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RESISTIVE TRANSDUCERS
Lecture 11Instructor : Dr Alivelu M Parimi
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RESISTIVE
POTENTIOMETERS Loading Effect of Potentiometers
The usual situation with use of potentiometer is that output
voltage is fed to a meter or recorder that draws some current
from the potentiometer. Thus a more realistic circuit is as
shown in Figure
2
Schematic of Loaded
Potentiometer
Using concept of voltage divider concept,
K1mK1
K
R||RRR
R||R
e
e
xmxp
xm
ex
0
where
K =m
p
t
i
p
x
R
Rm&
x
x
R
R
When K = 0, i.e. x i=0, e0= 0 V , wiper is on one extreme [negative side of supply] and
whole of eexis dropped across resistor.
When K=1, i.e. xi = xt, e0 = eex, wiper is on other extreme [ positive side of supply ] and
whole of supply is tapped
Choice of Rp thus must be influenced by a
tradeoff between loading and sensitivity
considerations
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RESISTIVE
POTENTIOMETERS
3
Rm = detector is of infinite impedance( ideal detector) i.e. m = 0 ; Ke
e
ex
0
When m = 0 , input-output curve is a straight line and e0is open circuit voltage.
When Rm , m >0 , there is a nonlinear relation between e0 and xi. This deviation from
linearity is shown in Figure 4.3.
Error = (output voltage under no load) - ( output voltage at loaded condition )
= eex.K - K1mK1K.eex
=
m
KK
KKeex1
1
12
At K = 0 and K = 1, error = 0. At all other points error is positive, since voltage of loaded
potentiometer is less than unloaded potentiometer. The position of wiper at which maximum
error occurs could be found by differentiating error expression w.r.t. K. For all values of m,
maximum error is encountered for values of K around 0.6 - 0.7.
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RESISTIVITE
POTENTIOMETERS
4
A variable pot has a total resistance of 2.2 kand is fed from 10 V DC supply. The output is
connected to a load resistance of 5.1 k. Tabulate errors for wiper positions from 0 to 1.0 in
increments of 0.1
Error = eex.
p
m
2
R
RK1K
1KK
K 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Error/Eex 0 0.037 0.013 0.25 0.37 0.48 0.573 0.58 0.52 0.3363 0.0
It may be observed that maximum error is for K between 0.7 and 0.8
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Resolution of Potentiometers
The resolution of potentiometer is strongly influenced by the
construction of the resistance element.
A single slide-wire as the resistance element gives an
essentially continuous step less resistance variation as the
wiper travels over it.
Slide wire resistance elements, also called non-wire wound
resistance elements provide improved resolution and life;
however, they are more temperature-sensitive, have a high
wiper contact resistance.
Elements of both cermet and conductive plastic are available
in the form of flat strips or films and thus present a smooth
surface to the wiper. They are conventionally described as
having infinitesimal resolution.5
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Resolution of Potentiometers
To get sufficiently high resistancevalues in small space, the wire woundresistance element is widely used.
The resistance wire is wound in amandrel or card which is then formed
into a circle or helix if a rotationaldevice is desired as shown in Figure
With such a construction the variation
of resistance is not a linear continuouschange, but actually proceeds in smallsteps as the wiper moves from oneturn of the wire to the next as shownin figure 6
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Resolution of Potentiometers
This phenomenon results in a fundamental limitation on the resolutionin terms of resistance-wire size.
For instance, if a translational device has 500 turns of resistance wire ona card 1 inch long, motion changes smaller than 0.002 inch cannot bedetected. The actual limit for wire spacing according to current practiceis between 500 and 1,000 turns per inch. For translational devices,
resolution is thus limited to 0.001 to 0.002 inches. Another approach to increased resolution involves the use of multiturn
potentiometers.
The resistance element is in the form of a helix, and the wiper travelsalong a lead screw. The number of wires per inch of element is stilllimited, but an increase in resolution can be obtained by introducinggearing between the shaft whose motion is to be measured and thepotentiometer shaft.
For example, one rotation of the measured shaft could cause 10rotations of the potentiometer shaft; thus the resolution of measured-shaft motion is increased by a factor of 10.
For translational devices, various motion-amplifying mechanisms couldbe used in similar fashion.
7
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Example
8
Suppose we have two resistors of 10 and 330 both having power rating of 0.25W. I
both resistors are connected to 6V battery then power dissipated by 330 resistor is PD=
W109.0330
66
R
V 2
and power dissipated by 10 resistors is
10
66= 3.6W.
Then 10 resistor will burn, since power dissipated by it exceeds its rated capacity. Smaller
resistance will carry more current and burnout (principle used in fuse)
A control potentiometer is rated as 150 Ohm, 1W (derate at 10 mW/oC above 65
oC).
Thermal resistance is 30oC/W. Can it be used with a 10V supply at 80
otemperature?
Problem
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RESISTANCE STRAIN GAGES
Strain measurement is generally used for testing the performance ofa particular device when subjected to vibration, bending,compression and tension, torque etc.
They are used in industry, aerospace, medical, automotive sector,material testing research etc
. Strain Gages in general are applied in two types of tasks, one ofthem being experimental stress analysis of machines and structuresand the other being in the development of force, torque, pressure,flow and acceleration transducers.
Strain Gage works on the basic principle of change in the resistanceupon application of strain.
Both Strain Gages and Potentiometer are resistive transducers. Thebasic difference is that Potentiometer resistance is varied manuallyor automatically by wiper motion, while Strain Gages exhibitschange in resistance by mechanical deformation or stress. 9
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RESISTANCE STRAIN GAGES
10
Consider a conductor of uniform cross sectional area A and length L, as shown in Figure 4.7.
Fig. 4.7: Wire with length L and area of cross--section A
It is made of a material with resistivity () and the resistance R of such a conductor is given
by
R =A
L
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Basic Concepts, RESISTANCE
STRAIN GAGES
11
If this conductor is now stretched or compressed, its resistance will change because of
dimensional changes (length and cross sectional area) and because of a fundamental property
of materials called piezoresistance which indicates a dependence of resistivity () on the
mechanical strain. R depending on the basic parameters. Taking natural logarithmic and
differentiating expression of resistance. To find expression for sensitivity of gage, it is
required to findL/dL
R/dRwhich is fractional change in resistance per unit applied strain.
ln R = ln + ln Lln A
A
dA
L
dLd
R
dR
R =A
L
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12
A
dA
L
dLd
R
dR
D
dD2
A
dA;
L/dL
/d
L/dL
A/dA1
L/dL
R/dR
= Poissons ratio =L/dL
D/dD
soL/dL
R/dR= 1 + 2+
L/dL
/d
L/dL
R/dR
is called Gage factor, so
Gage factor =
effectcepiezoresistoduechangeceresischangeareatodue
changeceresis
changelengthtodue
changeceresisLdL
d
LdL
RdR
tantan
tantan/
/21
/
/
Basic Concepts, RESISTANCE
STRAIN GAGES
This is the principle of the resistance gage. The termLdL
d
/
/can also be expressed as ,E
where is the longitudinal piezoresistance and E is the modulus of elasticity. Poissonsratio is always between 0 and 0.5 for all the materials.
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Strain Gages
Desirable features of Strain Gages are:
High value of gage factor which will lead to enhanced
sensitivity
High Gage resistance to minimize the effects of
undesirable variation of resistance in measurement circuitry(connecting leads, terminals, etc.)
Linear relationship between resistance vs strain
Good spatial resolution, ideally measuring strain at a
point Insensitive to changes in ambient temperature
High frequency response for dynamic strain
measurements 13
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Problem
14
A Strain Gage is bonded to a steel beam which is 10 cm long having cross-sectional area o
4 cm2. Youngs modulus of elasticity (Ysteel) is 20.7 x 10
102m
N.
Gage resistance is 240 ,
Gage factor is 2.2. Upon application of load, resistance changes by 0.0013 . Calculate the
change in length and amount of force applied.
Solution
=L
Land Gage factor = 2.2
L/L
R/R
m
m
L
L 61046.22.2
240/0013.0
Y = Youngs Modulus =Strain
Stressso Stress = Y.= (20.7 x 10
10) N/
m
2( 2.46 x 10
-6)
= 50.922 x 104
2m
N
F = Stress x Area = (50.922 x 104 2mN )x ( 4 x 10-4m2)= 203.688 N
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Classification of Strain Gages
Unbonded Metal Wire Gage
Bonded Metal Wire Gage
Bonded Metal Foil Gage
Vacuum Deposited Thin Metal Film Gage.
Sputter Deposited Thin Metal Film Gage.
Bonded Semiconductor Gage
Diffused Semiconductor Gage 15
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The Unbonded Metal Wire
Gage
16
It employs a set of preloaded resistance wires
connected in a Wheatstone Bridge
configuration as shown in the Figure
At the initial preload resistance the strains and the resistances of the four wires are nominally equal, which gives a
balanced bridge, and e0 = 0. Application of a small input motion increases the tension in the two wires ( 1 & 3) and
decreases in the other two ( 2& 4) causing corresponding resistances to change and making the bridge unbalanced. The
output voltage of bridge being proportional to the input motion.
The wires may be made of various Copper-Nickel, Manganin, Chrome Nickel, or Nickel-Iron alloys.
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The Bonded Metal-Wire Gage
A grid of fine wire is cemented to the specimen surface where
the strain is to be measured.
Embedded in the matrix of cement, the wires cannot buckle
and thus faithfully follow both the tensile and the compressive
strains of the specimen. Since materials and wire sizes are similar to those of the
unbonded gage, gage factors and resistances are comparable.
17
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The Bonded Metal-Foil Gage
Bonded Metal Foil Gages use identical or similar materials to
wire gages that are used today for most general purpose
stress analysis tasks and many transducers. The sensing
elements are formed from sheets less than 0.0002 inches
thick by Photoetching process which allows greater flexibilitywith regard to the shape. The various shapes of this type of
the Strain Gage
18
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Evaporation-deposited and sputtering -
deposited thin-metal film gages
Thin-film gages exhibit improved time and temperature
stability.
Both evaporation-deposited and sputter-deposited form all
the gage elements directly on the strain surface; they are not
separately attached as with bonded gages. Resistances and gage factors of film gages usually are similar
to those of the bonded foil strain gages.
19
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To study
Bonded Semiconductor Gage
Diffused Semiconductor Gage
20
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Strain Gage Bridge
Arrangements Strain Gage Bridge Arrangements
Quarter Bridge
Half Bridge
Full bridge
21
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Problem
A resistance strain gage having gage factor 3.5 has
contribution of 1.7 due to piezoresistive effect. Calculate the
contribution of Poissons ratio in Gage Factor.
22
Solution
(G.F.) = 1 + 2 + E
2 = (G.F.)1E
= 3.511.7 = 0.8
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Problem
Strain Gage with gage resistance of 350and gage factor of 2
is used in Wheatstone Bridge with resistances of other three
arms being 350. If strain of 1450 microns is applied, find the
bridge output voltage if excitation voltage is 10V.
23
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Bonded Semiconductor Gage
strain sages depend on the piezoresistive effects of Silicon or
Germanium and measure the change in resistance with stress
as opposed to strain. The semiconductor bonded strain gage is
a wafer with the resistance element diffused into a substrate
of Silicon. The wafer element usually is not provided with abacking, and bonding it to the strained surface requires great
care as only a thin layer of epoxy is used to attach it as shown
in Figure
24
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Strain Gage Bridge
Arrangements Strain Gage Bridge Arrangements
Quarter Bridge
Half Bridge
Full bridge
25
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Quarter Bridge
26
Quarter Bri dge
The strain gage bridge circuit shown in Figure 4.14, in which one arm is occupied by strain
gage is known as Quarter Bridge. The strain gage may be measuring deflection caused by
orce, pressure, vibration, torque etc.
Fig. 4.14: Quarter Bridge Strain Gage Circuit
Physical realization of this is shown in Figure 4.15, where strain gage bonded on cantilever
orms one arm of the bridge.
Fig. 4.15 : Quarter Bridge Arrangement for Cantilever Beam
We analyze this circuit for finding the expression for output voltage in terms of change in
resistance.
Assume RRRR 321
Voltage source = Vs
Output voltage = Vo
If due to tensile force strain gauge resistance changes to RR
2
1
RR2
RRVV so
RR22
RR2R2R2Vs
R2R4
RVs
if RR ,
R
RVV so
4 ( as 2R
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Half Bridge
27
The strain gage bridge circuit shown in Figure 4.16, in which two arms are occupied bystrain gages is known as Half Bridge .
Fig. 4.16 : Half Bridge Strain Gage Circuit
Physical realization of half bridge is shown in Figure 4.17, where strain gages bonded on
pper and lower side of cantilever form two arms of the bridge. Figure 4.17(a) shows the
cantilever under no load leading and corresponding balanced bridge. Figure 4.17(b) shows
he loaded beam and unbalanced bridge.
Suppose one strain gauge(upper one ) undergoes tension RR and the other(lower one)
undergoes compression, RR
Voltage source = Vs
Output voltage = V0
2
1
R2
RRVV
so
R
RRR
2
Vs
R
R
2
Vs
output voltage is directly proportional to R, resulting in linear relationship between V0and
R.
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Full bridge
28
Figure 4.18 shows the Full bride circuit in which all the arms of the bridge are constituted by
active strain gages. One possible physical arrangement of strain gages can be thought of as:
wo strain gages on the upper side of cantilever undergoing tension, and the two on lower
side of cantilever beam undergoing compression.
Fig. 4.18 : Full Bridge Strain Gage Circuit
Voltage source = Vs
Output voltage = Vo
R2
RR
R2
RRVV so
R2R2
Vs
R
RVs
It can be observed that Sensitivity of Quarter bridge < Half bridge< Full bridge.
Full bridge always gives linear output while for quarter bridge and half bridge where the two
arms are occupied by opposite arms, linear relationship is attained only for small changes in
R .