Absolute position sensing using sets of windings of different pitches providing respective indications of phase proportional to displacement

For enabling a resolver to have absolute position sensing over a wide displacement range while still obtaining the resolution, accuracy and precision obtainable by operation in an incremental mode, the resolver is provided with a number of terminals for providing offset pitch phase indications as a function of position. A microcomputer is programmed to execute a decoding procedure for reading the offset pitch phase indications and from them computing the absolute position. This method is applicable to linear as well as rotary position sensing. By using multiplexing, digital signal processing and large-scale circuit integration of interfacing the resolver to the microcomputer, the method can achieve absolute position sensing with high reliability and low cost. The offset pitch phase indications are readily provided by inductive coupling between a multiplicity of windings, including a set of offset pitch windings connected to the terminals.

BACKGROUND OF THE INVENTION 
1. Field of the Invention. 
The present invention relates to position sensors in which displacement is 
indicated by the phase of an electrical signal. 
2. Description of the Background Art. 
The shaft angle transducer is a fundamental component in modern control 
technology. By employing a mechanical coupling mechanism such as a rack 
and pinion or a spooled band, a shaft angle transducer can monitor linear 
as well as angular displacement. Linear displacement, however, can also be 
measured directly by differential or linear variable phase transformers, 
and ferromagnetic position transducers. See, e.g., Rhod Zimmerman, 
"Resolvers As Velocity and Position Encoding Devices," PCMI, Sept. 1986, 
pp. 47-54; Don Overcash, "Selecting the Proper Position Sensor," Control 
Engineering, Sept. 1986, pp. 294-302. 
Differential or linear variable phase transformers offer many advantages 
such as infinite resolution, ruggedness, input/output isolation, and 
operation over wide temperature ranges. A kind of variable phase 
transformer sold under the trademark "Inductosyn" is also capable of very 
high accuracy. As described in Tripp et al. U.S. Pat. No. 2,799,835, this 
kind of variable phase transformer includes two relatively moveable 
inductor supports. A first one of the supports carries a pair of first and 
second windings each in the form of a flat metallic ribbon following a 
sinuous path along the direction of relative displacement between the two 
supports. The first and second windings are mounted in positional phase 
quadrature relation with respect to each other and are excited in 
electrical phase quadrature by respective sine and cosine signals. The 
second support carries a third winding similar to the first and second 
windings. The third winding is also aligned along the direction of 
relative displacement and is positioned for mutual coupling with the first 
and second windings. Therefore, the third winding provides an electrical 
signal having a phase indicating the relative displacement between the 
supports. 
The "Inductosyn," however, must be used as an incremental device for 
sensing displacements in excess of the wavelength of the windings, because 
a relative displacement of one wavelength between the two supports results 
in the same phase indication. For some other kinds of position sensing 
variable phase transformers, attempts have been made to obtain accurate 
absolute position sensing over a relatively wide range. Pauwels et al. 
U.S. Pat. No. 4,282,485, for example, discloses a linear variable phase 
transformer employing multi-layer helical coils in which the sine and 
cosine driven windings have a density of windings which is a sinusoidal 
function of position along the length of the transformer. Shimizu et al. 
U.S. Pat. No. 4,604,575 discloses a rotational position detection system 
including a first rotary variable phase transformer detecting an absolute 
rotational position within a complete circumference, a second rotary 
variable phase transformer detecting absolute rotational position within 
an integral submultiple of a complete circumference, and means for 
combining the positions detected by the two transformers to obtain an 
indication of absolute rotational position. 
SUMMARY OF THE INVENTION 
Accordingly, the primary object of the present invention is to provide an 
absolute position sensor which indicates displacement over a wide range 
while obtaining the accuracy of an incremental position sensor. 
A specific object of the present invention is to provide an "Inducfosyn" 
type of variable phase transformer with absolute position sensing along 
its entire length. 
Another object of the invention is to provide a low-cost absolute position 
sensor of high accuracy for use in a microcomputer system.

While the invention is susceptible to various modifications and alternative 
forms, specific embodiments thereof have been shown by way of example and 
will be further described in detail. It should be understood, however, 
that it is not intended to limit the invention to the particular forms 
disclosed, but, on the contary, the intention is to cover all 
modifications, equivalents, and alternatives falling within the spirit and 
scope of the invention as defined by the appended claims. 
DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Turning now to the drawings, there is shown in FIG. 1 a schematic diagram 
of an "Inductosyn" type of variable phase transformer 20 for sensing 
linear displacement. The variable phase transformer 20 includes a first 
inductor support 21 and a second inductor support 22 which are moveable 
relative to each other along an axial direction 23. The first support 21 
carries a pair of windings W.sub.1 and W.sub.1 each in the form of a flat 
metallic ribbon following a sinuous path along the axial direction 23. The 
windings W.sub.1 and W.sub.1 are mounted in positional phase quadrature 
relation with respect to each other and are driven by respective cosine 
and sine signals. (Sometimes, however, these kind of resolvers use 
three-phase driven windings instead of two-phase driven windings.) The 
second support 22 carries a third winding W.sub.s similar to the first and 
second windings W.sub.1 and W.sub.1. The third winding is also aligned 
along the axial direction and is positioned for mutual coupling with the 
first and second windings. Therefore, the third winding W.sub.s provides 
an electrical signal having a phase .theta..sub.d indicating the relative 
displacement between the two supports 21, 22. The electrical signal from 
the third winding, however, only gives an incremental indication of 
displacements between the two supports in excess of one wavelength 
.lambda., of the windings, because a relative displacement of one 
wavelength between the two supports results in the same phase indication. 
In other words, for the variable-phase transformer 20, the first and second 
windings W.sub.1 and W.sub.1 comprise a set or pair of windings, each 
winding in the set being disposed in a periodic spatial pattern having the 
same pitch or wavelength .lambda..sub.1 and extending over a distance or 
range including multiple cycles. When used in connection with the third 
winding W.sub.s, the windings W.sub.1 and W.sub.1 permit an electrical 
signal cos(wt+.theta..sub.d) to be generated having a phase .theta..sub.d 
proportional to the relative displacement between the two supports 21, 22. 
The phase .theta..sub.d itself is a periodic function of the relative 
displacement over a range of displacement corresponding to the distance or 
range over which the set or pair of periodic windings W.sub.1 and W.sub.1 
extend. In particular, the phase .theta..sub.d as a function of the 
relative displacement varies continuously over a range of at least two pi 
(2.pi.) radians and is periodic with the same wavelength .lambda..sub.1 as 
the first and second windings W.sub.1 and W.sub.1. The set or pair of 
periodic windings can therefore be considered as defining a phase pattern 
(P.sub.1 in FIG. 2) giving rise to a phase .theta..sub.d that is a 
corresponding periodic function of the relative displacement between the 
two supports 21, 22. 
In accordance with an important aspect of the present invention, the phase 
ambiguity of the "Inductosyn" type of position sensor is resolved by 
providing additional sets of periodic windings, each set of windings 
defining a respective offset pitch pattern (for example patterns P.sub.2 
and P.sub.3 in FIG. 2) having a different respective pitch or wavelength 
(for example .lambda..sub.2 or .lambda..sub.3 in FIG. 2). If the support 
21 is longer than the support 22, the respective offset pitch phase 
patterns are most easily established by placing additional pairs of driven 
windings on the support 21, with each pair of driven windings being 
similar to the windings W.sub.1 and W.sub.1 but having a different pitch 
or wavelength. Alternatively, if the support 21 is shorter than the 
support 22, the offset pitch phase patterns are most easily established by 
providing multiple pick-up windings on the support 22, with each pickup 
winding having a different pitch or wavelength. The alternative method 
requires fewer windings, but in such a case the pick-up windings extend 
over a greater distance and are therefore more susceptible to noise 
pick-up. Consequently, for most applications, it is preferable to use a 
support 22 that is smaller than the support 21 as shown in FIG. 1, and to 
practice the present invention by providing multiple pairs of driven 
windings on the support 21. 
Turning now to FIG. 2, there is shown a schematic diagram of three phase 
patterns P.sub.1, P.sub.2, and P.sub.3 each having multiple wavelengths. 
As introduced above, each phase pattern can be provided by a respective 
pair of driven windings driven by sine and cosine signals for the case in 
which multiple pairs of driven windings are used, or alternatively each 
phase pattern can be provided by a respective pick-up winding for the case 
in which multiple pick-up windings are used. In FIG. 2 the second 
wavelength .lambda..sub.2 is 4/3 of first wavelength .lambda..sub.1 and 
the third wavelength .lambda..sub.3 is 16/15 of first wavelength 
.lambda..sub.1. 
In accordance with an important aspect of the present invention, the phase 
patterns have respective wavelengths which are about the same but are 
offset from each other, preferably according to: 
##EQU1## 
where N.sub.1, N.sub.2, . . . , N.sub.(M-1) are integers. These 
relationships readily permit the phase pattern P.sub.2 to provide absolute 
position sensing over N.sub.1 wavelengths .lambda..sub.1, the phase 
pattern P.sub.3 to provide absolute position sensing over N.sub.2 N.sub.1 
wavelengths .lambda..sub.1, and so on. To facilitate the use of binary 
arithmetic, preferably the N's are powers of two, for example, four, eight 
or sixteen. The phase patterns in FIG. 2 correspond to N's equal to four. 
As further described below, the maximum values that can be selected for 
the N's are determined by the precision of the phase measurements. 
In accordance with another aspect of the present invention, an absolute 
position measurement is made by successively obtaining respective phase 
measurements for each of the phase patterns, and applying a decoding 
procedure. The respective phase measurements are obtained by operating an 
electronic multiplexer which selects the respective set of driven windings 
or the respective pick-up winding for the respective phase pattern. For 
using binary arithmetic in the decoding procedure, the phase measurements 
are preferably made so that a range of 0 to 360 degrees is represented by 
an unsigned binary number from 0 to one minus an integral power of two, 
for example, from 0 to 255 representable with eight binary bits. 
Turning now to FIG. 3, there is shown a graph of the normalized value or 
count C obtained as a function of displacement from the null position for 
each of the phase patterns in FIG. 2. In order to apply a decoding 
procedure shown and described below in connection with FIGS. 20 and 21, 
the measured phase values are normalized, by subtracting predetermined 
constant phase offsets if necessary, to obtain a zero phase value or count 
C at a central null or zero position. The offsets in the pitch of the 
respective phase patterns is evident from the differences between the 
respective slopes for the phase patterns. Each phase pattern has the same 
phase value at a multitude of different displacement values. Each 
displacement value, however, has associated with it a unique set of three 
respective phase values for the phase patterns. Therefore, a decoding 
procedure can determine the absolute displacement from the three 
respective phase values measured for any given displacement within the 
displacement range in FIG. 3. 
Turning now to FIGS. 4 to 6, there is shown a linear position sensor 
employing the present invention. The sensor is housed in an extruded 
aluminum rail 30. An elongated support 31 for a plurality of pairs of 
driven windings (.phi..sub.1, .phi..sub.1, .phi..sub.2, .phi..sub.2, 
.phi..sub.3, .phi..sub.3) is secured in the bottom of the rail 30 by set 
screws 32. Preferably the support is an insulating material such as glass 
fiber reinforced plastic. For high accuracy, ferromagnetic materials are 
typically not used, but if high accuracy is not of prime importance, the 
substrate can be loaded with iron or ferrite powder to increase the 
magnetic coupling between the driven windings and the pick-up winding and 
thereby provide an increased output singal level. The driven windings 
32.sup.1 are laminated or wound onto the substrate 31, as shown and 
further described below in connection with FIGS. 9-11. 
A pick-up winding is carried by a slider 33 which slides over the substrate 
31. To position the slider, a control bracket 34 is fastened to the slider 
33. The control bracket protrudes above the rail 30 for connection as a 
follower to whatever is providing the displacement to be sensed. A pair of 
rubber or plastic seals 35, 36 cover the top of the rail 30 and join 
forming an elongated slit through which the control bracket slides. In 
order to provide a connection between the pick-up winding in the slider 33 
and a shielded twisted pair 37 mounted to the end portion 40 of the rail 
30, a pair of resilient bands 38, 39 connect the control bracket 34 to the 
end portion 40 of the rail. The band 38 carries electrical conductors 
conveying the pick-up signal. Preferably the resilient bands are Mylar 
strips, and the electrical conductors are copper foil strips adhesively 
bonded or laminated into the resilient band 38. 
The control bracket 34 and slider 33 are further shown in FIG. 7. 
Preferably the control bracket is made of sheet brass that is cut, bent to 
shape and spot welded together at 41. Holes 42 are provided for riviting 
the control bracket 34 to the resilient bands 38, 39. To urge the slider 
into contact with the substrate 31, resilient fingers 43 are formed in the 
control bracket. 
Shown in FIG. 8 are pick-up coils 50, 51, 52 in the bottom of the slider 
33. The slider 33 is made of plastic and can be loaded with iron or 
ferrite powder to increase the coupling of the pick-up coils with the 
driven windings. The coils are rectangular multi-turn pancake coils that 
are slightly skewed to improve the linearity of the phase with respect to 
displacement. The coils are spaced one-half wavelength from each other, 
and the middle coil 51 is connected in opposite polarity with respect to 
the end coils 50, 52. To reduce noise and distortion caused by capacitive 
coupling to the coils 50, 51, 52, an electrostatic shield 53 in the form 
of a comb is laid over the coils. The electrostatic shield is connected to 
the ground lead or shield wires of the electrical conductors 37 conveying 
the pick-up signal. 
Turning now to FIG. 9, there is shown a schematic diagram of a machine for 
aligning and laminating multiple driven windings in precise phase 
registration with each other. Perforated plastic film of the kind used for 
motion picture film is laminated to copper foil and the windings of the 
required wavelengths are etched in the copper foil in the required 
registration with the perforations by using printed or photolithographic 
techniques. The films carrying the various windings are conveyed over 
tensioning rollers 60 to a pair of driven laminating rollers 61 and 62. 
The rollers are sprocketed to maintain proper registration between the 
film layers. Before reaching the laminating rollers, the films receive 
adhesive 63 for bonding the films together. 
Driven windings can also be wound rather than laminated on the substrate. 
Winding by hand is facilitated by the use of a substrate having closely 
spaced slots for receiving the windings. As shown in FIG. 10, an embossing 
roller 71 can be used to emboss a plastic strip 70 to provide the slots 
72. The embossing could also be done during an extrusion process. 
Preferably the plastic strip 70 is loaded with iron or ferrite powder to 
increase the coupling between the driven windings and the pick-up winding. 
The winding of a driven winding 73 on the slotted substrate 72 is shown in 
FIG. 11. The first wavelength .lambda..sub.1 is chosen to have an integral 
number of slots, such as 16 as shown. The positions of the other windings 
are quantized by the positions of the slots. This quantization introduces 
some phase non-linearity in the response from the other windings. The 
phase non-linearity may necessitate the use of an additional pair of 
driven windings. Preferably the uppermost winding in each slot of the 
substrate is covered by a wire from an electrostatic shield 74 in the form 
of a comb. 
The use of a slotted substrate comprising iron or ferrite powder 
considerably increases the degree of coupling between the driven windings 
and the pick-up winding. To eliminate the need for an electrical 
connection to the pick-up coil, a micropower FM transmitter could be 
energized solely by the signal received by the pick-up winding from the 
driven windings. The use of such a transmitter is shown in FIGS. 12-13. 
As shown in FIG. 12, a linear position sensor 80 similar to that shown in 
FIGS. 4-6 is provided with a slider 81 mounted to a control bracket 82. A 
micropower FM transmitter 83 and a sliding capacitor 84 are also mounted 
to the control bracket 82. The sliding capacitor 84 capacitively couples 
the output of the FM transmitter 83 to a strip transmission line 
comprising a plastic strip 86 mounted to the rail 87 of the position 
sensor 80, and a strip of copper foil 85 adhesively bonded to the plastic 
strip 86. The strip transmission line extends along the length of the rail 
86. 
A schematic diagram of the micro-power FM transmitter 83 is shown in FIG. 
13. A signal at about 20 KHz is received by the pick-up coil 90 which is 
tuned to the frequency of the signal by a capacitor 91. The received 
signal is rectified by a full wave doubler circuit including a pair of 
germanium crystal diodes 92, 93 and a pair of capacitors 94, 95. The 
rectified signal powers a selected one of two transistor oscillators 
having respective tuned circuits 96, 97 which are adjusted to different 
frequencies. The transistor oscillators also include respective 
transistors 98, 99, resonating capacitors 100, 101, feedback capacitors 
102, 103, and biasing resistors 104, 105. 
So that a particular one of the transistor oscillators are selected for 
oscillation in response to the polarity of the signal across the pick-up 
coil 90, the transistors 98, 99 share a common emitter resistor 106 and RF 
bypass capacitor 107 so as to form a differential pair and function as a 
differential amplifier at the 20 KHz frequency. The signal across the 
pick-up coil 90 is fed to the transistor 99 through a resistor 108, 
causing conduction to periodically switch from one transistor to the 
other, and therefore causing the frequency of oscillation to periodically 
shift from the frequency of one transistor oscillator to the other. The 
frequencies of oscillation, for example, are slightly above and below the 
standard FM intermediate frequency of 10.7 MHz so that a standard FM 
limiter and discriminator 109 may be used to detect the FM modulated 
signal. The limiter and discriminator is, for example, an integrated 
circuit such as RCA Corporation part No. CA3075. The limiter and 
discriminator receives the signal from one end of the strip transmission 
line 85. 
Turning now to FIG. 14, there is shown a longitudinal cross-sectional view 
of an alternative embodiment 120 of a linear position sensor of the 
present invention employing helical windings. The linear position sensor 
120 has the advantage that the sense winding and the driven windings are 
relatively fixed with respect to each other so that flexible electrical 
connections or other means are not required for communicating signals from 
the relatively moving windings. Instead of relatively displacing the 
pick-up winding with respect to the driven windings to obtain a phase 
signal indicating displacement, a displaceable ferromagnetic core 121 
magnetically couples the driven windings and the pick-up winding in such a 
way that the pick-up winding receives a signal having a phase indicating 
displacement of the core 121. 
As shown in FIG. 14, the core 121 is disposed inside a tube 122 upon which 
are wound a two-layer pick-up winding 123 and offset pitch driven windings 
124, 125, 126, and 127 for the respective phases .phi..sub.1, .phi..sub.1, 
.phi..sub.2, .phi..sub.2. For displacing the core 121, it is secured to 
the end of a rod 128. In order to eliminate electrostatic coupling between 
the pick-up winding 123 and the driven windings 124, 125, 126, 127, an 
electrostatic shield 129 in the form of a layer of metal foil is wound on 
the pick-up winding, and the driven windings are wound over the shield. 
As shown in FIG. 15, the shield 129 is wound over the pick-up winding 123 
with overlapping portions separated by an insulating layer 130. The shield 
129, for example, is a strip of aluminum foil, and the insulating layer is 
a strip of adhesive tape. This form of construction permits magnetic flux 
at the operating frequency to pass from the driven windings to the pick-up 
winding, while attenuating higher frequency noise and harmonic distortion. 
Returning for a moment to FIG. 14, the shield 129 is preferably connected 
to the shield 131 of a shielded twisted pair for conveying the signal 
received by the pick-up winding 123. Preferably all of the windings are 
magnetically shielded by an external magnetic shield 132 which also 
improves the coupling between the driven windings and the pick-up 
windings. As shown in FIG. 14, the magnetic shield is made of epoxy resin 
loaded with ferrite powder. The ferrite powder is mixed with epoxy glue, 
and the mixture is painted on the windings so that it hardens over the 
windings. In FIG. 14 the thickness of the windings has been exaggerated 
for the sake of illustration. The tube 121 as well as the windings should 
be thin so as to provide a short air gap between the core 121 and the 
shield 132 so as to maximize the magnetic coupling between the pick-up 
winding and the driven windings via the core. The core 121, for example, 
has a length of 10 mm, and a diameter of 5.4 mm. The coils are wound with 
0.125 mm diameter wire, giving 8 turns per mm. The driven windings extend 
over 80 mm, or four wavelengths of 20 mm per wavelength. The two layer 
pick-up winding extends over 90 mm. With these dimensions and at an 
operating frequency of 15.625 kHz, the pick-up winding resonated with a 
0.08 uF capacitor and therefore had an impedance of about 130 ohms. 
The electrical connections for the windings of the sensor 120 are shown in 
FIG. 16. Each of the windings is formed of a continuous length of wire, 
but each of the driven windings 124, 125, 126, 127 has a number of 
sections that are about a quarter wavelength long. Also, adjacent quarter 
wave sections are wound with opposite sense. Preferably this is done by 
winding one half of each driven winding in a clockwise direction, and 
winding the other half in a counter-clockwise direction. The direction 
changes, for example, at the nodes 133, and the quarter wave section 134 
is wound clockwise and the quarter wave section 135 is wound 
counter-clockwise. 
If the length of the core 121 is very short in comparison to the length of 
the windings, there may be substantial unbalanced parasitic magnetic 
coupling between the driven windings and the pick-up winding. In this case 
it is advisable to null out the imbalance of each driven winding by 
winding a few additional turns 136 as needed. These additional turns are 
wound by hand while the respective driven winding is energized at the 
operating frequency and the signal in the pick-up winding is measured, in 
order to null out the measured signal. 
For the sensor 120 of FIG. 14, the core 121 is about a half wavelength 
long, and the windings are about four wavelengths long. If the sensor is 
to be longer than this, it is advisable to use a segmented core having a 
number of magnetically permeable half-wavelength sections centered at 
wavelength intervals, as shown in FIG. 17. In the sensor 120', the core 
121' includes three ferromagnetic sections 137 separated by 
half-wavelengths spacers 138. The sensor 120' has a two-layer pick-up 
winding and driven windings 139 for six phases. It should be noted that 
the thickness of the windings in FIG. 17 has been exaggerated for the sake 
of illustration. 
It should apparent that the technique of using a ferromagnetic slider to 
couple relatively fixed driven and pick-up windings can be used with the 
laminated or slot-wound windings, and in such cases an electrostatic 
shield in the form of a grounded comb should be laminated or interlaid 
between the driven windings and the pick-up winding. The helical winding 
geometry, however, provides relatively high mutual inductance between the 
driven windings and the pick-up windings, and relatively low 
self-inductance, so that it functions most like a transformer, and returns 
a high signal level. The slot-wound geometry may return a high signal 
level but has appreciable self-inductance which may have to be cancelled 
out by selecting resonating capacitors for shunting the windings, but 
drift in the capacitance or self-inductance values causes a phase shift 
and therefore some loss in precision of position measurement. The 
laminated windings provide low self-inductance but also low mutual 
inductance, so high accuracy can be obtained, but relatively high drive 
current and a preamplifier near the position sensor may be required to 
obtain a sufficiently high signal to noise ratio for repeatable 
measurements within the high resolution of the digital phase sensing 
provided with the circuitry described below in connection with FIGS. 23 
and 24. 
Turning now to FIGS. 18 and 19 there is shown a rotary position sensor 140 
employing the present invention. As is conventional, the sensor 140 has a 
control shaft 141 journaled to a mounting bushing 142 which is affixed to 
a disc-shaped plate 143. A cover 144 fits onto the plate 143. 
To sense the angular position of the control shaft 141 with respect to the 
plate 143, a field member 145 formed of ferrite-loaded plastic is secured 
to the plate 143, and an armature member 147, also formed of 
ferrite-loaded plastic, abuts the field member and is secured to the 
control shaft. Multi-phase driven windings are provided on an 
annular-shaped multi-layer printed circuit board 146 mounted on the 
annular face of the field member 145. To give a phase-linear response over 
an entire 360 degrees of angular position, the driven windings should have 
an integral number of wavelengths per 360 degrees, for example, a first 
pair of driven windings have 16 wavelengths per 360 degrees, a second pair 
of driven windings has 12 wavelengths per 360 degrees, and a third pair of 
driven windings has 15 wavelengths per 360 degrees, corresponding to the 
example in FIG. 3. To sense the phase of the magnetic field provided by 
the driven windings at a selected angular position, the armature member is 
formed with grooves into which are wound pick-up windings 148 which abut 
the printed circuit board 146. The pick-up windings 148 are similar to the 
pick-up windings 50-52 of FIG. 8. 
In order to convey the signal from the pick-up windings 148 to external 
lead wires 149, the pick-up windings are connected to an annular coil 150 
formed in the armature member 147, and two of the lead wires 149 are 
connected to an annular coil 151 formed in the field member 145. The 
annular coils 150, 151 therefore form a rotary transformer. The other lead 
wires are connected to the driven windings in the printed circuit board 
146. 
There has now been described linear and rotary position sensors for 
generating electrical signals which provide respective offset pitch phase 
indications C.sub.1, C.sub.2, . . . C.sub.M of displacement. In accordance 
with a feature of the present invention, the offset pitch phase 
indications are combined to form a position value by successively 
employing a procedure for justifying a high and low precision value and 
combining them. A specific procedure, named "PRECIS", is included in the 
program listing of Appendix I. The procedure is used as shown in FIG. 20. 
The indication C.sub.1 approximately gives the least significant portion 
of the absolute position, N.sub.1 times the difference C.sub.1 -C.sub.2 
gives the next least significant portion of the absolute position plus 
about C.sub.1, and so on, and N.sub.1 *N.sub.2 * . . . *N.sub.M-1 times 
the difference C.sub.1 -C.sub.M gives approximately the absolute position. 
The various portions can be computed with precision by truncation, and 
then combined by multiplication and addition, but before truncation the 
fraction of the prior subtotal representing the less significant portions 
should be subtracted and one-half of the truncation quantization should be 
added. Therefore, the absolute position is given by: 
EQU C.sub.1 +N.sub.1 *TRUN(C.sub.1 -C.sub.2 -ST.sub.1 /N.sub.1 
+HQ.sub.1)+N.sub.1 *N.sub.2 *TRUN(C.sub.1 -C.sub.3 -ST.sub.2 /N.sub.2 
+HQ.sub.2)+. . . +N.sub.1 *N.sub.2 * . . . *N.sub.M-1 TRUN(C.sub.1 
-C.sub.M -ST.sub.M-1 +HQ.sub.M-1) 
where ST.sub.1 =C.sub.1, ST.sub.2 =ST.sub.1 +N.sub.1 *TRUN(C.sub.1 -C.sub.2 
-ST.sub.1 +HQ.sub.1), etc. The procedure PRECIS in effect performs the 
elementary operation L+N*TRUN(H-L/N+HQ). 
Turning now to FIG. 21, there is shown a flowchart 160 of the PRECIS 
procedure implemented in binary arithmetic. It is assumed that the N's are 
powers of 2, such that N=2.sup.K. In the first step 161 the operand L is 
left shifted right by K places to perform a division by N. Then in step 
162, the left-shifted operand L is subtracted from H and a 
half-quantization value of 0 . . . 010 . . . 0 is added in order to 
compute H-L/N+HQ. In step 163 the sum is truncated by logically anding the 
sum with the mask 1 . . . 100 . . . 0. Finally, in step 164, the sum is 
logically or'ed with the left-shifted operand L, to obtain a 
left-justified value of L+N*TRUN(H-L/N+HQ). 
As an example, suppose M=2 so that there are two phase counts C.sub.1 and 
C.sub.2, and further assume that C.sub.1 and C.sub.2 are measured with 
eight bit precision, and the absolute position is 010001001101 binary. If 
the counts were entirely accurate, then one would measure L=C.sub.1 
=01001101 and H=C.sub.1 -C.sub.2 =01000101. In step 161 the left-shifted 
value of L is 000001001101, and in step 162 the sum is computed as 
010001000000-000001001101+000010000000=010010000011. In step 162 the sum 
is truncated to 010000000000 and in step 163 the sum becomes 010001001101 
as it should be. However, even if the value of H were as high as 01001100 
or as low as 00111101 the procedure would give the correct absolute 
position. Therefore, so long as the differences between the phase counts 
have four bit precision (i.e., an eight-bit count is precise to within 
+00000111 and -00001000 relative to the count C.sub.1), then the absolute 
position can be resolved to within four additional bits by the sensing of 
an additional phase count. 
Turning now to FIG. 22, there is shown an integrated circuit 170 for use 
with a conventional microcomputer 171 for energizing the driven windings 
172 of a position sensor 173 of the present invention and for processing 
the signal from a pick-up winding 174 to obtain phase counts. As shown, 
the integrated circuit 170 has 32 pins, and it is preferably fabricated 
using a CMOS process. Pin 175 receives a power supply voltage such as 5 
volts, and pin 176 is a ground connection. 
To provide a time base for generating quadrature-phase excitation signals 
for the driven windings 172 and for resolving the relative phase of the 
signal from the pick-up winding 174, the integrated circuit 170 includes 
an oscillator 177 having pins 178, 179 for connections to a resonator or 
tank circuit such as a quartz crystal, ceramic resonator, or as shown, an 
inductor 180 and capacitors 181 and 182. The oscillator 177 preferably 
oscillates at about 4 MHz or higher to provide quadrature-phase 
excitations signals at about 30 kHz or more. The excitation frequency is 
generated by a seven-stage synchronous binary counter 178. 
In order to generate the quadrature-phase excitation signals, the output of 
the phase counter 183 is fed to a sine/cosine generator 186. The sine and 
cosine waveforms appear on pins 198, 199 which may be shunted to ground by 
capacitors 200, 201 in order to suppress switching harmonics and to cancel 
the effect of inductance in the driven windings 172 so that relatively 
undistorted sinusoidal waveforms appear across the driven windings. 
In order to selectively energize the driven windings 172, the integrated 
circuit 170 includes respective transmission gates 202 which are enabled 
by respective signals from a latch 203. The integrated circuit 170 also 
includes a chip-select gate 204 to enable the microcomputer 171 to address 
the integrated circuit 170 and a latch-select gate 205 to enable the 
microcomputer to write to the latch 203 by asserting an address on 
chip-select and control pins 206 and by passing data over a bidirectional 
data bus to data bus pins 207. 
To provide a sufficient amount of current for driving the driven windings 
172 of the position sensor 173, a bipolar integrated circuit 208 is wired 
between the driven windings and output pins 209 for the transmission gates 
202. The integrated circuit 209 includes respective super-beta transistors 
210 in emitter follower configuration with respective current limiting 
resistors 211. To reduce leakage currents in the super-beta transistors 
210, the transmission gates 202 should have NMOS devices for shunting the 
output pins 209 to ground when the transmission gates are off. 
For receiving the signal from the pick-up winding 174, the integrated 
circuit includes a comparator 212 having signal and offset inputs on a set 
of pins 213. An optional potentiometer 214 may be used to adjust the 
offset of the comparator, for example, to provide a zero adjustment for 
the position sensor. Interconnected between the pick-up winding 174 and 
the comparator 212 is a circuit for biasing and protection from 
electrostatic discharge and electromagnetic pulse interference, including 
a bridge 215 of protection diodes clamping the leads of the pick-up 
windings to between ground and the supply voltage, a capacitor 216 
resonating with the inductance of the pick-up coil, biasing resistors 217, 
218, and resistor-capacitor lowpass filters 219, 220 protecting each of 
the inputs of the comparator 212 from high-speed pulses. If the position 
sensor 172 is mounted in close proximity to the integrated circuit 170, 
however, it may be unnecessary to use the diode bridge 215 or the 
resistor-capacitor filters 219, 220. 
In order to sense the relative phase of the signal from the pick-up winding 
174, the output of the comparator 212 is sampled by a delay flip-flop 221 
and used to clock a latch receiving the phase count from the phase counter 
183. A second flip-flop 221' is also used to guarantee a fast-rising clock 
to the latch 222 under all signal conditions. Therefore, the latch 222 
functions as a phase register for indicating the phase of the signal from 
the pick-up winding 174. To eliminate a critical race condition, the delay 
flip-flops 221, 221' are clocked by an inverter 223 driven by the 
oscillator 177. 
In order to provide increased phase resolution, the least significant bit 
of the phase count is provided by sampling the signal from the pick-up 
winding coincident with a clock transition of opposite polarity to the 
clock transition coincident with the sampling of the signal from the 
pick-up winding for the purpose of clocking the phase register 222. By 
employing this technique, the phase of the signal from the pick-up winding 
can be resolved with one extra bit of precision without requiring an 
increase in the frequency of the oscillator 177. In FIG. 22, the least 
significant bit of the phase count is provided by delay flip-flops 224, 
224' clocked by the oscillator 177. Also in FIG. 22 the complement output 
of the flip-flop 224' is fed to the least significant data input of the 
phase register 222, and the data output of the flip-flop 221' is fed to 
the clock input of the phase register which is active upon a rising 
transition or edge from the flip-flop 221'. 
To permit the microcomputer to address and read the phase count from the 
phase register 222, the phase register has tristate outputs which are 
connected to the data bus 207 and which are enabled by a gate 230 when the 
integrated circuit is addressed and the read/write signal is active for a 
read operation. 
Turning now to FIG. 23 there is shown a schematic diagram of a circuit 
using individual 4000 series CMOS integrated circuits for demonstrating 
the feasibility of the integrated circuit 170 of FIG. 22 and for operation 
with a Motorola 6800 microprocessor programmed as shown in Appendix I. A 4 
MHz oscillator is provided by an inverter 301, capacitors 302 and 303, an 
inductor 304. The inverter is, for example, part no. 4069, the capacitors 
are 120 picofarad, and the inductor is about 25 microhenries. The output 
of the inverter is buffered by inverters 305 and 306. 
A phase counter includes a binary divider formed by a delay flip-flop 307 
(part No. 4013) and 4-bit synchronous counters 308 and 309 (part No. 
4029). A delay flip-flop is used because it can clock about twice as fast 
as a 4-bit synchronous counter (5 MHz for the 4013, but only about 2.5 MHz 
for the 4029). A quadrature-phase sine-cosine generator is provided by an 
inverter 310, exclusive-or gates 311, 312, 313 (part No. 4030), resistors 
314, 315 (10K ohm), resistors 316, 317 (22K ohm), and capacitors 318, 319 
(470 picofarads). The quadrature-phase signals are selectively directed 
through transmission gates 320, 321, 322, and 323 (part No. 4016). To 
drive the driven windings 124, 125, 126, 127 of the resolver 120 of FIG. 
4, there are provided respective emitter follower circuits including NPN 
bipolar transistors 324 and resistors 325 (150 ohms). The windings 124, 
125 are driven when a SEL A/B signal on line 326 is high, and otherwise an 
inverter 327 enables transmission gates 321 and 323 to drive the windings 
126 and 127. To provide both manual as well as computer operation of the 
demonstration circuit, the line 326 is shunted to ground through a 
resistor 328 (100K ohms) and is selectively connectable to the power 
supply through a resistor 329 (4.7K ohms) and a switch 330. The switch is 
effective when the microcomputer is disconnected from the circuits in FIG. 
23. 
The signal from the pick-up winding 123 is fed to a comparator 331 (e.g. 
National Semiconductor part No. LM311, RCA Corp. CA311). The leads from 
the pick-up winding 123 are shunted with a capacitor 332 to resonate with 
the inductance of the pick-up winding at the operating frequency (for a 4 
MHz clock, the operating frequency is 31.25 kHz and a typical capacitance 
value is 0.015 microfarad). A resistor 333 (22K ohms) biases the 
comparator inputs to ground. 
Two quad D latches 334, 335 (part No. 74C175) provide a phase register. The 
phase register has true outputs which are fed to an input port (P.sub.0 
-P.sub.7) of the microcomputer, and complement outputs which drive an 
array 336 of light-emitting diodes connected via current-limiting 
resistors 337. The least significant input of the phase register is 
provided by a delay flip-flop 338 (part No. 4013). The phase register is 
clocked by the output of another delay flip-flop 339 (part no. 4013). An 
inverter 340 ensures that the two delay flip-flops 338, 339 are clocked 
alternately by the buffer inverter 306. 
The program listing in Appendix I is executed to enable a Motorola 6800 
microprocessor to operate the test circuit of FIG. 23. The computer 
program assumes that the I/O port P.sub.0 -P.sub.7 is a Motorola 6820 PIA 
having a control A register at address F009 and corresponding data 
direction and I/O registers at address F008. The terminal CRA2 for the PIA 
is used to supply the SEL A/B signal to line 326 of FIG. 24, and the 
terminal CRA1 of the PIA is used to receive the complement output of the 
flip-flop 339 of FIG. 24 as an interrupt signal. Every time that a phase 
count C.sub.i is clocked into the phase register 334, 335, the 
microcomputer executes the interrupt procedure MIVEC beginning at address 
0400. The interrupt procedure increments an interrupt counter (at address 
0200) upon each interrupt. When the interrupt counter reaches a value of 
six, the count in the phase register 334, 335 is read and stored in memory 
(at address 0201) as the A phase count and then the SEL A/B signal is 
switched to select B. When the interrupt counter reaches a value of twelve 
(C hexadecimal), the interrupt counter is cleared, the count in the phase 
register is read and stored in memory (at address 0202) as the B phase 
count and the SEL A/B signal is switched back to select B. Therefore, the 
microcomputer periodically excites the A driven windings 124, 125, obtains 
the phase count C.sub.A, excites the B driven windings, 126, 127, and 
obtains the phase count C.sub.B. 
In the executive program beginning at address 0400, the PIA is set up in a 
procedure named START. Then the absolute position is computed from the A 
and B phase counts which are stored and periodically updated in memory at 
addresses 0201 and 0202, respectively. In the procedure named COMPUTE the 
difference between the A and B phase counts is computed and stored as a 
two byte integer number in the memory locations 0204 and 0205 which store 
the SUM parameter for the PRECIS subroutine. The PRECIS subroutine is 
called to determine the absolute position, which ends up in the SUM memory 
locations 0204 and 0205. In a procedure named DISPLAY, the value of the 
absolute position is displayed by calling an internal subroutine residing 
in the microcomputer's operating system at address BDFF. Upon returning, 
execution jumps back to the COMPUTE procedure. In this way the absolute 
position of the core in the resolver 120 is continuously determined and 
indicated by the microcomputer. 
In view of the above, there has been disclosed a method for enabling an 
"Inductosyn" type of variable phase transformer to sense absolute 
position. Also, for low-cost applications where the utmost in accuracy and 
precision is not required, there have been disclosed absolute position 
sensors for linear and rotary position sensing, and for providing high 
signal levels when driven with low excitation currents. The position 
sensors can be fabricated using either capital-intensive techniques as in 
the case of the laminated windings, or labor-intensive techniques as in 
the case of lap-wound and helical wound coils (although a 
numerically-controlled lathe could be used to wind the helical coils with 
a variably programmed pitch for obtaining a sinusoidal density along the 
length of the sensor for each driven winding). For use with any of the 
position sensors, there has also been provided an integrated circuit for 
interfacing to the data bus of a microcomputer. 
APPENDIX I. 
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Motorola MC6800 Program Listing 
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0200 INTERRUPT COUNTER 
0201 PHASE A (4) Switch Top 
0202 PHASE B (3) Switch Bottom 
0203 SUM HIGH 
0204 SUM LOW 
0205 DIFFERENCE HIGH 
0206 DIFFERENCE LOW 
0400 B6 LDA A $0200 MIVEC Rotine 
0401 02 
0402 00 
0403 4C INC A Increment Interrupt Counter 
0404 B7 
0405 02 STA A $0200 
0406 00 
0407 81 CMP A $06 
0408 06 
0409 26 BNE SKIPA 
040A 0C 
040B B6 LDA A $F008 
040C F0 
040D 08 
040E B7 STA A $0201 
040F 02 
0410 01 
0411 86 LDA A #$37 Select Phase B 
0412 37 
0413 B7 STA A $F009 
0414 F0 
0415 09 
0416 3B RT1 
0417 81 CMP A $OC 
0418 0C 
0419 2C BGE SKIPB 
041A 01 
041B 3B RT1 
041C 7F CLR $0200 SKIPB 
041D 02 Reset Interrupt Counter 
041E 00 
041F B6 LDA A $F008 Sample Phase B 
0420 F0 
0421 08 
0422 B7 STA A $0202 
0423 02 
0424 02 
0425 86 LDA A #$3F Select Phase A 
0426 3F 
0427 B7 STA A $F009 
0428 F0 
0429 09 
042A 3B RT1 
0440 BD JRS #FEID START Executive Program 
0441 FE 
0442 1D Clear Display 
0443 86 LDA A #$3F 
0444 3F 
0445 B7 STA A $F009 Initialize PIA 
0446 F0 
0447 09 
0448 7F CLR $0200 Initialize Interrupt Counter 
0449 02 
044A 00 
044B 0E CLI Enable Interrupt 
044C B6 LDA A $0201 COMPUTE Routine 
044D 02 
044E 01 
044F 16 TAB 
0450 F0 SUB B $0202 
0451 02 
0452 02 
0453 F7 STA B $0205 
0454 02 
0455 05 
0456 7F CLR $0206 
0457 02 
0458 06 
0459 80 SUB A #$6C 
045A 6C 
045B B7 STA A $0203 
045C 02 
045D 03 
045E 7F CLR $0204 
045F 02 
0460 04 
0461 8D BSR PRECIS 
0462 14 
0463 CE LDX #$2600 DISPLAY Routine 
0464 26 
0465 00 Reset Display Pointer 
0466 FF STX #$0102 
0467 01 
0468 02 
0469 B6 LDA A $0203 
046A 02 
046B 03 
046C BD JSR DISPLAY 
046D FF 
046E 6D 
046F B6 LDA A $0204 
0470 02 
0471 04 
0472 BD JSR DISPLAY 
0473 FF 
0474 6D 
0475 20 BRA COMPUTE 
0476 D5 
0477 74 LSR $0203 PRECIS Subroutine 
0478 02 
0479 03 
047A 76 ROR $0204 
047B 02 
047C 04 
047D 74 LSR $0203 
047E 02 
047F 03 
0480 76 ROR $0204 
0481 02 
0482 04 
0483 B6 LDA A $0206 
0484 02 
0485 04 
0486 B0 SUB A $0204 
0487 02 
0488 06 
0489 B6 LDA A $0205 
048A 02 
048B 05 
049C B2 SUBC A $0205 
048D 02 
048E 03 
048F 8B ADD A #$20 
0490 20 
0491 84 AND A #$CO 
0492 C0 
0493 BA ORA A $0203 
0494 02 
0495 03 
0496 B7 STA A $0203 
0497 02 
0498 03 
0499 39 
RTS 
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