U.S. patent application number 09/861965 was filed with the patent office on 2002-11-21 for magnetoresistor sensor die.
Invention is credited to Schroeder, Thaddeus.
Application Number | 20020171416 09/861965 |
Document ID | / |
Family ID | 25337240 |
Filed Date | 2002-11-21 |
United States Patent
Application |
20020171416 |
Kind Code |
A1 |
Schroeder, Thaddeus |
November 21, 2002 |
MAGNETORESISTOR SENSOR DIE
Abstract
A single die MR array composed of a plurality of MR elements,
wherein each MR element is composed of a number of serially
connected MR segments. The MR elements are arranged and configured
so as to produce a variety of MR array geometries. In one form, an
MR array is formed to provide angular sensing schemes wherein
angular measurement redundancy is incorporated therein. In a second
form, an MR array is formed to provide angular sensing schemes
wherein angular measurement redundancy and reference redundancy are
incorporated therein.
Inventors: |
Schroeder, Thaddeus;
(Rochester Hills, MI) |
Correspondence
Address: |
MARGARET A. DOBROWITSKY
DELPHI TECHNOLOGIES, INC.
Legal Staff, Mail Code 480-414-420
P. O. Box 5052
Troy
MI
48007-5052
US
|
Family ID: |
25337240 |
Appl. No.: |
09/861965 |
Filed: |
May 21, 2001 |
Current U.S.
Class: |
324/207.21 ;
324/207.25 |
Current CPC
Class: |
G01D 5/145 20130101 |
Class at
Publication: |
324/207.21 ;
324/207.25 |
International
Class: |
G01B 007/14 |
Claims
1. A magnetoresistor sensor comprising: a single die comprising an
array of magnetoresistor elements, said array comprising a first
magnetoresistor element having a first area, a second
magnetoresistor element having second area and a third
magnetoresistor element having a third area, wherein each
magnetoresistor element comprises a series of magnetoresistor
segments arranged linearly in a respectively predetermined pattern
which thereby defines the respective area thereof, wherein said
second magnetoresistor element is located between and adjacent to
said first and third magnetoresistor elements, and wherein said die
has a center; and an article having an end superposably adjacent
said die in concentric relation to said center and in perpendicular
relation to said die, wherein a first magnetic irregularity and a
second magnetic irregularity are mutually diametrically disposed at
said end; wherein said end is rotatable with respect to said die
such that the first magnetic irregularity is always superposed said
first magnetoresistor element, and wherein the second magnetic
irregularity is always superposed said third magnetoresistor
element; and wherein said first and third areas are much smaller
than said second area.
2. The sensor of claim 1, wherein said array further comprises a
fourth magnetoresistor element having a fourth area, said fourth
magnetoresistor element being located between said third and first
magnetoresistor elements, wherein said fourth magnetoresistor
element comprises a series of the magnetoresistor segments arranged
linearly in a respectively predetermined pattern which thereby
defines the fourth area, and wherein said first and third areas are
much smaller than said second and fourth areas.
3. The sensor of claim 1, further comprising an electronic circuit
connected to said first, second and third magnetoresistor elements
such that said first magnetoresistor element has a resistance R1
responsive to the magnetic field locally thereat, said second
magnetoresistor element has a resistance R2 over a predetermined
resistance range responsive to the magnetic field locally thereat,
and said third magnetoresistor element has a resistance R3
responsive to the magnetic field locally thereat, wherein a
rotative position of the end relative to the die is related to R2
as a function of R1 and R3 defining respective maximum and minimum
resistances in a predetermined proportion of the resistance range
of R2.
4. The sensor of claim 3, further comprising a bias magnet located
superposably adjacent said die so as to provide a magnetic field at
said die, wherein said first magnetic irregularity comprises a
ferromagnetic material and wherein said second magnetic
irregularity comprises a substantially nonmagnetic material,
wherein said first and second magnetic irregularities locally
affect the magnetic field at the die.
5. The sensor of claim 3, wherein said first magnetic irregularity
comprises a bias magnet and said second magnetic irregularity
comprises a substantially nonmagnetic material.
6. The sensor of claim 2, further comprising an electronic circuit
connected to said first, second, third and fourth magnetoresistor
elements such that said first magnetoresistor element has a
resistance R1 responsive to the magnetic field locally thereat,
said second magnetoresistor element has a resistance R2 over a
predetermined resistance range responsive to the magnetic field
locally thereat, said third magnetoresistor element has a
resistance R3 responsive to the magnetic field locally thereat, and
said fourth magnetoresistor element has a resistance R4 over the
predetermined resistance range responsive to the magnetic field
locally thereat, wherein a rotative position of the end relative to
the die is related to R2 and R4 redundantly as a function of R1 and
R3 defining respective maximum and minimum resistances in a
predetermined proportion of the resistance range.
7. The sensor of claim 6, further comprising a bias magnet located
superposably adjacent said die so as to provide a magnetic field at
said die, wherein said first magnetic irregularity comprises a
ferromagnetic material and wherein said second magnetic
irregularity comprises a substantially nonmagnetic material,
wherein said first and second magnetic irregularities locally
affect the magnetic field at the die.
8. The sensor of claim 6, wherein said first magnetic irregularity
comprises a bias magnet and said second magnetic irregularity
comprises a substantially nonmagnetic material.
9. A magnetoresistor sensor comprising: a single die comprising an
array of magnetoresistor elements, said array comprising a first
magnetoresistor element having a first area, a second
magnetoresistor element having second area a third magnetoresistor
element having a third area, a fourth magnetoresistor element
having a fourth area, a fifth magnetoresistor element having a
fifth area, and a sixth magnetoresistor element having a sixth
area, wherein each magnetoresistor element comprises a series of
magnetoresistor segments arranged linearly in a respectively
predetermined pattern which thereby defines the respective area
thereof, wherein said first and second magnetoresistor elements are
mutually adjacent and located between said sixth and third
magnetoresistor elements such that said first magnetoresistor
element is adjacent said sixth magnetoresistor element and said
second magnetoresistor element is adjacent said third
magnetoresistor element, wherein said fourth and fifth
magnetoresistor elements are mutually adjacent and located between
said sixth and third magnetoresistor elements such that said fourth
magnetoresistor element is adjacent said third magnetoresistor
element and said fifth magnetoresistor element is adjacent said
sixth magnetoresistor element, and wherein said die has a center;
and an article having an end superposably adjacent said die in
concentric relation to said center and in perpendicular relation to
said die, wherein a first magnetic irregularity and a second
magnetic irregularity are mutually diametrically disposed at said
end; wherein said end is rotatable with respect to said die such
that the first magnetic irregularity is always superposed said
first and second magnetoresistor elements, and wherein the second
magnetic irregularity is always superposed said fourth and fifth
magnetoresistor elements; and wherein said first, second, fourth
and fifth areas are much smaller than said third and sixth
areas.
10. The sensor of claim 9, further comprising an electronic circuit
connected to said first, second, third, fourth, fifth and sixth
magnetoresistor elements such that said first magnetoresistor
element has a resistance R1 responsive to the magnetic field
locally thereat, said second magnetoresistor element has a
resistance R2 responsive to the magnetic field locally thereat,
said third magnetoresistor element has a resistance R3 over a
predetermined resistance range responsive to the magnetic field
locally thereat, said fourth magnetoresistor element has a
resistance R4 responsive to the magnetic field locally thereat,
said fifth magnetoresistor element has a resistance R5 responsive
to the magnetic field locally thereat, and said sixth
magnetoresistor element has a resistance R6 over the predetermined
resistance range responsive to the magnetic field locally thereat,
wherein a rotative position of the end relative to the die is
related redundantly to R3 and R6 as a function of R1 and R2 in
mutual redundancy and R4 and R5 in mutual redundandcy defining
respective maximum and minimum resistances in a predetermined
proportion of the resistance range.
11. The sensor of claim 10, further comprising a bias magnet
located superposably adjacent said die so as to provide a magnetic
field at said die, wherein said first magnetic irregularity
comprises a ferromagnetic material and wherein said second magnetic
irregularity comprises a substantially nonmagnetic material,
wherein said first and second magnetic irregularities locally
affect the magnetic field at the die.
12. The sensor of claim 10, wherein said first magnetic
irregularity comprises a bias magnet and said second magnetic
irregularity comprises a substantially nonmagnetic material.
Description
TECHNICAL FIELD
[0001] The present invention relates to magnetoresistor arrays used
for magnetic position sensors.
BACKGROUND OF THE INVENTION
[0002] The use of magnetoresistors (MRs) and Hall devices as
position sensors is well known in the art. For example, a
magnetically biased differential MR sensor may be used to sense
angular position of a rotating toothed wheel, as for example
exemplified by U.S. Pat. Nos. 4,835,467, 5,731,702, and
5,754,042.
[0003] In such applications, the magnetoresistor (MR) is biased
with a magnetic field and electrically excited, typically, with a
constant current source or a constant voltage source. A magnetic
(i.e., ferromagnetic) object moving relative and in close proximity
to the MR, such as a toothed wheel, produces a varying magnetic
flux density through the MR, which, in turn, varies the resistance
of the MR. The MR will have a higher magnetic flux density and a
higher resistance when a tooth of the moving target wheel is
adjacent to the MR than when a slot of the moving target wheel is
adjacent to the MR.
[0004] Increasingly more sophisticated spark timing and emission
controls introduced the need for crankshaft sensors capable of
providing precise position information during cranking. Various
combinations of magnetoresistors and single and dual track toothed
or slotted wheels (also known as encoder wheels and target wheels)
have been used to obtain this information (see for example U.S.
Pat. Nos. 5,570,016, 5,731,702, and 5,754,042).
[0005] The shortcoming of MR devices is their temperature
sensitivity. They have a negative temperature coefficient of
resistance and their resistance can drop as much as 50% when heated
to 180 degrees Celsius. Generally, this led to the use of MR
devices in matched pairs for temperature compensation.
Additionally, it is preferable to drive MR devices with current
sources since, with the same available power supply, the output
signal is nearly doubled in comparison with a constant voltage
source.
[0006] To compensate for the MR resistance drop at higher
temperatures, and thus, the magnitude decrease of the output signal
resulting in decreased sensitivity of the MR device, it is also
desirable to make the current of the current source automatically
increase with the MR temperature increase. This is shown in U.S.
Pat. No. 5,404,102 in which an active feedback circuit
automatically adjusts the current of the current source in response
to temperature variations of the MR device. It is also known that
air gap variations between the MR device and ferromagnetic
materials or objects will affect the resistance of MR devices with
larger air gaps producing less resistance and decreased output
signals.
[0007] Single element magnetic field sensors composed of, for
example, an indium antimonide or indium arsenide epitaxial film
strip supported on, for example, a monocrystalline elemental
semiconductor substrate, are also known. The indium antimonide or
indium arsenide film is, for example, either directly on the
elemental semiconductor substrate or on an intermediate film that
has a higher resistivity than that of silicon. A conductive contact
is located at either end of the epitaxial film, and a plurality of
metallic (gold) shorting bars are on, and regularly spaced along,
the epitaxial film. Examples thereof are exemplified by U.S. Pat.
Nos. 5,153,557, 5,184,106 and 5,491,461.
[0008] Most noncontacting magnetic angle position sensors use a
Hall sensor and a rotating magnetic field. Since the Hall sensor
output signal is proportional to the normal component of the
magnetic field, its output is a sinusoidal function of the angle of
rotation. Only within a relatively small angular range is the
output proportional to the angle of rotation. Depending on the
required accuracy, this range may be as small as .+-.30 degrees
with a .+-.1.3% full scale error and, practically, never greater
than .+-.50 degrees with almost a .+-.10% full scale error. Another
approach relies on varying the air gap between a Hall sensor and a
magnetic target. This allows a greater angular range. However, it
is an inherently error prone method due to the high degree of non
linearity in the relation between the magnetic field strength and
the air gap.
[0009] Compound semiconductor MRs, such as those manufactured from
lnSb, InAs, etc., are simply two-terminal resistors with a high
magnetic sensitivity and thus, are very suitable for the
construction of single die MR array geometries suitable for use as
large range angular position sensors (in most cases one terminal of
all the MR elements can be common).
[0010] Ultimately, such MR arrays could be integrated on the same
die with appropriate processing circuitry. For example, if the MR
array was fabricated on a Si substrate then the processing
circuitry would be also Si based. For higher operating
temperatures, silicon-on-insulator (SOI) could be used. A
potentially lower cost alternative to the SOl approach would be to
take advantage of the fact that MRs are currently fabricated on
GaAs, a high temperature semiconductor, and thus, to fabricate the
integrated processing circuitry from GaAs (or related lnP) using
HBT (Heterojunction Bipolar Transistor) or HEMT (High Electron
Mobility Transistor) structures. This technology is now easily
available and inexpensive through the explosive growth of the
cellular phone industry.
[0011] Accordingly, what remains needed is a compact and
inexpensive die having at least one array of magnetic sensing
elements and configured so as to produce a variety of array
geometries suitable for specialized angular sensing schemes capable
of self compensation over wide ranges of temperature and air gaps,
wherein an array is defined as having three or more MR
elements.
SUMMARY OF THE INVENTION
[0012] The present invention is a compact and inexpensive single
die having at least one MR array composed of a plurality of MR
elements, wherein each MR element is composed of a number of
serially connected MR segments. The MR elements are arranged and
configured so as to produce a variety of MR array geometries
suitable for specialized angular sensing schemes.
[0013] The present invention is a noncontacting large angular range
(approaching 180 degrees) angular magnetoresistor position sensor
array incorporated on a die capable of self compensation over wide
temperature ranges and air gaps.
[0014] According to a first aspect of the present invention, an MR
array is formed of a plurality of MR elements, wherein each MR
element is composed of a plurality of uniformly arranged, serially
connected MR segments. The arrangement is such as to provide an MR
array suitable for angular sensing schemes wherein angular
measurement redundancy is incorporated therein.
[0015] According to a second aspect of the present invention, an MR
array is formed of a plurality of MR elements, wherein each MR
element is composed of a plurality of uniformly arranged, serially
connected MR segments. The arrangement is such as to provide an MR
array suitable for angular sensing schemes wherein angular
measurement redundancy and reference redundancy are incorporated
therein.
[0016] According to a preferred method of fabrication, an indium
antimonide epitaxial film is formed, then masked and etched to
thereby provide epitaxial mesas characterizing the MR elements.
Shorting bars, preferably of gold, are thereupon deposited, wherein
the epitaxial mesa not covered by the shorting bars provides the MR
segments. The techniques for fabricating epitaxial mesas with
shorting bars are elaborated in U.S. Pat. No. 5,153,557, issued
Oct. 6, 1992, U.S. Pat. No. 5,184,106, issued Feb. 2, 1993 and U.S.
Pat. No. 5,491,461, issued Feb. 13, 1996, each of which being
hereby incorporated herein by reference.
[0017] Accordingly, it is an object of the present invention to
provide an MR die comprising at least one MR array according to the
first and second aspects of the present invention which is capable
of detecting angular movement of a ferromagnetic or magnetic target
in relation to the MR array.
[0018] This and additional objects, features and advantages of the
present invention will become clearer from the following
specification of a preferred embodiment.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] FIG. 1A is a schematic representation of a single die MR
array according to a first aspect of the present invention.
[0020] FIG. 1B is a detailed depiction of an MR element of the
single die MR array of FIG. 1A.
[0021] FIG. 1C is a detail view of a portion of an MR element of
FIG. 1A, seen by way of example at circle 1C of FIG. 1B.
[0022] FIG. 2 is a schematic representation of a single die MR
array according to the second aspect of the present invention.
[0023] FIG. 3A depicts a first example of the preferred environment
of use of the present invention.
[0024] FIG. 3B is a view seen along line 3B-3B of FIG. 3A.
[0025] FIG. 4A depicts a second example of the preferred
environment of use of the present invention.
[0026] FIG. 4B is a view seen along line 4B-4B of FIG. 4A.
[0027] FIG. 5A is a schematic representation of a single die MR
array according to the first aspect of the present invention
depicting an angular displacement of the first or second example of
the preferred environment of use of the present invention according
to FIG. 3A or FIG. 4A.
[0028] FIG. 5B is a schematic representation of a single die MR
array according to the second aspect of the present invention
depicting an angular displacement of the first or second example of
the preferred environment of use of the present invention according
to FIG. 3A or FIG. 4A.
[0029] FIG. 6 shows a first example of an analog circuit
implementing the first aspect of the present invention.
[0030] FIG. 7 shows a second example of an analog circuit
implementing the first aspect of the present invention.
[0031] FIG. 8 shows an example of a circuit employing a digital
processor implementing the first aspect of the present
invention.
[0032] FIG. 9 shows a first example of an analog circuit
implementing the second aspect of the present invention.
[0033] FIG. 10 shows a second example of an analog circuit
implementing the second aspect of the present invention.
[0034] FIG. 11 shows an example of a circuit employing a digital
processor implementing the second aspect of the present
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0035] FIG. 1A is a schematic representation of an MR die 10 on
which an MR array 12 according to a first aspect of the present
invention is depicted. The MR array 12 is comprised of four
magnetoresistor elements, MR1, MR21, MR22, and MR3 wherein MR1
spans the angle A1, MR21 spans the angle A21, MR22 spans the angle
A22, and MR3 spans the angle A3. The shape of the MR array 12 is,
preferably, circular, as depicted in FIG. 1A, but may be otherwise.
MR21 and MR22 are the angle measuring elements whereas MR1 and MR3
are reference elements. MR22 is intended to provide a redundant
angle measurement as required by many throttle position sensor
specifications. If redundancy is not required, MR22 may be absent.
Generally, and as shown in FIG. 1A, angles A1 and A3 are equal and
angles A21 and A22 are equal, but this is not a fundamental
requirement.
[0036] FIG. 1B and 1C show a portion of the MR die 10, in
particular MR element MR1 of the MR array 12. Structurally, MR
element MR1 consists of a plurality of MR segments 22 demarcated by
uniform shorting bars 24 which are preferably gold. The MR segments
22 are each uniformly matched to the others (that is, the MR
segments are identical). By way of preferred example, each MR
segment 22 is composed of indium antimonide (InSb) epitaxial film
mesas. Each epitaxial film mesa is provided, by way of preferred
example, by forming an indium antimonide epitaxial film, then
masking and etching it. The shorting bars 24, which demarcate the
MR segments 22, are composed of gold bars deposited upon the MR
segments. Bonding pads (contacts or terminals) 26, preferably also
of gold, are provided at the ends of each MR element. Also,
connecting strips 28 are also preferably of gold. The other MR
elements of the MR array 12 are similarly constructed of MR
segments demarcated by shorting bars, bonding pads and connecting
strips.
[0037] FIG. 2 is a schematic representation of an MR die 100 on
which an MR array 120 according to a second aspect of the present
invention is depicted. The MR array 120 is comprised of six
magnetoresistor elements, MR11, MR12, MR21', MR22', MR31, and MR32
wherein MR11 spans the angle A11, MR12 spans the angle A12, MR21'
spans the angle A21', MR22' spans the angle A22', MR31 spans the
angle A31, and MR32 spans the angle A32. The shape of the MR array
120 is, preferably, circular, as depicted in FIG. 2, but may be
otherwise. MR21' and MR22' are the angle measuring elements whereas
MR11, MR12, MR31, and MR32 are reference elements. MR22' is
intended to provide a redundant angle measurement as required by
many throttle position sensor specifications and MR12 and MR32
provide redundant reference elements. Generally, and as shown in
FIG. 2, angles A11, A12, A31, and A32 are equal and angles A21 '
and A22' are equal, but this is not a fundamental requirement.
[0038] The MR array 120 is generally fabricated according to the
method previously described for the MR array 12' of FIG. 1B,
including the respective conductive contact at each opposing end of
each MR element.
[0039] FIGS. 3A and 3B depict a first example of the preferred
environment of use of the present invention. The single MR sensor
30, preferably stationary, employs an MR die 10 of FIG. 1A or an MR
die 100 of FIG. 2 which is biased by a permanent magnet 32, wherein
the MR sensor is coaxially aligned with the axis 36 of a magnetic
(i.e. ferromagnetic) shaft 34 such that the surface of the MR die
lies in a plane perpendicular to the axis of the magnetic shaft.
The magnetic shaft 34 can rotate clockwise 38 or counterclockwise
40 about the axis 36 of the shaft. The end 42 of the shaft 34
adjacent the sensor 30 has a notch 44 such that a tooth 46 and slot
48 are formed, thereby creating a rotating tooth and slot such that
the die 10 or 100 experiences a maximum magnetic flux density on
those portions thereof adjacent to the tooth and a minimum magnetic
flux density on those portions thereof adjacent to the slot.
[0040] FIGS. 4A and 4B depict a second example of the preferred
environment of use of the present invention. The single MR sensor
50, preferably stationary, is comprised of an MR die 10 of FIG. 1A
or an MR die 100 of FIG. 2, a magnetic (i.e. ferromagnetic) layer
52, and a circuit board 54. The circuit board 54 may be located
elsewhere, if desired. The layer 52, preferably less than one
millimeter thick, increases the sensitivity of the sensor to
magnetic fields and is optional. The sensor 50 is coaxially aligned
with the axis 56 of a nonmagnetic shaft 58 such that the surface of
the MR die 10 or 100 lies in a plane perpendicular to the axis of
the shaft. The shaft 58 can rotate clockwise 60 or counterclockwise
62 about the axis 56 of the shaft. On the end 64 of the shaft 58
adjacent the sensor 50 is attached a magnet assembly 66 which
rotates with the shaft and is coaxially aligned with the shaft 58.
The magnet assembly 66 has a permanent magnet 68, preferably in the
form of a semicircular disk, such that one half of the area of the
end 64 of the shaft 58 is covered, thereby forming a tooth whereas
the other half of the area of the end of the shaft is covered with
a nonmagnetic material 70 thereby forming a slot by which a
rotating tooth and slot is created such that the die 10 or 100
experiences a maximum magnetic flux density on those portions
thereof adjacent to the tooth and a minimum magnetic flux density
on those portions thereof adjacent to the slot.
[0041] FIG. 5A is a schematic representation of a single die MR
array 10 according to the first aspect of the present invention of
the first or second example of the preferred environment of use of
the present invention according to FIG. 3A or 4A. The shaded
portion 72 of the overlay 74 represents the tooth 46 or 68,
respectively, whereas the unshaded portion 78 represents the slot
48 or 70. FIG. 5A depicts, in this case, a clockwise rotation 76 of
the tooth 46 or 68 through an angular displacement A from an
initial position of zero degrees wherein at the initial position of
zero degrees, MR21 is totally under the slot 48 or 70 and MR22 is
totally under the tooth. The angular displacement A is limited
during clockwise rotation 76 such that the tooth 46 or 68 always
covers MR1 and the slot 48 or 70 always covers MR3 ensuring that
MR1 always experiences a maximum magnetic flux density and MR3
always experiences a minimum magnetic flux density whereas the
coverage of MR21 or MR22 varies from being totally under the slot
to being totally under the tooth by which the resistance of MR21,
R.sub.21, and MR22, R.sub.22, varies, preferably linearly, from a
minimum, R.sub.MIN, to a maximum, R.sub.MAX. MR1 is designed such
that its resistance, R.sub.1, is a fraction p of R.sub.MAX when
exposed to the maximum magnetic flux density and MR3 is designed
such that its resistance, R.sub.3, is a fraction q of R.sub.MIN
when exposed to the minimum magnetic flux density where p and q
have, preferably, values between greater than zero and one. Hence,
R.sub.1/p=R.sub.MAX and R.sub.3/q=R.sub.MIN. Values for p and q
greater than one are permissible but there does not appear to be
any benefit in doing so.
[0042] At an angular displacement A,
R.sub.21=(A/A21)*R.sub.1/p+(1-(A/A21))*R.sub.3/q (1)
and
R.sub.22=(1-(A/A22)*R.sub.1/p+(A/A22))*R.sub.3/q (2)
from which,
A=A21(R.sub.21-R.sub.3/q)/(R.sub.1/p-R.sub.3/q) (3)
and
A=A22(R.sub.1/p-R.sub.22)/(R.sub.1/p-R.sub.3/q) (4)
[0043] thereby enabling the angle A to be determined given p, q,
R.sub.1, R.sub.21, R.sub.3, and A21 or, redundantly, given p, q,
R.sub.1, R.sub.22, R.sub.3, and A22. Preferably, p, q, R.sub.1,
R.sub.3, A21, and A22 are known from the die characteristics and
R.sub.21, and R.sub.22 are variables to be determined from
measurements.
[0044] FIG. 5B is a schematic representation of a single die MR
array 100 according to the second aspect of the present invention
depicting an angular displacement of the first or second example of
the preferred environment of use of the present invention of FIG.
3A or FIG. 4A. The shaded portion 72' of the overlay 74' represents
the tooth 46 or 68 of FIG. 3 or FIG. 4, respectively, whereas the
unshaded portion 78' represents the slot 48 or 70. FIG. 5B depicts,
in this case, a clockwise rotation 76' of the tooth 46 or 68
through an angular displacement A' from an initial position of zero
degrees wherein at the initial position of zero degrees, MR21' is
totally under the slot 48 or 70 and MR22' is totally under the
tooth. The angular displacement A' is limited during clockwise
rotation 76' such that the tooth 46 or 68 always covers MR11 and
MR12 and the slot 48 or 70 always covers MR31 and MR32 ensuring
that MR11 and MR12 always experience a maximum magnetic flux
density and MR31 and MR32 always experience a minimum magnetic flux
density whereas the coverage of MR21' or MR22' varies from being
totally under the slot to being totally under the tooth by which
the resistance of MR21', R'.sub.21, and MR22', R'.sub.22, varies,
preferably linearly, from a minimum, R'.sub.MIN, to a maximum,
R'.sub.MAX. MR11 and MR12 are designed such that their resistances,
R.sub.11, and R.sub.12, are a fraction p' of R'.sub.MAX when
exposed to the maximum magnetic flux density and MR31 and MR32 are
designed such that their resistances, R.sub.31, and R.sub.32, are a
fraction q' of R'.sub.MIN when exposed to the minimum magnetic flux
density where p' and q' have, preferably, values between greater
than zero and one. Hence, R.sub.11/p'=R.sub.12/p'=R'.sub.MAX and
R.sub.31/q'=R.sub.32/q'=R'.sub.MIN. Values for p' and q' greater
than one are permissible but there does not appear to be any
benefit in doing so.
[0045] At an angular displacement A',
R'.sub.21=(A'/A2l')*R.sub.12/p'+(1-(A'/A21'))*R.sub.32/q' (5)
R'.sub.21=(A'/A2l')*R.sub.11/p'+(1-(A'/A21'))*R.sub.31/q' (6)
R'.sub.22=(1-(A'/A22')*R.sub.12/p'+(A'/A22'))*R.sub.32/q' (7)
and
R'.sub.22=(1-(A'/A22')*R.sub.11/p'+(A'/A22'))*R.sub.31/q' (8)
from which,
A'=A21'(R'.sub.21-R.sub.32/q')/(R.sub.12/p'-R.sub.32/q') (9)
A'=A21'(R'.sub.21-R.sub.31/q')/(R.sub.11/p'-R.sub.31/q') (10)
A'=A22'(R'.sub.12/p'-R'.sub.22)/(R.sub.12/p'-R.sub.32/q') (11)
and
A'=A22'(R'.sub.11/p'-R'.sub.22)/(R.sub.11/p'-R.sub.31/q') (12)
[0046] thereby enabling the angle A' to be determined with full
redundancy given p', q', R.sub.11, R.sub.12, R'.sub.21, R'.sub.22,
R.sub.31, R.sub.32, A21' and A22'. Preferably, p', q', R.sub.11,
R.sub.12, R.sub.31, R.sub.32, A21', and A22' are known from the die
characteristics and R'.sub.21 and R'.sub.22 are variables to be
determined from measurements.
[0047] FIG. 6 shows a first example of an analog circuit 600
implementing the first aspect of the present invention. V.sub.S is
the power supply voltage and i.sub.1, i.sub.1, i.sub.3 and i.sub.4
are matched constant current sources such that
i.sub.1=i.sub.2=i.sub.3=i.sub.4. V.sub.1, V.sub.21, V.sub.22, and
V.sub.3 are given by:
V.sub.1=i.sub.1*R.sub.1 (13)
V.sub.21=i.sub.2*R.sub.21 (14)
V.sub.22=i.sub.3*R.sub.22 (15)
and
V.sub.3=i.sub.4*R.sub.3 (16)
[0048] Amplifier 602 (i.e. an OP-AMP) has a preset gain of (1/p)
whereas amplifier 604 (i.e. an OP-AMP) has a preset gain of (1/q).
The output of differential amplifiers 606, 608, and 610 are,
respectively, (V.sub.1/p-V.sub.22), (V.sub.1/p-V.sub.3/q), and
(V.sub.21-V.sub.3/q). Single quadrant analog divider 612 has a
preset gain of A21 whereas single quadrant analog divider 614 has a
preset gain of A22 whereby, since the current sources are
matched,
V.sub.612=A21(V.sub.21-V.sub.3/q)/(V.sub.1/p-V.sub.3/q)=A21(R.sub.21-R.sub-
.3/q)/(R.sub.1/p-R.sub.3/q)=A (17)
and
V.sub.614=A22(V.sub.1/p-V.sub.22)/(V.sub.1/p-V.sub.3/q)=A22(R.sub.1/p-R.su-
b.22)/(R.sub.1/p-R.sub.3/q)=A (18)
[0049] thereby determining the angle of rotation A. Although not
explicitly shown, it is understood that all components have
appropriate power supply connections as needed and required,
including ground.
[0050] FIG. 7 shows a second example of an analog circuit 700
implementing the first aspect of the present invention. V'.sub.S is
the power supply voltage and i'.sub.2 and i'.sub.3 are matched
constant current sources such that i'.sub.2=i'.sub.3. Constant
current sources i'.sub.1, and i'.sub.4 are weighted such that
i'.sub.1=i'.sub.2/p and i'.sub.4=i'.sub.2/q. V'.sub.1, V'.sub.21,
V'.sub.22, and V'.sub.3 are given by:
V'.sub.1=i'.sub.2*R.sub.1/p (19)
V'.sub.21=i'.sub.2*R.sub.21 (20)
V'.sub.22=i'.sub.3*R.sub.22 (21)
and
V'.sub.3=i'.sub.2*R.sub.3/q. (22)
[0051] The output of differential amplifiers 702, 704, and 706 are,
respectively, (V.sub.1-V.sub.22), (V.sub.1-V.sub.3), and
(V.sub.21-V.sub.3). Single quadrant analog divider 708 has a preset
gain of A21 whereas single quadrant analog divider 710 has a preset
gain of A22 whereby,
V.sub.708=A21(V.sub.21-V.sub.3)/(V.sub.1-V.sub.3)=A21(R.sub.21-R.sub.3/q)/-
(R.sub.1/p-R.sub.3/q)=A (23)
and
V.sub.710=A22(V.sub.1-V.sub.22)/(V.sub.1-V.sub.3)=A22(R.sub.1/p-R.sub.22)/-
(R.sub.1/p-R.sub.3/q)=A (24)
[0052] thereby determining the angle of rotation A. Although not
explicitly shown, it is understood that all components have
appropriate power supply connections as needed and required,
including ground.
[0053] FIG. 8 shows an example of a circuit 800 employing a digital
processor 802 (i.e. digital signal processor, microcontroller,
microprocessor, etc.) implementing the first aspect of the present
invention. V".sub.S is the value of the supply voltage and is
implicitly known to the digital processor 802, for example, as an
input, or stored in the digital processor's memory. The parameters
p, q, A21, A22, R.sub.MAX, and R.sub.MIN are, preferably, stored in
memory also. The values of V",, V".sub.2, and V".sub.3 are input to
the digital processor 802 and can be expressed as:
V".sub.1=V".sub.S*(R.sub.3+R.sub.1+R.sub.22)/(R.sub.21+R.sub.3+R.sub.1+R.s-
ub.22) (25)
V".sub.2=V".sub.S*(R.sub.1+R.sub.22)/(R.sub.21+R.sub.3+R.sub.1+R.sub.22)
(26)
and
V".sub.3=V".sub.S*R.sub.22/(R.sub.21+R.sub.3+R.sub.1+R.sub.22).
(27)
[0054] The value of the output voltages V.sub.D1 and V.sub.D2 are
computed by the digital processor 802 and can be expressed as:
V.sub.D1=A21*{[(V".sub.S-V".sub.1)-(V".sub.1-V".sub.2)/q]/[(V".sub.2-V".su-
b.3)/p-(V".sub.1-V".sub.2)/q]} (29)
and
V.sub.D2=A22*{[(V".sub.2-V".sub.3)/p-V".sub.3]/[(V".sub.2-V".sub.3)/p-(V".-
sub.1-V".sub.2)/q]} (30)
[0055] which, using equations 25, 26, and 27, reduce to:
V.sub.D1=A21*(R.sub.21-R.sub.3/q)/(R.sub.1/p-R.sub.3/q)=A (31)
and
V.sub.D2=A22(R.sub.1/p-R.sub.22)/(R.sub.1/p-R.sub.3/q)=A (32)
[0056] thereby determining the angle of rotation A. The
implementation of the above procedure for the digital processor 802
is well known in the art.
[0057] FIG. 9 shows a first example of an analog circuit 900
implementing the second aspect of the present invention. V.sub.SS
is the power supply voltage and i.sub.11, i.sub.22, i.sub.33,
i.sub.44, i.sub.55, and i.sub.66 are matched constant current
sources such that
i.sub.11=i.sub.22=i.sub.33=i.sub.44=i.sub.55=i.sub.66. V.sub.11,
V.sub.12, V".sub.21, V".sub.22, V.sub.31 and V.sub.32 are given
by:
V.sub.11=i.sub.11*R.sub.11 (33)
V".sub.21=i.sub.22*R'.sub.21 (34)
V.sub.31=i.sub.33*R.sub.31 (35)
V.sub.32=i.sub.44*R.sub.32 (36)
V".sub.22=i.sub.55*R'.sub.22 (33)
and
V.sub.12=i.sub.66*R.sub.12. (33)
[0058] Amplifiers 902 and 904 (i.e. OP-AMPs) have a preset gain of
(1/p') whereas amplifiers 906 and 908 (i.e. OP-AMPs) have a preset
gain of (1/q'). The output of differential amplifiers 910, 912,
914, and 916 are, respectively, (V.sub.11/p'-V.sub.31/q'),
(V.sub.21-V.sub.31/q'), (V.sub.12/p'-V.sub.32/q'), and
(V.sub.12/p'-V".sub.22). Single quadrant analog divider 918 has a
preset gain of A21' whereas single quadrant analog divider 920 has
a preset gain of A22', whereby, since the current sources are
matched,
V.sub.918=A21(V".sub.21-V.sub.31/q')/(V.sub.11/p'-V.sub.31/q')=A21'(R'.sub-
.21-R.sub.31/q')/(R.sub.11/p'-R.sub.31/q')A' (39)
and
V.sub.920=A22'(V.sub.12/p'-V".sub.22)/(V.sub.12/p'-V.sub.32/q')=A22'(R.sub-
.12/p'-R'.sub.22)/(R.sub.12/p'-R.sub.32/q')=A' (40)
[0059] thereby determining the angle of rotation A'. Although not
explicitly shown, it is understood that all components have
appropriate power supply connections as needed and required,
including ground.
[0060] FIG. 10 shows a second example of an analog circuit 1000
implementing the second aspect of the present invention. V'.sub.SS
is the power supply voltage and i'.sub.22 and i'.sub.55 are matched
constant current sources such that i'.sub.22=i'.sub.55. Constant
current sources i'.sup.11, i'.sub.33=i'.sub.44, and i'.sub.66 are
weighted such that i'.sub.11=i'.sub.66=i'.sub.22/p' and
i'.sub.33=i'.sub.44=i'.sub.22/q'. V'.sub.11, V'.sub.12, V'".sub.21,
V'".sub.22, V'.sub.31, and V'.sub.31, and V'.sub.32 are given
by:
V'.sub.11=i'.sub.22*R.sub.11/p' (41)
V'".sub.21=i'.sub.22*R'.sub.21 (42)
V'.sub.31=i'.sub.22*R.sub.31/q' (43)
V'.sub.12=i'.sub.22*R.sub.32/q' (44)
V'".sub.22=i'.sub.22*R'.sub.22 (45)
and
V'.sub.12=i'.sub.22*R.sub.12/p'. (46)
[0061] The output of differential amplifiers 1002, 1004, 1006, and
1008 are, respectively, (V'.sub.11-V'.sub.31),
(V'".sub.21-V'.sub.31), (V'.sub.12-V'.sub.32), and
(V'.sub.12-V'".sub.22). Single quadrant analog divider 1010 has a
preset gain of A21' whereas single quadrant analog divider 1012 has
a preset gain of A22' whereby,
V.sub.1010=A21'(V'".sub.21-V'.sub.31)/(V'.sub.11-V'.sub.31)=A21'(R'.sub.21-
-R.sub.31/q')/(R.sub.11/p'-R.sub.31/q')=A' (47)
and
V.sub.1012=A22'(V'.sub.12-V'".sub.22)/(V'.sub.12-V'.sub.32)=A22'(R.sub.12/-
p'-R'.sub.22)/(R.sub.12/p'-R.sub.32/q')=A' (48)
[0062] thereby determining the angle of rotation A'. Although not
explicitly shown, it is understood that all components have
appropriate power supply connections as needed and required,
including ground.
[0063] FIG. 11 shows an example of a circuit 1100 employing a
digital processor 1102 (i.e. digital signal processor,
microcontroller, microprocessor, etc.) implementing the second
aspect of the present invention. V".sub.SS is the value of the
supply voltage and is implicitly known to the digital processor
1102, for example, as an input or stored in the digital processor's
memory. The parameters p', q', A21', A22', R'.sub.MAX, and
R'.sub.MIN are, preferably, stored in memory also. The values of
V.sub.A, V.sub.B, V.sub.C, and V.sub.D are input to the digital
processor 1102 and can be expressed as:
V.sub.A=V".sub.SS*(R'.sub.22+R.sub.32)/(R.sub.12+R'.sub.22+R.sub.32)
(49)
V.sub.B=V".sub.SS*R.sub.32/(R.sub.12+R'.sub.22+R.sub.32) (50)
V.sub.C=V".sub.SS*(R'.sub.21+R.sub.31)/(R.sub.11+R'.sub.21+R.sub.31)
(51)
and
V.sub.D=V".sub.SS*R.sub.31/(R.sub.11+R'.sub.21+R.sub.31) (52)
[0064] The value of the output voltages V'.sub.D1 and V'.sub.D2 are
computed by the digital processor 1102 and can be expressed as:
V'.sub.D1=A21'*{[(V.sub.C-V.sub.D)-V.sub.D/q']/[(V".sub.SS-V.sub.C)/p'-V.s-
ub.D/q]} (53)
and
V'.sub.D2=A22'*{[(V".sub.SS-V.sub.A)/p'-V.sub.B/q']/[(V".sub.SS-V.sub.A)/p-
'-V.sub.B/q']} (55)
[0065] which, using equations 49, 50, 51, and 52 reduce to:
V'.sub.D1=A21'(R'.sub.21-R.sub.31/q')/(R.sub.11/p'-R.sub.31/q')=A'
(55)
and
V'.sub.D2=A22'(R.sub.12/p'-R'.sub.22)/(R.sub.12/p'-R.sub.32/q')=A'
(56)
[0066] thereby determining the angle of rotation A'. The
implementation of the above procedure for the digital processor
1102 is well known in the art.
[0067] To those skilled in the art to which this invention
appertains, the above described preferred embodiment may be subject
to change or modification. Such change or modification can be
carried out without departing from the scope of the invention,
which is intended to be limited only by the scope of the appended
claims.
* * * * *