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Texas Instruments LDC1612 LDC1614 Linear Position Sensing (Rev. A) Application notes
(1)
Application Report
SNOA931A – April 2015 – Revised November 2019
LDC1612/LDC1614 Linear Position Sensing
Ben Kasemsadeh
ABSTRACT
This application note discusses two techniques for using LDC technology to measure the lateral position
of a conductive target. A comparison of each approach, along with design guidelines, is provided. This
application note focuses on the LDC1612 and LDC1614, but the same principles apply to other LDCs
such as:
• LDC100x
• LDC1041
• LDC1312
• LDC1314
1
2
3
4
Contents
Introduction ................................................................................................................... 2
Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target .......................... 2
Approach 2: Measuring Lateral Movement with a Stretched Coil and a Rectangular Target ..................... 8
Summary .................................................................................................................... 13
List of Figures
1
Lateral Movement of a Triangular Target at Position dx (Top View) .................................................. 2
2
Circular PCB Sensor Coil ................................................................................................... 3
3
Target Dimensions and Position ........................................................................................... 4
4
Linear Slider Position Versus Measured Inductance.................................................................... 5
5
Lateral Movement of a Rectangular Target at Position dx (Top View) ................................................ 8
6
Starting Position: dx = 0 mm (Top View) .................................................................................. 8
7
Final Position: dx = 100 mm (Top View) .................................................................................. 9
8
Final Position: dx = 100 mm (Side View)
9
Linear Slider Position Versus Measured Inductance .................................................................. 10
.................................................................................
9
List of Tables
Resolution at Different Target Distances
2
Standard Deviation at dx = 50 mm, dz = 2 mm ........................................................................... 6
3
Z-axis Dependence .......................................................................................................... 7
4
Resolution at Different Target Distances
5
6
(1)
................................................................................
1
...............................................................................
Standard Deviation at dx = 50 mm, dz = 2 mm .........................................................................
Z-axis Dependence ........................................................................................................
6
11
12
13
WEBENCH is a registered trademark of Texas Instruments.
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Introduction
1
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Introduction
Linear position sensing determines the position of a target that moves laterally across an inductive sensor
that is generating a magnetic field. An inductance-to-digital converter (LDC), like the LDC1612 or
LDC1614, senses inductance changes of an inductor that comes into proximity with a conductive target,
such as a piece of metal. The LDC measures this inductance shift to provide information about the
position of a conductive target over a sensor coil. The inductance shift is caused by eddy currents
generated in the target due to the magnetic field of the sensor. These eddy currents generate a secondary
magnetic field that opposes the sensor field, causing a shift in the observed inductance (see
http://www.ti.com/lsds/ti/data-converters/inductance-to-digital-converter.page).
Inductive sensing is ideally suited for this type of application because it is a contactless and magnet-free
technology that facilitates systems with very high measurement accuracy and high reliability at low system
cost.
There are two approaches to implement a linear position sensing system with an inductance-to-digital
converter. Both approaches utilize a PCB coil as a sensor.
1. A circular coil can be used to detect the position of a triangular conductive target.
2. A stretched coil design that produces a non-homogeneous AC magnetic field can be used to determine
the position of a rectangular conductive target.
2
Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target
2.1
Concept
Moving a triangular target from the tip to the widest point over a circular PCB sensor coil at a fixed target
distance dz decreases coil inductance as the metal exposure over the coil increases. The increase or
decrease in the amount of target metal exposed to the field in turn changes the eddy currents and the
strength of the secondary field. Figure 1 shows a diagram of the target movement over the sensor coil.
Metal Target
PCB Coil
tTravel Distancet
dX
Figure 1. Lateral Movement of a Triangular Target at Position dx (Top View)
2
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2.2
Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target
Coil and Target Design
A circular PCB coil as shown in Figure 2 can be used as a sensor. To maximize travel range, the sensor
coil diameter must match or exceed the widest end of the target that is to be measured. The example in
this application note uses a 29-mm PCB coil with 70 turns per layer on a 2-layer PCB. The coil diameter of
29 mm exceeds the 25-mm width of the target.
Texas Instruments provides two tools to assist with design of suitable PCB coils:
• WEBENCH® Inductive Sensing Designer can be used to design a suitable coil for this application:
http://www.ti.com/lsds/ti/analog/webench/inductive-sensing.page. An example that shows how to
design a suitable coil in WEBENCH® is provided at this site:
http://e2e.ti.com/blogs_/b/analogwire/archive/2014/09/17/inductive-sensing-five-minute-sensor-coildesign.
• Texas Instruments provides PCB layout scripts that generate coils for a variety of applications. Refer to
the application note LDC Sensor Design, and also the coil generation scripts available in the tools
section of the LDC product page.
Figure 2. Circular PCB Sensor Coil
A suitable target is an isosceles triangle that is made from metal such as aluminum or copper. Other metal
types, or plastic targets that have been painted with conductive paint are suitable alternatives but may
result in different performance.
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Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target
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The measurements in this application note use a copper target with dimensions and mechanical positions
as shown in Figure 3. The usable travel range of the target over the coil is limited to the range in which the
data output is monotonic and provides sufficient output code change for system requirements. To provide
output data monotonicity beyond the hypotenuse of the triangle, it is recommended to extend the target
shape beyond the hypotenuse of the triangle by the coil diameter to increase the maximum usable travel
distance. The diagram shows the target position in the starting position (dx = 0 mm) and the final position
(dx = 100 mm).
Starting Position (Top View)
Metal Target
PCB Coil
t25 mmt
29 mm
dX = 0 mm
tdXt
t70 mmt
t30 mmt
Final Position (Top View)
dX = 100 mm
tdXt
Final Position (Side View)
Metal Target
dZ =
2 mm
dX = 100 mm
PCB Coil
Figure 3. Target Dimensions and Position
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2.3
Performance
5600000
5500000
5400000
5300000
5200000
5100000
5000000
4900000
4800000
4700000
4600000
4500000
4400000
4300000
4200000
4100000
4000000
3900000
3800000
3700000
3600000
3500000
Output Code, dZ = 2 mm
Inductance (µH), dZ = 2 mm
0
10
20
30
40
50
60
Linear Slider Position (mm)
70
80
90
234
228
222
216
210
204
198
192
186
180
174
168
162
156
150
144
138
132
126
120
114
108
100
Inductance (µH)
LDC1612 Output Code (ch0)
Moving the target from dx = 0 mm to dx = 100 mm at a target distance of dz = 2 mm in 0.5 mm steps
results in the data output in Figure 4. Sliding the target from dx = 0 mm to dx = 100 mm decreases the
sensor inductance from 216.3 μH to 122.2 μH. This results in a code change from 3,998,031 to 5,316,099
codes over this range and therefore can be used to determine the slider position.
D001
Figure 4. Linear Slider Position Versus Measured Inductance
The effective resolution changes with target position, and decreases at the extremes of the target.
1. For example, the data shows that moving from dx = 50.0 mm to dx = 50.5 mm results in an output code
change of 12,630 codes (4,564,564 to 4,577,194). Therefore, the average code change over this range
is 25.3 codes per μm.
2. By contrast, moving from dx = 7.0 mm to dx = 7.5 mm results in an output code change by 54 codes
(3,998,249 to 3,998,303). Therefore, the average code increase over this range is 0.1 codes per μm.
To determine the lower end of system accuracy, it is necessary to include measurement noise addition to
resolution. Measurement noise is affected by the reference count of the device (RCOUNT). An RCOUNT
value of 0xFFFF was used to calculate this data, at which the standard deviation in output codes is 5.7
codes (refer to Table 2).
2.4
2.4.1
System Design Recommendations
Maximum Travel Range (dx)
For high-accuracy systems, in which the code change at the extremes is insufficient, it is recommended to
use a target whose length is longer than the required travel range such that accuracy requirements can be
met. The target in the example above may be suitable for a precision application in which 82-mm travel
range is required (13 mm ≤ dx ≤ 95 mm), because the effective resolution is ≥ 1 code per μm of travel in
this range.
By using an even narrower operating range, effective resolution can be improved further; for example, in
the travel range of 23.5 mm ≤ dx ≤ 82.5 mm, the effective resolution is ≥ 10 codes per μm of travel. Note
that the distance resolution is constrained by the standard deviation of the output code (see Table 2).
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Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target
2.4.2
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Coil Design: Quality Factor
The coil design must aim to maximize the quality factor (Q) of the sensor. A high Q sensor results in
higher noise immunity that leads to measurement accuracy and a lower dependence on temperature than
a low Q sensor.
Q is determined by Equation 1, Sensor Coil Quality Factor:
1
L
u
RS
C
Q
where
•
•
•
2.4.3
RS is the AC series resistance of the inductor, which increases with increasing frequency.
L is the sensor inductance.
C is the sensor capacitance.
(1)
Target Distance (dZ)
Since the magnetic field strength rapidly decays beyond one coil diameter distance, it is recommended to
keep the target distance less than one coil diameter to ensure precise measurements.
However, best measurement accuracy can be achieved if dz is kept even lower. A comparison of the
measurement output in the example above at three different target distances shows that the maximum
resolution can be achieved at the lowest dz height. When determining the minimum target distance that
can be used in a system, care must be taken that within the operating range, a drive current setting is
available that satisfies RP and maximum oscillation amplitude requirements.
Table 1. Resolution at Different Target Distances
2.4.4
dz
Output Code
at dx = 13 mm
Codes Increase
per μm Travel
at dx = 13 mm
Output Code
at dx = 50 mm
Codes Increase
per μm Travel
at dx = 50 mm
Output Code
at dx = 95 mm
Codes Increase
per μm Travel
at dx = 95 mm
1 mm
4,002,506
1.9 codes/μm
4,885,570
43.1 codes/μm
6,341,914
3.7 codes/μm
2 mm
4,001,197
1.4 codes/μm
4,564,564
25.3 codes/μm
5,315,157
1.0 codes/μm
3 mm
4,000,213
1.0 codes/μm
4,378,760
16.2 codes/μm
4,839,031
0.6 codes/μm
Reference Count
The conversion time of the LDC161x represents the number of reference clock cycles used to measure
the sensor frequency. It is set by the CHx_RCOUNT register for the channel. The reference count value
must be chosen to support the required resolution. A higher reference count value results in lower rms
noise at the expense of a longer conversion time. Table 2 shows the standard deviation over 1000
samples. The table shows that increasing the RCOUNT value from 0x00FF to 0xFFFF improves SNR by
33.8 dB. Standard deviation and measurement resolution must both be included to calculate the lower
limit on the system accuracy.
Note that as reference count is increased, the effective sample rate decreases.
Table 2. Standard Deviation at dx = 50 mm, dz = 2 mm
Conversion time
Standard Deviation
in Codes (1000 Samples)
Standard Deviation
in μm (1000 Samples)
0xFFFF
26.2 ms at fREF=40 MHz
5.7
0.36
0x0FFF
1.6 ms at fREF=40 MHz
20.6
1.29
0x00FF
0.1 ms at fREF=40 MHz
277.6
17.35
RCOUNT
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2.4.5
Approach 1: Measuring Lateral Movement with a Circular Coil and a Triangular Target
Output Linearization
The output is mostly linear over 60% of the travel range, and provided that the degree of linearization
during this range is sufficient to meet system accuracy requirements, no additional linearization is
necessary. However, a higher degree of linearization is often desired in order to minimize the required
target length, and to improve system accuracy. There are several approaches to improving the linearity of
the measurement::
1. The output code can be translated to travel distance by calculating the best-fit curve through the output
response. For this approach, system accuracy requirements dictate the minimum polynomial degree,
and therefore the required processing power of the microcontroller.
2. The output code can be translated to travel distance by employing a look-up table. This approach
requires little processing power, but requires memory for the look-up table.
3. Instead of using an isosceles triangle, the target shape can be altered such that the output response is
linear. To calculate the precise target shape to result in a linear output, either complex electromagnetic
modeling or complex iterative experimental modeling is required.
2.4.6
Z-axis Compensation
Figure 4 shows that the LDC depends on both dx and dz. If no measures are taken to compensate for
mechanical tolerances of the target distance, then any error introduced by the mechanical tolerance
introduces an error in dz. Table 3 shows the effect that a ± 10% tolerance of the target distance has on the
measurement. For example, the error that is introduced by a +0.2-mm target distance change causes a
-1.8-mm error in dx. While a system with a lower dz offers superior resolution than a system with higher dz,
it is also more dependent on z-axis tolerance. For example, an uncompensated system that has a 0.2-mm
tolerance in dz creates a larger dx error if dz = 1 mm than if dz = 3 mm.
Table 3. Z-axis Dependence
Output code (dx = 50 mm)
Error [codes]
Error [% of frequency]
Equivalent dx position change
dz = 1.8 mm
dz = 2.0 mm
dz = 2.2 mm
4,613,716
4,564,564
4,519,173
49,152
0
-45,391
1.08%
0%
0.99%
1,940 μm
0
-1,792 μm
Therefore, it is necessary to ensure that an error that is introduced by the mechanical tolerance of the
target height does not exceed resolution requirements.
In systems in which linear position must be determined more accurately than tolerances in target height
normally allow, a dual-coil coils can be used to compensate for the z-axis tolerance. Such a system
utilizes two coils; one coil whose objective it is to determine dx, and a second coil which is used to
determine dz. By using a two-dimensional look-up table or curve fitting, a higher degree of accuracy can
be achieved to determine dx over a range of dZ as it would be possible with a single-coil solution.
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Approach 2: Measuring Lateral Movement with a Stretched Coil and a Rectangular Target
3.1
Concept
As an alternative to shaping the target to produce a varying output when moving a target over a coil, it is
possible to instead shape the AC magnetic field that the coil produces. Figure 5 shows an example of
such a system, in which a rectangular target slides over a coil at a fixed target distance to produce an
LDC output that can be used to determine the target position dx.
Metal target
PCB coil
tTravel distancet
dX
Figure 5. Lateral Movement of a Rectangular Target at Position dx (Top View)
The advantage of choosing a stretched coil with rectangular target over a circular coil with triangular target
is that the target can be much smaller and also of a simpler shape. In many systems, where space for the
moving target is restricted, a stretched coil design may be a more feasible approach.
3.2
Coil and Target Design
To use a rectangular target for linear position sensing, the coil has to be shaped to produce a nonhomogeneous AC magnetic field. This can be achieved by ‘stretching’ a coil, such that it produces a
stronger AC magnetic field on one side than on the other. Figure 6 shows an example of such a coil. The
coil measures 100 * 15 mm, has 28 turns per layer on two layers, and a 3.3 mm loop stepping. The AC
magnetic field that the coil produces is strongest at the innermost turn, and decays towards the right side.
Therefore, the peak strength of the AC magnetic field lies left of the geometric center of the coil.
Texas Instruments provides PCB layout scripts that generate stretched coils for linear position sensing
applications. These sensor design generation scripts can be downloaded from www.ti.com/ldc. Application
report SNOA930 contains further information on LDC sensor design.
The target is a rectangular copper or aluminum target. Other metal types, or plastic targets that have been
painted with conductive paint, are suitable alternatives, but may result in different performance. Figure 6
through Figure 8 show the target position in the starting position (dx = 0 mm) and the final position (dx =
100 mm).
t15 mmt
tYTARGET = 25 mmt
Innermost Turn:
Highest Field Line Density
tdXt
t100 mmt
PCB Coil
Aluminum Target
tXTARGET = 14 mmt
Figure 6. Starting Position: dx = 0 mm (Top View)
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YTARGET = 25mm
PCB Coil
tdXt
Aluminum Target
Figure 7. Final Position: dx = 100 mm (Top View)
Aluminum Target
2 mm
PCB Coil
Figure 8. Final Position: dx = 100 mm (Side View)
The target length XTARGET impacts resolution and travel range. A longer target improves resolution, but
limits the usable travel range. The target width YTARGET must extend past the coil to ensure maximum metal
exposure.
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3.3
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Performance
6250000
98
6225000
97
6200000
96
6175000
95
6150000
94
6125000
93
6100000
92
6075000
91
6050000
90
6025000
89
6000000
88
5975000
87
5950000
86
5925000
Output Code, dZ = 2 mm
85
Inductance (µH), dZ = 2 mm
84
80
90
100
5900000
0
10
20
30
40
50
60
Linear Slider Position (mm)
70
Inductance (µH)
LDC1612 Output Code (ch0)
Moving a target from dx = 0 mm to dx = 100 mm at a target distance of dz = 2 mm in 0.5 mm steps results
in the data output seen in Figure 9 below. The target is a 14×25 mm aluminum target.
D002
Figure 9. Linear Slider Position Versus Measured Inductance
The graph that results from sliding the target from dx = 0 mm to dx = 100 mm can be broken up into three
distinct regions.
1. Between 0.0 mm and 15.0 mm, the target enters the magnetic field of the coil. This region can be used
to determine target position, but the resolution is less than in the center region. For example, moving
from dx = 5.0 mm to dx = 5.5 mm results in an output code change from 6,014,920 to 6,014,969, a 49
code change. Therefore, the average code increase over this range is 0.1 codes per μm.
2. The center region spans from 15.0 mm to 92.0 mm over which the sensor inductance decreases from
95.4 μH to 89.1 μH. This region can be used to most accurately determine target position. For
example, the data shows that moving from dx = 50.0 mm to dx = 50.5 mm results in an output code
change by 1,565 codes. Therefore, the average code increase over this range is 3.1 codes per μm.
3. Between dx = 92.0 mm and dx = 100.0 mm, the trend reverses, which is due to the drop in magnetic
field strength past the center coil loop. Since the LDC output codes cannot be uniquely mapped into
this region, use of this region poses significant system challenges for the small increase in target travel
range it provides.
To determine the lower end of system accuracy, it is necessary to include measurement noise addition to
resolution. Measurement noise is affected by the reference count of the device (RCOUNT). An RCOUNT
value of 0xFFFF was used to calculate this data, at which the standard deviation is 2.38 codes (refer to
Table 5).
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3.4
3.4.1
System Design Recommendations
Maximum Travel Range (dx)
The performance calculations in Section 3.3 show that not every region is suitable for measurement. The
region past the center coil loop (between dx = 92.0 mm and dx = 100.0 mm) is not monotonic and is
therefore unusable for this application. This limits the usable travel range to 92 mm.
Depending on system accuracy requirements, precision applications may also need to discard the region
between 0.0 mm and 15.0 mm. This leads to a usable travel range of 77 mm (77% of coil length). As a
result, the coil design length needs to extend beyond the required travel range.
3.4.2
Coil Design
The coil design must aim to maximize the quality factor (Q) of the sensor (refer to Equation 1). A high-Q
sensor results in higher noise immunity, which leads to measurement accuracy and a lower dependence
on temperature than a low-Q sensor.
3.4.3
Target Distance (dz)
Since the magnetic field strength rapidly decays beyond one coil diameter distance, it is recommended to
keep the target distance less than the coil diameter to ensure precise measurements. For non-circular
coils such as the one used in this example, the smaller coil dimension must be considered to be the coil
diameter.
However, best measurement accuracy can be achieved if dz is kept even lower. A comparison of the
measurement output in the example above at three different target distances shows that the maximum
resolution can be achieved at the lowest dz height. When determining the minimum target distance that
can be used in a system, care must be taken that within the operating range, a drive current setting is
available that satisfies RP and maximum oscillation amplitude requirements.
Table 4. Resolution at Different Target Distances
dz
Output Code
at dx = 15 mm
Codes Increase
per μm Travel
at dx = 15 mm
Output Code
at dx = 50 mm
Codes Increase
per μm Travel
at dx = 50 mm
Output Code
at dx = 92 mm
Codes Increase
per μm Travel
at dx = 92 mm
1 mm
6,022,444
1.5 codes/μm
6,142,007
4.7 codes/μm
6,354,896
7.2 codes/μm
2 mm
6,019,754
1.0 codes/μm
6,097,690
3.1 codes/μm
6,229,048
2.9 codes/μm
3 mm
6,018,212
0.7 codes/μm
6,071,355
2.1 codes/μm
6,155,486
0.9 codes/μm
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3.4.4
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Reference Count
The conversion time of the LDC161x represents the number of reference clock cycles used to measure
the sensor frequency. It is set by the CHx_RCOUNT register for the channel. The reference count value
must be chosen to support the required resolution. A higher reference count value results in lower rms
noise at the expense of a longer conversion time. Table 5 shows the standard deviation over 1000
samples. The table shows that increasing the RCOUNT value from 0x00FF to 0xFFFF improves SNR by
43.8 dB. Standard deviation and measurement resolution must both be included to calculate the lower
limit on the system accuracy.
Note that as reference count is increased, the effective sample rate decreases.
Table 5. Standard Deviation at dx = 50 mm, dz = 2 mm
RCOUNT
3.4.5
Conversion time
Standard Deviation
in Codes (1000 Samples)
Standard Deviation
in μm (1000 Samples)
0xFFFF
26.2 ms at fREF = 40 MHz
2.38
0.85
0x0FFF
1.6 ms at fREF = 40 MHz
15.85
5.66
0x00FF
0.1 ms at fREF = 40 MHz
370.40
132.28
Output Linearization
The output is mostly linear over 77% of the travel range, and provided that the degree of linearization
during this range is sufficient to meet system accuracy requirements, no additional linearization is
necessary. However, a higher degree of linearization is often desired in order to minimize the required coil
length, and to improve system accuracy. There are several approaches to improving the linearity of the
measurement:
1. The output code can be translated to travel distance by calculating the best-fit curve through the output
response. For this approach, system accuracy requirements dictate the minimum polynomial degree,
and therefore the required processing power of the microcontroller.
2. The output code can be translated to travel distance by employing a look-up table. This approach
requires little processing power, but requires memory for the look-up table.
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3.5
Approach 2: Measuring Lateral Movement with a Stretched Coil and a Rectangular Target
Z-axis Compensation
Figure 4 shows that the LDC depends on both dx and dz. If no measures are taken to compensate for
mechanical tolerances of the target distance, then any error introduced by the mechanical tolerance
introduces an error in dz. Table 5 shows the effect that a ± 10% tolerance of the target distance has on the
measurement. For example, the error that is introduced by a +0.2-mm target distance change causes a
-2.0-mm error in dx. While a system with a lower dz offers superior resolution than a system with higher dz,
it is also more dependent on z-axis tolerance. For example, an uncompensated system that has a 0.2-mm
tolerance in dz creates a larger dx error if dz = 1 mm than if dz = 3 mm.
Table 6. Z-axis Dependence
Output code (dx = 50 mm)
dz = 1.8 mm
dz = 2.0 mm
dz = 2.2 mm
4,613,716
4,564,564
4,519,173
Error [codes]
7,020
0
-6,336
Error [% of frequency]
0.12%
0%
0.10%
2.243 μm
0
-2,024 μm
Equivalent dx position change
Therefore, it is necessary to ensure that an error that is introduced by the mechanical tolerance of the
target height does not exceed resolution requirements.
In systems in which linear position must be determined more accurately than tolerances in target height
would normally allow, a dual-coil coils can be used to compensate for the z-axis tolerance. Such a system
utilizes two coils; one coil whose objective it is to determine dx, and a second coil which is used to
determine dz. By using a two-dimensional look-up table or curve fitting, a higher degree of accuracy can
be achieved to determine dx over a range of dZ as it would be possible with a single-coil solution.
4
Summary
Inductive sensing is an ideal sensing method for linear position sensing due to the contactless nature and
high reliability of the method.
Linear position can be measured either by using a circular coil and a triangular target, or by using a
stretched coil and a rectangular target. Space requirements for coil and target are the primary deciding
factors on which approach to use for a system:
• Using a circular coil and a triangular target offers excellent resolution in systems in which a target
length that is longer than the required travel range is acceptable. Texas Instruments provides the
WEBENCH® Inductive Sensing Designer and coil scripts that greatly simplify coil design for this
approach.
• Using a stretched coil and rectangular target is suitable for systems in which system space constraints
dictate use of a small target. Texas Instruments provides coil scripts that greatly simplify coil design for
this approach.
SNOA931A – April 2015 – Revised November 2019
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LDC1612/LDC1614 Linear Position Sensing
Copyright © 2015–2019, Texas Instruments Incorporated
13
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Updated sentence structure throughout ................................................................................................ 1
Fixed broken cross-reference to Table 5. ............................................................................................ 12
Changed LDC1000 to LDC100x throughout ......................................................................................... 13
Revision History
SNOA931A – April 2015 – Revised November 2019
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Copyright © 2015–2019, Texas Instruments Incorporated
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