by selecting conductor patterns, etc.
The repeat increments of the conductors are preferably selected such that the maximum repeat increment is less than about one half of the extent of the conductor struct-ure ~the con-ductor structure having an extent in a second direction that is different from the first direction). For example, each conductor may have at least three active portions.
The repeat increment of the at least one serpentine con-ductor may be non-uniform throughout, or at least in the position-determining portion of the conductor structure, i.e., the portion of the conductor structure relative to which the MD2/scg331.005 -9-location of the movable element is to be deter~ined with rela-tively good accuracy. The repeat increment of the at least one conductor may change any n~mber of tim~s over the full extent of the conductor.
In the preferred embodiments, there is at least a con-straint on the maximum repeat increment to provide noise im-munity, as described below.
The conductors are arranged for an axis of the grid in a pattern such that signals obtained for that axis from the con-ductors or from a conductor in the movable element (e.g., functioning as a coil at the freguency o interest) may be pro-cessed to provide binary numbers each unique to a small region of the active area in which a reference poin~ (e.g., coil center) of the movable element i~ located. Alternatively, the signals may uniquely represent an individual conductor run on or adjacent to which the reference point of the movable element is located, i.e., a conductor run adjacent to the small region. The small region for a given axis corresponds to the space between two im-mediately adjacent, active conductor portions for that axis, with a possible ambiguity of one space.
Thus, in the X axis, for example, the small region is a narrow rectangle or strip extending between two adjacent X-axis active conductor portions. The binary numbers representing ad-jacent small regions o~ a given axis (or adjacent conductor runs) differ by a single binary bit, i.e., only one bit changes if the conductor of the movable element is moved along the given axis MD2/scg331.005 -10-2 5: 3 9 ~

past a conductor run from one small region to the adjacent small region~ Thus, the binary numbers form a type of a Gray code with a possible ambiguity of one bit. The binary numbers defining the small region for the X axis grid and the small region for the Y
axis grid de~ine a smaller region bounded on opposite sides by the conductor runs of the respective axis (or the binary numbers define the point of intersection of an X axis run and a Y axis run). These small regions in each axis, or the smaller regions for the two axes, define coarse locations of the movable element.
Fine location within a region may be determined from the mag-nitudes of signals induced in selected runs by interpolation, or from the phase relationship of signals induced in selected runs.
The number of conductors and the number of conductor runs of conductor structures according to the invention depend on, among other things, the desired active area of the tablet and the desired resolution. If properly laid out in accordance with the invention, n serpentine conductors with 2n conductor runs will provide up to 2n-1 unique regions between adjacent conductor runs. However, if rigi~-constraints are placed on the repeat in-crements for the conductors, the uniquely identifiable regions resultiny from a given number of conductors will be less than 2n-1. For example, a relatively larye minimum repeat increment and/or a relatively small maximum~repeat increment, i.e., the permissible variation of the repeat increment between a minimum and a maximum is small, may result in a number of uniquely iden-tifiable regions which is substantially less than 2n-1. In the MD2/scg331.005 -11-2 ~ 3 ~ 7 limiting case where the minimum repeat increment equals the maxi-mum repeat increment (i.e., tha repeat increment is the same for all conductors and does not vary), only 2n uniquely identifiable regions may be defined.
For example, five conductors with 32 (25) conductor ac-tive portions will provide up to 31 (25-1) unique regions if the conductors are laid out in accordance with the invention. With a spacing o~ 0.250 inch between conductor active portions, an eight-inch grid span may be obtained.
With rPspect to maximum repeat increment, since the amplitude or magnitude (absolute value) of signal induced in (or by, depending on whether the system is movable element driven or conductor structure driven) runs of a serpentine conductor decreases with increasing distance in both directions away from the reference point of the movable element, the expected induced signal in adjacent runs for given signal levels must be sig- ~
nificantly greater than the expected noise le.vel. Therefore, a maximum distance is imposed on the spacing between adjacent runs of the same conductor.
With respect to the minimum repeat increment, the primary constraint thereon is that adjacent runs of the same conductor should be spaced so that the signal phase changes in a particular conductor as the movable element is moved past only one of the two adjacent runs of that same conductor. Another minimum repeat increment criterion relates to fine position determination. For, example, where mathematical interpolation is used, as described MD2/scg331.005 -12-f' ,t-.
2~3~3~
below, the repeat increment should be large enough to provide good linearity of signal level vs. distance between the signal induced in two conductor xuns used for interpolation. Maintain-ing such linearity enables the fine position to be determined directly from a mathamatical operation performed directly on cur- -rent magnitudes, as opposed to first performing a mathematical operation on signal values (e.g., forming a ratio) and then using the result of the mathematical operation with a look-up table to obtain the interpolated fine position.
Conflicting goals are presented between maximum and mini-mum repeat increments, i.e., to minimize errors, the minimum repeat increment is set as large as possible, and as close as possible to the maximum repeat increment (i.e., minimize the change in repeat increments between consecutive runs o~ the same conductor); and, for noise immunity, the maximum repeat incre-ment is set as small as possible.
The following relates to the constraint on maximum change in repeat increment. In most areas of a serpentine grid tablet, the total amplitude of the induced signal is the individual con-tributions of multiple conductor runs. For conductor runs that are equidistant from the reference point of tha movable element, the induced signals are aqual and opposite, and cancel. In such a case, the conductors equidistant from the movable element reference point make no contribution to the total of the induced signal, which introduces no interpolation error. Thus, inter-polation may be facilitated and interpolation accuracy may be im-MD2/scg331.005 -13-2 ~
proved by spacing the conductor runs immediately adjacent each side of the run closest to the movable element reference point equidistantly therefrom. However, since the conductors are fixed and the movable element is movable, the conductor runs immediate-ly adjacent th2 one closest to the movable element refe~ence point will seldom be equidistant from the reference point. In accordance with the invention, howe~er, it is possible to mini-mize the unequal spacing or imbalance of the two immediately ad-jacent conductor runs from the movable element reference point.
This is accomplished in accordance with the invention by imposinq a constraint on the maximum change in repeat increment from run to run of th~ conductors~
As indicated above, fine position may be determined by interpolation. Alternatively, two grid conductors may be ex-tended with the same repeat interval, and the fine position may be determined by the phase of induced signals as disclosed in the Bailey '963 Patent cited above. The use o~ two such conductors relieves somewhat the minimum repeat increment constraint.
A conductor structure according to the invention for a position-determining device which includes a movable element and determines the location of the movable element relative to the conductor structure, comprises at least three conductors each of which includes a plurality of, preferably at least three, active portions or runs extending substantially in a first direction substantially in or adjacent a common plane substantially paral-lel to each other. The conductors each have repeat increments MD2/scg331.005 -14-~ r ~ ~3 3 ~ r7 which space adjacent active portions of the same conductor, and means couple the spaced active portions of same conductors in series. The conductors are arranged in a pattern such that:
spaces between the active portions of all of the conductors ~or each of the conductor active portions) may-be uniquely identified by a unique binary number, respective binary digits of each of the unique binary numbers corresponding to respective conductors, whereby upon interaction betw~en the movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to the binary digits which are indicative of the location of the movable element r~lative to the conductor structure; and the repeat increment of at least one of the conductors is non-uniform.
Stated another way, adjacent active portions of the same condl-ctor are separated by first spaces and adjacent active por-tions of all of the conductors are separated by second spaces, and the spaced active portions of same conductors are coupled in series. The conductors are arranged in a pattern such that: at least two of the first spaces between adjacent active portions of at least one of the conductors are different; and each of the second spaces between adjacent active pcrtions of all of the con-ductors (or the conductor runs themselves) may be uniquely iden-tified by a unique binary number, respective binary digits of each of the unique binary numbers corresponding to respective conductors, wherehy upon interaction between the movahle element and respective conductors binary logic signals may be ohtained MD2/scg331.005 -15-k~ 2 ~

corresponding to the binary digits which are indicative of the location of the movable element relative to the conductor ~truc-ture.
The repeat increment, or first spaces, of the at least one conductor mayl but need not, be constrained by a maximum repeat increment (first space), or by a minim~n repeat increment (first space) or a maximum change in repeat increm~nts (first spaces) between consecutive runs of a same conductor, all selected, for example, as described herein, or combinations thereof.
Preferably, the repeat increment (first space) is less than one-half of the extent of the conductor structure for noise immunity.
In the preferred embodiments, the repeat increment (first space) is constrained by a maximum value for noise immunity, and by a minimum value such that the phase of the induced signals changes as the movable element is moved past a conductor run.
Where mathematical interpolation is to be employed for fine posi-tion determination, the minimum repeat increment (first space) is further constrained to provide substantially linear signals for interpolation, and the maximum change in consecutive repeat in-crements (first spaces) is restrained.
A conductor system according to the invention for a position-determining device which includes a movable element and determines the location of the movable element relative to the MD2/scg331.0Q5 -16-conductor syste~, comprises first and second conductor structures as descri~ed above, one for each axis.
Apparatus according to the invention for determining the location oP a movable element relative to a given area, com-prises: a cond~ctor structure or system as described above which interacts with the movable element when the movable element is on or ad~acent the given area and upon energization of at least one of the conductor structure (system~ and the element; means for energizing one of the conductor structure (system) and the mov-able element to cause location-determining signals to be present in the other; and means for processing the location-determining signals in the other of the conductor structure (system) and the movable element. The processing means includes first means for obtaining from the location-determining signals binary signals corresponding to the binary digits which identify the spaces be-tween all conductor runs (second spaces) or the conductor runs, and which are indicative of the location of the movable element relative to the given area.
A conductor system according to the invention for a position-determining device which includes a movable element and determines the location of the movable element relative to the conductor system comprises first and second conductor structures as described above for the first conductor structure, one for each axis.
In the preferred embodiments, for each of the first and second conductor structures, the second spaces (or basic spacing) MD2~scq331.005 -17-between adjacent conductor active portions of all conductors of the respective conductor structure are equal; two adjacent active portions of the same conductor are separated by at least one ac-tive portion of another conductor; and the processing means in-cludes means for storing sets o~ binary nu~bers corresponding to locations of the movable element relative to the given area, and means for comparing the stored sets of binary numbers and the binary numbers obtained from the binary signals to determine the location of the movable element relative to the given area.
According to one embodiment, the first means of the pro-cessing means determines a coarse location of the movable element from the binary numbers. The coarse location corresponds to a location of the movable element, with respect to each of the con-ductor structures, ~etween two conductor active portions, i.e., in a second space. The processing means includes second means for determining a fine location of the movable element, with respect to each of the conductor structures, between the two con-ductor active portions or on one of them. For each of the con-ductor structures, the processing means in a preferred embodiment provides the amplitudes of the position-determining signals, and the second means performs a mathematical interpolation from selected amplitudes of selected position-determining signals.
According to another embodiment, two conductors of the first and second conductor structures each have a plurality of active portions which are equally spaced with respect to adjacent active portions of both of the two conductors and which are MD2/scg331~005 -18-2~3~3~

equally spaced with respect to active portions of the same con-ductor. The second means processes the position-determining sig-nals in the two additional conductors for each of the first and second conductor structures to determine the fine location.
A method according to the invention determines a layout of a conductor structure of n conductors having the character-istics described above. The method comprises: (1) inserting into the layout one of the conductors at a time such that at least two of the first spaces between adjacent active portions of at least -one of the conductors are different, (2) after each conductor is inserted into the layout, determining whether selected conditions are satisfied; (3) if selected conditions are satisfied in step (2), repeating steps (1) and (2) for the next conductor until n conductors have been inserted into the layout; if selected condi-tions are not satisfied in step (2), then removing the last con-ductor inserted into the }ayout and then repeating steps (1) and (2) for another conductor laid out differently from the removed conductor.
A method according to the invention for determining the location of a movable element relative to a conductor structure of the types described above which interacts with the movable element when the movable element is adjacent the conductor struc-ture upon energization of at least one of the conductor structure and the movable element, comprises: energizing one of the con-ductor structure and the movable element; and processing signals obtained from the other of the conductor structure and movable MD2/scg331.005 -19-i~ r ~3~7 element to provide a unique binary number which uniquely identi-fies a space or at least one conductor active portion close to the movable element. A fine location may then be detsrmined using, for example, magnitude interpolation or the phase rela-tionship of signals on the conductors.
The above and other objects, aspects, features and ad-vantages of the invention will be more readily perceived from the description of the preferred embodiments thereof taken in con-junction with the accompanying drawings and appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
- Th~ invention is illustrated by way of example and not limitation in the figures of the accompanyiny drawings in which like references denote the same or corresponding parts, and in which:
Figs. lA and lB are schematic diagrams o~ a conventional electromagnetic-type digiti2er grid showing the phases of the currents induced in the grid conductors for two locations of a coil relative to the grid;
_ Figs. 2A and 2B are schematic diagrams of a conventional electromagnetic-type digitizer grid having three serpentine grid conductors showing the phases of the currents induced in the grid conductors for two locations of a coil relative to the grid;
Fig. 3 is a schematic view of both axes of a five con-ductor per axis grid structure according to the invention;
Fig. 4 is a schematic diagram showing current induced in a serpentine grid conductor as a function of the distance of the MD2/scg331.005 -20-conductor runs of the sa~e conductor from the center of a coil which interacts with the conductor, which is referred to in con nection with a description of how the maximum repeat increment is determined for a serpentine conductor according to the invention;
Fig. 5 is a schematic diagram showing current induced-in a serpentine conductor as a function of the distance of the con-ductor runs from the center oE a coil which interacts with the conductor, which is referrPd to in connection with a description of how the minimum repeat increment is determined for a ser-pentine conductor according to the invention;
Fig. 6 is a schematic diagram showing the induced current waveform with respect to the three closest conductor runs of a serpentine conductor grid structure, which is referred to :in con-nection with a description of interpolation of the location of the center of a coil with respect to the serpentine canductor grid structure;
Fig. 7 is a schematic diagram of a single axis of a six teen conductor grid structure according to the invention;
Fig. 8 is a schematic diagram of a single axis of another sixteen conductor grid structure according to the invention;
Fig. 9A is a functional block diagram of signal process-ing circuitry for a transducer driven digitizer system which in-- corporates for both axes the grid structure depicted in Fig. 8;
Fig. 9B is a functional block diagram of signal process-ing circuitry for a grid driven digitizer system which in-corporates for both axes the grid structure depicted in Fig. 8;

MD2/scg331.005 -21-2 ~

Fig. 10 is a flow chart illustrating operation of the grid structure and signal processing circuitry of Fig. 9A;
Fig. 11 is flow chart illustrating a fine position inter-polation routine in the flow chart of Fig. 10;
Fig. 12 is a schematic view illustratin~-the grid con-ductors selected for fine position determination in the flow chart of Fig. 11;
Fig. 13 is a schematic view of a two conductor serpentine fine location or secondary grid which is independent of the coarse grid;
Fig. 14 is a schematic view of a two conductor ser-pentine, fine location or secondary grid incorporated into a coarse or primary grid; and Fig. 15 is a flow chart illustrating selection of ser-pentine grid conductor patterns in accordance with the invention.

DESCRIPI ION OF TH_E PREFERRE~ EMBODIMENTS
The digitizer system and the conductor structures and systems illustrated in the drawings and described below are of the electromagnetic type. ~owever, the invention is not limited to such digitizers systems and such conductor structures and sys-tems. In an electromagnetic system, the conductors of the con-ductor structure or grid are electrical conductors, the conductor in the movable element is a an inductor or coil, and the movable element reference point is the center of the coil.
Figsu lA and lB depict a portion of the X-axis grid 10 of a convention~l electromagnetic-type digitizer system of the type ~D2/scg331.005 -22-r in which a coil 12 in a cursor or stylus (not shown) energized by an ac signal induces currents in the individual grid conductors 14, 15, 16, 17, 18, 19, ... N. Each conductor 14-N crosses the active area once, so that separate conductors are required, as shown. The current in conductors_14-N is sensed by sequentially closing respective switches 22 to sequentially couple each con-ductor to processing circuitry 23. The position oE the center of a coil 12 relative to grid 10 may be determined from the phase (direction) and/or magnitudes of the currents induced in the grid conductors 14-N. In that type of digitizer system, the currents induced in the conductors on one side of coil 12 have ane phase while the cur~ents induced in the conductors on the other side of coil 12 have the opposite phase. For example, with the center of coil 12 positioned between conductors 16 and 17, and current flowing counterclockwise in coil 12, as shown ~y the arrow asso-ciated with coil 12 in Fig. lA, the current direction in con-ductors 14-16 is down and the current direction in conductors 17-N is up. With the center of coil 12 between conductors 17 and 18 and coil current counterclockwise, as depicted in Fig. lB, the-current direction in conductors 14-17 is up and the current direction in conductors 18-N is down. The magnitudes of the cur-rents depend upon the relative closeness of the coil to the respective conductors. The prior art discloses a number of tech-niques for uniquely determining the position of coil 12 relative to grid 10 using such current phases and/or magnitudes.

MD2/scg331.005 -23-3 ~
Figs. lA and lB (and Figs. 2A, ~B, 3, 7 and 8) for simplicity show the diameter of coil 12 to be less than the spac-ing between adjacent grid conductors. While coil 12, particular-ly when it is disposed in a cursor, may have a diameter larger than the spacing b~ween adjacent grid conductors, a current phase analysis similar to that described above may be used to lo-cate the center of the coil relative to grid 10.
In Figs. 2A and 2B, X axis grid 25 includes three con-ductors 29-31 each run in a serpentine path, and each having a plurality of parallel, spaced active conductor portions or runs 2~a, 29b, 29c, 29d; 30a, 30b; 31a, 31b, running in opposite directions and interconnected by connecting portions 33, 34, 35, respectively, running perpendicular to the active portions. The basic conductor spacing "W'l between runs of all conductors is uniform, and the repeat increment for each conductor i9 constant, _although the repeat increments for different conductors may be different. The X axis grid 25 depicted in Figs. 2A and 2B is confiqured and operated similar to the one depicted in Fig. 7 of U.S. Patent No. 3,705,956 of Dertou~os, mentione-a above, to lo-cate the position of the center of coil 12 relative to grid 25, except that in Figs. 2A and 2B, coil 12 is energized to induce currents in grid 25, while in Fig. 7 of the Dertouzos '956 Patent, the grid conductors are energized to induce currents in the coil. The net amplitude or magnitude of the current induced in a particular conductor is the sum of the individual currents induced in the individual conductor active portions, the con-~MD2/scg331.005 -24-2 ~ .3 ~
ductor active portion closest to the coil providing the greatest contribution to the net ourrent summation for that conductor.
For example, in Fig. 2A where the center of coil 12 is in space S~ between conduc~or active portions 30a and 29b, the net curre~t induced in conductor 29 is the summation of the individu-al currents induced in conductor active portions 29a, 29b, 29c and 29d, with conductor portion 29b providing the greatest con-tribution since it is the closest to coil 12 of the conductor ac-tive portions of conductor 29. (Conductor portions 2sa and 29c make approximately equal but opposite contributions to the net current, and conductor portion 29d is relatively far from coil 12.) ~s such, the phase o~ the current induced in conductor 29 is determinad by the current induced in conductor portion 29b.
Similarly, the currents induced in conductor portions 30a and 31a make the greatest contribution to the net current in conductors 30 and 31, respectively. In Fig. 2B where the center of coil 12 is in space S3 between conductor portions 29b and 31a, conductor portions 29b, 30a and 31a make the greatest contributions to the current in the respective conductors.
By assigning a binary logic level to the net current phase in each conductor, and forming binary numbers from the logic levels o~tained from the net current phases in all of the grid conductors when coil 12 is energized, a binary number is ob-tained which uniquely identifies two conductor active portions between which, or on one of which, coil 12 is located. (Alterna-tively, the binary number may identify a conductor run.) For ex-MD2/scg331.005 -25-ample, when the center of coil 12 is located in space S2 between conductor active portions 30a and 2sb and for a counterclockwise energizing current in coil 12, as depicted in Fig. 2A, the net current phase is out of conductors 29 and 30, and into conductor 31. By assigning the binary logic level "01l to net current out of a conductor, the net currents induced in conductors 31-29, respectively, produce the binary number "100", which uniquely identifies space S2 between conductor active portions 30a and 29b tor one of the conductor active portions 30a or 2gb). In Fig.
2B, the center of coil 12 located in space S3 between conductor active portions 29b and 31a with a counterclockwise energizing current induces currents to produce the binary number "101".
Processing circuitry 37 processes the signals received from con-ductors 2g-31 and provides signals representing the position of the center of coil 12 relative to X grid 25.
The seven binary numbers identifying the seven spaces Sl-S7 between adjacent conductor active portions form a Gray-type code given in Table I below ~with the conductor order being "31, 30, 29").

MD2~scg331.005 -26-$~
~BL~ I
Code Sl 1~ 0 s3 101 s7 011 The description above demonstrates operation of a ser pentine grid digitizer system for coarse coil location. Inter-polation may be used to locate the coil center within a space be-tween adjacent conductor active portions or on a conductor active portion. Further description of serpentine grid patterns and op-eration thereof to obtain the location of the coil relative thereto is found in the above-cited patents. However, as men-tioned above with respect to the prior approaches, as the number of conductors and the number of coarse locations increase, either the nu~ber of unique spaces that may be identified with a given conductor run spacing and a given numbar of conductors is reduced, or the distance between adjacent active conductor por-tions becomes too large so as to present signal level or noise problems.
In accordance with the invention, n serpentine conductors are laid out with with the repeat increment of at least one of the conductors being non-uniform, at least in the position-determining portion of the grid to provide up to 2n-1 uniquely identifiable spaces in a serpentine grid system.
Fig. 3 shows a grid system 40 incorporating the invention for an approximately six inch by six inch active area 42. Grid MD2/scg331.005 -27-f ~3(~

40 includes an X axis grid 44 and a Y axis grid 45, each compris-ing five conductors 46x-50x and 46y-50y. Conductors 51x and 51y are common returns for the X axis grid 44 and the Y axis grid 45, respectively. Conductors 46x-50x and 46y-50y are coupled to respective inputs of respective multiplexers (not shown), -~
generally as shown in Fig. 9A or 9B and discussed below in con nection with the X axis grid shown in Fig. 8. Since the X axis grid 44 and the Y axis grid 45 may be the same, the following description of ~he X axis grid 44 ~pplies also to the Y axis grid 45.
Each of the X axis conductors ~6x-50x includes a plurality of ~paced, parallal active portions or runs 53 extend-inq in the Y direction. The active portions of the Y axis grid conductors extend in the X direction normal to the X axis active portions, and the X axis and Y axis grid conductors are insulated from each other. Adjacent active portions 53 of each conductor are connected by connecting portions 54 which extend in the X
direction outside of active area 42. The active portions 53 of all conductors 46x-50x are spaced by spaces 58 (second spaces).
Each of conductors 46x-50x and 46y-50y are electrically insulated from each other by extending them in different closely-spaced planes that are insulated in known manner from each other. The different conductors of a same axis may be insulated from each other in other ways, e.g., at the crossover or intersecting points. It is preferred that the conductor runs of all con-ductors be uniformly spaced. However, they need not be. Uniform MD2/scg331.005 -28~

f~ f 2 ~

spacing is preferred because it facilitates fine location determination using interpolation techniques. Thus, with reference to Fig. 3, the "basic" spacing 58 between runs of all conductors 46x 50x is uniform. Each individual conductor 46x-50x is run in a serpentine path from one-side of X axis grid 44 to the other. (However, it is not necessary that all conductors in a particular grid be run in a serpentine fashion, and a grid may include non-serpentinely run conductors.) Each conductor 46x-50x includes from five to eight active portions 53, and the X axis grid 44 laid out as shown in Fig. 3 has a total of 31 active por-tions, only 25 of which lie in active area 42. Thus, active area 42 for the X axis includes twenty-four spaces 58.
In order to uniquely identify in a Gray-type code each of the spaces 58 of the X axis grid 44 in active area 42 (or the conductor runs), with a constraint on the maximum repeat incre-ment for each conductor in accor~ance with the invention, at least one of conductors 46x-50x has a non-uniform spacing (first spaces) between its activs portions 53, i.e., at least one of those conductors is run in a serpentine path with a non-uniform repeat increment. In the particular embodiment depicted in Fig.
3, all of conductors 46x-50x have a non-uniform repeat increment.
The repeat increments of conductors 46x-50x may ~e determined manually or with computer assistance using, for example, the al-gorithm flow charted in Fig. 15. Patterns of five serpentine conductors other than the one depicted in Fig. 3, with a con-straint on the maximum repeat increment of the conductors, will MD2/scg331.005 -29-2~3~
provide up to thir-ty one uniquely identifiable regions or spaces 58 (or conductor runs) in a Gray-type code.
A constraint on the minimum conductor repeat increment is also preerably imposed in accordance with the invention, as dis-cussed herein.
A constraint is also preferably imposed in accordance with the invention on the maximum change permitted in repeat in-crement from one run to the next consecutive run of any con-ductor.
Tha repeat increments for the embodiment depicted in Fig.
3 are set forth in Table II below. The maximum repeat increment is 7 and the minimum repeat increment is 3. To minimize non-linearity in connection with mathematical interpolation, con-ductor run imbalance is held to a minimum, i.e., the maximum ~-hange in the repeat increment between consecutive runs of the same conductor is limited to 2, i.e., the repeat increment may change by 1 or 2 from one run to the next consecutiva run of any same conductor. The actual spacing between adjacent active por-tions 53 of the same conductor is a multiple of the basic spacing 58 between adjacent active portions 53 of all conductors. Thus, for a basic spacing 58 of 0.250 inch, a repeat increment of 4 equals one inch.

MD2/scg331.005 -30-T~BL~ II 2~3~7 Conductor Re~eat Increment 46x 4, 4J 4, 5,4, 4, 3 47x 5, 7, 6, 7 48x 3, ~, 5, 6, 4, 3 49x 7, 6, 7, 6 50x 4, 4, 3, 4 Constraints on the maximum and minimum repeat increments, and for the maximum change in repeat increment between consecu-tive runs of the same conductor for serpentine grid conductor structures according to the invention are determined in consider-ation of the following.
With respect to maximum repeat increment, referring to Fig. 4, the amplitude or magnitude (absolute value) of current ID
induced in ~coil driven) or by (grid driven) serpentine conductor 60 decreases with increasing distance in both directions away from the center 62 of coil 12. If the closest run or active por-tion of a conductor is at distance D from the center 62 of coil 12, the current magnitude ¦ID¦ induced in that conductor run for given signal levels must be significantly greater than the ex-pected noise level, ¦IN¦, e.g., ¦ID¦ must be greater than ¦IN¦.
The maximum distance D is selected for "one sided current'l, i.e.,current induced in a conductor in the beginning and ending areas of the grid where the coil center 62 may be located on one side of one run of a conductor, rather than between two runs of the same conductor. Since in most of the active area, the center 62 of coil 12 will be between two runs of the same conductor, and the induced current will be additive from the two runs between MD2/scg331.005 -31-which the coil center is located, an even greater noise margin is provided.
With respect to the minimum repeat increment, the primary constraint thereon is that adjacent runs o the same conductor s~ould be spac~d so that the current phase changes in a particu-lar conductor as the coil 12 is moved past only one of the two adjacent runs of that same conductor. Another minimum repeat in-crement criterion relates to fine position determination. For, example, where mathematical interpolation is used as described below, the repeat increment should be large enough to provide good linearity of signal level vs. distance between any two ad-jacent runs of the conductor. Maintaining such linearity enables the fine position to be determined directly from a mathematical operation performed directly on current magnitudes, as opposed to first performing a mathematical operation on current values (e.g., forming a ratio) and then using the result of the mathe-matical operation with a look-up table to obtain the interpolated fine position.
A worse case estimate of error relative to ¦Imin¦ used for interpolation is ¦I(max incr) - I(min incr)¦. Thereforel conflicting goals are presented, i.e., set the minimum repeat in-crement as larg~ as possible, and as close as possible to the maximum repeat increment (i.e., minimize the change in repeat in-crement between consecutive runs of the same conductor) to mini-mize fine position determination errors; and set the maximum repeat increment as small as possible for noise immunity.

MD2/scg331.005 -32-20~9~
If the amplitude of the induced current is to be used for interpolation, then it is preferable that the current amplitude used be that of the current induced in the conductor run closest to the center of the coil, and with negligible or no contribution from the adjacent run of the same conductor. The reason for this is that the slope of current amplitude vs. distance from coil center is approximately linaar in the region closest to the con-cerned conductor run.
Referring to Fig. 5, serpentine conductor 64 includes runs C1, C2, and C3 which are at distances dl, d2, and d3, respectively, from the center 62 of coil 12; and the center 62 of coil 12 is located closest to conductor run Cl. The total cur-rent amplitude IT in conductor 64 used for interpolation, which is approximately equal to the sum of the currents induced in the individual runs (IT = I(d~) t I(d2) + I(d3)), must be approxi-mately equal to I(d2) for good linearity. ~f the minimum current which will be used for interpolation is Imin, then the current amplitude contribution I(d2) of conductor run C2 is selected to be at least O.9(Imin). In other words, the maximum I(dl) and I~d3) contributions of conductor runs C1 and C3 are selected to be less than O.l(Imin). This imposes a constraint on the close-ness of conductor run C2 to conductor runs C1 and C3, i.e., the minimum repeat increment. The larger the minimum repeat incre-ment, the more accurate the interpolation may be.
In most areas of a serpentine grid tablet, the total amplitude of the induced current IT is the individual contribu-MD2/scg331.005 -33-.. . ... ,. ... j.. _., ~, . .. .. .

2 ~3 ~3 ~
tions of multiple conductor runs, e.g., the contributions of I(dl), I(d2) and Itd3) (Fig. 5! in conductor runs Cl, C2 and C3, as described above. Referring to Fig. 5, the current introduced by the I(d2~ contribution is of the opposite polarity to the cur~
rent introduced by the I(d3) contribution. If conductor runs Cl and C3 are equidistant from coil center 62, i.e., dl=d2, then the currents in conductor runs Cl and C3 are equal and opposite, and cancel. In such a case, the total current in conductor 64 will bP I(d2), which introduces no interpolation error. Thus, inter-polation may be facilitated and interpolation accuracy may be im-proved by spacing the conductor runs immediately adjacent each side of the run closest to the coil center equidistantly there-from. For example, conductor run Cl and conductor run C3 would b~ spaced equally from conductor run C2, i.e. Rl=R2. However, since the conductors are fixed and the coil is movable, the con-ductor runs immediately adjacent the one closest to the coil cen-ter will seldom be equidistant from the coil center. Also, it is not possible for all runs of a serpentine conductor having a non-uniform repeat increment to be equidistantly spaced from adjacent conductor runs.
However, it is possible to minimize the unequal spaciny or imbalance of the two immediately adjacent conductor runs from the coil center. This is accomplished in accordance with the in-vention by imposing a constraint on the maximum change in repeat increment from run to run of the conductors. For example, limit-ing the maximum change in repeat increment to 2 limits the im-MD2/scg331.005 -34-2~3~7 balance in relative positioning of conductor runs immedlately ad-jacent the one closest to the coil center, and places the immedi-ately adjacent conductor runs sufficiently close to equidistant from the coil center for various locations of the coil so that the current contributions in the two immediately adjacent runs substantially cancel.
However, since the repeat increments and change in repeat increments are known, and the location of adjacent runs of a con-ductor are Xnown, the imbalance at all points on the grid is known and may be compensated. Preferably, such compensation is accomplished by changing the sensed current amplitudes in accor-dance with the known imbalance. One way to implement the com pensation is by means of a looX-up table in which the coarse tablet location indexes the table, which then provides scaling factors for the current amplitudes to compensate for the im-balance~
Another parameter to be selected in providing a ser-pentine grid structure according to the invention is the basic conductor spacing 'IS'', which impacts on resolution for coarse location determination and accuracy for fine location determina-tion. In order to impose a minimum current magnitude ¦Imin¦
criterion for the current used in interpolation, the choice of conductor runs used in interpolation must not be limited to the two between which the coil center is positioned. Referring to Fig. 6, the center of the coil is represented by zero crossing (or phase reversal point~ 62, and the minimum acceptable current MD2/scg331.005 -35-.. ........ .. .. .... . .. , . ... ,, ,, , ,,,,,, , , , ,,, , ~,, , ,, , ~ ,. . .. . . .

- ` 2 ~ 3 ~
magnitude for interpolation is ~ n¦ which occur on the current curve given distances in both directions from zero crossing 62.
It is possible that a conductor run B be located such that it is closer to zero crossing 62 than the ¦Imin¦ point. Therefore, the current in run B can not be used for interpolation, and inter-polation must be permitted using the currents in runs A and C, despite the location of zero crossing 52 between runs B and C.
This introduces other conflicting objectives. In order for run B to be located between runs A and C with uniform basic spacing S, the spacing L between runs A and C must be twice the basic spacing S. Since the spacing L should be much less than the coil diameter to minimize non-linearity, these criteria sug-gest spacing adjacent conductor runs closely. However, for a given conductor span (tablet width), closely spaced conductor runs sugges~ a large nu~ber o~ con~uctors, thus, presenting addi-tional conflicting objectives.
With no minimum/maximum repeat increment criteria, N con-ductors can be laid out to produce 2n-l unique areas. For an overall tablet length L, the basic conductor spacing must be greater than or equal to L/(2n 1). As constraints on repeat in-crement criteria are imposed, however, the number of feasible combinations of uniquely identifiable spaces may decrease from the unconstrained 2n-1 combinations. In the limiting case, set-ting the minimum and maximum repeat increments equal to each other and egual to n*~basic conductor run spacing) constrains the MD2/scg331.005 -36~

2 0 3 ~ P"!
number of possible unique combinations to 2n (each conductor can be run once in each direction parallel to the axis).
Typica}ly, the standard or basic conductor spacing is constrained to be less than twice the coil diameter; and for ergonomic reasons, cursor coils are usually less than an inch in diameter. The standard conductor spacing is thus the first para-meter to be set, and is in the order of approximately 0.250 inch.
The maximum tablet length is selected typically be marketing criteria. With these two parameters set, the number of unique regions or spaces per axis is defined as: L/ (standard conductor spacing).
The number of unique regions required then defines the minimum number of conductors n, such that 2n is greater than or e~ual to the nu~ber of unique regions or spaces required. The conductor spacing may be modified at this stage if, with the selected number of conductors, the desired accuracy and precision is not achieved as the tablet length increases in a particu}ar axis.
The minimum/maximum repeat increments are selected to typically be in the order of 3 to 5 times the diameter of the coil. Since the error phenomena is expected to be a square-law function of the distance, the currents induced in adjacent con-ductor runs of the same conductor with these repeat increment limits is expected to be less than 0.1 of the peak value of Imin.
To reduce interpolation errors, a minimum repeat incre-ment of about ~ * coil diameter and a maximum basic conductor MD2/scg331.005 -37-.. ~,_, . . .. .. _ . . _ ~ .. . . .. , . , .. , _~_ , . . .. . ... . , .. ,, . .. . ... . _, ., _ , _ _ spacing of about coil diameter/~ are preferred. The preferred number of conductors is obtained from the following ratio: mini-mum repeat increment/basic conductor spacing. Thus, ~he minimum numher of conductors preferred is 8 (4D/(D/2)=8). These paramet ers (minimum repeat increment and basic conductor spacing) directly affect the achievable accuracy, and can be modified as required to achieve an economically feasible number of con-ductors. As digital electronic components typically come in mul-tiples o~ 8 inpu~s/ou~puts, the choice is usually between 8 or 16 conductors. The preferred implementation is 8 conductors if that can provide the desired tablet length L in a given axis (L ~ 256 * basic conductor spacing), and the coil charact~ristics are such that the errors induced by minimum repeat increment criteria are acceptable, provided that L/ (basic conductor spacing) combina-tions can be ~ound while imposing the maximum repeat increment criterion. A ~6 conductor implementation requires mora com-ponents, but is typically much easier to design in view of the multitude of competing requirementsO An eight conductor grid may provide up to 28 l or 255 spaces or regions, and a sixteen conductor grid ~ay provide up to 216 -1 or 65535 spaces or regions. The actual number of unique spaces provided depends upon the constraints imposed on the conductor repeat increment.
Referring again to Fig. 3, processing circuitry (not shown in Fig. 3) provides a unique binary number identifying the position of the center 62 of coil 12 for each space 58, which identifies the two active conductor portions 53 defining the par-MD2/scg331.005 -38-2~i3~.q~
ticular space 58 between which the coil center 62 lies. For ex-ample, the binary number "01000" identifies (locates coil canter 62 in) space S10 in Fig. 3; the binary number ~01010" identifies space Sll; the binary number "01011" identifies space S12; the binary number ~11011" identifies space S13; etc. The arrows in Fig. 3 associated with conductor active portions 53 correspond to current phases in the conductor active portions when the coil center 62 is located in space S10 (coil dri~en system with cur-rent in coil 12 counterclocXwise). The full Gray-type code for all of spaces 58 in Fig. 3 may be obtained as described above in connection with Figs. 2A and 2B.
The tablet length in a given axis depends upon the basic spacing between adjacent conductor active portions, the number of conductors, and the repeat increments for each conductor (i.e., the number of active portions per conductor). For the X axis grid 44 depicted in Fig. 3, for a basic conductor active portion spacing of 0.250 inch, with five conductors and a repeat incre-ment of from 4-8 (each conductor having from 5-~ active por-tions), which provide 30 conductors active portions and 29 spaces, a maximum tablet length of 7.25 inches is obtained, of which about six inches is the active area.
The binary numbers identifying the spaces or regions in the Y axis grid 45 may similarly be obtained. The Y axis grid 45 may be identical to that for the X axis (but rotated 90 degrees) for a square active area, or smaller or larger depending upon the particular geometry desired for the active area. As such, the Y

MD2/scg331.005 -39-~ ~ 3 ~
axis grid 45 may have the same number as~ or more or less than, the number of conductors in the X axis grid.
The grid for a particular axis will typically include 8 or 16 conductors, as described above, because multiplexers and other digital electronic components are typically available with 8 or 16 inputsfoutputs. Fig. 7 shows an X axis grid 70 which in-cludes sixteen conductors 72-87, each having from 3-4 active por-tions 90. Conductor 88 is the common return for conductors 72-87. The conductors (and the X axis and Y axis grids) are insu-lated from each other as described above for grid 40 of Fig. 3.
In the Fig. 7 embodiment, the total number of conductor active portions 90 is fifty-five, and the total number of spaces 92 be-tween conductor active portions 90 is fifty-four. For a basic conductor run spacing 92 of 0.~0 inch, the span of X axis grid 70 is 13.5 inches, and the active area 83 is 12 inches. Con-ductors 72-87 are arranged in a patt~rn such that currents in-duced by a coil 12 centered in the different spaces 92 provide a Gray-type binary code as described above. For example, the cen-ter 62 of coil 12 is in space S34, the binary number obtained from conductors 72-~7 is "0001111111111110"; space S35 provides ~0000111111111110~; and space S36 provides "0000011111111110".
The repeat increment for conductors 72-37 of X axis grid 70 varies from a repeat increment of fourteen to a repeat incre-ment of eighteen, which for a basic spacing 92 of 0.250 inch, is from 3.5 inches to 4.0 inches. To minimize non-linearity in con-nection with mathematical interpolation, conductor run imbalance MD2/scg331.005 -40-2~39~
is held to a minimum, i.e., the maximum change in the repeat in-crement between consecutive runs of the same conductor is limited to 2. Table III below lists the repeat increments for each of conductors 72-~7.
TABL~ III

Conductor Increment Spacinq 72 15, 14, 14 73 15, 14, 15 74 15, 16, 14 1~, 15, 14 76 16, 18 77 16, 14, 16 78 1~, 18 79 16, 14, 15 15, 18 81 16, 14, 14 82 16, 18 83 16, 14 84 16, 18 18, 18 ~6 1~, 18 87 18, 18 Fiy. 8 shows an X axis grid 100 which includes sixteen conductors 102-117 each having from 15-18 active portions. Con-ductor 11~ is the common return for conductors 102-117. The con-ductors ~and the X axis and Y axis grids) are insulated from each other as described above for grid 40 of Fig. 3. In the Fig. 8 embodiment, the total nu~ber of conductor active portions 120 is 256, and the total number of spaces 122 between conductor active portions is 2550 For a basic spacing 122 of 0.200 inch, the length or span of X axis grid 100 is 51 inches, and the active area is 48 inches. Conductors 102-117 are arranged in a pattern such that currents induced by a coil centered in the different spaces 122 provide a Gray~type binary code as described above.

MD2/scg331.005 -41-2 ~
The repeat increment ~or conductors 102-117 of X axis grid 100 varies from a repeat increment of fourteen to a repeat increment of eighteen, which for a basic spacing 122 of 0.200 inch, is from 2.8 inches to 3.6 inches. The maximum change in the repeat increment between consecutive runs of the same con-ductor is limite~ to 2 (conductor run imbalance is held to a min-imum), as in the embodiments of Figs. 3 and 7, to minimize non-linearity in connection with mathematical interpolation. Table IV below lists the repeat increments for each of conductors 102-117.

MD2/scg331.005 ~42-~3~}`~

TABLE IV
Conductor Increment Spacinq 102 15, 14, 14, 15, 15, 15, 14, 14, 15, 14, 15, 14, 14, 14, 15, 15, 14 103 15, 14, 15, 14, 16, 14, 16, 14, 14, 14, 14, 16, 14, 16, 15, 15, 14 10~ 15, 16, 14, 14, 15, 15, 15, 14, 14, 15, 14, 15, 14, 14, 14, 15, 15 105 16, 15, 14, 15, 14, 16, 14, 16, 14, 14, 14, 14, 16, 14, 16t 15, 15 106 16, 18, 17, 15, 14, 15, 15, 15, 14 16, 14, 1~, 15, 17, 18 107 16, 14, 16, 14, 14, 15, 15, 15, 14, 14, 15, 14, 15, 14, 14, 14, 15 108 16, 18, 16, 18, 18, 18, 18, 18, 18 18, 17, 15, 14, 14 109 16, 14, 15, 15, 14, 15, 14, 1~, 14, 16, 14, 14, 14, 14, 16, 14, 16 110 16, 18, 18, 18, 18, 16, 18, 18, 18, 18, 16, 18, 18, 18 111 16, 14, 14, 16~ 14, 14, 16, 14, 15, 14, 14, 15, 16, 14, 16, 14 112 16, 18, 18, 18, 18, 17, 17, 18, 18, 18, 17, 16, 14, 1~
113 16, 14, 16, 14, 16, 14, 16, 18, 18, 18, 16, 18, 18, 18 114 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18 115 18, 18, 18, 18, 18, 18, 18, 18, 1~, 18, 18, 18, 18 116 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18 117 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, MDZ/scg331.005 -43-~9~
E`or the Fig. 8 embodiment described in the preceding par-agraph, the minimum spacing between adjacent conductor active portions of the same conductor is 2.8 inches, or a repeat incre-ment of 14.
Signal ~cquisition and processing to obtain the signals representing the coordinates of th~ movable element relative to the digitizer active area ara described below in connection with Figs. 9-ll. Referring first to Fig. 9A, coil driven digitizer system 130 according to the invention comprises digitizer tablet 131 which includes X and Y axes grids 100 and lO1 similar to X
axis grid 100 of Fig. 8, and signal acquisition and processing circuitry 132. One end of each of X axis grid conductors lO~x-111x is coupled to an X axis multiplexer 133, and one end of each of Y axis grid conductors 102y-117y is coupled to a Y axis multi-plexer 153. Multiplexers 133, 153 may be conventional 16-to-1 multiplexers (or two, ~-to-l multiplexers). Respective opposite ends of X axis grid conductors 102x-117x are connected to ground, and respective opposite ends of Y axis grid conductors 102y-117y are connected to ground. Output 155 of multiplexer 133 and out-put 156 of multiplexer 153 are coupled to current sensing ,~ ,rz amplifier 148. Microprocessor 160 via X/Y select lines 152, 153 enables one of multiplexers 133, 153 at a time, and via address bus 154 selects one grid line at a time to be coupled from an in-put of the enabled multiplexer 133, 153 to the output 155, 156 of the enabled multiplexer 133, 153.

HD2~scg331.005 -44-2~339$'~ ~
Microprocessor 150 is coupled to read only memory (ROM) 160 (e.g., EPROM) containing the program for operating digitizer system 130, a look-up table for correlating binary nu~bers cor-responding to the current phases in the individual conductors of grids 100, 101 to a coarse tablet location, and a look-up table for scaling current amplitudes used for interpolation, as de-scribed above. Microprocessor lSO also includes temporary read/write memory for storing the digital signals corresponding to the induced currents detected in the individual grid con-ductors. Such temporary memory may simply be registers or random access memory (RAM).
Current sensing amplifier 148 is coupled to an analog-to-digital (A/D) converter 162 which is in turn coupled to micro-processor 150. Current sensing amplifier 148 may include cir-cuitry for introducing a dc offsat to the currents sensed from X/Y multiplexers 133, 153, as described below.
As mentioned above, digitizer system 130 is coil driven, i.e., coil 12 is energized and the signals induced in grid con-ductors 102x-117x and 102y-117y are sampled and processed to ob-tain the coordinates of coil 12 relative to the active area 172 of tablet 131. Coil 12 is tuned to the frequency of interest and induces a current in each of grid conductors 102x-117x and 102y-117y depending on the position of coil 12. Microprocessor 150 outputs clock pulses at a given frequency, e.g., lOKHz. to 20 KHz., to driver 176, which provides sufficient current to coil 12. Microprocessor 150 is programmed in ~nown manner to associa-MD2/scg331.005 -45-~ ~ 3 ~
te currents sampled on the grid conductors with phasing of the signals supplied to coil 12.
Processing circuitry 132 is shown functionally in Fig.
9A, and may be implemented by discrete components, or by a micro-controller or microcomputer including all or some of the func tional blocks depicted. For example, an ~os6-family micro-controller, available from Intel Corp., with associated support circuitry may imple.ment microprocessor 150, A/D converter 162, ROM 160 and driver 176, depending upon the particular micro-controller selected. If sufficient input/output pins are avail-able, microprocessor 150 may also implement multiplexers 133, 153. Current sensing amplifier 148 may be implemented by conven-tional operational amplifier circui~ry. If not implemented by microprocessor 150, ROM 160 may be implemented by conventional EPROM chips, etc. Strobe signal lines, a clock and other conven-tional components or parts o~ processing circuitry 132 have not been shown and are known to those of skill in the art.
Referring next to the flow chart in FigO 10, digitizer system 130 is operated according to a main routine 200 as fol-lows. The magnitudes and phases o~ the current ~ignals induced in each of the sixteen conductors o~ the X axis grid conductors 102x-1}7x and the Y axis grid conductors 102y-117y for the posi-tion of coil 12 on active area 172 are obtained and temporarily stored in internal registers of microprocessor 150 according to routines 201 and 202. For the cursor-driven system 130 of Fig.
9A, each grid conductor 102x-117x and 102y-117y is sequentially MD2/scg331.005 -46-coupled to current sensing amplifier 148, which interjects a dc offset to the sensed current signals and amplifies the sensed current signals, providing voltage output signals proportional to the amplified current signals. For example, the voltage output signals may have a dc offset of 2.0 volts, so that voltages be-tween o and 2.0 are 180 degrees out of phase with voltages above 2.o volts. These voltage signals are supplied to A/D converter 162 which converts the positive analog voltages to digital sig-nals and supplies them to microprocessor 150 which causes the digital representations of the analog voltages to be stored in internal registers. Microprocessor 150 is programed to recognize stored voltages below 2~0 volts as corresponding to grid currents of one phase, and to recogni~e stored voltages above 2.0 volts as corresponding to currents of the opposite phase.
The binary number described above which represents the coarse location of the center of coil 12 within a particular space or regions between two immediately adjacent conductor ac-tive portions for the X axis and for the Y axis is then determined by microprocessor 150 according to routine 204. Mi-croprocessor 150 accomplishes that by ordering the phases of the stored voltage signals in accordance with the multiplexing se-quence of the grid conductors for each axis.
The binary numbers obtained in routine 204 are indexed by microprocessor 150 according to routine 206 in a look-up table contained in ROM 160, which supplies the coordinates of the coarse location, i.e., the particular region between conductor MD2/scg331.005 -47-active portions or each axis in which the center of coil 12 lies. If mathematical interpolation is used to determine fine location, the indexed location of the ROM look-up table also identifies the conductors which are to be used in the fine loca-~ion determination for each axis.
However, fine location may be determined largely indepen-dently of the coarse position determination, i.e., a number of techniques may be used for fine position detennination, and mi-croprocessor 150 determines fine position according to routine 208. It is preferre~ that fine location of coil 12 for each axis be determined by mathema~ical interpolation according to, for ex-ample, routine 208A flow charted in Fig. 11. Alternatively, fine location may be determined as described below, or using current phases in a pair of conductors as described in the Bailey '963 Patent.
Referring again to Fig. 10, microprocessor 150 in routine 210 then determines the precise X and Y coordinates of the cursor from the coarse and fine location determinations for each axis.
Fine position may be determined by interpolation as fol-lows. Because there may be some ambiguity as to which two con-ductors to use for interpolation, and to implement use of a mini-mum current magnitude (IImin¦) for interpolation, as discussed above, step 206 of main routine 200 (Fig. 10) identifies for each axis, more than two conductors, e.g., four conductors. As sho~n in Fig. 12, those four conductors for each axis are designated "A", "B", "C", and "D". ~eferring to Fig. 11, in step 212 of MD2/scg331.005 -48-r~
routine 208A, the magnitudes (i.e., absolute values) of the cur-rents in conductors A, B, C, D are obtained. In steps 214, the current magnitudes in conductors B and C are compared. If they are the same, then the fine position is midway between conductors B and C (step 216). If the current magnitude is greater in con-ductor C, then the current magnitudes in conductors A and C are used for interpolation (step 218). I~ the current magnltude is greater in conductor B, then the current magnitudes in conductors B and D are used for interpolation (step 220). Actual interpola-tion is then mathematically performed in either step 218 or step 220 by taking the ratio of the signal magnitudes in the two con-ductors of interest. For example, if conductors B and D are to be used, the ratio is:

l Bl ¦B¦+¦D¦
An alternate embodiment ~or determining fine position is as follows. A 'Ifine location" or "secondary" conductor structure or grid is either disposed adjacent the "primary" or "coarse location" grid (so that it is independent of the primary or coarse location grid), or a fine location grid is disposed a part of the primary grid structure. A separate, independent, secondary two-conductor serpentine grid is described below.
Referring to Fig. 13, serpentine grid 250 comprises two ser-pentine conductors 252, 253 each having a constant repeat incre-ment and with equal basic conductor run spacing W. Three or four conductors instead of two may be run in a similar serpentine pat-MD2/scg331.005 -49-tern to minimize non-linearity errors as the distance from the coil center increases.
The current induced in each run of each conductors 252 and 253 i5 a function o~ the distance of the respective run from the center of a coil (not shown) inducing the current. With uniform basic conductor run spacing W, the composite current in-d~ced in each conductor is primarily a function of the distance from the coil center to the nearest conductor run. Ignoring edge e~fects, the current induced when the coil is centered over a conductor run will be 0; moving th~ coil to one side of that con-ductor run increases the current, and moving the coil to the other side decreases the current. The current peaks (i.e., a maximum positive peak or a maximum negati~e peak) when the edge of the coil is approximately tangent to the conductor run. Thus, as the coil i5 moved across the surface of the secondary grid 250, the induced current will be a sinusoidal-like wa~eform, the precise shape of which is a function of the coil diameter rela-tive to the basic conductor run spacing.
For example, if the coil diameter is much larger than the basic conductor spacing, the induced current waveforms will be triangle~like (saw tooth) because as the coil is moved across the grid there will be times when two or more conductor runs will be within the coil diameter so the inducèd currents conflict with each, and other times when a conductor run is tangent to the coil edge. If the coil diameter is less than the conductor spacing W, the induced current waveform will be sinusoidal-like with flat-MD2~scg331.005 -50-2 ~ S~
tened peak~ (trapezoidal-like) corresponding to the times that the coil edges are spaced from the conductor runs, which ac-centuates the tangential effect.
About the induced current zero point (the center of the coil is above a conductor run), regardless of the repeat pattern, the induced current is for the most part approximately linear vs.
distance from the center of the coil.
Referring to Fig. 13, it has been found that choosing a repeat increment equal to the coil diameter produces a set of in-duced currents such that lia¦/(¦ia¦ + ¦ib¦) produces a quotient hetween O and 1 which is directly proportional to the distance from the "a" conductor; ia being the smaller current magnitude and ib the larger.
The advantage o using the ¦ia¦/(¦ia¦ + ¦ib¦) ratio is that the division makes the quotient independent of the amplitude of the induced current and the drive current need not be con-sistent from digitizer tablet-to-digitizer tablet, and the cursor distance above the grid need not bs fixed. For improved accuracy a polynomial fit can be employed instead of the sample linear model described above, i.e.:
x = Ao + Al [¦ia~ ia¦ + ¦ib¦)] + A2[¦ia¦/(¦ia¦/(¦ia¦ + ¦ib¦)}2 + ... + An [¦ia¦/(¦ia¦ + ¦ib¦)]n.
Ao thru An may be found by building or simulating a model of the grid and collecting the ¦ia¦/(¦ia¦ + ¦ib¦) quotient of various points on the grid (at known location x). Then a polynomial c~rve fitting program may be applied using (¦x - location of MD2/scg331.005 -51-2 ~3 3 ~
"a"¦) as the independent variable, and lial/(lial + ¦ib¦) as the dependent variable. The number of terms on the polynomial may be determined to minimize calculations while maximizing accuracy.
With the increment repeat spacing of secondary grid 250 equal to the diameter of coil 12, fine cycle "F" (two repeat in-crements for a conductor 252 or 253) may be determined to be a distance corrasponding to twice the coil diameter. If the maxi mum repeat increment for a coarse grid conductor is in the order of 4-8 coil diameters (for noise immunity) and basic spacing for the coarse grid conductor runs is equal to that for the fine grid~ then 2-4 conductors are required for 4-16 possible runs (2n), or an active area of 8-32 coil diameters. Reducing the basic coarse location spaces to half the fine grid cycle enables twice the number of conductors to be used, i.e., 4-8 conductors, for an active area of 32-256 coil diameters. Reducing the basic coarse grid spacing even further provide similar increases in the number of possible options and overall grid size. Table V
presents these parameters for various numbers o~ conductors and coil diameters.

MD2/scg331.005 -52-~3~'3~'~
TABLB Y

Conductors Conductors Run Spacing Possible Active Area (nL (In Coil Diameters~ Spaces l2nL (In Coil_Diameters) 4 l/4 16 4 6 l/4 64 16 8 l/4 256 6~
0 l/4 1024 256 6 l/4 6~536 1~384 As mentioned above, the fin~ location or secondary grid may form part of the coarse, primary grid. In that case, two conductors are constrained to have constant spacing, as shown in Fig. 14 and Table V.
Either approach, however, requires that the fine grid repeat increment be twice the diameter of the coil for opt:imal accuracy. A smaller r~peat increment will be les~ efficient and potentially less accurate due to conflicting current inductions.
A large fine cycle width will be less sensitive to repeat pat-terns but would not be accurate as both conductors could be "far away" (into the non-linear region) from the coil centerO
Still another approach uses two grid wires and current phasing as described in the Bailey ' 963 Patent.
As indicated above, the particular grid conductor pat-terns which satisfy the minimum and maximum repeat increments, and which are capable of identifying the spaces between conductor MD2/scg331.005 -53-2 0 3 ~ 3 l~ I
active portion~ in a Gray-type binary code may be determined manually or with computer assistance. Fig. 15 is a flow chart of an algorithm for laying out a grid conductor pattern for an axis of the grid. The following parameters are input as givens: num-ber of grid line locations (or conductor runs or active por-tions), referred to as "goal grid #," which are sequentially num-bered so that conductor active portion #l corresponds to the first grid line location, conductor active portion #2 corresponds to the second grid line location, e~c.; number of grid con-ductors, referred to as "max wire #"; minimum repeat increment, "Rmin": and maximum repeat increment, I'Rmax."
The "generate pattern" algorithm 300 flow charted in Fig.
15 then determines and prints a grid pattern which satisfies the above. Step 302 sets the grid line location to #1, i.e., sets the location of the first conductor active portion to the first grid line locationO Step 304 determines whether the highest grid line location designated is greater than or equal to the goal grid line location (goal grid #). If it is, the algorithm con-siders that a pattern has been determined which satisfies the goals and repeat maximum and minimum increments, and in step 306 prints the pattern and in step 308 stops. If the highest grid line location designated is not greater than or equal to the goal grid #, then the algorithm proceeds to step 310 in which the con-ductor number is set to #1. If in step 312 the number of grid conductors does not exceed the maximum number of conductors (max wire #), then the algorithm proceeds to step 314, which MD2/scg331.005 -54-2 ~ rll determines tha bit pattern (blnary number) of the overall pattern generated to this point including the conductor active portion placed at the last grid line location considered.
Step 316 d~termines if that binary number is unique, i.e., whether that binary number was generated already for a pre-vious stage of the pattern. If it is unique, then in step 318 the distance between this last placed conductor active portion and the adjacent one for the same conductor, i.e., the last repeat increment for that conductor is determined. If that repeat increment is within the minimum and maximum repeat incre-ments, as determined in step 320, then in step 322, that con-ductor is selected for that grid line location, and the informa-tion is storedO The grid line location is then incremented in step 324 and the algorithm proceeds to step 304 to determine the conductor to be placed in the next grid line location ~steps 310-324) or the grid pattern is printed and the algorithm stopped (steps 306-308).
I~ in step 312 the conductor number exceeds the max wire ~, then the algorithm proceeds to step 326 in which the grid line location number is decremen~ed. If the decremented grid line number in step 326 is zero, then a desired grid pattern is not possible within the goal parameters. In step 328, the conductor number is reset back to the one selected for the decremented grid line location. Step 330 then increments the conductor number and the algorithm proceeds to step 312. The loop formed by steps 326, 328 and 330 is cycl~d, and the grid line location decre-MD2/scg331.005 -55-3 ~
mented until the conductor number is lesg than the max wire ~, as determined in s~ep 312. This loop enables ~he algorithm to back trac~ to a particular point and then process forward with a dif-erent pattern until a desired grid pattern is determined. Thus, the algorithm does not have to look forward ~ut is allowed to proceed until it determines that the pattern generated to that point does not satisfy the goals, at which po:int, the algorithm ~ack tracks.
I~ in step 320, the minimum and maximum repeat increments are not satisfied, the conductor num~er is incremented and the next conductor tried starting with step 312.
The algorithm flow charted in Fig. 15 will provide one grid pattern satisfying the goal parameters. There may be others, which may be determined with the aid o~ already-generated grid pattarns, or by use of other algorithms, or by modifying the Fig. 15 algorithm. For example, in addition the maximum and ~inimum repeat increment constraints, the constraint on the maxi-mum change in repeat increment between consecutive runs of a con-ductor may be imposed to enhance ~he cancella~ion effect of in-duced currents for runs adjacent the one closest to the coil cen-ter, as describP above in connection with Fig. 3 and Table III.
As indicated above, it will be easier to generate desired grid patterns when a number of conductors exceeding the absolute mini-mum required is utilized.
Fig. 9B shows a digitizer system 130B which is grid driven, i.e., conductors 102x-117x and 102y-117y are sequentially MD2/scg331.005 -56-energlzed, and the currents induced in coil 12 are sampled. Mul-tiplexers 133 and 153 sequentially switch one end of each of the grid conductors to ground while an energizing signal is applied from driver 1~6b to the other ends which are connected together and to driver 176b. Current sensing ampli~ier 148b, which is coupled to coil 12, senses and amplifies signals induced in coil 12 generally as described above for siqnals induced in the grid conductors of system 130. A/D converter 162B converts the analog signals to digital signals which are supplied to microprocessor 150. Signal acquisition and processing is generally as described above for coil driven system 130 of Fig. sA, with changes that are apparent due to ~.e dual nature of coil and grid driven sys-tems. As discussed above for Fig. sA, Fig 9B is a functional block diagram, and may be implemented, except perhaps for current sensing amplifying 148b, ~y a microcontroller (e.g. Intel 8096 family) or a microcomputer.
As is the case with most digitizer grid structuras, "edge effect" errors may be present in areas closP to the conductor connecting portions and the ground and returns of the conductors.
Such errors may be avoided or minimized by defining an active area su tably spaced from such connecting portions, returns and ground. Alternatively, such ~'edge effects~ may be compensated.
Certain changes and modifications of the embodiments of the invention herein disclosed will be readily apparent to those of skill in the art. ~oreover, uses of the invention other than for coordinated determination in ~ digitizer system will also be MD2/scg331.005 -57-2 ~ 3 ~
readily apparent to those of skill in the art. It is the ap-plicant's intention to cover by the claims all such uses and all those changes and modifications which could be made to the em-b~diments of the i.nvention herein chosen for the purposes of dis-closure which do not depart from the spirit and scope of the in--vention.

MD2/scg331.005 -58-

Claims

1. A conductor structure for a position-determining device which includes a movable element and determines the loca-tion of said movable element relative to said conductor struc-ture;
said conductor structure comprising;
at least first, second and third conductors each of which includes at least three active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;
said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con-ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform.

MD2/scg331.005

2. A conductor structure fox a position-determining device which includes a movable element and determines the loca-tion of said movable element relative to said conductor struc-ture;
said conductor structure comprising;
at least first, second and third conductors each of which includes at least three active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;
said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con-ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform in a position determining area of said conductor structure.

MD2/scg331.005

3. A conductor structure for a position-determining device which includes a movable element and determines the loca-tion of said movable element relative to said conductor struc-ture;
said conductor structure comprising;
at least first, second and third conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;
said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con-ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure;
(b) the-repeat increment of at least one of said con-ductors is non-uniform; and (c) the repeat increment of said conductors is con-strained by a maximum repeat increment that is determined in re-lation to desired noise immunity.

MD2/scg331.005

4. A conductor structure for a position-determining device which includes a movable element and determines the loca-tion of said movable element relative to said conductor struc-ture;
said conductor structure comprising;
at least first, second and third conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors is series;
said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con-ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform; and (c) the repeat increment of said conductors is con-strained by a maximum repeat increment that is determined in re-MD2/scg331.005 lation to desired noise immunity, or a minimum repeat increment or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations of a maximum repeat incre-ment, a minimum repeat increment and a maximum change in consecu-tive repeat increments.

5. The conductor structure of claim 4 wherein the repeat increment is constrained by a minimum value and by a maximum value.

6. The conductor structure of claim 4 wherein the repeat increment is constrained by a minimum value, by a maximum value and by maximum change in consecutive repeat increments.

7. Apparatus for determining the location of a movable element relative to a given area comprising:
a conductor structure which interacts with said element when said element is on or adjacent said given area and upon energization of at least one of said conductor structure and said element;
said conductor structure comprising:
at least first, second and third conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;

MD2/scg331.005 said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con-ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform and the repeat increment of said at least one conductor is constrained by a maximum repeat increment, or a minimum repeat increment or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations of a maximum repeat increment, a minimum repeat increment and a max-imum change in consecutive repeat increments.
said apparatus including:
means for energizing one of said conductor structure and said movable element to cause location-determining signals to be present in the other;
means for processing said location-determining signals in the other of said conductor structure and said movable element, said processing means including first means for obtaining from said location-determining signals binary signals corresponding to said binary digits which identify said conductor runs and are in-MD2/scg331.005 dicative of the location of said movable element relative to said given area.

8. The apparatus of claim 7 wherein the repeat increment is constrained by a minimum value and by a maximum value.

9. The apparatus of claim 7 wherein the repeat increment is constrained by a minimum value, by a maximum value and by max-imum change in consecutive repeat increments.

10. A conductor system for a position-determining device which includes a movable element and determines the location of said movable element relative to said conductor system;
said conductor system comprising first and second con-ductor structures;
said first conductor structure comprising:
at least first, second and third conductors each of which includes a plurality of active portions extending substantially in a-first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;
said second conductor structure comprising:
at least fourth, fifth and sixth conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said fourth, fifth and six-MD2/scg331.005 th conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same fourth, fifth and sixth conductors in series;
said conductors of said first conductor structure and said conductors of said second conductor structure being arranged in respective patterns such that for each pattern:
(a) each of said active portions of all of said con-ductors or spaces therebetween of each conductor structure may be uniquely identified by a unique binary number with respect to that conductor structure, respective binary digits of each of said unique binary numbers corresponding to respective con-ductors, whereby upon interaction between said movable element and respective conductors binary logic signals may be obtained corresponding to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform and the repeat increment of said at least one conductor is constrained by a maximum repeat increment, or a minimum repeat increment or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations of a maximum repeat increment, a minimum repeat increment and a max-imum change in consecutive repeat increments.

11. The conductor system of claim 10 wherein the repeat increment is constrained by a minimum value and by a maximum value.

MD2/scg331.005

12. The conductor system of claim 10 wherein the repeat increment is constrained by a minimum value, by a maximum value and by maximum change in consecutive repeat increments.

13. Apparatus for determining the location of a movable element relative to a given area comprising:
a conductor system which interacts with said movable ele-ment when said movable element is on or adjacent said given area and upon energization of at least one of said conductor system and said movable element;
said conductor system comprising first and second con ductor structures;
said first conductor structure comprising:
at least first, second and third conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same conductors in series;
said second conductor structure comprising:
at least fourth, fifth and sixth conductors each of which includes a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said fourth, fifth and six-MD2/scg331.005 th conductors each having repeat increments which space adjacent active portions of the same conductor; and means for coupling the spaced active portions of same fourth, fifth and sixth conductors in series;
said conductors of said first conductor structure and said conductors of said second conductor structure being arranged in respective patterns such that for each pattern:
(a) each of said active portions or spaces therebetween of all of said conductors of each conductor structure may be uniquely identified by a unique binary number with respect to that conductor structure, respective binary digits of each of said unique binary numbers corresponding to respective con-ductors, whereby upon interaction between said movable element and respective conductors binary logic signals may be obtained corresponding to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is-non-uniform and the repeat increment of said at least one conductor is constrained by a maximum repeat increment, or a minimum repeat increment or a maximum change in repeat increments between consecutive runs of a same conductor, or combinations of a maximum repeat increment, a minimum repeat increment and a max-imum change in consecutive repeat increments.
said apparatus including:

MD2/scg331.005 means for energizing one of said conductor system and said movable element to cause location-determining signals to be present in the other;
means for processing said location-determining signals in the other of said conductor system and said movable element, said processing means including first means for obtaining from said location-determining signals binary signals corresponding to said binary digits which identify said conductor active portions and are indicative of the location of said movable element relative to said given area.

14. The apparatus of claim 13 wherein the repeat incre-ment is constrained by a minimum value and by a maximum value.

15. The apparatus of claim 13 wherein the repeat incre-ment is constrained by a minimum value, by a maximum value and by maximum change in consecutive repeat increments.

16. A conductor structure for a position-determining device which includes a movable element and determines the loca-tion of said movable element relative to said conductor struc-ture;
said conductor structure comprising;
at least first, second and third conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first spaces and adjacent MD2/scg331.005 active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of same conductors in series;
said conductor structure having an extent in a second direction that is different from said first direction;
said conductors being arranged in a pattern such that:
(a) at least two of said first spaces between adjacent active portions of at least one of said conductors are different;
(b) the maximum first space between any two adjacent ac-tive portions of the same conductor is less than one-half of said extent of said conductor structure; and (c) each of said second spaces between adjacent active portions or said active portions of all of said conductors may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors, whereby upon interaction between said mov-able element and respective conductors binary logic signals may be obtained corresponding to said binary digits which are indica-tive of the location of said movable element relative to said conductor structure.

17. The conductor structure of claim 16 wherein each of said conductors has a first end and a second end, the first ends of said conductors being uniquely addressable and the second ends of said conductors being coupled together.

MD2/scg331.005

18. The conductor structure of claim 16 wherein said first and second directions are perpendicular to each other.

19. The conductor structure of claim 16 wherein two or more of said second spaces between adjacent conductor active por-tions of all conductors are equal.

20. The conductor structure of claim 16 wherein two ad-jacent active portions of the same conductor are separated by at least one active portion of another conductor.

21. Apparatus for determining the location of a movable element relative to a given area comprising:
a conductor structure which interacts with said element when said element is on or adjacent said given area and upon energization of at least one of said conductor structure and said element;
said conductor structure comprising:
at least first, second and third conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first spaces and adjacent active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of same conductors in series;
said conductor structure having an extent in a second direction that is different from said first direction;

MD2/scg331.005 said conductors being arranged in a pattern such that:
(a) at least two of said first spaces between adjacent active portions of at least one of said conductors are different;
(b) the maximum first space between any two adjacent ac-tive portions of the same conductor is less than one-half of said extent of said conductor structure; and (c) each of said second spaces between adjacent active portions or said active portions of all of said conductors may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors;
said apparatus including:
means for energizing one of said conductor structure and said movable element to cause location-determining signals to be present in the other;
means for processing said location-determining signals in the other of said conductor structure and said movable element, said processing means including first means for obtaining from said location-determining signals binary signals corresponding to said binary digits which identify said second spaces and are in-dicative of the location of said movable element relative to said given area.

22. The apparatus of claim 21 wherein said first and second directions are perpendicular to each other.

23. The apparatus of claim 21 wherein two or more of said second spaces between adjacent conductor active portions of all conductors are equal.

MD2/scg331.005

24. The apparatus of claim 21 wherein two adjacent ac-tive portions of the same conductor are separated by at least one active portion of another conductor.

25. The apparatus of claim 21 wherein said processing means includes means for storing sets of binary numbers cor-responding to locations of said element relative to said given area, and means for comparing said stored sets of binary numbers and said binary numbers obtained from said binary signals to determine said location of said element relative to said given area.

26. The apparatus according to claim 22 wherein said first means of said processing means determines a coarse location of said movable element from said binary numbers relative to said given area, said coarse location corresponding to a location of said movable element between two conductor active portions, said processing means including second means for determining a fine location of said movable element relative to said given area cor-responding to a location between said two conductor active por-tions or on one of them.

27. The apparatus according to claim 26 wherein said processing means provides the amplitudes of said position-determining signals, and said second means performs a mathemati-cal interpolation from selected amplitudes of selected position-determining signals.

28. The apparatus according to claim 26 wherein said conductor structure comprises two additional conductors each hav-MD2/scg331.005 ing a plurality of active portions extending substantially in said first direction substantially in or adjacent said common plane substantially parallel to each other, said active portions of said two additional conductors being equally spaced with respect to adjacent active portions of both of said two con-ductors and equally spaced with respect to active portions of the same conductor, said second means processing position-determining signals in said two additional conductors to determine said fine location.

29. A conductor system for a position-determining device which includes a movable element and determines the location of said movable element relative to said conductor system;
said conductor system comprising first and second con-ductor structures;
said first conductor structure comprising:
at least first, second and third conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first spaces and adjacent active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of same conductors in series;
said first conductor structure having an extent in a sec-ond direction that is different from said first direction;

MD2/scg331.005 said second conductor structure comprising:
at least fourth, fifth and sixth conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first spaces and adjacent active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of the same of said fourth, fifth and sixth conductors in series;
said second conductor structure having an extent in said first direction;
said conductors of said first conductor structure and said conductors of said second conductor structure being arranged in respective patterns such that for each pattern:
(a) at least two of said first spaces between adjacent active portions of at least one of said conductors are different;
(b) the maximum first space between any two adjacent ac-tive portions of the same conductor is less than one-half of said extent of said conductor structure; and (c) each of said second spaces between adjacent active portions or said active portions of all of said conductors may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors.

MD2/scg331.005

30. The conductor system of claim 29 wherein said first and second directions are perpendicular to each other.

31. The conductor system of claim 29 wherein, for each of said first and second conductor structures, said second spaces between adjacent conductor active portions of all conductors of the respective conductor structure are equal.

32. The conductor system of claim 29 wherein, for each of said first and second conductor structures, two adjacent ac-tive portions of the same conductor are separated by at least one active portion of another conductor.

33. The conductor system of claim 29 wherein said pro-cessing means includes means for storing sets of binary numbers corresponding to locations of said element relative to said con-ductor system, and means for comparing said stored sets of binary numbers and said binary numbers obtained from said binary signals to determine said location of said movable element relative to said conductor system.

34. The conductor system of claim 29 wherein said first means of said processing means determines a coarse location of said movable element from said binary numbers, said coarse loca-tion corresponding to a location of said movable element, with respect to each of said conductor structures, between two con-ductor active portions, said processing means including second means for determining a fine location of said movable element, with respect to each of said conductor structures, between said two conductor active portions or on one of them.

MD2/scg331.005

35. The conductor system of claim 34 wherein, for each of said conductor structures, said processing means provides the amplitudes of said position-determining signals, and said second means performs a mathematical interpolation from selected amplitudes of selected position-determining signals.

36. The conductor system of claim 34 wherein said first and second conductor structures each comprises two additional conductors which each have a plurality of active portions extend-ing substantially in said first or second direction, respective-ly, substantially in or adjacent said common plane substantially parallel to each other, said active portions of said two addi-tional conductors being equally spaced with respect to adjacent active portions of both of said two conductors and equally spaced with respect to active portions of the same conductor, said sec-ond means processing position-determining signals in said two ad-ditional conductors for each of said first and second conductor structures to determine said fine location.

37. Apparatus for determining the location of a movable element relative to a given area comprising:
a conductor system which interacts with said movable ele-ment when said movable element is on or adjacent said given area and upon energization of at least one of said conductor system and said movable element;
said conductor system comprising first and second con-ductor structures;
said first conductor structure comprising:

MD2/scg331.005 at least first, second and third conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first space and adjacent active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of same conductors in series;
said first conductor structure having an extent in a sec-ond direction that is different from said first direction;
said second conductor structure comprising:
at least fourth, fifth and sixth conductors each of which include a plurality of active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other adjacent active portions of the same conductor being separated by first spaces and adjacent active portions of all of said conductors being separated by sec-ond spaces; and means for coupling the spaced active portions of the same of said fourth, fifth and sixth conductors in series;
said second conductor structure having an extent in said first direction;
said conductors of said first conductor structure and said conductors of said second conductor structure being arranged in respective patterns such that for each pattern:

MD2/scg331.005 (a) at least two of said first spaces between adjacent active portions of at least one of said conductors are different;
(b) the maximum first space between any two adjacent ac-tive portions of the same conductor is less than one-half of said extent of said conductor structure; and (c) each of said second spaces between adjacent active portions or said active portions of all of said conductors may be uniquely identified by a unique binary number, respective binary digits of each of said unique binary numbers corresponding to respective conductors;
said apparatus including:
means for energizing one of said conductor system and said movable element to cause location-determining signals to be present in the other;
means for processing said location-determining signals in the other of said conductor system and said movable element, said processing means including first means for obtaining from said location-determining signals binary signals corresponding to said binary digits which identify said second spaces and are indicaca-tive of the location of said movable element relative to said given area.

38. The apparatus of claim 37 wherein, for each of said first and second conductor structures, said second spaces between adjacent conductor active portions of all conductors of the respective conductor structure are equal.

MD2/scg331.005

39. The apparatus of claim 38 wherein, for each of said first and second conductor structures, two adjacent active por-tions of the same conductor are separated by at least one active portion of another conductor.

40. The apparatus of claim 37 wherein said processing means includes means for storing sets of binary numbers cor-responding to locations of said movable element relative to said given area, and means for comparing said stored sets of binary numbers and said binary numbers obtained from said binary signals to determine said location of said movable element relative to said given area.

41. The apparatus of claim 37 wherein said first means of said processing means determines a coarse location of said movable element from said binary numbers, said coarse location corresponding to a location of said movable element, with respect to each of said conductor structures, between two conductor ac-tive portions, said processing means including second means for determining a fine location of said movable element, with respect to each of said conductor structures, between said two conductor active portions or on one of them.

42. The apparatus claim 37 wherein, for each of said conductor structures, said processing means provides the amplitudes of said position-determining signals, and said second means performs a mathematical interpolation from selected amplitudes of selected position-determining signals.

MD2/scg331.005

43. The apparatus of claim 37 wherein said first and second conductor structures each comprises two additional con-ductors which each have a plurality of active portions extending substantially in said first or second direction, respectively, substantially in or adjacent said common plane substantially parallel to each other, said active portions of said two addi-tional conductors being equally spaced with respect to adjacent active portions of both of said two conductors and equally spaced with respect to active portions of the same conductor, said sec-ond means processing position-determining signals in said two ad-ditional conductors for each of said first and second conductor structures to determine said fine location.

44. A method of determining a layout of a conductor structure of n conductors having the following characteristics:
each of said n conductors including a plurality of ac-tive portions extending substantially in a first direction sub-stantially in or adjacent a common plane substantially parallel to each other, adjacent active portions of the same conductor being separated by first spaces and adjacent active portions of all of said conductors being separated by second spaces, and the spaced active portions of same conductors being coupled in series;
said conductors being arranged in a pattern such that the following conditions are satisfied:
(a) said conductors have N total active portions;

MD2/scg331.005 (b) the first space between any two adjacent active por-tions of the same conductor does not exceed a maximum value; and (c) each of said second spaces between adjacent active portions or said active portions of all of said conductors may be uniquely identified by a unique binary number;
said method comprising the steps of:
(1) inserting into said layout one of said conductors at a time such that at least two of said first spaces between ad-jacent active portions of at least one of said conductors are different;
(2) after each conductor is inserted into said layout, determining whether conditions (a) - (c) are satisfied;
(3) if conditions (a) - (c) are satisfied in step (2), repeating steps (i) and (2) for the next conductor until n con-ductors have been inserted into said layout;
(4) if conditions (a) - (c) are not satisfied in step (2), then removing the last conductor inserted into said layout and then repeating steps (1) and (2) for another conductor laid out differently from the removed conductor.

45. The method according to claim 44 wherein step (2) additionally determines whether said conductor structure layout satisfies the additional condition (d) that the first space be-tween any two adjacent active portions of the same conductor is not less than a minimum value, wherein step (3) is performed if conditions (a) - (d) are satisfied, and wherein step (4) is per-formed if conditions (a) - (d) are not satisfied.

MD2/scg331.005

46. A method for determining the location of a movable element relative to a conductor structure which interacts with said movable element when said movable element is adjacent said conductor structure upon energization of at least one of said conductor structure and said movable element; said conductor structure comprising at least first, second and third conductors each of which include s at least three active portions extending substantially in a first direction substantially in or adjacent a common plane substantially parallel to each other, said con-ductors each having repeat increments which space adjacent active portions of the same conductor, the spaced active portions of same conductors being coupled in series;
said conductors being arranged in a pattern such that:
(a) each of said active portions of all of said con--ductors or spaces therebetween may be uniquely identified by a unique binary number, respective binary digits of each of said -unique binary numbers corresponding to respective conductors, whereby upon interaction between said movable element and respec-tive conductors binary logic signals may be obtained correspond-ing to said binary digits which are indicative of the location of said movable element relative to said conductor structure; and (b) the repeat increment of at least one of said con-ductors is non-uniform;
said method comprising the steps of:
energizing one of said conductor structure and said mov-able element; and MD2/scg331.005 processing signals obtained from the other of said con-ductor structure and movable element to provide a unique binary number which uniquely identifies a space or conductor active por-tion close to said movable element.

MD2/scg331.005

47. The conductor structure of claim 1, 2, 3 or 4 wherein, for each of said first, second and third conductors, two adjacent active portions of the same conductor are separated by at least one active portion of another conductor.

48. The conductor structure of claim 1, 2, 3 or 4 wherein, for each of said first, second and third conductors, said conductor active portions are equally spaced.

49. The conductor structure of claim 1, 2, 3 or 4 wherein each of said first, second and third conductors has a first end and a second end, the first ends of said conductors being uniquely addressable and the second ends of said conductors being coupled together.

50. The apparatus of claim 7 wherein, for each of said first, second and third conductors, two adjacent active portions of the same conductor are separated by at least one active por-tion of another conductor.

51. The apparatus of claim 7 wherein, for each of said first, second and third conductors, said conductor active por-tions are equally spaced.

52. The apparatus of claim 7 wherein each of said first, second and third conductors has a first end and a second end, the first ends of said conductors being uniquely addressable and the second ends of said conductors being coupled together.

53. The system of claim 10 wherein, for each of said first through sixth conductors, two adjacent active portions of MD15.SCG331.AMD

the same conductor are separated by at least one active portion of another conductor.

54. The system of claim 10 wherein, for each of said first through sixth conductors, said conductor active portions are equally spaced.

55. The system of claim 10 wherein each of said first through sixth conductors has a first end and a second end, the first ends of said conductors being uniquely addressable and the second ends of said first, second and third conductors being coupled together and the second ends of said fourth, fifth and sixth conductors being coupled together.

56. The apparatus of claim 13 wherein, for each of said first through sixth conductors, two adjacent active portions of the same conductor are separated by at least one active portion of another conductor.

57. The apparatus of claim 13 wherein, for each of said first through sixth conductors, said conductor active portions are equally spaced.

58. The apparatus of claim 13 wherein each of said first though sixth conductors has a first end and a second end, the first ends of said first through sixth conductors being uniquely addressable and the second ends of said first, second and third conductors being coupled together and the second ends of said fourth, fifth and sixth conductors being coupled together.

59. The conductor structure of claim 16 wherein said maximum space between any two adjacent active portions of the MD15.SCG331.AMD

same conductor is determined in relation to desired noise im-munity.

60. The conductor structure of claim 16 wherein said conductors are arranged in a pattern such that there is a minimum space between any two adjacent active portions of the same con-ductor or there is a maximum change in first spaces between any two adjacent active portions of the same conductor, or both, which space and change are determined in consideration of approx-imate linear mathematical interpolation of the movable device relative to said conductor structure.

61. The apparatus of claim 21 wherein said maximum space between any two adjacent active portions of the same conductor is determined in relation to desired noise immunity.

62. The apparatus of claim 21 wherein said conductors are arranged in a pattern such that there is a minimum space be-tween any two adjacent active portions of the same conductor or there is a maximum change in first spaces between any two ad-jacent active portions of the same conductor, or both, which space and change are determined in consideration of approximate linear mathematical interpolation of the movable device relative to said conductor structure.

63. The conductor system of claim 29 wherein for each conductor structure said maximum space between any two adjacent active portions of the same conductor is determined in relation to desired noise immunity.

MD15.SCG331.AMD

64. The conductor system of claim 29 wherein said con-ductors of each of said conductor structures are arranged in a pattern such that there is a minimum space between any two ad-jacent active portions of the same conductor or there is a maxi-mum change in first spaces between any two adjacent active por-tions of the same conductor, or both, which space and change are determined in consideration of approximate linear mathematical interpolation of the movable device relative to the respective conductor structure.

65. The apparatus of claim 37 wherein for each conductor structure said maximum space between any two adjacent active por-tions of the same conductor is determined in relation to desired noise immunity.

66. The apparatus of claim 37 wherein said conductors of each of said conductor structures are arranged in a pattern such that there is a minimum space between any two adjacent active portions of the same conductor or there is a maximum change in first spaces between any two adjacent active portions of the same conductor, or both, which space and change are determined in con-sideration of approximate linear mathematical interpolation of the movable device relative to the respective conductor struc-ture.