Chapter 3: Sensors

CHAPTER 3: SENSORS
SECTION 3.1: POSITIONAL SENSORS
LINEAR VARIABLE DIFFERENTIAL TRANSFORMERS (LVDT)
HALL EFFECT MAGNETIC SENSORS
RESOLVERS AND SYNCHROS
INDUCTOSYNS
ACCELEROMETERS
3.1
3.1
3.6
3.9
3.13
3.15
iMEMS® ANGULAR-RATE-SENSING GYROSCOPE
GYROSCOPE DESCRIPTION
CORIOLIS ACCELEROMETERS
MOTION IN 2 DIMENSIONS
CAPACITIVE SENSINGS
IMMUNITY TO SHOCK AND VIBRATION
REFERENCES
3.19
3.19
3.20
3.21
3.23
3.25
3.27
SECTION 3.2: TEMPERATURE SENSORS
INTRODUCTION
SEMICONDUCTOR TEMPERATURE SENSORS
CURRENT OUT TEMPERATURE SENSORS
CURRENT AND VOLTAGE OUTPUT TEMPERATURE SENSORS
THERMOCOUPLE PRINCIPLES AND COLD-JUNCTION
COMPENSATION
AUTO-ZERO AMPLIFIER FOR THERMOCOUPLE
MEASUREMENTS
RESISTANCE TEMPERATURE DETECTORS (RTDs)
THERMISTORS
DIGITAL OUTPUT TEMPERATURE SENSORS
THERMOSTATIC SWITCHES AND SET-POINT CONTROLLERS
MICROPROCESSOR TEMPERATURE MONITORING
REFERENCES
SECTION 3.3: CHARGE COUPLED DEVICES (CCDs)
REFERENCES
SECTION 3.4: BRIDGE CIRCUITS
INTRODUCTION
AMPLIFING AND LINEARIZING BRIDGE OUTPUTS
DRIVING REMOTE BRIDGES
SYSTEM OFFSET MINIMIZATION
REFERENCES
SECTION 3.5: STRAIN, FORCE, PRESSURE
AND FLOW MEASUREMENTS
STRAIN GAGES
3.29
3.29
3.31
3.33
3.34
3.38
3.45
3.47
3.52
3.56
3.58
3.61
3.64
3.65
3.68
3.69
3.69
3,75
3.80
3.84
3.87
3.89
3.89
BASIC LINEAR DESIGN
SECTION 3.5: STRAIN, FORCE, PRESSURE
AND FLOW MEASUREMENTS (CONT)
SEMICONDUCTOR STRAIN GAGES
BRIDGE SIGNAL CONDITION CIRCUITS
REFERENCES
3.92
3.95
3.99
SENSORS
POSITIONAL SENSORS
CHAPTER 3: SENSORS
SECTION 3.1: POSITIONAL SENSORS
Linear Variable Differential Transformers (LVDTs)
The linear variable differential transformer (LVDT) is an accurate and reliable method
for measuring linear distance. LVDTs find uses in modern machine-tool, robotics,
avionics, and computerized manufacturing.
The LVDT (see Figure 3.1) is a position-to-electrical sensor whose output is proportional
to the position of a movable magnetic core. The core moves linearly inside a transformer
consisting of a center primary coil and two outer secondary coils wound on a cylindrical
form. The primary winding is excited with an AC voltage source (typically several kHz),
inducing secondary voltages which vary with the position of the magnetic core within the
assembly. The core is usually threaded in order to facilitate attachment to a
nonferromagnetic rod which in turn in attached to the object whose movement or
displacement is being measured.
+
THREADED
CORE
VA
~
VOUT = VA – VB
AC
SOURCE
VB
1.75"
_
VOUT
VOUT
SCHAEVITZ
E100
_
POSITION +
_
POSITION +
Figure 3.1: Linear Variable Differential Transformer (LVDT)
The secondary windings are wound out of phase with each other, and when the core is
centered the voltages in the two secondary windings oppose each other, and the net
3.1
BASIC LINEAR DESIGN
output voltage is zero. When the core is moved off center, the voltage in the secondary
toward which the core is moved increases, while the opposite voltage decreases. The
result is a differential voltage output which varies linearly with the core's position.
Linearity is excellent over the design range of movement, typically 0.5% or better. The
LVDT offers good accuracy, linearity, sensitivity, infinite resolution, as well as
frictionless operation and ruggedness.
A wide variety of measurement ranges are available in different LVDTs, typically from
±100 µm to ±25 cm. Typical excitation voltages range from 1 V to 24 VRMS, with
frequencies from 50 Hz to 20 kHz.
Note that a true null does not occur when the core is in center position because of
mismatches between the two secondary windings and leakage inductance. Also, simply
measuring the output voltage VOUT will not tell on which side of the null position the
core resides.
ABSOLUTE
VALUE
+
AC
SOURCE
FILTER
+
~
VOUT
_
ABSOLUTE
VALUE
_
FILTER
LVDT
+ VOUT
_
POSITION +
_
Figure 3.2: Improved LVDT Output Signal Processing
A signal conditioning circuit which removes these difficulties is shown in Figure 3.2
where the absolute values of the two output voltages are subtracted. Using this technique,
both positive and negative variations about the center position can be measured. While a
diode/capacitor-type rectifier could be used as the absolute value circuit, the precision
rectifier shown in Figure 3.3 is more accurate and linear. The input is applied to a V/I
converter which in turn drives an analog multiplier. The sign of the differential input is
3.2
SENSORS
POSITIONAL SENSORS
detected by the comparator whose output switches the sign of the V/I output via the
analog multiplier. The final output is a precision replica of the absolute value of the input.
These circuits are well understood by IC designers and are easy to implement on modern
bipolar processes.
gm STAGE
+
INPUT
MULTIPLIER
×
V/I
OUTPUT
_
+
±1
_
COMPARATOR
Figure 3.3: Precision Absolute Value Circuit
(Full Wave Rectifier)
The industry-standard AD598 LVDT signal conditioner shown in Figure 3.4 (simplified
form) performs all required LVDT signal processing. The on-chip excitation frequency
oscillator can be set from 20 Hz to 20 kHz with a single external capacitor. Two absolute
value circuits followed by two filters are used to detect the amplitude of the A and B
channel inputs. Analog circuits are then used to generate the ratiometric function
[A – B]/[A + B]. Note that this function is independent of the amplitude of the primary
winding excitation voltage, assuming the sum of the LVDT output voltage amplitudes
remains constant over the operating range. This is usually the case for most LVDTs, but
the user should always check with the manufacturer if it is not specified on the LVDT
data sheet. Note also that this approach requires the use of a 5-wire LVDT.
A single external resistor sets the AD598 excitation voltage from approximately 1 VRMS
to 24 VRMS. Drive capability is 30 mARMS. The AD598 can drive an LVDT at the end of
300 feet of cable, since the circuit is not affected by phase shifts or absolute signal
magnitudes. The position output range of VOUT is ±11 V for a 6 mA load and it can
drive up to 1000 feet of cable. The VA and VB inputs can be as low as 100 mV RMS.
The AD698 LVDT signal conditioner (see Figure 3.5 ) has similar specifications as the
AD598 but processes the signals slightly differently and uses synchronous demodulation.
The A and B signal processors each consist of an absolute value function and a filter. The
A output is then divided by the B output to produce a final output which is ratiometric
and independent of the excitation voltage amplitude. Note that the sum of the LVDT
secondary voltages does not have to remain constant in the AD698.
3.3
BASIC LINEAR DESIGN
AD598
~
AMP
EXCITATION
OSCILLATOR
+
VA
ABS
VALUE
FILTER
A–B
A+B
ABS
VALUE
_
VB
5-WIRE LVDT
FILTER
AMP
VOUT
FILTER
Figure 3.4: AD598 LVDT Signal Conditioner (Simplified)
AD698
EXCITATION
~
AMP
REFERENCE
OSCILLATOR
VB
B
+
A
B
VA
FILTER
AMP
VOUT
A
A, B = ABSOLUTE VALUE + FILTER
_
4-WIRE LVDT
Figure 3.5: AD698 LVDT Signal Conditioner (Simplified)
The AD698 can also be used with a half-bridge (similar to an auto-transformer) LVDT as
shown in Figure 3.6. In this arrangement, the entire secondary voltage is applied to the B
processor, while the center-tap voltage is applied to the A processor. The half-bridge
LVDT does not produce a null voltage, and the A/B ratio represents the range-of-travel of
the core.
3.4
SENSORS
POSITIONAL SENSORS
AD698
EXCITATION
~
AMP
REFERENCE
OSCILLATOR
+
B
A
B
FILTER
AMP
VOUT
A
_
A, B = ABSOLUTE VALUE + FILTER
HALF BRIDGE LVDT
Figure 3.6: Half-Bridge LVDT Configuration
It should be noted that the LVDT concept can be implemented in rotary form, in which
case the device is called a rotary variable differential transformer (RVDT). The shaft is
equivalent to the core in an LVDT, and the transformer windings are wound on the
stationary part of the assembly. However, the RVDT is linear over a relatively narrow
range of rotation and is not capable of measuring a full 360º rotation. Although capable
of continuous rotation, typical RVDTs are linear over a range of about ±40º about the
null position (0º). Typical sensitivity is 2 to 3mV per volt per degree of rotation, with
input voltages in the range of 3VRMS at frequencies between 400 Hz and 20 kHz. The 0º
position is marked on the shaft and the body.
3.5
BASIC LINEAR DESIGN
Hall Effect Magnetic Sensors
If a current flows in a conductor (or semiconductor) and there is a magnetic field present
which is perpendicular to the current flow, then the combination of current and magnetic
field will generate a voltage perpendicular to both (see Figure 3.7). This phenomenon is
called the Hall Effect, was discovered by E. H. Hall in 1879. The voltage, VH, is known
as the Hall Voltage. VH is a function of the current density, the magnetic field, and the
charge density and carrier mobility of the conductor.
T
CONDUCTOR
OR
SEMICONDUCTOR
I
I
VH
I
= CURRENT
B = MAGNETIC FIELD
T
B
= THICKNESS
VH = HALL VOLTAGE
Figure 3.7: Hall Effect Sensor
The Hall effect may be used to measure magnetic fields (and hence in contact-free
current measurement), but its commonest application is in motion sensors where a fixed
Hall sensor and a small magnet attached to a moving part can replace a cam and contacts
with a great improvement in reliability. (Cams wear and contacts arc or become fouled,
but magnets and Hall sensors are contact free and do neither.) Since VH is proportional to
magnetic field and not to rate of change of magnetic field like an inductive sensor, the
Hall Effect provides a more reliable low speed sensor than an inductive pickup.
Although several materials can be used for Hall effect sensors, silicon has the advantage
that signal conditioning circuits can be integrated on the same chip as the sensor. CMOS
processes are common for this application. A simple rotational speed detector can be
made with a Hall sensor, a gain stage, and a comparator as shown in Figure 3.8. The
circuit is designed to detect rotation speed as in automotive applications. It responds to
small changes in field, and the comparator has built-in hysteresis to prevent oscillation.
Several companies manufacture such Hall switches, and their usage is widespread.
3.6
SENSORS
POSITIONAL SENSORS
There are many other applications, particularly in automotive throttle, pedal, suspension,
and valve position sensing, where a linear representation of the magnetic field is desired.
The AD22151 is a linear magnetic field sensor whose output voltage is proportional to a
magnetic field applied perpendicularly to the package top surface (see Figure 3.9). The
AD22151 combines integrated bulk Hall cell technology and conditioning circuitry to
minimize temperature related drifts associated with silicon Hall cell characteristics.
ROTATION
I
GAIN
B
HALL
CELL
VH
COMPARATOR
WITH
HYSTERESIS
+
_
VOUT
VTHRESHOLD
MAGNETS
Figure 3.8: Hall Effect Sensor Used as a Rotational Sensor
The architecture maximizes the advantages of a monolithic implementation while
allowing sufficient versatility to meet varied application requirements with a minimum
number of external components. Principal features include dynamic offset drift
cancellation using a chopper-type op amp and a built-in temperature sensor. Designed for
single +5 V supply operation, low offset and gain drift allows operation over a –40ºC to
+150ºC range. Temperature compensation (set externally with a resistor R1) can
accommodate a number of magnetic materials commonly utilized in position sensors.
Output voltage range and gain can be easily set with external resistors. Typical gain range
is usually set from 2 mV/Gauss to 6 mV/Gauss. Output voltage can be adjusted from
fully bipolar (reversible) field operation to fully unipolar field sensing. The voltage
output achieves near rail-to-rail dynamic range (+0.5 V to +4.5 V), capable of supplying
1 mA into large capacitive loads. The output signal is ratiometric to the positive supply
rail in all configurations.
3.7
BASIC LINEAR DESIGN
VCC = +5V
VCC / 2
VCC / 2
R2
+
TEMP
REF
R1
_
R3
_
VOUT
AD22151
+
CHOPPER
AMP
VOUT =
1 + R3
R2
0.4mV
Gauss
OUTPUT
AMP
NONLINEARITY = 0.1% FS
Figure 3.9: AD22151 Linear Output Magnetic Field Sensor
3.8
SENSORS
POSITIONAL SENSORS
Resolvers and Synchros
Machine-tool and robotics manufacturers have increasingly turned to resolvers and
synchros to provide accurate angular and rotational information. These devices excel in
demanding factory applications requiring small size, long-term reliability, absolute
position measurement, high accuracy, and low-noise operation.
A diagram of a typical synchro and resolver is shown in Figure 3.10. Both synchros and
resolvers employ single-winding rotors that revolve inside fixed stators. In the case of a
simple synchro, the stator has three windings oriented 120º apart and electrically
connected in a Y-connection. Resolvers differ from synchros in that their stators have
only two windings oriented at 90º.
S1
S2
STATOR
SYNCHRO
ROTOR
ROTOR
R1
θ
S1 TO S3 = V sin ωt sin θ
S3 TO S2 = V sin ωt sin (θ + 120°)
S2 TO S1 = V sin ωt sin (θ + 240°)
V sin ωt
R2
S3
ROTOR
S4
R1
STATOR
V sin ωt
S1 TO S3 = V sin ωt sin θ
S4 TO S2 = V sin ωt sin (θ + 90°)
= V sin ωt cos θ
S2
STATOR
R2
S3
RESOLVER
S1
Figure 3.10: Synchros and Resolvers
Because synchros have three stator coils in a 120º orientation, they are more difficult than
resolvers to manufacture and are therefore more costly. Today, synchros find decreasing
use, except in certain military and avionic retrofit applications.
Modern resolvers, in contrast, are available in a brushless form that employ a transformer
to couple the rotor signals from the stator to the rotor. The primary winding of this
transformer resides on the stator, and the secondary on the rotor. Other resolvers use
more traditional brushes or slip rings to couple the signal into the rotor winding.
Brushless resolvers are more rugged than synchros because there are no brushes to break
or dislodge, and the life of a brushless resolver is limited only by its bearings. Most
resolvers are specified to work over 2 V to 40 VRMS and at frequencies from 400 Hz to
3.9
BASIC LINEAR DESIGN
10 kHz. Angular accuracies range from 5 arc-minutes to 0.5 arc-minutes. (There are 60
arc-minutes in one degree, and 60 arc-seconds in one arc-minute. Hence, one arc-minute
is equal to 0.0167 degrees).
In operation, synchros and resolvers resemble rotating transformers. The rotor winding is
excited by an AC reference voltage, at frequencies up to a few kHz. The magnitude of the
voltage induced in any stator winding is proportional to the sine of the angle, θ, between
the rotor coil axis and the stator coil axis. In the case of a synchro, the voltage induced
across any pair of stator terminals will be the vector sum of the voltages across the two
connected coils.
For example, if the rotor of a synchro is excited with a reference voltage, Vsinωt, across
its terminals R1 and R2, then the stator's terminal will see voltages in the form:
S1 to S3 = V sinωt sinθ
S3 to S2 = V sinωt sin (θ + 120º)
S2 to S1 = V sinωt sin (θ + 240º),
Eq. 3-1
Eq. 3-2
Eq. 3-3
where θ is the shaft angle.
In the case of a resolver, with a rotor AC reference voltage of Vsinωt, the stator's
terminal voltages will be:
S1 to S3 = V sinωt sin θ
S4 to S2 = V sinωt sin(θ + 90º) = V sinωt cosθ.
Eq. 3-4
Eq. 3-5
It should be noted that the 3-wire synchro output can be easily converted into the
resolver-equivalent format using a Scott-T transformer. Therefore, the following signal
processing example describes only the resolver configuration.
A typical resolver-to-digital converter (RDC) is shown functionally in Figure 3.11. The
two outputs of the resolver are applied to cosine and sine multipliers. These multipliers
incorporate sine and cosine lookup tables and function as multiplying digital-to-analog
converters. Begin by assuming that the current state of the up/down counter is a digital
number representing a trial angle, ϕ. The converter seeks to adjust the digital angle, ϕ,
continuously to become equal to, and to track θ, the analog angle being measured. The
resolver's stator output voltages are written as:
V1 = V sinωt sinθ
V2 = V sinωt cosθ
Eq. 3-6
Eq. 3-7
where θ is the angle of the resolver's rotor. The digital angle ϕ is applied to the cosine
multiplier, and its cosine is multiplied by V1 to produce the term:
V sinωt sinθ cosϕ.
3.10
Eq. 3-8
SENSORS
POSITIONAL SENSORS
V sin ωt
ROTOR REFERENCE
V sin ωt sin
θ
COSINE
MULTIPLIER
STATOR
INPUTS
V sin ωt sin θ cos ϕ
_
ϕ
V sin ωt cos θ
SINE
MULTIPLIER
+
V sin ωt cos θ sin ϕ
ϕ
UP / DOWN
COUNTER
V sin ωt [sin (θ – ϕ )]
DETECTOR
ERROR
K sin (θ – ϕ )
INTEGRATOR
VCO
ϕ = DIGITAL ANGLE
VELOCITY
LATCHES
ϕ
WHEN ERROR = 0,
ϕ = θ ± 1 LSB
Figure 3.11: Resolver to Digital Converter (RDC)
The digital angle ϕ is also applied to the sine multiplier and multiplied by V2 to product
the term:
V sinωt cosθ sinϕ.
Eq. 3-9
These two signals are subtracted from each other by the error amplifier to yield an AC
error signal of the form:
V sinωt [sinθ cosϕ – cosθ sinϕ].
Eq. 3-10
Using a simple trigonometric identity, this reduces to:
V sinωt [sin (θ –ϕ)].
Eq. 3-11
The detector synchronously demodulates this AC error signal, using the resolver's rotor
voltage as a reference. This results in a DC error signal proportional to sin(θ–ϕ).
3.11
BASIC LINEAR DESIGN
The DC error signal feeds an integrator, the output of which drives a voltage-controlledoscillator (VCO). The VCO, in turn, causes the up/down counter to count in the proper
direction to cause:
sin (θ – ϕ) → 0.
Eq. 3-12
θ – ϕ → 0,
Eq. 3-13
ϕ=θ
Eq. 3-14
When this is achieved,
and therefore
to within one count. Hence, the counter's digital output, ϕ, represents the angle θ. The
latches enable this data to be transferred externally without interrupting the loop's
tracking.
3.12
SENSORS
POSITIONAL SENSORS
Inductosyns
Synchros and resolvers inherently measure rotary position, but they can make linear
position measurements when used with lead screws. An alternative, the Inductosyn™
(registered trademark of Farrand Controls, Inc.) measures linear position directly. In
addition, Inductosyns are accurate and rugged, well-suited to severe industrial
environments, and do not require ohmic contact.
The linear Inductosyn consists of two magnetically coupled parts; it resembles a
multipole resolver in its operation (see Figure 3.12). One part, the scale, is fixed (e.g.
with epoxy) to one axis, such as a machine tool bed. The other part, the slider, moves
along the scale in conjunction with the device to be positioned (for example, the machine
tool carrier).
The scale is constructed of a base material such as steel, stainless steel, aluminum, or a
tape of spring steel, covered by an insulating layer. Bonded to this is a printed-circuit
trace, in the form of a continuous rectangular waveform pattern. The pattern typically has
a cyclic pitch of 0.1 inch, 0.2 inch, or 2 millimeters. The slider, about 4 inches long, has
two separate but identical printed circuit traces bonded to the surface that faces the scale.
These two traces have a waveform pattern with exactly the same cyclic pitch as the
waveform on the scale, but one trace is shifted one-quarter of a cycle relative to the other.
The slider and the scale remain separated by a small air gap of about 0.007 inch.
V sin ωt sin
2πX
S
V sin ωt cos
2πX
S
V sin ωt
SLIDER
EXPANDED
SCALE
S
X
SCALE
TRACES
SLIDER
TRACES
SINE
COSINE
TWO WINDINGS SHIFTED
BY 1/4 PERIOD (90°)
Figure 3.12: Linear Inductosyn
3.13
BASIC LINEAR DESIGN
Inductosyn operation resembles that of a resolver. When the scale is energized with a sine
wave, this voltage couples to the two slider windings, inducing voltages proportional to
the sine and cosine of the slider's spacing within the cyclic pitch of the scale. If S is the
distance between pitches, and X is the slider displacement within a pitch, and the scale is
energized with a voltage V sinωt, then the slider windings will see terminal voltages of:
V (sine output)
= V sinωt sin[2πX/S]
Eq. 3-15
V (cosine output)
= V sinωt cos[2πX/S].
Eq. 3-16
As the slider moves the distance of the scale pitch, the voltages produced by the two
slider windings are similar to those produced by a resolver rotating through 360º. The
absolute orientation of the Inductosyn is determined by counting successive pitches in
either direction from an established starting point. Because the Inductosyn consists of a
large number of cycles, some form of coarse control is necessary in order to avoid
ambiguity. The usual method of providing this is to use a resolver or synchro operated
through a rack and pinion or a lead screw.
In contrast to a resolver's highly efficient transformation of 1:1 or 2:1, typical
Inductosyns operate with transformation ratios of 100:1. This results in a pair of
sinusoidal output signals in the millivolt range which generally require amplification.
Since the slider output signals are derived from an average of several spatial cycles, small
errors in conductor spacing have minimal effects. This is an important reason for the
Inductosyn's very high accuracy. In combination with 12-bit RDCs, linear Inductosyns
readily achieve 25 microinch resolutions.
Rotary inductosyns can be created by printing the scale on a circular rotor and the slider's
track pattern on a circular stator. Such rotary devices can achieve very high resolutions.
For instance, a typical rotary Inductosyn may have 360 cyclic pitches per rotation, and
might use a 12-bit RDC. The converter effectively divides each pitch into 4096 sectors.
Multiplying by 360 pitches, the rotary Inductosyn divides the circle into a total of
1,474,560 sectors. This corresponds to an angular resolution of less than 0.9 arc seconds.
As in the case of the linear Inductosyn, a means must be provided for counting the
individual pitches as the shaft rotates. This may be done with an additional resolver
acting as the coarse measurement.
3.14
SENSORS
POSITIONAL SENSORS
Accelerometers
Accelerometers are widely used to measure tilt, inertial forces, shock, and vibration. They
find wide usage in automotive, medical, industrial control, and other applications.
Modern micromachining techniques allow these accelerometers to be manufactured on
CMOS processes at low cost with high reliability. Analog Devices iMEMS® (Integrated
Micro Electro Mechanical Systems) accelerometers represent a breakthrough in this
technology. A significant advantage of this type of accelerometer over piezoelectric-type
charge-output accelerometers is that DC acceleration can be measured (e.g. they can be
used in tilt measurements where the acceleration is a constant 1g).
The basic unit cell sensor building block for these accelerometers is shown in Figure
3.13. The surface micromachined sensor element is made by depositing polysilicon on a
sacrificial oxide layer that is then etched away leaving the suspended sensor element. The
actual sensor has tens of unit cells for sensing acceleration, but the diagram shows only
one cell for clarity. The electrical basis of the sensor is the differential capacitor (CS1 and
CS2) which is formed by a center plate which is part of the moving beam and two fixed
outer plates. The two capacitors are equal at rest (no applied acceleration). When
acceleration is applied, the mass of the beam causes it to move closer to one of the fixed
plates while moving further from the other. This change in differential capacitance forms
the electrical basis for the conditioning electronics shown in Figure 3.14.
AT REST
CS1
CS2
APPLIED ACCELERATION
CENTER
PLATE
TETHER
BEAM
CS1
= CS2
CS1
< CS2
FIXED
OUTER
PLATES
DENOTES ANCHOR
Figure 3.13: ADXL-Family Micromachined Accelerometers
(Top View of IC)
3.15
BASIC LINEAR DESIGN
APPLIED ACCELERATION
SYNC
CS2 > CS1
0°
PLATE
CS1
A1
BEAM
OSCILLATOR
PLATE
CS2
SYNCHRONOUS
DEMODULATOR
180°
A2
VOUT
Figure 3.14: Accelerometer Internal Signal Conditioning
The sensor's fixed capacitor plates are driven differentially by a 1 MHz square wave: the
two square wave amplitudes are equal but are 180º out of phase. When at rest, the values
of the two capacitors are the same, and therefore the voltage output at their electrical
center (i.e., at the center plate attached to the movable beam) is zero. When the beam
begins to move, a mismatch in the capacitance produces an output signal at the center
plate. The output amplitude will increase with the acceleration experienced by the sensor.
The center plate is buffered by A1 and applied to a synchronous demodulator. The
direction of beam motion affects the phase of the signal, and synchronous demodulation
is therefore used to extract the amplitude information. The synchronous demodulator
output is amplified by A2 which supplies the acceleration output voltage, VOUT.
An interesting application of low-g accelerometers is measuring tilt. Figure 3.15 shows
the response of an accelerometer to tilt. The accelerometer output on the diagram has
been normalized to 1g fullscale. The accelerometer output is proportional to the sine of
the tilt angle with respect to the horizon. Note that maximum sensitivity occurs when the
accelerometer axis is perpendicular to the acceleration. This scheme allows tilt angles
from –90º to +90º (180º of rotation) to be measured. However, in order to measure a full
360º rotation, a dual-axis accelerometer must be used.
3.16
SENSORS
POSITIONAL SENSORS
+90°
X
X
1g
Acceleration
θ
0°
–90°
+1g
Acceleration = 1g × sin θ
θ
0g
–90°
0°
+90°
–1g
Figure 3.15: Using an Accelerometer to Measure Tilt
Figure 3.16 shows a simplified block diagram of the ADXL202 dual axis ±2 g
accelerometer. The output is a pulse whose duty cycle contains the acceleration
information. This type of output is extremely useful because of its high noise immunity,
and the data is transmitted over a single wire. Standard low cost microcontrollers have
timers which can be easily used to measure the T1 and T2 intervals. The acceleration in g
is then calculated using the formula:
A(g) = 8 [T1/T2 – 0.5] .
Eq. 3-17
Note that a duty cycle of 50 % (T1 = T2) yields a 0g output. T2 does not have to be
measured for every measurement cycle. It need only be updated to account for changes
due to temperature. Since the T2 time period is shared by both X and Y channels, it is
necessary to only measure it on one channel. The T2 period can be set from 0.5 ms to
10 ms with an external resistor.
Analog voltages representing acceleration can be obtained by buffering the signal from
the XFILT and YFILT outputs or by passing the duty cycle signal through an RC filter to
reconstruct its DC value.
A single accelerometer cannot work in all applications. Specifically, there is a need for
both low-g and high-g accelerometers. Low-g devices are useful in such applications as
tilt measurements, but higher-g accelerometers are needed in applications such as airbag
crash sensors.
3.17
BASIC LINEAR DESIGN
+3.0V TO +5.25V
VDD
CX
VDD
XFILT
SELF TEST
XOUT
X
SENSOR
OSCILLATOR
DEMOD
32kΩ
ADXL202
DUTY
CYCLE
MODULATOR
32kΩ
Y
µC
YOUT
DEMOD
SENSOR
CY
T2
T1
YFILT
T2
RSET
A(g) = 8 (T1 /T2 – 0.5)
0g = 50% DUTY CYCLE
T2 = RSET/125MΩ
Figure 3.16: ADXL202 ±2g Dual Axis Accelerometer
3.18
SENSORS
POSITIONAL SENSORS
iMEMS® Angular-Rate-Sensing Gyroscope
The new ADXRS150 and ADXRS300 gyros, with full-scale ranges of 150°/s and 300°/s,
represent a quantum jump in gyro technology. The first commercially available surfacemicromachined angular rate sensors with integrated electronics, they are smaller—with
lower power consumption, and better immunity to shock and vibration—than any gyros
having comparable functionality.
Gyroscope Description
Gyroscopes are used to measure angular rate—how quickly an object turns. The rotation
is typically measured in reference to one of three axes: yaw, pitch, or roll. Figure 3.17
shows a diagram representing each axis of sensitivity relative to a package mounted to a
flat surface. Depending on how a gyro normally sits, its primary axis of sensitivity can be
one of the three axes of motion: yaw, pitch, or roll. The ADXRS150 and ADXRS300 are
yaw-axis gyros, but they can measure rotation about other axes by appropriate mounting
orientation. For example, at the right of Fig. 3.17 a yaw-axis device is positioned to
measure roll.
Fig. 3.17: Gyro Axes of Rotational Sensitivity
A gyroscope with one axis of sensitivity can also be used to measure other axes by
mounting the gyro differently, as shown in the right-hand diagram. Here, a yaw-axis
gyro, such as the ADXRS150 or ADXRS300, is mounted on its side so that the yaw axis
becomes the roll axis.
As an example of how a gyro could be used, a yaw-axis gyro mounted on a turntable
rotating at 33 1/3 rpm (revolutions per minute) would measure a constant rotation of 360°
3.19
BASIC LINEAR DESIGN
times 33 1/3 rpm divided by 60 seconds, or 200°/s. The gyro would output a voltage
proportional to the angular rate, as determined by its sensitivity, measured in millivolts
per degree per second (mV/°/s). The full-scale voltage determines how much angular rate
can be measured, so in the example of the turntable, a gyro would need to have a fullscale voltage corresponding to at least 200°/s. Full-scale is limited by the available
voltage swing divided by the sensitivity. The ADXRS300, for example, with 1.5 V fullscale and a sensitivity of 5 mV/°/s, handles a full-scale of 300°/s. The ADXRS150, has a
more limited full-scale of 150°/s but a greater sensitivity of 12.5 mV/°/s.
One practical application is to measure how quickly a car turns by mounting a gyro inside
the vehicle; if the gyro senses that the car is spinning out of control, differential braking
engages to bring it back into control. The angular rate can also be integrated over time to
determine angular position—particularly useful for maintaining continuity of GPS-based
navigation when the satellite signal is lost for short periods of time.
Coriolis Acceleration
Analog Devices’ ADXRS gyros measure angular rate by means of Coriolis acceleration.
The Coriolis effect can be explained as follows, starting with Figure 3.16. Consider
yourself standing on a rotating platform, near the center. Your speed relative to the
ground is shown as the arrow lengths in Figure 3.18. If you were to move to a point near
the outer edge of the platform, your speed would increase relative to the ground, as
indicated by the longer blue arrow. The rate of increase of your tangential speed, caused
by your radial velocity, is the Coriolis acceleration (after Gaspard G. de Coriolis, 17921843—a French mathematician).
Figure 3.18: Coriolis acceleration example.
3.20
SENSORS
POSITIONAL SENSORS
If Ω is the angular rate and r the radius, the tangential velocity is Ωr. So, if r changes at
speed, v, there will be a tangential acceleration Ωv. This is half of the Coriolis
acceleration. There is another half from changing the direction of the radial velocity
giving a total of 2Ωv. If you have mass, M, the platform must apply a force, 2MΩv, to
cause that acceleration, and the mass experiences a corresponding reaction force.
Motion in 2 dimensions
Consider the position coordinate, z = rεiθ, in the complex plane. Differentiating with
respect to time, t, the velocity is:
dz
dr
=
ε
dt
dt
jθ
+ ir
dθ jθ
ε
dt
Eq. 3-19
The two terms are the respective radial and tangential components, the latter arising from
the angular rate. Differentiating again, the acceleration is:
2
d2 z
d2r jθ
dr dθ jθ
dr dθ jθ
d2θ jθ
dθ jθ
+
i
ε
+
i
ε
+
ir
ε -r
ε
=
ε
2
2
2
dt
dt dt
dt dt
dt
dt
dt
Eq. 3-20
The first term is the radial linear acceleration and the fourth term is the tangential
component arising from angular acceleration. The last term is the familiar centripetal
acceleration needed to constrain r. The second and third terms are tangential and are the
Coriolis acceleration components. They are equal, respectively arising from the changing
direction of the radial velocity and from the changing magnitude of the tangential
velocity. If the angular rate and radial velocities are constant,
dθ
= Ω
dt
Eq.3-21
dr
dt = v
Eq. 3-22
and
then
d2 z
= I 2 Ω v εiθ
dt2
Ω2 r εiθ
Eq. 3-23
where the angular component, iεiθ, indicates a tangential direction in the sense of positive
θ for the Coriolis acceleration, 2Ωv, and –εiθ indicates towards the center (i.e.,
centripetal) for the Ω2r component
The ADXRS gyros take advantage of this effect by using a resonating mass analogous to
the person moving out and in on a rotating platform. The mass is micromachined from
3.21
BASIC LINEAR DESIGN
polysilicon and is tethered to a polysilicon frame so that it can resonate only along one
direction.
Figure 3.19 shows that when the resonating mass moves toward the outer edge of the
rotation, it is accelerated to the right and exerts on the frame a reaction force to the left.
When it moves toward the center of the rotation, it exerts a force to the right, as indicated
by the arrows.
Figure 3.19: Coriolis Effect Demo 1
Figure 3.20: Schematic of the gyro’s mechanical structure.
To measure the Coriolis acceleration, the frame containing the resonating mass is
tethered to the substrate by springs at 90° relative to the resonating motion, as shown in
Figure 3.20. This figure also shows the Coriolis sense fingers that are used to capacitively
sense displacement of the frame in response to the force exerted by the mass, as described
Figure 3.19, a demonstration of the Coriolis effect in response to a resonating silicon
3.22
SENSORS
POSITIONAL SENSORS
mass suspended inside a frame. The orange arrows indicate the force applied to the
structure, based on status of the resonating mass.
In figure 3.21 the frame and resonating mass are displaced laterally in response to the
Coriolis effect. The displacement is determined from the change in capacitance between
the Coriolis sense fingers on the frame and those attached to the substrate.
further on. If the springs have a stiffness, K, then the displacement resulting from the
reaction force will be 2 ΩvM/K
Figure 3.21: Displacement due to the Coriolis Effect
Figure 3.21, which shows the complete structure, demonstrates that as the resonating
mass moves, and as the surface to which the gyro is mounted rotates, the mass and its
frame experience the Coriolis acceleration and are translated 90° from the vibratory
movement. As the rate of rotation increases, so does the displacement of the mass and the
signal derived from the corresponding capacitance change.
It should be noted that the gyro may be placed anywhere on the rotating object and at any
angle, so long as its sensing axis is parallel to the axis of rotation. The above explanation
is intended to give an intuitive sense of the function and has been simplified by the
placement of the gyro.
Capacitive Sensing
ADXRS gyros measure the displacement of the resonating mass and its frame due to the
Coriolis effect through capacitive sensing elements attached to the resonator, as shown in
Figures 3.19, 20, and 21. These elements are silicon beams inter-digitated with two sets
of stationary silicon beams attached to the substrate, thus forming two nominally equal
capacitors. Displacement due to angular rate induces a differential capacitance in this
system. If the total capacitance is C and the spacing of the beams is g, then the
differential capacitance is 2 ΩvMC/gK, and is directly proportional to the angular rate.
The fidelity of this relationship is excellent in practice, with nonlinearity less than 0.1%.
3.23
BASIC LINEAR DESIGN
The ADXRS gyro electronics can resolve capacitance changes as small as 12 x 10–21
farads (12 zeptofarads) from beam deflections as small as 0.00016 Angstroms
(16 femtometers). The only way this can be utilized in a practical device is by situating
the electronics, including amplifiers and filters, on the same die as the mechanical sensor.
The differential signal alternates at the resonator frequency and can be extracted from the
noise by correlation.
These sub atomic displacements are meaningful as the average positions of the surfaces
of the beams, even though the individual atoms on the surface are moving randomly by
much more. There are about 1012 atoms on the surfaces of the capacitors, so the
statistical averaging of their individual motions reduces the uncertainty by a factor of
106. So why can’t we do 100 times better? The answer is that the impact of the air
molecules causes the structure to move—although similarly averaged, their effect is far
greater! So why not remove the air? The device is not operated in a vacuum because it is
a very fine, thin film weighing only 4 micrograms; its flexures, only 1.7 microns wide,
are suspended over the silicon substrate. Air cushions the structure, preventing it from
being destroyed by violent shocks—even those experienced during firing of a guided
shell from a howitzer (as demonstrated recently)
Figure 3.22: Photograph of mechanical sensor.
Figure 3.22 shows that the ADXRS gyros include two structures to enable differential
sensing in order to reject environmental shock and vibration.
3.24
SENSORS
POSITIONAL SENSORS
Integration of electronics and mechanical elements is a key feature of products such as
the ADXRS150 and ADXRS300, because it makes possible the smallest size and cost for
a given performance level. Figure 3.23 is a photograph of the ADXRS die, highlighting
the integration of the mechanical rate sensor and the signal conditioning electronics.
Figure 3.23: Photograph of ADXRS gyro die
The ADXRS150 and ADXRS300 are housed in an industry-standard package that
simplifies users’ product development and production. The ceramic package—a 32-pin
ball grid-array, (BGA)—measures 7 mm wide by 7 mm deep by 3 mm tall. It is at least
100 times smaller than any other gyro having similar performance. Besides their small
size, these gyros consume 30 mW, far less power than similar gyros. The combination of
small size and low power make these products ideally suited for consumer applications
such as toy robots, scooters, and navigation devices.
Immunity to Shock and Vibration
One of the most important concerns for a gyro user is the device’s ability to reliably
provide an accurate angular rate-output signal—even in the presence of environmental
shock and vibration. One example of such an application is automotive rollover detection,
in which a gyro is used to detect whether or not a car (or SUV) is rolling over. Some
rollover events are triggered by an impact with another object, such as a curb, that results
in a shock to the vehicle. If the shock saturates the gyro sensor, and the gyro cannot filter
it out, then the airbags may not deploy. Similarly, if a bump in the road results in a shock
or vibration that translates into a rotational signal, the airbags might deploy when not
needed—a considerable safety hazard!
3.25
BASIC LINEAR DESIGN
As can be seen, the ADXRS gyros employ a novel approach to angular rate-sensing that
makes it possible to reject shocks of up to 1,000 g — they use two resonators to
differentially sense signals and reject common-mode external accelerations that are
unrelated to angular motion. This approach is, in part, the reason for the excellent
immunity of the ADXRS gyros to shock and vibration. The two resonators in Figure 3.22
are mechanically independent, and they operate anti-phase. As a result, they measure the
same magnitude of rotation, but give outputs in opposite directions. Therefore, the
difference between the two sensor signals is used to measure angular rate. This cancels
non-rotational signals that affect both sensors. The signals are combined in the internal
hard-wiring ahead of the very sensitive preamplifiers. Thus, extreme acceleration
overloads are largely prevented from reaching the electronics—thereby allowing the
signal conditioning to preserve the angular rate output during large shocks. This scheme
requires that the two sensors be well-matched, precisely fabricated copies of each other.
3.26
SENSORS
POSITIONAL SENSORS
REFERENCES
1.
Herman Schaevitz, “The Linear Variable Differential Transformer”, Proceedings of the SASE,
Volume IV, No. 2, 1946.
2.
Dr. Ernest D.D. Schmidt, “Linear Displacement - Linear Variable Differential Transformers –
LVDTs”, Schaevitz Sensors, http://www.schaevitz.com.
3.
E-Series LVDT Data Sheet, Schaevitz Sensors, http://www.schaevitz.com.
Schaevitz Sensors is now a division of Lucas Control Systems, 1000 Lucas Way, Hampton, VA
23666.
4.
Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New
York, 1991.
5.
Harry L. Trietley, Transducers in Mechanical and Electronic Design, Marcel Dekker, Inc.,
1986.
6.
AD598 and AD698 Data Sheet, Analog Devices, Inc., http://www.analog.com.
7.
Bill Travis, “Hall-Effect Sensor ICs Sport Magnetic Personalitie”s, EDN, April 9, 1998,
pp. 81-91.
8.
AD22151 Data Sheet, Analog Devices, Inc., http://www.analog.com.
9.
Dan Sheingold, Analog-Digital Conversion Handbook, Third Edition, Prentice-Hall, 1986.
10.
F. P. Flett, “Vector Control Using a Single Vector Rotation Semiconductor for Induction and
Permanent Magnet Motor”s, PCIM Conference, Intelligent Motion, September 1992
Proceedings, Available from Analog Devices.
11.
F. P. Flett, “Silicon Control Algorithms for Brushless Permanent Magnet Synchronous
Machines”, PCIM Conference, Intelligent Motion, June 1991 Proceedings, Available from
Analog Devices.
12.
P.J.M. Coussens, et al, “Three Phase Measurements with Vector Rotation Blocks in Mains and
Motion Control”, PCIM Conference, Intelligent Motion, April 1992 Proceedings, Available
from Analog Devices.
13.
Dennis Fu, “Digital to Synchro and Resolver Conversion with the AC Vector Processor
AD2S100”, Available from Analog Devices.
14.
Dennis Fu, “Circuit Applications of the AD2S90 Resolver-to-Digital Converter, AN-230”, Analog
Devices.
15.
Aengus Murray and P. Kettle, “Towards a Single Chip DSP Based Motor Control Solution”,
Proceedings PCIM - Intelligent Motion, May 1996, Nurnberg Germany, pp. 315-326. Also
available at http://www.analog.com.
16.
D. J. Lucey, P. J. Roche, M. B. Harrington, and J. R. Scannell, “Comparison of Various Space
Vector Modulation Strategies”, Proceedings Irish DSP and Control Colloquium, July 1994,
Dublin, Ireland, pp. 169-175.
17.
Niall Lyne, “ADCs Lend Flexibility to Vector Motor Control Application”, Electronic Design,
May 1, 1998, pp. 93-100.
3.27
BASIC LINEAR DESIGN
18.
3.28
Frank Goodenough, “Airbags Boom when IC Accelerometer Sees 50g,” Electronic Design,
August 8, 1991.
SENSORS
TEMPERATURE SENSORS
SECTION 3.2: TEMPERATURE SENSORS
Introduction
Measurement of temperature is critical in modern electronic devices, especially
expensive laptop computers and other portable devices with densely packed circuits
which dissipate considerable power in the form of heat. Knowledge of system
temperature can also be used to control battery charging as well as prevent damage to
expensive microprocessors.
Compact high power portable equipment often has fan cooling to maintain junction
temperatures at proper levels. In order to conserve battery life, the fan should only
operate when necessary. Accurate control of the fan requires a knowledge of critical
temperatures from the appropriate temperature sensor.
Accurate temperature measurements are required in many other measurement systems
such as process control and instrumentation applications. In most cases, because of lowlevel nonlinear outputs, the sensor output must be properly conditioned and amplified
before further processing can occur.
Except for IC sensors, all temperature sensors have nonlinear transfer functions. In the
past, complex analog conditioning circuits were designed to correct for the sensor
nonlinearity. These circuits often required manual calibration and precision resistors to
achieve the desired accuracy. Today, however, sensor outputs may be digitized directly
by high resolution ADCs. Linearization and calibration is then performed digitally,
thereby reducing cost and complexity.
Resistance Temperature Devices (RTDs) are accurate, but require excitation current and
are generally used in bridge circuits. Thermistors have the most sensitivity but are the
most non-linear. However, they are popular in portable applications such as measurement
of battery temperature and other critical temperatures in a system.
Modern semiconductor temperature sensors offer high accuracy and high linearity over
an operating range of about –55ºC to +150ºC. Internal amplifiers can scale the output to
convenient values, such as 10 mV/ºC. They are also useful in cold-junctioncompensation circuits for wide temperature range thermocouples. Semiconductor
temperature sensors can be integrated into multi-function ICs which perform a number of
other hardware monitoring functions.
Figure 3.24 lists the most popular types of temperature transducers and their
characteristics.
3.29
BASIC LINEAR DESIGN
THERMOCOUPLE
RTD
THERMISTOR
SEMICONDUCTOR
Widest Range:
Range:
Range:
Range:
–184ºC to +2300ºC
–200ºC to +850ºC
0ºC to +100ºC
–55ºC to +150ºC
High Accuracy and
Fair Linearity
Poor Linearity
Linearity: 1ºC
Repeatability
Accuracy: 1ºC
Needs Cold Junction
Requires
Requires
Compensation
Excitation
Excitation
Low-Voltage Output
Low Cost
High Sensitivity
Requires Excitation
10mV/K, 20mV/K,
or 1µA/K Typical
Output
Figure 3.24: Types of Temperature Sensors
3.30
SENSORS
TEMPERATURE SENSORS
Semiconductor Temperature Sensors
Modern semiconductor temperature sensors offer high accuracy and high linearity over
an operating range of about –55°C to +150°C. Internal amplifiers can scale the output to
convenient values, such as 10 mV/°C. They are also useful in cold-junctioncompensation circuits for wide temperature range thermocouples.
All semiconductor temperature sensors make use of the relationship between a bipolar
junction transistor's (BJT) base-emitter voltage to its collector current:
VBE =
kT ⎛ I c ⎞
ln ⎜ ⎟
q
⎝ Is ⎠
Eq. 3-24
where k is Boltzmann's constant, T is the absolute temperature, q is the charge of an
electron, and Is is a current related to the geometry and the temperature of the transistors.
(The equation assumes a voltage of at least a few hundred mV on the collector, and
ignores Early effects.)
If we take N transistors identical to the first (see Figure 3.25) and allow the total current
Ic to be shared equally among them, we find that the new base-emitter voltage is given by
the equation
VN =
kT ⎛ I c ⎞
ln ⎜
⎟
q
⎝ N ⋅ Is ⎠
Eq. 3-25
IC
IC
ONE TRANSISTOR
VBE
VBE =
N TRANSISTORS
VN
kT ⎛ IC ⎞
ln⎜ ⎟
q ⎝ IS ⎠
VN =
ΔVBE = VBE − VN =
kT ⎛ IC ⎞
ln⎜
⎟
q ⎝ N ⋅ IS ⎠
kT
ln(N)
q
INDEPENDENT OF IC, IS
Figure 3.25: Basic Relationships for Semiconductor Temperature Sensors
3.31
BASIC LINEAR DESIGN
Neither of these circuits is of much use by itself because of the strongly temperature
dependent current Is, but if we have equal currents in one BJT and N similar BJTs then
the expression for the difference between the two base-emitter voltages is proportional to
absolute temperature and does not contain Is.
ΔVBE = VBE − VN =
ΔVBE = VBE − VN =
kT ⎛ I c ⎞ kT ⎛ I c ⎞
ln ⎜ ⎟ −
ln ⎜
⎟
q
q
⎝ Is ⎠
⎝ N ⋅ Is ⎠
kT
q
⎡ ⎛ Ic ⎞
⎛ Ic ⎞⎤
⎟⎥
⎢ ln ⎜ ⎟ − ln ⎜
⎝ N ⋅ I s ⎠ ⎥⎦
⎢⎣ ⎝ I s ⎠
⎡⎛ I c ⎞
⎤
⎢⎜ ⎟
⎥
kT ⎢⎝ I s ⎠
⎥ = kT ln ( N )
ΔVBE = VBE − VN =
ln
⎛ Ic ⎞⎥
⎢
q
q
⎜
⎟⎥
⎢
⎝ N ⋅ Is ⎠ ⎦
⎣
Eq.3-26
Eq.3-27
Eq. 3-28
+VIN
R
+
I2 ≅ I 1
Q2
NA
ΔVBE = VBE − VN =
kT
ln(N )
q
"BROKAW CELL"
R
VBANDGAP = 1.205V
Q1
A
VN
VBE
(Q1)
R2
VPTAT = 2
R1 kT
ln(N)
R2 q
R1
Figure 3.26: Classic Bandgap Temperature Sensor
The circuit shown in Figure 3.26 implements the above equation and is known as the
"Brokaw Cell" (see Reference 10). The voltage ΔVBE = VBE – VN appears across
resistor R2. The emitter current in Q2 is therefore ΔVBE/R2. The op amp's servo loop
and the resistors, R, force the same current to flow through Q1. The Q1 and Q2 currents
3.32
SENSORS
TEMPERATURE SENSORS
are equal and are summed and flow into resistor R1. The corresponding voltage
developed across R1 is proportional to absolute temperature (PTAT) and given by:
. VP TAT =
2R1( VBE − VN )
R2
=2
R1 kT
ln ( N )
R2 q
Eq. 3-29
The bandgap cell reference voltage, VBANDGAP, appears at the base of Q1 and is the
sum of VBE(Q1) and VPTAT. VBE(Q1) is complementary to absolute temperature
(CTAT), and summing it with VPTAT causes the bandgap voltage to be constant with
respect to temperature (assuming proper choice of R1/R2 ratio and N to make the
bandgap voltage equal to 1.205 V). This circuit is the basic band-gap temperature sensor,
and is widely used in semiconductor temperature sensors.
Current Out Temperature Sensors
This type of temperature sensor produces a current output proportional to absolute
temperature. For supply voltages between 4 V and 30 V the device acts as a high
impedance constant current regulator with an output proportional to absolute temperature
with a typical transfer function of 1 µA/°K. This means that at 25°C there will be 298 µA
flowing in the loop.
A current output temperature sensor such as the AD590 is particularly useful in remote
sensing applications. These devices are insensitive to voltage drops over long lines due to
their high impedance current outputs. The output characteristics also make this type of
device easy to multiplex: the current can be switched by a simple logic gate as shown in
the figure.
Zone 1
Zone 2
Zone 3
Zone 4
Current Output
Temperature
Sensor (AD590)
AD590
CMOS
Gates
AD590
AD590
AD590
1mV/°K
1K
Figure 3.27: Multiplexed AD590 Application
3.33
BASIC LINEAR DESIGN
Current and Voltage Output Temperature Sensors
The concepts used in the bandgap temperature sensor discussion above can be used as the
basis for a variety of IC temperature sensors to generate either current or voltage outputs.
VS = +5V
0.1µF
REFERENCE
I(VS )
ADC
+
VOUT
INPUT
–
R(T)
GND
AD22100
VOUT =
VS
22.5 mV
∗ 1.375V +
∗ TA
°C
5V
Figure 3.28: Ratiometric Voltage Output Sensor
In some cases, it is desirable for the output of a temperature sensor to be ratiometric with
its supply voltage. The AD22100 (see Figure 3.29) has an output that is ratiometric with
its supply voltage (nominally 5 V) according to the equation:
V OUT =
VS
22.5 mV
* TA
∗ 1.375 V +
°C
5V
Eq.3-30
The circuit shown in Figure 3.28 uses the AD22100 power supply as the reference to the
ADC, thereby eliminating the need for a precision voltage reference.
The thermal time constant of a temperature sensor is defined to be the time required for
the sensor to reach 63.2% of the final value for a step change in the temperature.
Figure 3.29 shows the thermal time constant of the ADT45/ADT50 series of sensors with
the SOT-23-3 package soldered to 0.338" x 0.307" copper PC board as a function of air
flow velocity. Note the rapid drop from 32 seconds to 12 seconds as the air velocity
increases from 0 (still air) to 100 LFPM. As a point of reference, the thermal time
constant of the ADT45/ADT50 series in a stirred oil bath is less than 1 second, which
verifies that the major part of the thermal time constant is determined by the case.
3.34
SENSORS
TEMPERATURE SENSORS
The power supply pin of these sensors should be bypassed to ground with a 0.1 µF
ceramic capacitor having very short leads (preferably surface mount) and located as close
to the power supply pin as possible. Since these temperature sensors operate on very little
supply current and could be exposed to very hostile electrical environments, it is
important to minimize the effects of EMI/RFI on these devices. The effect of RFI on
these temperature sensors is manifested as abnormal DC shifts in the output voltage due
to rectification of the high frequency noise by the internal IC junctions. In those cases
where the devices are operated in the presence of high frequency radiated or conducted
noise, a large value tantalum electrolytic capacitor (>2.2 µF) placed across the 0.1 µF
ceramic may offer additional noise immunity.
35
SOT-23-3 SOLDERED TO 0.338" x 0.307" Cu PCB
V+ = 2.7V TO 5V
NO LOAD
30
25
TIME
CONSTANTSECONDS
20
15
10
5
0
0
100
200
300
400
500
600
700
AIR VELOCITY - LFPM
Figure 3.29: Thermal Response in Forced Air for SOT-23-2 Package
3.35
BASIC LINEAR DESIGN
Thermocouple Principles and Cold-Junction Compensation
Thermocouples are small, rugged, relatively inexpensive, and operate over the widest
range of all temperature sensors. They are especially useful for making measurements at
extremely high temperatures (up to +2300°C) in hostile environments. They produce only
millivolts of output, however, and require precision amplification for further processing.
They also require cold-junction-compensation (CJC) techniques which will be discussed
shortly. They are more linear than many other sensors, and their non-linearity has been
well characterized. Some common thermocouples are shown in Figure 3.30. The most
common metals used are Iron, Platinum, Rhodium, Rhenium, Tungsten, Copper, Alumel
(composed of Nickel and Aluminum), Chromel (composed of Nickel and Chromium) and
Constantan (composed of Copper and Nickel).
TYPICAL
NOMINAL
ANSI
USEFUL
SENSITIVITY
DESIGNATION
RANGE (ºC)
(µV/ºC)
38 to 1800
7.7
B
0 to 2300
16
C
Chromel - Constantan
0 to 982
76
E
Iron - Constantan
0 to 760
55
J
Chromel - Alumel
–184 to 1260
39
K
Platinum (13%)/Rhodium-
0 to 1593
11.7
R
0 to 1538
10.4
S
–184 to 400
45
T
JUNCTION MATERIALS
Platinum (6%)/ RhodiumPlatinum (30%)/Rhodium
Tungsten (5%)/Rhenium Tungsten (26%)/Rhenium
Platinum
Platinum (10%)/RhodiumPlatinum
Copper-Constantan
Figure 3.30: Common Thermocouples
Figure 3.31 shows the voltage-temperature curves of three commonly used
thermocouples, referred to a 0°C fixed-temperature reference junction. Of the
thermocouples shown, Type J thermocouples are the most sensitive, producing the largest
output voltage for a given temperature change. On the other hand, Type S thermocouples
are the least sensitive. These characteristics are very important to consider when
designing signal conditioning circuitry in that the thermocouples' relatively low output
signals require low-noise, low-drift, high-gain amplifiers.
To understand thermocouple behavior, it is necessary to consider the non-linearities in
their response to temperature differences. Figure 3.31 shows the relationships between
sensing junction temperature and voltage output for a number of thermocouple types (in
3.36
SENSORS
TEMPERATURE SENSORS
all cases, the reference cold junction is maintained at 0°C). It is evident that the responses
are not quite linear, but the nature of the non-linearity is not so obvious.
Figure 3.32 shows how the Seebeck coefficient (the change of output voltage with
change of sensor junction temperature - i.e., the first derivative of output with respect to
temperature) varies with sensor junction temperature (we are still considering the case
where the reference junction is maintained at 0°C).
When selecting a thermocouple for making measurements over a particular range of
temperature, we should choose a thermocouple whose Seebeck coefficient varies as little
as possible over that range.
THERMOCOUPLE OUTPUT VOLTAGE (mV)
60
50
TYPE K
40
TYPE J
30
20
TYPE S
10
0
-10
-250
0
250
500
750
1000
1250
1500
1750
TEMPERATURE (°C)
Figure 3.31: Thermocouple Output Voltages for Type J, K and S
Thermocouples
For example, a Type J thermocouple has a Seebeck coefficient which varies by less than
1 µV/°C between 200 and 500°C, which makes it ideal for measurements in this range.
Presenting these data on thermocouples serves two purposes: First, Figure 3.30 illustrates
the range and sensitivity of the three thermocouple types so that the system designer can,
at a glance, determine that a Type S thermocouple has the widest useful temperature
range, but a Type J thermocouple is more sensitive. Second, the Seebeck coefficients
provide a quick guide to a thermocouple's linearity. Using Figure 3.31, the system
designer can choose a Type K thermocouple for its linear Seebeck coefficient over the
range of 400°C to 800°C or a Type S over the range of 900°C to 1700°C. The behavior
of a thermocouple's Seebeck coefficient is important in applications where variations of
3.37
BASIC LINEAR DESIGN
temperature rather than absolute magnitude are important. These data also indicate what
performance is required of the associated signal conditioning circuitry.
70
TYPE J
SEEBECK COEFFICIENT - µV/ °C
60
50
TYPE K
40
30
20
TYPE S
10
0
-250
0
250
500
1000
750
1250
1500
1750
TEMPERATURE (°C)
Figure 3.32: Thermocouple Seebeck Coefficient vs. Temperature
To use thermocouples successfully we must understand their basic principles. Consider
the diagrams in Figure 3.33.
A. THERMOELECTRIC VOLTAGE
C. THERMOCOUPLE MEASUREMENT
Metal A
Metal A
V1 – V2
Metal A
V1
Thermoelectric
EMF
Metal B
T1
V1
T1
T2
Metal B
D. THERMOCOUPLE MEASUREMENT
B. THERMOCOUPLE
Copper
Metal A
R
Metal A
V
Metal A
T3
T1
T2
Metal B
R = Total Circuit Resistance
I = (V1 – V2) / R
V2 V1
T4
T1
T2
Metal B
V = V1 – V2, If T3 = T4
Figure 3.33: Thermocouple Basics
3.38
Copper
Metal A
I
V1
V2
V2
SENSORS
TEMPERATURE SENSORS
If we join two dissimilar metals at any temperature above absolute zero, there will be a
potential difference between them (their "thermoelectric e.m.f." or "contact potential")
which is a function of the temperature of the junction (Figure 3.33A). If we join the two
wires at two places, two junctions are formed (Figure 3.33B). If the two junctions are at
different temperatures, there will be a net e.m.f. in the circuit, and a current will flow
determined by the e.m.f. and the total resistance in the circuit (Figure 3.33B). If we break
one of the wires, the voltage across the break will be equal to the net thermoelectric e.m.f.
of the circuit, and if we measure this voltage, we can use it to calculate the temperature
difference between the two junctions (Figure 3.33C). We must always remember that a
thermocouple measures the temperature difference between two junctions, not the
absolute temperature at one junction. We can only measure the temperature at the
measuring junction if we know the temperature of the other junction (often called the
"reference" junction or the "cold" junction).
But it is not so easy to measure the voltage generated by a thermocouple. Suppose that
we attach a voltmeter to the circuit in Figure 3.33C (Figure 3.33D). The wires attached to
the voltmeter will form further thermojunctions where they are attached. If both these
additional junctions are at the same temperature (it does not matter what temperature),
then the "Law of Intermediate Metals" states that they will make no net contribution to
the total e.m.f. of the system. If they are at different temperatures, they will introduce
errors. Since every pair of dissimilar metals in contact generates a thermoelectric e.m.f.
(including copper/solder, kovar/copper [kovar is the alloy used for IC leadframes] and
aluminum/kovar [at the bond inside the IC]), it is obvious that in practical circuits the
problem is even more complex, and it is necessary to take extreme care to ensure that all
the junction pairs in the circuitry around a thermocouple, except the measurement and
reference junctions themselves, are at the same temperature.
Thermocouples generate a voltage, albeit a very small one, and do not require excitation.
As shown in Figure 3.33D, however, two junctions (T1, the measurement junction and
T2, the reference junction) are involved. If T2 = T1, then V2 = V1, and the output voltage
V = 0. Thermocouple output voltages are often defined with a reference junction
temperature of 0ºC (hence the term cold or ice point junction), so the thermocouple
provides an output voltage of 0 V at 0ºC. To maintain system accuracy, the reference
junction must therefore be at a well-defined temperature (but not necessarily 0ºC). A
conceptually simple approach to this need is shown in Figure 3.34. Although an ice/water
bath is relatively easy to define, it is quite inconvenient to maintain.
Today an ice-point reference, and its inconvenient ice/water bath, is generally replaced by
electronics. A temperature sensor of another sort (often a semiconductor sensor,
sometimes a thermistor) measures the temperature of the cold junction and is used to
inject a voltage into the thermocouple circuit which compensates for the difference
between the actual cold junction temperature and its ideal value (usually 0°C) as shown
in Figure 3.35. Ideally, the compensation voltage should be an exact match for the
difference voltage required, which is why the diagram gives the voltage as f(T2) (a
function of T2) rather than KT2, where K is a simple constant. In practice, since the cold
3.39
BASIC LINEAR DESIGN
METAL A
METAL A
V1 – V(0°C)
T1
V1
METAL B
V(0°C)
ICE
BATH
T2
0°C
Figure 3.34: Classic Cold-Junction Compensation
Using an Ice-Point (0°C) Reference Junction
V(OUT)
V(COMP)
COPPER
METAL A
T1
SAME
TEMP
V(T1)
COPPER
TEMPERATURE
COMPENSATION
CIRCUIT
METAL A
V(T2)
T2
TEMP
SENSOR
METAL B
V(COMP) = f(T2)
V(OUT)
ISOTHERMAL BLOCK
= V(T1) – V(T2) + V(COMP)
IF V(COMP) = V(T2) – V(0°C), THEN
V(OUT)
= V(T1) – V(0°C)
Figure 3.35: Using a Temperature Sensor for Cold-Junction Compensations
junction is rarely more than a few tens of degrees from 0°C, and generally varies by little
more than ±10°C, a linear approximation (V = KT2) to the more complex reality is
sufficiently accurate and is what is often used. (The expression for the output voltage of a
thermocouple with its measuring junction at T°C and its reference at 0°C is a polynomial
of the form V = K1T + K2T2 + K3T3 + ..., but the values of the coefficients K2, K3, etc.
3.40
SENSORS
TEMPERATURE SENSORS
are very small for most common types of thermocouple. References 8 and 9 give the
values of these coefficients for a wide range of thermocouples.)
When electronic cold-junction compensation is used, it is common practice to eliminate
the additional thermocouple wire and terminate the thermocouple leads in the isothermal
block in the arrangement shown in Figure 3.36. The Metal A-Copper and the Metal BCopper junctions, if at the same temperature, are equivalent to the Metal A-Metal B
thermocouple junction in Figure 3.35.
COPPER
V(OUT) = V1 – V(0°C)
T2
METAL A
COPPER
T1
V1
METAL B
TEMPERATURE
COMPENSATION
CIRCUIT
TEMP
SENSOR
COPPER
T2
ISOTHERMAL BLOCK
Figure 3.36: Terminating Thermocouple Leads Directly to an Isothermal Block
The circuit in Figure 3.37 conditions the output of a Type K thermocouple, while
providing cold-junction compensation, for temperatures between 0ºC and 250ºC. The
circuit operates from single +3.3 V to +12 V supplies and has been designed to produce
an output voltage transfer characteristic of 10 mV/ºC.
A Type K thermocouple exhibits a Seebeck coefficient of approximately 41 µV/ºC;
therefore, at the cold junction, the TMP35 voltage output sensor with a temperature
coefficient of 10 mV/ºC is used with R1 and R2 to introduce an opposing cold-junction
temperature coefficient of –41 µV/ºC. This prevents the isothermal, cold-junction
connection between the circuit's printed circuit board traces and the thermocouple's wires
from introducing an error in the measured temperature. This compensation works
extremely well for circuit ambient temperatures in the range of 20ºC to 50ºC. Over a
250ºC measurement temperature range, the thermocouple produces an output voltage
change of 10.151 mV. Since the required circuit's output full-scale voltage change is
2.5 V, the gain of the circuit is set to 246.3. Choosing R4 equal to 4.99 kΩ sets R5 equal
to 1.22 MΩ. Since the closest 1% value for R5 is 1.21 MΩ, a 50 kΩ potentiometer is
used with R5 for fine trim of the full-scale output voltage. Although the OP193 is a
single-supply op amp, its output stage is not rail-to-rail, and will only go down to about
0.1 V above ground. For this reason, R3 is added to the circuit to supply an output offset
voltage of about 0.1V for a nominal supply voltage of 5 V. This offset (10°C) must be
3.41
BASIC LINEAR DESIGN
subtracted when making measurements referenced to the OP193 output. R3 also provides
an open thermocouple detection, forcing the output voltage to greater than 3 V should the
thermocouple open. Resistor R7 balances the DC input impedance of the OP193, and the
0.1 µF film capacitor reduces noise coupling into its non-inverting input.
3.3V TO 5.5V
0.1µF
TMP35
TYPE K
THERMO
COUPLE
R5*
1.21MΩ
R4*
4.99kΩ
R1*
24.9kΩ
P1
50kΩ
0 °C < T < 250 °C
–
R3*
1.24MΩ
CHROMEL
–
OP193
Cu
+
COLD
JUNCTION
+
R7*
4.99kΩ
Cu
R2*
102Ω
ALUMEL
VOUT
0.1 - 2.6V
R6
100kΩ
10mV/°C
0.1µF
FILM
* USE 1% RESISTORS
ISOTHERMAL
BLOCK
Figure 3.37: Using a Temperature Sensor
for Cold-Junction Compensation (TMP35)
The AD594/AD595 is a complete instrumentation amplifier and thermocouple cold
junction compensator on a monolithic chip (see Figure 3.38). It combines an ice point
reference with a precalibrated amplifier to provide a high level (10 mV/°C) output
directly from the thermocouple signal. Pin-strapping options allow it to be used as a
linear amplifier-compensator or as a switched output set-point controller using either
fixed or remote set-point control. It can be used to amplify its compensation voltage
directly, thereby becoming a stand-alone Celsius transducer with 10 mV/°C output. In
such applications it is very important that the IC chip is at the same temperature as the
cold junction of the thermocouple, which is usually achieved by keeping the two in close
proximity and isolated from any heat sources.
The AD594/AD595 includes a thermocouple failure alarm that indicates if one or both
thermocouple leads open. The alarm output has a flexible format which includes TTL
drive capability. The device can be powered from a single-ended supply (which may be
as low as +5 V), but by including a negative supply, temperatures below 0°C can be
measured. To minimize self-heating, an unloaded AD594/AD595 will operate with a
supply current of 160 µA, but is also capable of delivering ±5 mA to a load.
The AD594 is precalibrated by laser wafer trimming to match the characteristics of type J
(iron/constantan) thermocouples, and the AD595 is laser trimmed for type K
3.42
SENSORS
TEMPERATURE SENSORS
(chromel/alumel). The temperature transducer voltages and gain control resistors are
available at the package pins so that the circuit can be recalibrated for other thermocouple
types by the addition of resistors. These terminals also allow more precise calibration for
both thermocouple and thermometer applications. The AD594/AD595 is available in two
performance grades. The C and the A versions have calibration accuracies of ±1°C and
±3°C, respectively. Both are designed to be used with cold junctions between 0 to +50°C.
The circuit shown in Figure 7.11 will provide a direct output from a type J thermocouple
(AD594) or a type K thermocouple (AD595) capable of measuring 0 to +300°C.
+5V
0.1µF
BROKEN
THERMOCOUPLE
ALARM
4.7kΩ
OVERLOAD
DETECT
TYPE J: AD594
TYPE K: AD595
THERMOCOUPLE
VOUT
10mV/°C
AD594/AD595
+A
–
–
G
+
+
G
+
ICE
POINT
COMP
–TC
+TC
Figure 3.38: AD594/AD595 Monolithic Thermocouple Amplifier
with Cold-Junction Compensation
The AD596/AD597 are monolithic set-point controllers which have been optimized for
use at elevated temperatures as are found in oven control applications. The device coldjunction compensates and amplifies a type J/K thermocouple to derive an internal signal
proportional to temperature. They can be configured to provide a voltage output
(10mV/°C) directly from type J/K thermocouple signals. The device is packaged in a
10-pin metal can and is trimmed to operate over an ambient range from +25°C to
+100°C. The AD596 will amplify thermocouple signals covering the entire –200°C to
+760°C temperature range recommended for type J thermocouples while the AD597 can
accommodate –200°C to +1250°C type K inputs. They have a calibration accuracy of
±4°C at an ambient temperature of 60°C and an ambient temperature stability
specification of 0.05°C/°C from +25°C to +100°C.
None of the thermocouple amplifiers previously described compensate for thermocouple
non-linearity, they only provide conditioning and voltage gain. High resolution ADCs
3.43
BASIC LINEAR DESIGN
such as the AD77XX family can be used to digitize the thermocouple output directly,
allowing a microcontroller to perform the transfer function linearization as shown in
Figure 3.39. The two multiplexed inputs to the ADC are used to digitize the
thermocouple voltage and the cold-junction temperature sensor outputs directly. The
input PGA gain is programmable from 1 to 128, and the ADC resolution is between 16
and 22 bits (depending upon the particular ADC selected). The mIcrocontroller performs
both the cold-junction compensation and the linearization arithmetic.
3V OR 5V
(DEPENDING ON ADC)
0.1µF
AIN1+
CONTROL
REGISTER
TMP35
AIN1–
THERMO
COUPLE
MUX
AIN2+
AIN2–
PGA
ΣΔ
ADC
OUTPUT
REGISTER
G=1 TO 128
AD77XX SERIES
(16-22 BITS)
SERIAL
INTERFACE
TO MICROCONTROLLER
Figure 3.39: AD77XX ΣΔ ADC Used with TMP35 Temperature Sensor
for Cold-Junction Compensation
3.44
SENSORS
TEMPERATURE SENSORS
Auto-zero Amplifier for Thermocouple Measurements
In addition to the devices mentioned above, ADI has released an auto-zero
instrumentation amplifier, the AD8230, designed to amplify thermocouple and bridge
outputs. Through the use of auto-zeroing, this product has an offset voltage drift of less
than 50 nV/°C which is 1,000 times less than the signal produced by a typical
thermocouple. This allows very accurate measurement of the thermocouple signal. In
addition, the instrumentation amplifier architecture rejects common mode voltages that
often appear when using thermocouples for temperature measurement. This product is
typically used in applications involving a bank of thermocouples with one temperature
reference point which is compensated for in the system micro-controller. Other
applications include highly accurate bridge transducer measurements.
Auto-zeroing is a dynamic offset and drift cancellation technique that reduces input
referred voltage offset to the µV level and voltage offset drift to the nV/°C level. A
further advantage of dynamic offset cancellation is the reduction of low frequency noise,
in particular the 1/f component.
The AD8230 is an instrumentation amplifier that uses an auto-zeroing topology and
combines it with high common-mode signal rejection. The internal signal path consists of
an active differential sample-and-hold stage (pre-amp) followed by a differential
amplifier (gain amp). Both amplifiers implement auto-zeroing to minimize offset and
drift. A fully differential topology increases the immunity of the signals to parasitic noise
and temperature effects. Amplifier gain is set by two external resistors for convenient TC
matching.
GAIN AMP
PREAMP
–VS
CHOLD
V+IN
VDIFF
+VCM
CSAMPLE
V–IN
+
–
–
+
VOUT
CHOLD
–VS
VREF
RG
RF
3
0
1
3
6
0
5
0
Figure 3.40: Phase A of the Sampling Phase
3.45
BASIC LINEAR DESIGN
The signal sampling rate is controlled by an on-chip, 6 kHz oscillator and logic to derive
the required nonoverlapping clock phases. For simplification of the functional
description, two sequential clock phases, A and B, are used to distinguish the order of
internal operation as depicted in the first figure, respectively.
During Phase A, the sampling capacitors are connected to the inputs. The input signal’s
difference voltage, VDIFF, is stored across the sampling capacitors, CSAMPLE. Since the
sampling capacitors only retain the difference voltage, the common-mode voltage is
rejected. During this period, the gain amplifier is not connected to the preamplifier so its
output remains at the level set by the previously sampled input signal held on CHOLD, as
shown in the second figure.
GAIN AMP
PREAMP
–VS
CHOLD
V+IN
VDIFF
+VCM
CSAMPLE
V–IN
+
–
–
+
VOUT
CHOLD
–VS
VREF
RG
RF
4
0
-1
3
6
0
5
0
Figure 3.41: Phase B of the Sampling Phase
In Phase B, the differential signal is transferred to the hold capacitors refreshing the value
stored on CHOLD. The output of the preamplifier is held at a common-mode voltage
determined by the reference potential, VREF. In this manner, the AD8230 is able to
condition the difference signal and set the output voltage level. The gain amplifier
conditions the updated signal stored on the hold capacitors, CHOLD.
The AD8230 may be used to condition thermocouples as shown in the figure. It has
voltage overload protection and an RFI filter in front. Input overload protection is
provided by the BAV199 diodes at each input.
3.46
SENSORS
TEMPERATURE SENSORS
Resistance Temperature Detectors (RTDs)
The Resistance Temperature Detector, or the RTD, is a sensor whose resistance changes
with temperature. Typically built of a platinum (Pt) wire wrapped around a ceramic
bobbin, the RTD exhibits behavior which is more accurate and more linear over wide
temperature ranges than a thermocouple. Figure 3.42 illustrates the temperature
coefficient of a 100Ω RTD and the Seebeck coefficient of a Type S thermocouple. Over
the entire range (approximately –200°C to +850°C), the RTD is a more linear device.
Hence, linearizing an RTD is less complex.
„ Platinum (Pt) the Most Common
„ 100Ω, 1000Ω Standard Values
„ Typical TC = 0.385% / °C,
0.385Ω / °C for 100Ω Pt RTD
„ Good Linearity - Better than Thermocouple,
Easily Compensated
11.5
0.400
RTD
RESISTANCE
TC, ΔΩ / °C
100Ω Pt RTD
10.5
TYPE S
THERMOCOUPLE
0.375
9.50
0.350
TYPE S
THERMOCOUPLE
SEEBECK
COEFFICIENT,
µV / °C
8.50
0.325
7.50
0.300
0.275
6.50
0
400
800
5.50
TEMPERATURE - °C
Figure 3.42: Resistance Temperature Detectors (RTD)
Unlike a thermocouple, however, an RTD is a passive sensor and requires current
excitation to produce an output voltage. The RTD's low temperature coefficient of
0.385%/°C requires similar high-performance signal conditioning circuitry to that used
by a thermocouple; however, the voltage drop across an RTD is much larger than a
thermocouple output voltage. A system designer may opt for large value RTDs with
higher output, but large-valued RTDs exhibit slow response times. Furthermore, although
the cost of RTDs is higher than that of thermocouples, they use copper leads, and
thermoelectric effects from terminating junctions do not affect their accuracy. And
finally, because their resistance is a function of the absolute temperature, RTDs require
no cold-junction compensation.
3.47
BASIC LINEAR DESIGN
Caution must be exercised using current excitation because the current through the RTD
causes heating. This self-heating changes the temperature of the RTD and appears as a
measurement error. Hence, careful attention must be paid to the design of the signal
conditioning circuitry so that self-heating is kept below 0.5°C. Manufacturers specify
self-heating errors for various RTD values and sizes in still and in moving air. To reduce
the error due to self-heating, the minimum current should be used for the required system
resolution, and the largest RTD value chosen that results in acceptable response time.
Another effect that can produce measurement error is voltage drop in RTD lead wires.
This is especially critical with low-value 2-wire RTDs because the temperature
coefficient and the absolute value of the RTD resistance are both small. If the RTD is
located a long distance from the signal conditioning circuitry, then the lead resistance can
be ohms or tens of ohms, and a small amount of lead resistance can contribute a
significant error to the temperature measurement. To illustrate this point, let us assume
that a 100Ω platinum RTD with 30-gauge copper leads is located about 100 feet from a
controller's display console. The resistance of 30-gauge copper wire is 0.105 Ω/ft, and the
two leads of the RTD will contribute a total 21 Ω to the network which is shown in
Figure 3.43. This additional resistance will produce a 55°C error in the measurement!
The leads' temperature coefficient can contribute an additional, and possibly significant,
error to the measurement. To eliminate the effect of the lead resistance, a 4-wire
technique is used.
R = 10.5Ω
COPPER
100Ω
Pt RTD
R = 10.5Ω
COPPER
RESISTANCE TC OF COPPER = 0.40%/°C @ 20°C
RESISTANCE TC OF Pt RTD
= 0.385%/ °C @ 20°C
Figure 3.43: A 100 Ω Pt RTD with 100 Feet of 30- Gauge Lead Wires
In Figure 3.44, a 4-wire, or Kelvin, connection is made to the RTD. A constant current is
applied though the FORCE leads of the RTD, and the voltage across the RTD itself is
measured remotely via the SENSE leads. The measuring device can be a DVM or an
instrumentation amplifier, and high accuracy can be achieved provided that the
measuring device exhibits high input impedance and/or low input bias current. Since the
SENSE leads do not carry appreciable current, this technique is insensitive to lead wire
3.48
SENSORS
TEMPERATURE SENSORS
length. Sources of errors are the stability of the constant current source and the input
impedance and/or bias currents in the amplifier or DVM.
RTDs are generally configured in a four-resistor bridge circuit. The bridge output is
amplified by an instrumentation amplifier for further processing. However, high
resolution measurement ADCs such as the AD77XX series allow the RTD output to be
digitized directly. In this manner, linearization can be performed digitally, thereby easing
the analog circuit requirements.
FORCE
LEAD
RLEAD
100Ω
Pt RTD
I
FORCE
LEAD
SENSE
LEAD
RLEAD
TO HIGH - Z
IN-AMP OR ADC
SENSE
LEAD
Figure 3.44: Four-Wire or Kelvin Connection to Pt RTD
For Accurate Measurements
Figure 3.45 shows a 100 Ω Pt RTD driven with a 400 µA excitation current source. The
output is digitized by one of the AD77XX series ADCs. Note that the RTD excitation
current source also generates the 2.5 V reference voltage for the ADC via the 6.25 kΩ
resistor. Variations in the excitation current do not affect the circuit accuracy, since both
the input voltage and the reference voltage vary ratiometrically with the excitation
current. However, the 6.25 kΩ resistor must have a low temperature coefficient to avoid
errors in the measurement. The high resolution of the ADC and the input PGA (gain of 1
to 128) eliminates the need for additional conditioning circuits.
The ADT70 is a complete Pt RTD signal conditioner which provides an output voltage of
5 mV/°C when using a 1 kΩ RTD (see Figure 3.46). The Pt RTD and the 1 kΩ reference
resistor are both excited with 1mA matched current sources. This allows temperature
measurements to be made over a range of approximately –50°C to +800°C.
3.49
BASIC LINEAR DESIGN
3V OR 5V
(DEPENDING ON ADC)
+VREF
RREF
6.25kΩ
–VREF
+
400µA
100Ω
Pt RTD
CONTROL
REGISTER
AIN1+
MUX
PGA
–
ΣΔ
ADC
OUTPUT
REGISTER
AIN1–
G=1 TO 128
AD77XX SERIES
(16-22 BITS)
SERIAL
INTERFACE
TO MICROCONTROLLER
Figure 3.45: Interfacing a Pt RTD to a High Resolution ΣΔ ADC
+5V
0.1µF
1kΩ Pt
RTD
ADT70
+
2.5V
REFERENCE
1kΩ REF
RES
–
MATCHED
1mA SOURCES
SHUT
DOWN
+
INST
AMP
–
GND
REF
OUT = 5mV/ °C
RG = 50kΩ
-1V TO -5V
Note: Some Pins Omitted
for Clarity
Figure 3.46: Conditioning the Pt RTD Using the ADT70
3.50
SENSORS
TEMPERATURE SENSORS
The ADT70 contains the two matched current sources, a precision rail-to-rail output
instrumentation amplifier, a 2.5 V reference, and an uncommitted rail-to-rail output op
amp. The ADT71 is the same as the ADT70 except the internal voltage reference is
omitted. A shutdown function is included for battery powered equipment that reduces the
quiescent current from 3 mA to 10 µA. The gain or full-scale range for the Pt RTD and
ADT701 system is set by a precision external resistor connected to the instrumentation
amplifier. The uncommitted op amp may be used for scaling the internal voltage
reference, providing a "Pt RTD open" signal or "over temperature" warning, providing a
heater switching signal, or other external conditioning determined by the user. The
ADT70 is specified for operation from –40°C to +125°C and is available in 20-pin DIP
and SOIC packages.
3.51
BASIC LINEAR DESIGN
Thermistors
Similar in function to the RTD, thermistors are low-cost temperature-sensitive resistors
and are constructed of solid semiconductor materials which exhibit a positive or negative
temperature coefficient. Although positive temperature coefficient devices are available,
the most commonly used thermistors are those with a negative temperature coefficient.
Figure 3.47 shows the resistance-temperature characteristic of a commonly used NTC
(Negative Temperature Coefficient) thermistor. The thermistor is highly non-linear and,
of the three temperature sensors discussed, is the most sensitive.
40
ALPHA THERMISTOR, INCORPORATED
RESISTANCE/TEMPERATURE CURVE 'A'
10 kΩ THERMISTOR, #13A1002-C3
30
THERMISTOR
RESISTANCE
kΩ
20
10
Nominal Value @ 25 °C
0
0
20
40
60
80
100
TEMPERATURE - °C
Figure 3.45: Resistance Characteristics of a 10 kΩ NTC Thermistors
The thermistor's high sensitivity (typically, –44,000 ppm/°C at 25°C, as shown in
Figure 3.46), allows it to detect minute variations in temperature which could not be
observed with an RTD or thermocouple. This high sensitivity is a distinct advantage over
the RTD in that 4-wire Kelvin connections to the thermistor are not needed to
compensate for lead wire errors. To illustrate this point, suppose a 10 kΩ NTC
thermistor, with a typical 25°C temperature coefficient of –44,000 ppm/°C, were
substituted for the 100 Ω Pt RTD in the example given earlier, then a total lead wire
resistance of 21 Ω would generate less than 0.05°C error in the measurement. This is
roughly a factor of 500 improvement in error over an RTD.
3.52
SENSORS
TEMPERATURE SENSORS
-60000
ALPHA THERMISTOR, INCORPORATED
RESISTANCE/TEMPERATURE CURVE 'A'
10 kΩ THERMISTOR, #13A1002-C3
-50000
THERMISTOR
TEMPERATURE
COEFFICIENT
ppm/ °C
-40000
-30000
-20000
0
20
40
60
80
100
TEMPERATURE - °C
Figure 3.46: Temperature Coefficient of a 10 kΩ NTC Thermistor
However, the thermistor's high sensitivity to temperature does not come without a price.
As was shown in Figure 3.46, the temperature coefficient of thermistors does not
decrease linearly with increasing temperature as it does with RTDs; therefore,
linearization is required for all but the narrowest of temperature ranges. Thermistor
applications are limited to a few hundred degrees at best because they are more
susceptible to damage at high temperatures. Compared to thermocouples and RTDs,
thermistors are fragile in construction and require careful mounting procedures to prevent
crushing or bond separation. Although a thermistor's response time is short due to its
small size, its small thermal mass makes it very sensitive to self-heating errors.
Thermistors are very inexpensive, highly sensitive temperature sensors. However, we
have shown that a thermistor's temperature coefficient varies from –44,000 ppm/°C at
25°C to –29,000 ppm/°C at 100°C. Not only is this non-linearity the largest source of
error in a temperature measurement, it also limits useful applications to very narrow
temperature ranges if linearization techniques are not used.
It is possible to use a thermistor over a wide temperature range only if the system
designer can tolerate a lower sensitivity to achieve improved linearity. One approach to
linearizing a thermistor is simply shunting it with a fixed resistor. Paralleling the
thermistor with a fixed resistor increases the linearity significantly. As shown in
Figure 3.47, the parallel combination exhibits a more linear variation with temperature
compared to the thermistor itself. Also, the sensitivity of the combination still is high
compared to a thermocouple or RTD. The primary disadvantage to this technique is that
linearization can only be achieved within a narrow range.
3.53
BASIC LINEAR DESIGN
40
30
RESISTANCE
kΩ
20
THERMISTOR
PARALLEL COMBINATION
10
0
0
20
40
60
80
100
TEMPERATURE - °C
Figure 3.47: Linearization of NTC Thermistor Using a 5.17 kΩ Shunt Resistor
The value of the fixed resistor can be calculated from the following equation:
R=
RT 2 ⋅ ( RT1 + RT 3 ) − 2 ⋅ RT1 ⋅ RT 3
,
RT1 + RT 3 − 2 ⋅ RT 2
Eq. 3-31
where RT1 is the thermistor resistance at T1, the lowest temperature in the measurement
range, RT3 is the thermistor resistance at T3, the highest temperature in the range, and
RT2 is the thermistor resistance at T2, the midpoint, T2 = (T1 + T3)/2.
For a typical 10 kΩ NTC thermistor, RT1 = 32,650 Ω at 0°C, RT2 = 6,532 Ω at 35°C,
and RT3 = 1,752 Ω at 70°C. This results in a value of 5.17 kΩ for R. The accuracy
needed in the signal conditioning circuitry depends on the linearity of the network. For
the example given above, the network shows a non-linearity of – 2.3°C / + 2.0 °C.
The output of the network can be applied to an ADC to perform further linearization as
shown in Figure 7.21. Note that the output of the thermistor network has a slope of
approximately –10 mV/°C, which implies a 12-bit ADC has more than sufficient
resolution.
3.54
SENSORS
TEMPERATURE SENSORS
226µA
VOUT ≈ 0.994V @ T = 0°C
VOUT ≈ 0.294V @ T =70°C
ΔVOUT/ΔT ≈ −10mV/°C
10kΩ NTC
THERMISTOR
AMPLIFIER
OR ADC
5.17kΩ
LINEARIZATION
RESISTOR
LINEARITY ≈ ± 2°C, 0°C TO +70°C
Figure 3.48: Linearized Thermistor Amplifier
3.55
BASIC LINEAR DESIGN
Digital Output Temperature Sensors
Temperature sensors which have digital outputs have a number of advantages over those
with analog outputs, especially in remote applications. Opto-isolators can also be used to
provide galvanic isolation between the remote sensor and the measurement system. A
voltage-to-frequency converter driven by a voltage output temperature sensor
accomplishes this function, however, more sophisticated ICs are now available which are
more efficient and offer several performance advantages.
The TMP03/TMP04 digital output sensor family includes a voltage reference, VPTAT
generator, sigma-delta ADC, and a clock source (see Figure 3.49). The sensor output is
digitized by a first-order sigma-delta modulator, also known as the "charge balance" type
analog-to-digital converter. This converter utilizes time-domain oversampling and a high
accuracy comparator to deliver 12 bits of effective accuracy in an extremely compact
circuit.
The output of the sigma-delta modulator is encoded using a proprietary technique which
results in a serial digital output signal with a mark-space ratio format (see Figure 3.50)
that is easily decoded by any microprocessor into either degrees centigrade or degrees
Fahrenheit, and readily transmitted over a single wire. Most importantly, this encoding
method avoids major error sources common to other modulation techniques, as it is
clock-independent. The nominal output frequency is 35 Hz at +25ºC, and the device
operates with a fixed high-level pulse width (T1) of 10ms.
+VS = 4.5 TO 7V
REFERENCE
VOLTAGE
TEMP
SENSOR
VPTAT
CLOCK
(1MHz)
SIGMA-DELTA
ADC
OUTPUT
(TMP04)
OUTPUT
(TMP03)
TMP03/TMP04
GND
Figure 3.49: Digital Out Temperature Sensor: TMP03/04
3.56
SENSORS
TEMPERATURE SENSORS
T1
T2
⎛ 400 × T1⎞
TEMPERATURE (° C) = 235 − ⎜
⎟
⎝
T2 ⎠
⎛ 720 × T1⎞
TEMPERATURE (° F) = 455 − ⎜
⎟
⎝
T2 ⎠
„
„
„
„
„
„
„
T1 Nominal Pulse Width = 10ms
±1.5°C Error Over Temp, ±0.5°C Non-Linearity (Typical)
Specified –40°C to +100°C
Nominal T1/T2 @ 0°C = 60%
Nominal Frequency @ +25°C = 35Hz
6.5mW Power Consumption @ 5V
TO-92, SO-8, or TSSOP Packages
Figure 3.50: TMP03/TMP04 Output Format
The TMP03/TMP04 output is a stream of digital pulses, and the temperature information
is contained in the mark-space ratio per the equations:
⎛ 400 × T1 ⎞
Tem per a t u r e ( ° C ) = 235 − ⎜
⎟
⎝ T2 ⎠
Eq. 3-32
⎛ 720 × T1 ⎞
Tem per a t u r e ( ° F ) = 455 − ⎜
⎟.
⎝ T2 ⎠
Eq. 3-33
Popular microcontrollers, such as the 80C51 and 68HC11, have on-chip timers which can
easily decode the mark-space ratio of the TMP03/TMP04. A typical interface to the
80C51 is shown in Figure 3.51. Two timers, labeled Timer 0 and Timer 1 are 16 bits in
length. The 80C51's system clock, divided by twelve, provides the source for the timers.
The system clock is normally derived from a crystal oscillator, so timing measurements
are quite accurate. Since the sensor's output is ratiometric, the actual clock frequency is
not important. This feature is important because the microcontroller's clock frequency is
often defined by some external timing constraint, such as the serial baud rate.
Software for the sensor interface is straightforward. The microcontroller simply monitors
I/O port P1.0, and starts Timer 0 on the rising edge of the sensor output. The
microcontroller continues to monitor P1.0, stopping Timer 0 and starting Timer 1 when
the sensor output goes low. When the output returns high, the sensor's T1 and T2 times
are contained in registers Timer 0 and Timer 1, respectively. Further software routines
can then apply the conversion factor shown in the equations above and calculate the
temperature.
3.57
BASIC LINEAR DESIGN
+5V
XTAL
0.1µF
V+
OSCILLATOR
÷12
TIMER 0
TMP04
OUT
CPU
P1.0
GND
TIMER
CONTROL
TIMER 1
80C51 MICROCONTROLLER
NOTE:
ADDITIONAL
PINS OMITTED
FOR CLARITY
Figure 3.51: Interfacing a TMP04 to a Microcontroller
Thermostatic Switches and Setpoint Controllers
Temperature sensors used in conjunction with comparators can act as thermostatic
switches. ICs such as the AD22105 accomplish this function at low cost and allow a
single external resistor to program the setpoint to 2ºC accuracy over a range of –40ºC to
+150ºC (see Figure 3.52). The device asserts an open collector output when the ambient
temperature exceeds the user-programmed setpoint temperature. The ADT05 has
approximately 4ºC of hysteresis which prevents rapid thermal on/off cycling. The ADT05
is designed to operate on a single supply voltage from +2.7 V to +7.0 V facilitating
operation in battery powered applications as well as industrial control systems. Because
of low power dissipation (200 µW @ 3.3 V), self-heating errors are minimized, and
battery life is maximized. An optional internal 200 kΩ pull-up resistor is included to
facilitate driving light loads such as CMOS inputs.
The setpoint resistor is determined by the equation:
R SE T =
39 M Ω° C
− 90 .3 k Ω .
TSE T ( ° C ) + 281.6 ° C
Eq.3-34
The setpoint resistor should be connected directly between the RSET pin (Pin 4) and the
GND pin (Pin 5). If a ground plane is used, the resistor may be connected directly to this
plane at the closest available point.
The setpoint resistor can be of nearly any resistor type, but its initial tolerance and
thermal drift will affect the accuracy of the programmed switching temperature. For most
3.58
SENSORS
TEMPERATURE SENSORS
applications, a 1% metal-film resistor will provide the best tradeoff between cost and
accuracy. Once RSET has been calculated, it may be found that the calculated value does
not agree with readily available standard resistors of the chosen tolerance. In order to
achieve a value as close as possible to the calculated value, a compound resistor can be
constructed by connecting two resistors in series or parallel.
AD22105
+VS = 2.7V TO 7V
200kΩ
RPULL-UP
TEMP
SENSOR
OUT
0.1µF
SETPOINT
RSET
Figure 3.52: AD22105 Thermostatic Switch
The TMP01 is a dual setpoint temperature controller which also generates a PTAT output
voltage (see Figure 3.53). It also generates a control signal from one of two outputs when
the device is either above or below a specific temperature range. Both the high/low
temperature trip points and hysteresis band are determined by user-selected external
resistors.
The TMP01 consists of a bandgap voltage reference combined with a pair of matched
comparators. The reference provides both a constant 2.5 V output and a PTAT output
voltage which has a precise temperature coefficient of 5 mV/K and is 1.49 V (nominal) at
+25ºC. The comparators compare VPTAT with the externally set temperature trip points
and generate an open-collector output signal when one of their respective thresholds has
been exceeded.
Hysteresis is also programmed by the external resistor chain and is determined by the
total current drawn out of the 2.5 V reference. This current is mirrored and used to
generate a hysteresis offset voltage of the appropriate polarity after a comparator has
been tripped. The comparators are connected in parallel, which guarantees that there is no
hysteresis overlap and eliminates erratic transitions between adjacent trip zones.
3.59
BASIC LINEAR DESIGN
TMP01
VREF
TEMPERATURE
SENSOR AND
VOLTAGE
REFERENCE
2.5V
R1
–
SET
HIGH
V+
OVER
+
R2
SET
LOW
+
WINDOW
COMPARATOR
UNDER
–
R3
GND
HYSTERESIS
GENERATOR
VPTAT
Figure 3.53: TMP01 Programmable Setpoint Controller
3.60
SENSORS
TEMPERATURE SENSORS
Microprocessor Temperature Monitoring
Today's computers require that hardware as well as software operate properly, in spite of
the many things that can cause a system crash or lockup. The purpose of hardware
monitoring is to monitor the critical items in a computing system and take corrective
action should problems occur.
Microprocessor supply voltage and temperature are two critical parameters. If the supply
voltage drops below a specified minimum level, further operations should be halted until
the voltage returns to acceptable levels. In some cases, it is desirable to reset the
microprocessor under "brownout" conditions. It is also common practice to reset the
microprocessor on power-up or power-down. Switching to a battery backup may be
required if the supply voltage is low.
Under low voltage conditions it is mandatory to inhibit the microprocessor from writing
to external CMOS memory by inhibiting the Chip Enable signal to the external memory.
Many microprocessors can be programmed to periodically output a "watchdog" signal.
Monitoring this signal gives an indication that the processor and its software are
functioning properly and that the processor is not stuck in an endless loop.
The need for hardware monitoring has resulted in a number of ICs, traditionally called
"microprocessor supervisory products," which perform some or all of the above
functions. These devices range from simple manual reset generators (with debouncing) to
complete microcontroller-based monitoring sub-systems with on-chip temperature
sensors and ADCs. Analog Devices' ADM-family of products is specifically to perform
the various microprocessor supervisory functions required in different systems.
CPU temperature is critically important in the Pentium microprocessors. For this reason,
all new Pentium devices have an on-chip substrate PNP transistor which is designed to
monitor the actual chip temperature. The collector of the substrate PNP is connected to
the substrate, and the base and emitter are brought out on two separate pins of the
Pentium II.
The ADM1021 Microprocessor Temperature Monitor is specifically designed to process
these outputs and convert the voltage into a digital word representing the chip
temperature. The simplified analog signal processing portion of the ADM1021 is shown
in Figure 3.54.
The technique used to measure the temperature is identical to the "ΔVBE" principle
previously discussed. Two different currents (I and N·I)are applied to the sensing
transistor, and the voltage measured for each. In the ADM1021, the nominal currents are
I = 6 µA, (N = 17), N·I = 102 µA.
3.61
BASIC LINEAR DESIGN
The change in the base-emitter voltage, ΔVBE, is a PTAT voltage and given by the
equation:
ΔVBE =
kT
ln ( N ) .
q
Eq. 3-35
Figure 3.54 shows the external sensor as a substrate transistor, provided for temperature
monitoring in the microprocessor, but it could equally well be a discrete transistor. If a
discrete transistor is used, the collector should be connected to the base and not grounded.
To prevent ground noise interfering with the measurement, the more negative terminal of
the sensor is not referenced to ground, but is biased above ground by an internal diode. If
the sensor is operating in a noisy environment, C may be optionally added as a noise
filter. Its value is typically 2200 pF, but should be no more than 3000 pF.
VDD = +3V TO +5.5V
I
µP
REMOTE
SENSING
TRANSISTOR
IBIAS
N×I
OSCILLATOR
D+
C
D–
kT
ΔVBE = q ln N
SPNP
BIAS
DIODE
65kHz
LOWPASS
FILTER
GAIN
=G
VOUT
TO ADC
CHOPPER
AMPLIFIER
AND RECTIFIER
kT
VOUT = G • q ln N
Figure 3.54: ADM1021 Microprocessor Temperature Monitor
Input Signal Conditioning Circuits
To measure ΔVBE, the sensing transistor is switched between operating currents of I and
N·I. The resulting waveform is passed through a 65 kHz lowpass filter to remove noise,
then to a chopper-stabilized amplifier which performs the function of amplification and
synchronous rectification. The resulting DC voltage is proportional to ΔVBE and is
digitized by an 8-bit ADC. To further reduce the effects of noise, digital filtering is
performed by averaging the results of 16 measurement cycles.
In addition, the ADM1021 contains an on-chip temperature sensor, and its signal
conditioning and measurement is performed in the same manner.
3.62
SENSORS
TEMPERATURE SENSORS
One LSB of the ADC corresponds to 1ºC, so the ADC can theoretically measure from –
128ºC to +127ºC, although the practical lowest value is limited to –65ºC due to device
maximum ratings. The results of the local and remote temperature measurements are
stored in the local and remote temperature value registers, and are compared with limits
programmed into the local and remote high and low limit registers as shown in
Figure 3.55. An ALE RT output signals when the on-chip or remote temperature is out of
range. This output can be used as an interrupt, or as an SMBus alert.
The limit registers can be programmed, and the device controlled and configured, via the
serial System Management Bus (SMBus). The contents of any register can also be read
back by the SMBus. Control and configuration functions consist of: switching the device
between normal operation and standby mode, masking or enabling the ALE RT output,
and selecting the conversion rate which can be set from 0.0625 Hz to 8 Hz.
D–
SIGNAL CONDITIONING
AND ANALOG MUX
ADDRESS POINTER
REGISTER
TEMP
SENSOR
ONE-SHOT
REGISTER
CONVERSION RATE
REGISTER
LOCAL TEMPERATURE
VALUE REGISTER
8-BIT
ADC
BUSY
D+
REMOTE TEMPERATURE
VALUE REGISTER
LOCAL TEMPERATURE
LOW LIMIT COMPARATOR
LOCAL TEMPERATURE
LOW LIMIT REGISTER
LOCAL TEMPERATURE
HIGH LIMIT COMPARATOR
LOCAL TEMPERATURE
HIGH LIMIT REGISTER
REMOTE TEMPERATURE
LOW LIMIT COMPARATOR
REMOTE TEMPERATURE
LOW LIMIT REGISTER
REMOTE TEMPERATURE
HIGH LIMIT COMPARATOR
REMOTE TEMPERATURE
HIGH LIMIT REGISTER
RUN/STANDBY
EXTERNAL DIODE OPEN CIRCUIT
CONFIGURATION
REGISTER
STBY
STATUS
REGISTER
INTERRUPT
MASKING
ALERT
SMBUS INTERFACE
TEST VDD NC GND GND NC NC TEST
SDATA
SCLK
ADD0
ADD1
Figure 3.55: ADM1021 Simplified Block Diagram
3.63
BASIC LINEAR DESIGN
REFERENCES
1.
Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New
York, 1991.
2.
Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980.
3.
Walt Kester, Editor, 1992 Amplifier Applications Guide, Section 2, 3, Analog Devices, Inc.,
1992.
4.
Walt Kester, Editor, System Applications Guide, Section 1, 6, Analog Devices, Inc., 1993.
5.
Dan Sheingold, Nonlinear Circuits Handbook, Analog Devices, Inc.
6.
James Wong, Temperature Measurements Gain from Advances in High-precision Op Amps,
Electronic Design, 15 May 1986.
7.
OMEGA Temperature Measurement Handbook, Omega Instruments, Inc.
8.
Handbook of Chemistry and Physics, CRC.
9.
Paul Brokaw, A Simple Three-Terminal IC Bandgap Voltage Reference, IEEE Journal of Solid
State Circuits, Vol. SC-9, December, 1974.
3.64
SENSORS
CHARGE COUPLED DEVICES
SECTION 3.3: CHARGE COUPLED DEVICES (CCDs)
Charge coupled devices (CCDs) contain a large number of small photocells called
photosites or pixels which are arranged either in a single row (linear arrays) or in a matrix
(area arrays). CCD area arrays are commonly used in video applications, while linear
arrays are used in facsimile machines, graphics scanners, and pattern recognition
equipment.
The linear CCD array consists of a row of image sensor elements (photosites, or pixels)
which are illuminated by light from the object or document. During one exposure period
each photosite acquires an amount of charge which is proportional to its illumination.
These photosite charge packets are subsequently switched simultaneously via transfer
gates to an analog shift register. The charge packets on this shift register are clocked
serially to a charge detector (storage capacitor) and buffer amplifier (source follower)
which convert them into a string of photo-dependent output voltage levels (see
Figure 3.56). While the charge packets from one exposure are being clocked out to the
charge detector, another exposure is underway. The analog shift register typically
operates at frequencies between 1 and 10 MHz.
EXPOSURE
CLOCKS
TRANSFER
CLOCKS
PHOTO-SITES (PIXELS)
TRANSFER GATE
RESET
LEVEL
SHIFT
CLOCKS
+V
CCD
OUTPUT
ANALOG TRANSPORT
SHIFT REGISTER
CH
SAMPLE VIDEO/
SAMPLE RESET
FFT SWITCH
-V
Figure 3.56: Linear CCD Array
The charge detector readout cycle begins with a reset pulse which causes a FET switch to
set the output storage capacitor to a known voltage. The switching FETs capacitive
feedthrough causes a reset glitch at the output as shown in Figure 3.57. The switch is then
opened, isolating the capacitor, and the charge from the last pixel is dumped onto the
capacitor causing a voltage change. The difference between the reset voltage and the final
3.65
BASIC LINEAR DESIGN
voltage (video level) shown in Figure 9.87 represents the amount of charge in the pixel.
CCD charges may be as low as 10 electrons, and a typical CCD output sensitivity is
0.6 µV/electron. Most CCDs have a saturation output voltage of about 1 V (see
Reference 16).
RESET
GLITCH
CCD
OUTPUT
VIDEO
LEVEL
RESET
LEVEL
ΔV
RESET
LEVEL
RESET
LEVEL
VIDEO
LEVEL
PIXEL PERIOD
VIDEO
LEVEL
t
Figure 3.57: CCD Output Waveform
Since CCDs are generally fabricated on MOS processes, they have limited capability to
perform on-chip signal conditioning. Therefore the CCD output is generally processed by
external conditioning circuits.
CCD output voltages are small and quite often buried in noise. The largest source of
noise is the thermal noise in the resistance of the FET reset switch. This noise may have a
typical value of 100 to 300 electrons rms (approximately 60 to 180 mVrms). This noise
occurs as a sample-to-sample variation in the CCD output level and is common to both
the reset level and the video level for a given pixel period. A technique called correlated
double sampling (CDS)is often used to reduce the effect of this noise. Figure 9.88 shows
two circuit implementations of the CDS scheme. In the top circuit, the CCD output drives
both SHAs. At the end of the reset interval, SHA1 holds the reset voltage level. At the
end of the video interval, SHA2 holds the video level. The SHA outputs are applied to a
difference amplifier which subtracts one from the other. In this scheme, there is only a
short interval during which both SHA outputs are stable, and their difference represents
ΔV, so the difference amplifier must settle quickly.
Another arrangement is shown in the bottom half of Figure 3.58, which uses three SHAs
and allows either for faster operation or more time for the difference amplifier to settle. In
this circuit, SHA1 holds the reset level so that it occurs simultaneously with the video
level at the input to SHA2 and SHA3. When the video clock is applied simultaneously to
SHA2 and SHA3, the input to SHA2 is the reset level, and the input to SHA3 the video
3.66
SENSORS
CHARGE COUPLED DEVICES
level. This arrangement allows the entire pixel period (less the acquisition time of SHA2
and SHA3) for the difference amplifier to settle.
METHOD #1
SHA 1
CCD
OUTPUT
RESET CLOCK
-
VIDEO CLOCK
+
OUTPUT
SHA 2
SHA 2
SHA 1
CCD
OUTPUT
RESET
CLOCK
METHOD #2
-
VIDEO
CLOCK
OUTPUT
+
SHA 3
Figure 3.58: Correlated Double Sampling (CDS)
3.67
BASIC LINEAR DESIGN
REFERENCES:
1.
Walt Kester, Editor, 1992 Amplifier Applications Guide, Section 2, 3, Analog Devices, Inc.,
1992.
2.
Walt Kester, Editor, System Applications Guide, Section 1, 6, Analog Devices, Inc., 1993.
3.
Optoelectronics Data Book, EG&G Vactec, St. Louis, MO, 1990.
4.
Silicon Detector Corporation, Camarillo, CA, Part Number SD-020-12-001
5.
Photodiode 1991 Catalog, Hamamatsu Photonics, Bridgewater, NJ
6.
Ralph Morrison, Grounding and Shielding Techniques in Instrumentation, Third Edition,
John Wiley, Inc., 1986.
7.
Henry W. Ott, Noise Reduction Techniques in Electronic Systems, Second Edition, John
Wiley, Inc., 1988.
8.
An Introduction to the Imaging CCD Array, Technical Note 82W-4022, Tektronix, Inc.,
Beaverton, OR., 1987.
9.
Handbook of Chemistry and Physics, CRC.
3.68
Data Sheet.
SENSORS
BRIDGE CIRCUITS
SECTION 3-4: BRIDGE CIRCUITS
An Introduction to Bridges
This section discusses the fundamental bridge circuit concept. To gain greatest
appreciation of these ideas, it should be studied along with those sections discussing
precision op amp in Chapters 1. These sections can be read sequentially if the reader
already understands the design issues related to precision op amp applications.
Resistive elements are some of the most common sensors. They are inexpensive, and
relatively easy to interface with signal-conditioning circuits. Resistive elements can be
made sensitive to temperature, strain (by pressure or by flex), and light. Using these basic
elements, many complex physical phenomena can be measured, such as: fluid or mass
flow (by sensing the temperature difference between two calibrated resistances), dewpoint humidity (by measuring two different temperature points), etc.
‹ Strain Gages
120Ω, 350Ω, 3500Ω
‹ Weigh-Scale Load Cells
350Ω - 3500Ω
‹ Pressure Sensors
350Ω - 3500Ω
‹ Relative Humidity
100kΩ - 10MΩ
‹ Resistance Temperature Devices (RTDs)
100Ω , 1000Ω
‹ Thermistors
100Ω - 10MΩ
Figure 3.59: Sensor resistances used in bridge circuits span a wide dynamic
range
Sensor element resistance can range from less than 100 Ω to several hundred kΩ,
depending on the sensor design and the physical environment to be measured. Figure
3.59 indicates the wide range of sensor resistance encountered. For example, RTDs are
typically 100 Ω or 1000 Ω. Thermistors are typically 3500 Ω or higher.
Resistive sensors such as RTDs and strain gages produce relatively small percentage
changes in resistance, in response to a change in a physical variable such as temperature
or force. For example, platinum RTDs have a temperature coefficient of about
0.385%/°C. Thus, in order to accurately resolve temperature to 1ºC, the overall
measurement accuracy must be much better than 0.385 Ω when using a 100 Ω RTD.
Strain gages present a significant measurement challenge because the typical change in
resistance over the entire operating range of a strain gage may be less than 1% of the
3.69
BASIC LINEAR DESIGN
nominal resistance value. Accurately measuring small resistance changes is therefore
critical when applying resistive sensors.
A simple method for measuring resistance is to force a constant current through the
resistive sensor, and measure the voltage output. This requires both an accurate current
source and an accurate means of measuring the voltage. Any change in the current will be
interpreted as a resistance change. In addition, the power dissipation in the resistive
sensor must be small and in accordance with the manufacturer's recommendations, so that
self-heating does not produce errors. As a result, the drive current must be small, which
tends to limit the resolution of this approach.
VB
THE WHEATSTONE BRIDGE:
R4
R3
VO = VB ⎛⎜
R1
⎝ R1 + R4
−
R2 ⎞
⎟
R2 + R3 ⎠
AT BALANCE,
VO
R1 R2
=
VO = 0 if
R4 R3
R1
R2
Figure 3.60: The basic Wheatstone bridge produces an output null when the
ratios of sidearm resistances match
A resistance bridge, shown in Figure 3.60, offers an attractive alternative for measuring
small resistance changes accurately. This is a basic Wheatstone bridge (actually
developed by S. H. Christie in 1833), and is a prime example. It consists of four resistors
connected to form a quadrilateral, a source of excitation voltage VB (or, alternately, a
current) connected across one of the diagonals, and a voltage detector connected across
the other diagonal. The detector measures the difference between the outputs of the two
voltage dividers connected across the excitation voltage, VB. The general form of the
bridge output VO is noted in the figure.
There are two principal ways of operating a bridge such as this. One is by operating it as
a null detector, where the bridge measures resistance indirectly by comparison with a
similar standard resistance. On the other hand, it can be used as a device that reads a
resistance difference directly, as a proportional voltage output.
When R1/R4 = R2/R3, the resistance bridge is said to be at a null, irrespective of the
mode of excitation (current or voltage, AC or DC), the magnitude of excitation, the mode
of readout (current or voltage), or the impedance of the detector. Therefore, if the ratio of
3.70
SENSORS
BRIDGE CIRCUITS
R2/R3 is fixed at K, a null is achieved when R1 = K·R4. If R1 is unknown and R4 is an
accurately determined variable resistance, the magnitude of R1 can be found by adjusting
R4 until an output null is achieved. Conversely, in sensor-type measurements, R4 may be
a fixed reference, and a null occurs when the magnitude of the external variable (strain,
temperature, etc.) is such that R1 = K·R4.
Null measurements are principally used in feedback systems involving electromechanical
and/or human elements. Such systems seek to force the active element (strain gage, RTD,
thermistor, etc.) to balance the bridge by influencing the parameter being measured.
VB
R
VB
R
VO:
Linearity
Error:
R
VO
R+ΔR
VB
4
R
R+ΔR
VO
R
VB
ΔR
ΔR
R +
2
0.5%/%
(A) Single-Element
Varying
R
R−ΔR
R+ΔR
R
ΔR
ΔR
R +
2
0.5%/%
(B) Two-Element
Varying (1)
R−ΔR
VO
VO
R+ΔR
VB
2
VB
R+ΔR
VB ΔR
R
2
0
R−ΔR
VB
R+ΔR
ΔR
R
0
(C) Two-Element (D) All-Element
Varying
Varying (2)
Figure 3.61: The output voltage sensitivity and linearity of constant voltage drive
bridge configurations differs according to the number of active elements
For the majority of sensor applications employing bridges, however, the deviation of one
or more resistors in a bridge from an initial value is measured as an indication of the
magnitude (or a change) in the measured variable. In these cases, the output voltage
change is an indication of the resistance change. Because very small resistance changes
are common, the output voltage change may be as small as tens of millivolts, even with
the excitation voltage VB = 10 V (typical for a load cell application).
In many bridge applications, there may not just be a single variable element, but two, or
even four elements, all of which may vary. Figure 3.61 above shows a family of four
voltage-driven bridges, those most commonly suited for sensor applications. In the four
cases the corresponding equations for VO relate the bridge output voltage to the excitation
voltage and the bridge resistance values. In all cases we assume a constant voltage drive,
VB. Note that since the bridge output is always directly proportional to VB, the
measurement accuracy can be no better than that of the accuracy of the excitation
voltage.
3.71
BASIC LINEAR DESIGN
In each case, the value of the fixed bridge resistor “R” is chosen to be equal to the
nominal value of the variable resistor(s). The deviation of the variable resistor(s) about
the nominal value is assumed to be proportional to the quantity being measured, such as
strain (in the case of a strain gage), or temperature (in the case of an RTD).
The sensitivity of a bridge is the ratio of the maximum expected change in the output
voltage to the excitation voltage. For instance, if VB = 10 V, and the fullscale bridge
output is 10 mV, then the sensitivity is 1 mV/V. For the four cases of Figure 3.61,
sensitivity can be said to increase going left-right, or as more elements are made variable.
The single-element varying bridge of Figure 3.61A is most suited for temperature sensing
using RTDs or thermistors. This configuration is also used with a single resistive strain
gage. All the resistances are nominally equal, but one of them (the sensor) is variable by
an amount ΔR. As the equation indicates, the relationship between the bridge output and
ΔR is not linear. For example, if R = 100 Ω and ΔR = 0.1 Ω (0.1% change in resistance),
the output of the bridge is 2.49875 mV for VB = 10 V. The error is 2.50000 mV
– 2.49875 mV, or 0.00125 mV. Converting this to a % of fullscale by dividing by
2.5 mV yields an end-point linearity error in percent of approximately 0.05%. (Bridge
end-point linearity error is calculated as the worst error in % FS from a straight line
which connects the origin and the end point at FS, i.e., the FS gain error is not included).
If ΔR = 1 Ω, (1% change in resistance), the output of the bridge is 24.8756 mV,
representing an end-point linearity error of approximately 0.5%. The end-point linearity
error of the single-element bridge can be expressed in equation form:
Single-Element Varying Bridge End-Point Linearity Error ≈ % Change in Resistance ÷ 2
It should be noted that the above nonlinearity refers to the nonlinearity of the bridge
itself and not the sensor. In practice, most sensors themselves will exhibit a certain
specified amount of nonlinearity, which must also be accounted for in the final
measurement.
In some applications, the bridge nonlinearity noted above may be acceptable. But, if not,
there are various methods available to linearize bridges. Since there is a fixed relationship
between the bridge resistance change and its output (shown in the equations), software
can be used to remove the linearity error in digital systems. Circuit techniques can also be
used to linearize the bridge output directly, and these will be discussed shortly.
There are two cases to consider in the instance of a two-element varying bridge. In Case 1
(Figure 3.61B), both of the diagonally opposite elements change in the same direction.
An example would be two identical strain gages mounted adjacent to each other, with
their axes in parallel.
The nonlinearity for this case, 0.5%/%, the same as that of the single-element varying
bridge of Figure 3.61A. However, it is interesting to note the sensitivity is now improved
by a factor of 2, vis-à-vis the single-element varying setup. The two-element varying
bridge is commonly found in pressure sensors and flow meter systems.
3.72
SENSORS
BRIDGE CIRCUITS
A second case of the two-element varying bridge, Case 2, is shown in Figure 3.61C. This
bridge requires two identical elements that vary in opposite directions. This could
correspond to two identical strain gages: one mounted on top of a flexing surface, and
one on the bottom. Note that this configuration is now linear, and like two-element
varying Case 1, it has twice the sensitivity of the Figure 3.61A configuration. Another
way to view this configuration is to consider the terms R+ΔR and R–ΔR as comprising
two sections of a linear potentiometer.
The all-element varying bridge of Figure 3.61D produces the most signal for a given
resistance change, and is inherently linear. It is also an industry-standard configuration
for load cells constructed from four identical strain gages. Understandably, it is also one
of the most popular bridge configurations.
IB
IB
R
R
R
R−ΔR
VO
VO
R
R+ΔR
VO: IBR
4
ΔR
ΔR
R +
4
Linearity
Error:
R
R+ΔR
0.25%/%
(A) Single-Element
Varying
R
R+ΔR
R
ΔR
0
(B) Two-Element
Varying (1)
R+ΔR
IB
2
R−ΔR
VO
VO
R+ΔR
IB
2
IB
IB
ΔR
0
R−ΔR
IB
R+ΔR
ΔR
0
(C) Two-Element (D) All-Element
Varying
Varying (2)
Figure 3.62: The output voltage sensitivity and linearity of constant current drive
bridge configurations also differs according to the number of active elements
Bridges may also be driven from constant current sources, as shown in Figure 3.62, for
the corresponding cases of single, dual, dual, and four active element(s). As with the
voltage-driven bridges, the analogous output expressions are noted, along with the
sensitivities.
Current drive, although not as popular as voltage drive, does have advantages when the
bridge is located remotely from the source of excitation. One advantage is that the wiring
resistance doesn’t introduce errors in the measurement; another is simpler, less expensive
cabling. Note also that with constant current excitation, all bridge configurations are
linear except the single-element varying case of Figure 3.62A.
In summary, there are many design issues relating to bridge circuits, as denoted by
Figure 3.63 below. After selecting the basic configuration, the excitation method must be
3.73
BASIC LINEAR DESIGN
determined. The value of the excitation voltage or current must first be determined, as
this directly influences sensitivity. Recall that the fullscale bridge output is directly
proportional to the excitation voltage (or current). Typical bridge sensitivities are 1 mV/V
to 10 mV/V.
Although large excitation voltages yield proportionally larger fullscale output voltages,
they also result in higher bridge power dissipation, and thus raise the possibility of sensor
resistor self-heating errors. On the other hand, low values of excitation voltage require
more gain in the conditioning circuits, and also increase sensitivity to low level errors
such as noise and offset voltages.
‹ Selecting Configuration (1, 2, 4 - Element Varying)
‹ Selection of Voltage or Current Excitation
‹ Ratiometric Operation
‹ Stability of Excitation Voltage or Current
‹ Bridge Sensitivity: FS Output / Excitation Voltage
1mV / V to 10mV / V Typical
‹ Fullscale Bridge Outputs: 10mV - 100mV Typical
‹ Precision, Low Noise Amplification / Conditioning
Techniques Required
‹ Linearization Techniques May Be Required
‹ Remote Sensors Present Challenges
Figure 3.63: A number of bridge considerations impact design choices
Regardless of the absolute level, the stability of the excitation voltage or current directly
affects the overall accuracy of the bridge output, as is evident from the VB and IB terms in
the output expressions. Therefore stable references and/or ratiometric drive techniques
are required, to maintain highest accuracy.
Here, ratiometric simply refers to the use of the bridge drive voltage of a voltage-driven
bridge (or a current-proportional voltage, for a current-driven bridge) as the reference
input to the ADC that digitizes the amplified bridge output voltage. In this manner the
absolute accuracy and stability of the excitation voltage becomes a second order error.
Examples to follow illustrate this point further.
3.74
SENSORS
BRIDGE CIRCUITS
Amplifying and Linearizing Bridge Outputs
The output of a single-element varying bridge may be amplified by a single precision opamp connected as shown in Figure 3.64. Unfortunately this circuit, although attractive
because of relative simplicity, has poor overall performance. Its gain predictability and
accuracy are poor, and it unbalances the bridge due to loading from RF and the op amp
bias current. The RF resistors must be carefully chosen and matched to maximize
common mode rejection (CMR). Also, it is difficult to maximize the CMR while at the
same time allowing different gain options. Gain is dependent upon the bridge resistances
and RF. In addition, the output is nonlinear, as the configuration does nothing to address
the intrinsic bridge non-linearity. In summary, the circuit isn’t recommended for
precision use.
VB
RF
R
R
+VS
−
+
R
R+ΔR
RF
VS
2
Figure 3.64: Using a single op amp as a bridge amplifier
However, a redeeming feature of this circuit is that it is capable of single supply
operation, with a solitary op amp. Note that the RF resistor connected to the non-inverting
input is returned to VS/2 (rather than ground) so that both positive and negative ΔR
values can be accommodated, with the bipolar op amp output swing referenced to VS/2.
A much better approach is to use an instrumentation amplifier (in-amp) for the required
gain, as shown in Figure 3.65. This efficient circuit provides better gain accuracy, with
the in-amp gain usually set with a single resistor, RG. Since the amplifier provides dual,
high-impedance loading to the bridge nodes, it does not unbalance or load the bridge.
Using modern in-amp devices with gains ranging from 10-1000, excellent common mode
rejection and gain accuracy can be achieved with this circuit.
However, due to the intrinsic characteristics of the bridge, the output is still nonlinear
(see expression). As noted earlier, this can be corrected in software (assuming that the inamp output is digitized using an analog-to-digital converter and followed by a
microcontroller or microprocessor).
3.75
BASIC LINEAR DESIGN
The in-amp can be operated on either dual supplies as shown, or alternately, on a single
positive supply. In the figure, this corresponds to –VS = 0. This is a key advantageous
point, due the fact that all such bridge circuits bias the in-amp inputs at VB/2, a voltage
range typically compatible with amplifier bias requirements. In-amps such as the AD620
family, the AD623, and AD627 can be used in single (or dual) supply bridge
applications, provided their restrictions on the gain and input and output voltage swings
are observed.
VB
R
OPTIONAL RATIOMETRIC OUTPUT
VREF = VB
+V S
R
−
RG
VOUT =
VB
4
ΔR
R +
IN AMP
+
REF
ΔR
GAIN
2
V OUT
R
R+ΔR
-VS*
* SEE TEXT REGARDING
SINGLE-SUPPLY OPERATION
Figure 3.65: A generally preferred method of bridge amplification employs an
instrumentation amplifier for stable gain and high CMR
The bridge in this example is voltage driven, by the voltage VB. This voltage can
optionally be used for an ADC reference voltage, in which case it also is an additional
output, VREF.
Various techniques are available to linearize bridge outputs, but it is important to
distinguish between the linearity of the bridge equation (discussed earlier), and the sensor
response linearity to the phenomenon being sensed. For example, if the active sensor
element is an RTD, the bridge used to implement the measurement might have perfectly
adequate linearity; yet the output could still be nonlinear, due to the RTD device's
intrinsic nonlinearity. Manufacturers of sensors employing bridges address the
nonlinearity issue in a variety of ways, including keeping the resistive swings in the
bridge small, shaping complementary nonlinear response into the active elements of the
bridge, using resistive trims for first-order corrections, and others. In the examples which
follow, what is being addressed is the linearity error of the bridge configuration itself (as
opposed to a sensor element within the bridge).
Figure 3.66 shows a single-element varying active bridge circuit, in which an op amp
produces a forced bridge null condition. For this single-element varying case, only the op
amp feedback resistance varies, with the remaining three resistances fixed.
3.76
SENSORS
BRIDGE CIRCUITS
As used here, the op amp output provides a buffered, ground referenced, low impedance
output for the bridge measurement, effectively suppressing the VB/2 CM bridge
component at the op amp inputs.
VB
R
R
+
+VS
R
−
-VS
R+ΔR
VOUT = -VB
ΔR
2R
Figure 3.66: Linearizing a single-element varying bridge (Method 1)
The circuit works by adding a voltage in series with the variable resistance arm. This
voltage is equal in magnitude and opposite in polarity to the incremental voltage across
the varying element, and is linear with ΔR. As can be noted, the three constant “R”
valued resistances and the op amp operate to drive a constant current in the variable
resistance. This is the basic mechanism that produces the linearized output.
This active bridge has a sensitivity gain of two over the standard single-element varying
bridge (Figure 3.62A, again). The key point is that the bridge’s incremental resistance/
voltage output becomes linear, even for large values of ΔR. However, because of a still
relatively small output signal, a second amplifier must usually follow this bridge. Note
also that the op amp used in this circuit requires dual supplies, because its output must go
negative for conditions where ΔR is positive.
Another circuit for linearizing a single-element varying bridge is shown in Figure 3.67.
The top node of the bridge is excited by the voltage, VB. The bottom of the bridge is
driven in complementary fashion by the left op amp, which maintains a constant current
of VB/R in the varying resistance element, R + ΔR. Like the circuit of Figure 3.66, the
constant current drive for the single-element variable resistance provides the mechanism
for linearity improvement. Also, because of the fact that the bridge left-side center node
is ground-referenced by the op amp, this configuration effectively suppresses CM
voltages. This has the virtue of making the op amp selection somewhat less critical. Of
course, performance parameters of high gain, low offset/noise, and high stability are all
still needed.
3.77
BASIC LINEAR DESIGN
VB
VOUT =
R
R
VB
2
ΔR
R
1+
R2
R1
+VS
+
−
-VS
−
+
+VS
VOUT
R2
-VS
R+ΔR
R
R1
Figure 3.67: Linearizing a single-element varying bridge (Method 2)
The output signal is taken from the right-hand leg of the bridge, and is amplified by a
second op amp, connected as a non-inverting gain stage. With the scaling freedom
provided by the second op amp, the configuration is very flexible. The net output is
linear, and has a bridge-output referred sensitivity comparable to the single-element
varying circuit of Figure 3.66.
The circuit in Figure 3.67 requires two op amps operating on dual supplies. In addition,
paired resistors R1-R2 must be ratio matched and stable types, for overall accurate and
stable gain. The circuit can be a practical one using a dual precision op amp, such as an
AD708, the OP2177 or the OP213.
A closely related circuit for linearizing a voltage-driven, two-element varying bridge can
be adapted directly from the basic circuit of Figure 3.67. This form of the circuit, shown
in Figure 3.68, is identical to the previous single-element varying case, with the exception
that the resistance between VB and the op amp (+) input is now also variable (i.e., both
diagonal R + ΔR resistances vary, in a like manner).
For the same applied voltage VB, this form of the circuit has twice the sensitivity, which
is evident in the output expressions. A dual supply op amp is again required, and
additional gain may also be necessary.
The two-element varying bridge circuit shown in Figure 3.69 uses an op amp, a sense
resistor, and a voltage reference, set up in a feedback loop containing the sensing bridge.
The net effect of the loop is to maintain a constant current through the bridge of
IB = VREF/RSENSE. The current through each leg of the bridge remains constant (IB/2) as
the resistances change, therefore the output is a linear function of ΔR. An in-amp
provides the additional gain.
3.78
SENSORS
BRIDGE CIRCUITS
VB
R
R+ΔR
-
+
+VS
-VS
R+ΔR
R
⎡ ΔR ⎤
VOUT = -VB ⎢
⎥
⎣ R ⎦
Figure 3.68: Linearizing a two-element varying voltage-driven bridge (Method 1)
+VS
R
R+ΔR
ΔR
VOUT = IB
GAIN
2
−
RG
IB
IN AMP
+
R
R+ΔR
+VS
−
RSENSE
+
-VS*
IB
REF
VOUT
-VS*
* SEE TEXT REGARDING
SINGLE-SUPPLY OPERATION
VREF
Figure 3.70: Linearizing a two-element varying current-driven bridge (Method 2)
This circuit can be operated on a single supply with the proper choice of amplifiers and
signal levels. If ratiometric operation of an ADC is desired, the VREF voltage can be used
to drive the ADC.
3.79
BASIC LINEAR DESIGN
Driving Remote Bridges
Wiring resistance and noise pickup are the biggest problems associated with remotely
located bridges. Figure 3.71 shows a 350 Ω strain gage, which is connected to the rest of
the bridge circuit by 100 feet of 30 gage twisted pair copper wire. The resistance of the
wire at 25ºC is 0.105 Ω/ft, or 10.5 Ω for 100 ft. The total lead resistance in series with the
350 Ω strain gage is therefore 21 Ω. The temperature coefficient of the copper wire is
0.385%/ºC. Now we will calculate the gain and offset error in the bridge output due to a
+10ºC temperature rise in the cable. These calculations are easy to make, because the
bridge output voltage is simply the difference between the output of two voltage dividers,
each driven from a +10 V source.
+10V
100 FEET, 30 GAGE COPPER WIRE = 10.5Ω @ 25°C
TC = 0.385%/°C
ASSUME +10°C TEMPERATURE CHANGE
NUMBERS IN ( ) ARE @ +35°C
350Ω
350Ω
-
VO
+
RLEAD 10.5Ω (10.904Ω)
0 → 23.45mV
(5.44mV → 28.83mV)
STRAIN GAGE
350Ω → 353.5Ω FS
350Ω
RCOMP
21Ω
RLEAD 10.5Ω (10.904Ω)
OFFSET ERROR OVER TEMPERATURE = +23%FS
GAIN ERROR OVER TEMPERATURE = –0.26%FS
Figure 3.71: Wiring resistance related errors with remote bridge sensor
The fullscale variation of the strain gage resistance (with flex) above its nominal 350 Ω
value is +1% (+3.5 Ω), corresponding to a fullscale strain gage resistance of 353.5 Ω
which causes a bridge output voltage of +23.45 mV. Notice that the addition of the 21 Ω
RCOMP resistor compensates for the wiring resistance and balances the bridge when the
strain gage resistance is 350 Ω. Without RCOMP, the bridge would have an output offset
voltage of 145.63 mV for a nominal strain gage resistance of 350 Ω. This offset could be
compensated for in software just as easily, but for this example, we chose to do it with
RCOMP.
Assume that the cable temperature increases +10ºC above nominal room temperature.
This results in a total lead resistance increase of +0.404 Ω (10.5 Ω×0.00385/ºC×10ºC) in
each lead. Note: The values in parentheses in the diagram indicate the values at +35ºC.
The total additional lead resistance (of the two leads) is +0.808 Ω. With no strain, this
additional lead resistance produces an offset of +5.44 mV in the bridge output. Fullscale
strain produces a bridge output of +28.83 mV (a change of +23.39 mV from no strain).
3.80
SENSORS
BRIDGE CIRCUITS
Thus the increase in temperature produces an offset voltage error of +5.44 mV (+23%
fullscale) and a gain error of –0.06 mV (23.39 mV – 23.45 mV), or –0.26% fullscale.
Note that these errors are produced solely by the 30 gage wire, and do not include any
temperature coefficient errors in the strain gage itself.
The effects of wiring resistance on the bridge output can be minimized by the 3-wire
connection shown in Figure 3.72. We assume that the bridge output voltage is measured
by a high impedance device, therefore there is no current in the sense lead. Note that the
sense lead measures the voltage output of a divider: the top half is the bridge resistor plus
the lead resistance, and the bottom half is strain gage resistance plus the lead resistance.
The nominal sense voltage is therefore independent of the lead resistance. When the
strain gage resistance increases to fullscale (353.5 Ω), the bridge output increases to
+24.15 mV.
+10V
100 FEET, 30 GAGE COPPER WIRE = 10.5Ω @ 25°C
TC = 0.385%/°C
ASSUME +10°C TEMPERATURE CHANGE
NUMBERS IN ( ) ARE @ +35°C
350Ω
350Ω
-
VO
+
0 → 24.15mV
350Ω
RLEAD 10.5Ω (10.904Ω)
I=0
STRAIN GAGE
350Ω → 353.5Ω FS
(0 → 24.13mV)
RLEAD 10.5Ω (10.904Ω)
OFFSET ERROR OVER TEMPERATURE = 0%FS
GAIN ERROR OVER TEMPERATURE = –0.08%FS
Figure 3.72: Remote bridge wiring resistance errors are reduced with 3-wire
sensor connection
Increasing the temperature to +35ºC increases the lead resistance by +0.404 Ω in each
half of the divider. The fullscale bridge output voltage decreases to +24.13 mV because
of the small loss in sensitivity, but there is no offset error. The gain error due to the
temperature increase of +10ºC is therefore only –0.02 mV, or –0.08% of fullscale.
Compare this to the +23% fullscale offset error and the –0.26% gain error for the twowire connection shown in Figure 3.72.
The three-wire method works well for remotely located resistive elements which make up
one leg of a single-element varying bridge. However, all-element varying bridges
generally are housed in a complete assembly, as in the case of a load cell. When these
bridges are remotely located from the conditioning electronics, special techniques must
be used to maintain accuracy.
3.81
BASIC LINEAR DESIGN
Of particular concern is maintaining the accuracy and stability of the bridge excitation
voltage. The bridge output is directly proportional to the excitation voltage, and any drift
in the excitation voltage produces a corresponding drift in the output voltage.
For this reason, most all-element varying bridges (such as load cells) are six-lead
ssemblies: two leads for the bridge output, two leads for the bridge excitation, and two
sense leads. To take full advantage of the additional accuracy that these extra leads allow,
a method called Kelvin or 4-wire sensing is employed, as shown in Figure 3.73 below.
In this setup the drive voltage VB is not applied directly to the bridge, but goes instead to
the input of the upper precision op amp, which is connected in a feedback loop around
the bridge (+) terminal. Although there may be a substantial voltage drop in the +FORCE
lead resistance of the remote cable, the op amp will automatically correct for it, since it
has a feedback path through the +SENSE lead. The net effect is that the upper node of the
remote bridge is maintained at a precise level of VB (within the capability of the op amp
used, of course). A similar situation occurs with the bottom precision op amp, which
drives the bridge (-) terminal to a ground level, as established by the op amp input ground
reference. Again, the voltage drop in the –FORCE lead is relatively immaterial, because
of the sensing at the –SENSE terminal.
+
+VB
+FORCE
+SENSE
RLEAD
–
VO
– SENSE
– FORCE
RLEAD
–
+
Figure 3.73: A Kelvin sensing system with a 6-wire voltage-driven bridge
connection and precision op amps minimizes errors due to wire lead resistances
In both cases, the sense lines go to high impedance op amp inputs, thus there is minimal
error due to the bias current induced voltage drop across their lead resistance. The op
amps maintain the required excitation voltage at the remote bridge, to make the voltage
measured between the (+) and (-) sense leads always equal to VB.
3.82
SENSORS
BRIDGE CIRCUITS
Note— a subtle point is that the lower op amp will need to operate on dual supplies, since
the drive to the -FORCE lead will cause the op amp output to go negative. Because of
relatively high current in the bridge (~30 mA), current buffering stages at the op amp
outputs are likely advisable for this circuit.
Although Kelvin sensing eliminates errors due to voltage drops in the bridge wiring
resistance, the basic drive voltage VB must still be highly stable since it directly affects
the bridge output voltage. In addition, the op amps must have low offset, low drift, and
low noise. Ratiometric operation can be optionally added, simply by using VB to drive
the ADC reference input.
The constant current excitation method shown in Figure 3.74 below is another method for
minimizing the effects of wiring resistance on the measurement accuracy. This system
drives a precise current I through the bridge, proportioned as per the expression in the
figure. An advantage of the circuit in Figure 3.74 is that it only uses one amplifier.
I
RLEAD
4-LEAD
BRIDGE
VREF
+
–
VO
I
RLEAD
I=
VREF
RSENSE
I
RSENSE
Figure 3.74: A 4-wire current-driven bridge scheme also minimizes errors due to
wire lead resistances, plus allows simpler cabling
However, the accuracy of the reference, the sense resistor, and the op amp all influence
the overall accuracy. While the precision required of the op amp should be obvious, one
thing not necessarily obvious is that it may be required to deliver appreciable current,
when I is more than a few mA (which it will be with standard 350 Ω bridges). In such
cases, current buffering of the op amp is again in order.
Therefore for highest precision with this circuit, a buffer stage is recommended. This can
be as simple as a small transistor, since the bridge drive is unidirectional.
3.83
BASIC LINEAR DESIGN
System offset minimization
Maintaining an accuracy of 0.1% or better with a fullscale bridge output voltage of
20 mV requires that the sum of all offset errors be less than 20 µV. Parasitic
thermocouples are cases in point, and if not given due attention, they can cause serious
temperature drift errors. All dissimilar metal-metal connections generate voltages
between a few and tens of microvolts for a 1ºC temperature differential, are basic
thermocouple fact-of-life.
Fortunately however, within a bridge measurement system the signal connections are
differential, therefore this factor can be used to minimize the impact of parasitic
thermocouples.
THERMOCOUPLE VOLTAGE
≈ 35µV/ °C × (T1 – T2)
+ VB
T1
+
VO
IB +
VOS
+
T2
AMP
–
–
IB –
COPPER
TRACES
KOVAR
PINS
Figure 3.75: Typical sources of offset voltage within bridge measurement
systems
Figure 3.75 shows some typical sources of offset error that are inevitable in a system.
Within a differential signal path, only those thermocouple pairs whose junctions are
actually at different temperatures will degrade the signal. The diagram shows a typical
parasitic junction formed between the copper printed circuit board traces and the kovar
pins of an IC amplifier.
This thermocouple voltage is about 35 µV/ºC temperature differential. Note that this
package-PC trace thermocouple voltage is significantly less when using a plastic package
with a copper lead frame (recommended). Regardless of what package is used, all metalmetal connections along the signal path should be designed so that minimal temperature
differences occur between the sides.
The amplifier offset voltage and bias currents are further sources of offset error. The
amplifier bias current must flow through the source impedance. Any unbalance in either
the source resistances or the bias currents produce offset errors. In addition, the offset
voltage and bias currents are a function of temperature.
3.84
SENSORS
BRIDGE CIRCUITS
High performance low offset, low offset drift, low bias current, and low noise precision
amplifiers such as the AD707, the OP177 or OP1177 are required. In some cases,
chopper-stabilized amplifiers such as the AD8551/AD8552/AD8554 may be a solution.
AC bridge excitation such as that shown in Figure 3.76 below can effectively remove
offset voltage effects in series with a bridge output, VO.
The concept is simple, and can be described as follows. The net bridge output voltage is
measured under the two phased-sequence conditions, as shown. A first measurement
(top) drives the bridge at the top node with excitation voltage VB. This yields a first-phase
measurement output VA, where VA is the sum of the desired bridge output voltage VO and
the net offset error voltage EOS.
In the second measurement (bottom) the polarity of the bridge excitation is then reversed,
and a second measurement, VB, is made. Subtracting VB from VA yields 2VO, and the
offset error term EOS cancels as noted from the mathematical expression in the figure.
NORMAL
DRIVE
VOLTAGES
+ VB
EOS = SUM OF ALL OFFSET ERRORS
+
–
EOS
+
+
VA = VO + EOS
VO
–
-
VA – VB = (VO + EOS) – (– VO + EOS) = 2 VO
REVERSE
DRIVE
VOLTAGES
EOS
–
VO
+
–
+
+
VB = – VO + EOS
–
+ VB
Figure 3.76: AC bridge excitation minimizes system offset voltages
Obviously, a full implementation of this technique requires a highly accurate
measurement ADC such as the AD7730 (see Reference 5) as well as a microcontroller to
perform the subtraction.
Note that if a ratiometric reference is desired, the ADC must also accommodate the
changing polarity of the reference voltage, as well as sense the magnitude. Again, the
AD7730 includes this capability.
3.85
BASIC LINEAR DESIGN
A very powerful combination of bridge circuit techniques is shown in Figure 3.77, an
example of a high performance ADC. In Figure 3.77A is shown a basic DC operated
ratiometric technique, combined with Kelvin sensing to minimize errors due to wiring
resistance, which eliminates the need for an accurate excitation voltage.
The AD7730 measurement ADC can be driven from a single supply voltage of 5 V,
which in this case is also used to excite the remote bridge. Both the analog input and the
reference input to the ADC are high impedance and fully differential. By using the + and
– SENSE outputs from the bridge as the differential reference voltage to the ADC, there
is no loss in measurement accuracy if the actual bridge excitation voltage varies.
+5V
+FORCE
RLEAD
6-LEAD
BRIDGE
V3,4
Q3
Q1
DVDD
AVDD
+ SENSE
+SENSE
+ VREF
VO
– SENSE
– FORCE
+ FORCE
+5V/+3V
+ AIN
– AIN
(A) DC excitation
– SENSE
24 BITS
– VREF
RLEAD
VO
AD7730
ADC
GND
V1,2
V3,4
Q4
Q2
V1,2
+ FORCE
Q1,Q2
ON
Q1,Q2
ON
Q3,Q4
ON
Q3,Q4
ON
(B) AC excitation (simplified)
Figure 3.77: Ratiometric DC or AC operation with Kelvin sensing can be
implemented using the AD7730 ADC
To implement AC bridge operation of the AD7730, an "H" bridge driver of P-Channel
and N-Channel MOSFETs can be configured as shown in Figure 3.77B (note —
dedicated bridge driver chips are available, such as the Micrel MIC4427). This scheme,
added to the basic functionality of the AD7730 configuration of Figure 3.77A greatly
increases the utility of the offset canceling circuit, as generally outlined in the preceding
discussion of Figure 3.76.
Because of the on-resistance of the H-bridge MOSFETs, Kelvin sensing must also be
used in these AC bridge applications. It is also important that the drive signals be nonoverlapping, as noted, to prevent excessive MOSFET switching currents. The AD7730
ADC has on-chip circuitry which generates the required non-overlapping drive signals to
implement this AC bridge excitation. All that needs adding is the switching bridge as
noted in Figure 3.77B.
The AD7730 is one of a family of sigma-delta ADCs with high resolution (24 bits) and
internal programmable gain amplifiers (PGAs) and is ideally suited for bridge
applications. These ADCs have self- and system calibration features, which allow offset
and gain errors due to the ADC to be minimized. For instance, the AD7730 has an offset
drift of 5 nV/ºC and a gain drift of 2 ppm/ºC. Offset and gain errors can be reduced to a
few microvolts using the system calibration feature.
3.86
SENSORS
BRIDGE CIRCUITS
REFERENCES: BRIDGE CIRCUITS
1.
Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New
York, 1991.
2.
Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0916550-05-2.
3.
Sections 2, 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN:
0-916550-10-9.
4.
Sections 1, 6, Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0916550-13-3.
5.
Data sheet for AD7730 Bridge Transducer ADC, http://www.analog.com
3.87
BASIC LINEAR DESIGN
3.88
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
SECTION 3-5: STRAIN, FORCE, PRESSURE AND FLOW
MEASUREMENTS
Strain Gages
The most popular electrical elements used in force measurements include the resistance
strain gage, the semiconductor strain gage, and piezoelectric transducers. The strain gage
measures force indirectly by measuring the deflection it produces in a calibrated carrier.
Pressure can be converted into a force using an appropriate transducer, and strain gage
techniques can then be used to measure pressure. Flow rates can be measured using
differential pressure measurements, which also make use of strain gage technology.
These principles are summarized in Figure 3.78 below.
‹ Strain:
Strain Gage, PiezoElectric Transducers
‹ Force:
Load Cell
‹ Pressure:
Diaphragm to Force to Strain Gage
‹ Flow:
Differential Pressure Techniques
Figure 3.78: Strain gages are directly or indirectly the basis for a variety of
physical measurements
The resistance-based strain gage uses a resistive element which changes in length, hence
resistance, as the force applied to the base on which it is mounted causes stretching or
compression. It is perhaps the most well known transducer for converting force into an
electrical variable.
An unbonded strain gage consists of a wire stretched between two points. Force acting
upon the wire (area = A, length = L, resistivity = ρ) will cause the wire to elongate or
shorten, which will cause the resistance to increase or decrease proportionally according
to:
R = ρL/A
Eq. 3-36
and,
ΔR/R = GF·ΔL/L
Eq. 3-37
where GF = Gage factor (2.0 to 4.5 for metals, and more than 150 for semiconductors).
In this expression, the dimensionless quantity ΔL/L is a measure of the force applied to
the wire and is expressed in microstrains (1 µε = 10–6 cm/cm) which is the same as partsper-million (ppm).
3.89
BASIC LINEAR DESIGN
From equation 3-37, note that larger gage factors result in proportionally larger resistance
changes, hence this implies greater strain gage sensitivity. These concepts are
summarized in the drawing of Figure 3.79 below.
FORCE
R=
ΔR = GF • ΔL
R
L
STRAIN
SENSING
WIRE
AREA = A
LENGTH = L
RESISTIVITY =ρ
RESISTANCE = R
ΔL
L
FORCE
ρL
A
GF = GAGE FACTOR
2 TO 4.5 FOR METALS
>150 FOR SEMICONDUCTORS
= MICROSTRAINS ( με )
1 με = 1×10–6 cm / cm = 1 ppm
Figure 3.79: Operating principles of a basic unbonded strain gage
A bonded strain gage consists of a thin wire or conducting film arranged in a coplanar
pattern and cemented to a base or carrier. The basic form of this type of gage is shown in
Figure 3.80.
This strain gage is normally mounted so that as much as possible of the length of the
conductor is aligned in the direction of the stress that is being measured, i.e.,
longitudinally. Lead wires are attached to the base and brought out for interconnection.
Bonded devices are considerably more practical and are in much wider use than are the
aforementioned unbonded devices.
Perhaps the most popular version is the foil-type gage, produced by photo-etching
techniques, and using similar metals to the wire types. Typical alloys are of copper-nickel
(Constantan), nickel-chromium (Nichrome), nickel-iron, platinum-tungsten, etc. This
strain gage type is shown in Figure 3.81.
Gages having wire sensing elements present a small surface area to the specimen; this
reduces leakage currents at high temperatures and permits higher isolation potentials
between the sensing element and the specimen. Foil sensing elements, on the other hand,
have a large ratio of surface area to cross-sectional area and are more stable under
extremes of temperature and prolonged loading. The large surface area and thin cross
section also permit the device to follow the specimen temperature and facilitate the
dissipation of self-induced heat.
3.90
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
FORCE
‹ SMALL SURFACE AREA
‹ LOW LEAKAGE
‹ HIGH ISOLATION
FORCE
Figure 3.80: A bonded wire strain gage
FORCE
‹ PHOTO ETCHING TECHNIQUE
‹ LARGE AREA
‹ STABLE OVER TEMPERATURE
‹ THIN CROSS SECTION
‹ GOOD HEAT DISSIPATION
FORCE
Figure 3.81: A metal foil strain gage
3.91
BASIC LINEAR DESIGN
Semiconductor strain gages
Semiconductor strain gages make use of the piezoresistive effect in certain
semiconductor materials such as silicon and germanium in order to obtain greater
sensitivity and higher-level output.
Semiconductor gages can be produced to have either positive or negative changes when
strained. They can be made physically small while still maintaining a high nominal
resistance.
Semiconductor strain gage bridges may have 30 times the sensitivity of bridges
employing metal films, but are temperature sensitive and difficult to compensate. Their
change in resistance with strain is also nonlinear. They are not in as widespread use as the
more stable metal-film devices for precision work; however, where sensitivity is
important and temperature variations are small, they may have some advantage.
Instrumentation is similar to that for metal-film bridges but is less critical because of the
higher signal levels and decreased transducer accuracy. Figure 3.82 summarizes the
relative performance of metal and semiconductor strain gages.
PARAMETER
METAL
STRAIN GAGE
SEMICONDUCTOR
STRAIN GAGE
Measurement Range
0.1 to 40,000 με
0.001 to 3000 με
Gage Factor
2.0 to 4.5
50 to 200
Resistance, Ω
120, 350, 600, …, 5000
1000 to 5000
Resistance
Tolerance
0.1% to 0.2%
1% to 2%
Size, mm
0.4 to 150
Standard: 3 to 6
1 to 5
Figure 3.82: A comparison of metal and
semiconductor type strain gages
Strain gages can be used to measure force, as shown in Figure 3.82, where a cantilever
beam is slightly deflected by the applied force. Four strain gages are used to measure the
flex of the beam, two on the top, and two on the bottom. The gages are connected in a
four-element bridge configuration. Recall from the last section that this configuration
gives maximum sensitivity and is inherently linear. This configuration also offers firstorder correction for temperature drift in the individual strain gages.
Strain gages are low-impedance devices, consequently they require significant excitation
power to obtain reasonable levels of output voltage. A typical strain-gage based load cell
bridge will have a 350 Ω impedance and is specified as having a sensitivity in a range
3-10 millivolts full scale, per volt of excitation.
3.92
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
VB
RIGID BEAM
FORCE
R1
R1
R4
_
R3
+
VO
R2
R4
R2
R3
Figure 3.83: A beam force sensor using a strain gage bridge
FORCE
+VB
+SENSE
+VOUT
–VOUT
–SENSE
–VB
Figure 3.84: A load cell comprised of 4 strain gages is shown in physical (top)
and electrical (bottom) representations
The load cell is composed of four individual strain gages arranged as a bridge, as shown
in Figure 3.84. For a 10 V bridge excitation voltage with a rating of 3 mV/V, 30
millivolts of signal will be available at full scale loading.
3.93
BASIC LINEAR DESIGN
While increasing the drive to the bridge can increase the output, self-heating effects are a
significant limitation to this approach— they can cause erroneous readings, or even
device destruction. One technique for evading this limitation is to use a low duty cycle
pulsed drive signal for the excitation.
Many load cells have the ±"SENSE" connections as shown, to allow the signalconditioning electronics to compensate for DC drops in the wires (Kelvin sensing as
discussed in the last section). This brings the wires to a total of 6 for the fully
instrumented bridge. Some load cells may also have additional internal resistors, for
temperature compensation purposes.
Pressures in liquids and gases are measured electrically by a variety of pressure
transducers. A number of mechanical converters (including diaphragms, capsules,
bellows, manometer tubes, and Bourdon tubes) are used to measure pressure by
measuring an associated length, distance, or displacement, and to measure pressure
changes by the motion produced, as shown by Figure 3.85.
The output of this mechanical interface is then applied to an electrical converter such as a
strain gage, or piezoelectric transducer. Unlike strain gages, piezoelectric pressure
transducers are typically used for high-frequency pressure measurements (such as sonar
applications, or crystal microphones).
PRESSURE
SOURCE
STRAIN GAGE
MECHANICAL
OUTPUT
PRESSURE
SENSOR
(DIAPHRAGM)
SIGNAL
CONDITIONING
ELECTRONICS
Figure 3.85: Pressure sensors use strain gages for indirect pressure
measurement
There are many ways of defining flow (mass flow, volume flow, laminar flow, turbulent
flow). Usually the amount of a substance flowing (mass flow) is the most important, and
if the fluid's density is constant, a volume flow measurement is a useful substitute that is
generally easier to perform. One commonly used class of transducers, which measures
flow rate indirectly, involves the measurement of pressure.
Flow can be derived by taking the differential pressure across two points in a flowing
medium - one at a static point and one in the flow stream. Pitot tubes are one form of
3.94
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
device used to perform this function, where flow rate is obtained by measuring the
differential pressure with standard pressure transducers.
Differential pressure can also be used to measure flow rate using the venturi effect by
placing a restriction in the flow. Although there are a wide variety of physical parameters
being sensed, the electronics interface is very often strain gage based.
Bridge Signal Conditioning Circuits
The remaining discussions of this section deal with applications that apply the bridge and
strain gage concepts discussed thus far in general terms.
An example of an all-element varying bridge circuit is a fatigue monitoring strain sensing
circuit, as shown in Figure 3.86. The full bridge is an integrated unit, which can be
attached to the surface on which the strain or flex is to be measured. In order to facilitate
remote sensing, current mode bridge drive is used. The remotely located bridge is
connected to the conditioning electronics through a 4-wire shielded cable. The OP177
precision op amp servos the bridge current to 10mA, being driven from an AD589
reference voltage of 1.235V. Current buffering of the op amp is employed in the form of
the PNP transistor, for lowest op amp self-heating, and highest gain linearity.
+15V
7
2 –
10mA
8
AD620
0.1µF
1kΩ
100Ω
1
–15V
VOUT
6
–3.500V = –3500µε
+5.000V = +5000µε
5
3 +
1kΩ
499Ω
4
100Ω
+15V
1.7kΩ
2N2907A
8.2kΩ
1kΩ
6
1kΩ
+15V
7
STRAIN SENSOR:
Columbia Research Labs 2682
Range: –3500µε to +5000µε
Output: 10.25mV/1000µε
+1.235V
30.1kΩ
124Ω
4
OP177
+
3
–15V
–
2
AD589
27.4kΩ
+15V
+1.235V
Figure 3.86: A precision strain gage sensor amplifier using a remote currentdriven 1kΩ bridge, a buffered precision op amp driver, and a precision in-amp
100X gain stage
3.95
BASIC LINEAR DESIGN
The strain gauge produces an output of 10.25 mV/1000 με. The signal is amplified by the
AD620 in-amp, which is configured for a gain of 100 times, via an effective RG of 500 Ω.
Full-scale voltage calibration is set by adjusting the 100 Ω gain potentiometer such that,
for a sensor strain of –3500 με, the output reads –3.500 V; and for a strain of +5000 με,
the output registers +5.000 V. The measurement may then be digitized with an ADC
which has a 10 V fullscale input range.
The 0.1µF capacitor across the AD620 input pins serves as an EMI/RFI filter in
conjunction with the bridge resistance of 1 kΩ. The corner frequency of this filter is
approximately 1.6 kHz.
Another example is a load cell amplifier circuit, shown in Figure 3.87. This circuit is
more typical of a bridge workhorse application. It interfaces with a typical 350 Ω load
cell, and can be configured to accommodate typical bridge sensitivities over a range of
3-10 mV/V.
A 10.000 V bridge excitation excitation is derived from an AD588 10 V reference, with
an OP177 and 2N2219A used as a buffer. The 2N2219A is within the OP177 feedback
loop and supplies the necessary bridge drive current (28.57 mA). This insures that the op
amp performance will not be compromised. The Kelvin sensing scheme used at the
bridge provides for low errors due to wiring resistances, and a precision zener diode
reference, the AD588, provides lowest excitation drift and scaling with temperature
changes.
+15V
+15V
2N2219A
7
1kΩ
6
350Ω
+
4
–15V
3
350Ω
16
13
3
AD588
9
– 2
–
1
8
1
AD621B or
AD620B
(see text)
8
3
5
+
11
475Ω 100Ω
+15
7
12
6 8 10
4
2
350Ω
–15V
1
+10.000V
OP177
+10.000V
350Ω
+15V
2
6
Use with
AD620
VOUT
0 TO +10.000V FS
4
–15V
350Ω LOAD CELL
100mV FS
Figure 3.87: A precision 350Ω load cell amplifier, using a buffered voltage-driven
configuration with Kelvin sensing and a precision in-amp
3.96
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
To ensure highest linearity is preserved, a low drift instrumentation amplifier is used as
the gain stage. This design has a minimum number of critical resistors and amplifiers,
making the entire implementation accurate, stable, and cost effective. In addition to low
excitation voltage TC, another stability requirement is minimum in-amp gain TC. Both
factors are critical towards insuring stable circuit scaling over temperature.
With the use of the AD621B in-amp as shown, the scaling is for a precise gain of 100 (as
set by the pin 1-8 jumper), for lowest in-amp gain TC. The AD621B is specified for a
very low gain TC, only 5 ppm/°C. The gain of 100 translates a 100 mV fullscale bridge
output to a nominal 10 V output. Alternately, an AD620B could also be used, with the
optional gain network consisting of the fixed 475 Ω resistor, and 100 Ω potentiometer for
gain adjustment. This will provide a 50 ppm/°C gain TC for the in-amp, plus the TC of
the external parts (which should have low temperature coefficients).
While the lowest TC is provided by the fixed gain AD621 setup, it doesn’t allow direct
control of overall scaling. To retain the very lowest TC, scaling could be accomplished
via a software auto-calibration routine. Alternately, the AD588 and OP177 reference/op
amp stage could be configured for a variable excitation voltage (as opposed to a fixed
10.000 V as shown). Variable gain in the reference voltage driver will effectively alter
the excitation voltage as seen by the bridge, and thus provide flexible overall system
scaling. Of course, it is imperative that such a scheme be implemented with low TC
resistances.
As shown previously, a precision load cell is usually configured as a 350 Ω bridge.
Figure 3.88 shows a precision load cell amplifier, within a circuit possessing the
advantage of being powered from just a single power supply.
+VS
2
6
(VREF)
10kΩ
28.7Ω
1kΩ
1kΩ
10kΩ
+5.000V
REF195
1µF
4
196Ω
2
350Ω
8
1/2
OP213
350Ω
3
350Ω
–
+
4
1
G = 100
6
5
–
1/2
OP213
+
7
VOUT
350Ω
Figure 3.88: A single-supply load cell amplifier
As noted previously, the bridge excitation voltage must be both precise and stable,
otherwise it can introduce measurement errors. In this circuit, a precision REF195 5 V
reference is used as the bridge drive, allowing a TC as low as 5 ppm/°C. The REF195
3.97
BASIC LINEAR DESIGN
reference can also supply more than 30 mA to a load, so it can drive a 350 Ω bridge
(~14 mA) without need of a buffer. The dual OP213 is configured as a gain-of-100, two
op amp in-amp. The resistor network sets the gain according to the formula:
G =1+
10 k Ω
20 k Ω
+
= 100
1k Ω 196 Ω + 28.7 Ω
Eq. 3-38
For optimum CMR, the 10 kΩ/1 kΩ resistor ratio matching should be precise. Close
tolerance resistors (±0.5% or better) should be used, and all resistors should be of the
same type.
For a zero volt bridge output signal, the amplifier will swing to within 2.5 mV of 0 V.
This is the minimum output limit of the OP213. Therefore, if an offset adjustment is
required, the adjustment should start from a positive voltage at VREF and adjust VREF
downward until the output (VOUT) stops changing. This is the point where the amplifier
limits the swing. Because of the single supply design, the amplifier cannot sense input
signals which have negative polarity.
If linearity around or at zero volts input is required, or if negative polarity signals must be
processed, the VREF connection can be connected to a stable voltage which is mid-supply
(i.e., 2.5 V) rather than ground. Note that when VREF is not at ground, the output must be
referenced to VREF. An advantage of this type of referencing is that the output is now
bipolar, with respect to VREF.
The AD7730 24-bit sigma-delta ADC is ideal for direct conditioning of bridge outputs,
and requires no interface circuitry (see Reference 10). A simplified connection diagram
was shown in Figure 3.77A (again). The entire circuit operates on a single +5 V supply,
which also serves as the bridge excitation voltage. Note that the measurement is
ratiometric, because the sensed bridge excitation voltage is also used as the ADC
reference. Variations in the +5 V supply do not affect the accuracy of the measurement.
The AD7730 has an internal programmable gain amplifier which allows a fullscale bridge
output of ±10 mV to be digitized to 16-bit accuracy. The AD7730 has self and system
calibration features which allow offset and gain errors to be minimized with periodic
recalibrations.
A "chop" or AC mode option minimizes the offset voltage and drift and operates
similarly to a chopper-stabilized amplifier. The effective input voltage noise RTI will be
approximately 40 nV rms, or 264 nV peak-to-peak. This corresponds to a resolution of 13
ppm, or approximately 16.5-bits . Gain linearity is also approximately 16-bits.
3.98
SENSORS
STRAIN, FORCE, PRESSURE AND FLOW MEASUREMENTS
REFERENCES: STRAIN, FORCE, PRESSURE AND FLOW
MEASUREMENTS
1.
Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New
York, 1991.
2.
Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0916550-05-2.
3.
Sections 2, 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN:
0-916550-10-9.
4.
Sections 1, 6, Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0916550-13-3.
5.
Harry L. Trietley, Transducers in Mechanical and Electronic Design, Marcel Dekker, Inc., 1986.
6.
Jacob Fraden, Handbook of Modern Sensors, 2nd Ed., Springer-Verlag, New York, NY, 1996.
7.
The Pressure, Strain, and Force Handbook, Vol. 29, Omega Engineering, One Omega Drive, P.O.
Box 4047, Stamford CT, 06907-0047, 1995. http://www.omega.com
8.
The Flow and Level Handbook, Vol. 29, Omega Engineering, One Omega Drive, P.O. Box 4047,
Stamford CT, 06907-0047, 1995. (http://www.omega.com)
9.
Ernest O. Doebelin, Measurement Systems Applications and Design, 4th Ed., McGraw-Hill, 1990.
10. Data sheet for AD7730 Bridge Transducer ADC, http://www.analog.com
3.99
BASIC LINEAR DESIGN
NOTES:
3.100
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