sensors and actuators introduction to sensors · 5 potentiometer resistance of a material given by...
TRANSCRIPT
Department of Electrical Engineering
Electronic Systems
Sensors and Actuators Introduction to sensors
Sander Stuijk
2
DISPLACEMENT SENSORS (Chapter 7.1)
3 Applications
4 Sensor classification
sensor type quantity physical effect sensor
resistive displacement resistance potentiometer
inductive
displacement reluctance variable differential
transformer
inductive displacement Joule effect, Villari effect,
Wiedemann effect, Matteucci
effect
magnetostrictive
electromagnetic velocity Hall effect Hall effect
electromagnetic velocity Faraday’s law linear velocity
capacitive acceleration capacitance variable capacitor
capacitive acceleration capacitance differential capacitor
5 Potentiometer
resistance of a material given by
ρ – resistivity of material
l – length
A – cross-sectional area of material
change in the length changes the resistance of the material
A
lR
potentiometer (pot) is a variable resistor
pot wiper mechanically coupled to object
whose displacement must be measured
movement (linear or rotation) of object
causes change in resistance
6 Potentiometer
output voltage proportional to displacement
output voltage does not depend on the resistance RT
potentiometer is a ratio metric device
Vr
(1-α)RT
αRT vo dD
rr
T
Tr
T
To V
D
dV
DR
dRV
R
Rv
rr
T
Tr
TT
To VV
R
RV
RR
Rv
1
7 Potentiometer
output voltage proportional to displacement
what happens when a load Rm is connected to the sensor?
Thévenin equivalent circuit
open circuit voltage
output resistance
voltage across load
rr
T
Tr
TT
To VV
R
RV
RR
Rv
1
Vr
(1-α)RT
αRT Rmvm
Ro
Rmvovm
rr
T
To VV
R
Rv
T
TT
TTo R
RR
RRR
1
1
1
TTo RRR 1//
r
Tm
mo
om
mm V
RR
Rv
RR
Rv
1
8 Potentiometer
output voltage proportional to displacement
what happens when a load Rm is connected to the sensor?
voltage across load
sensor becomes linear when k >> 1(Rm >> RT)
relative error of the sensor
relative error depends on position of the wiper (i.e. it depends on α)
no error at the ends of the scale
rr
T
Tr
TT
To VV
R
RV
RR
Rv
1
r
Tm
mm V
RR
Rv
1
Tm RRk rm V
k
v
11
1
1
1
1
1
1
11
kkk
kk
V
VVk
k
v
vv
r
rr
o
om
9 Potentiometer
when is the maximal relative error reached?
maximal error reached when
maximal error
increasing load resistor decreases error
error is symmetrical around the center
0
d
d
21
211211
1
1
k
k
kd
d
d
d
21
21
k
k
d
d
2
1021
2v
d
dvu
d
duv
v
u
d
d
recall that
α
ε
k=1 25.0
25.0
1
15.0max
kk
10 Potentiometer – loading error
relative error (loading error) can be decreased by
increasing load resistor Rm
placing a resistor equal to Rm at the top side of the potentiometer
what is the output voltage of the sensor?
two options to compute output voltage
use Thévenin equivalent circuit
output voltage is voltage divider of two pair of parallel resistors
with
Vr
(1-α)RT
αRT Rmvm
Rm
r
xy
y
m VRR
Rv
mT
mTmTx
RR
RRRRR
1
1//1
mT
mTmTy
RR
RRRRR
//
11 Potentiometer – loading error
relative error (loading error) can be decreased by
increasing load resistor Rm
placing a resistor equal to Rm at the top side of the potentiometer
what is the output voltage of the sensor?
output voltage at α = 0.5
Vr
(1-α)RT
αRT Rmvm
Rm
r
xy
y
m VRR
Rv
T
m
R
Rk
r
mT
TTmm V
RR
RRRv
12 rm V
k
kv
12
1
rrm VVk
kv
2
1
5.0
5.05.05.0
additional resistor Rm enforces
vm = Vr/2 at central position
zero error at this point
12 Potentiometer – loading error
example – set zero error at any desired point
which value must R1 and R2 have such that a wiper displacement
of ±15% of its stroke around the position corresponding to ¼ of
the full-scale value produces a change in voltage of only 10% with
respect to the full-scale voltage?
use a = RT/R1 and b = RT/R2
Vr
(1-α)RT
αRT R2va
R1
r
TT
Ta V
RRRR
RRv
1////
//
12
2
r
T
T
T
T
T
T
V
RR
RR
RR
RR
RR
RR
1
1
1
1
2
2
2
2
r
TTTT
TT VRRRRRRRR
RRRR
2112
12
11
1
rm V
ba
av
1111
11
rm V
ba
av
11
11
13 Potentiometer – loading error
example – set zero error at any desired point
which value must R1 and R2 have such that a wiper displacement
of ±15% of its stroke around the position corresponding to ¼ of
the full-scale value produces a change in voltage of only 10% with
respect to the full-scale voltage?
two constraints
1) at α = 0.25 + 0.15 it must hold that va = (0.25 + 0.05)Vr
2) at α = 0.25 - 0.15 it must hold that va = (0.25 - 0.05)Vr
constraints imply
solving constraints yields
this implies
Vr
(1-α)RT
αRT R2va
R1
ba
a
625
1063.0
ba
a
990
1092.0
5.3a 6.9b
TRR 29.01 TRR 10.02
14 Potentiometer – loading error
relative error (loading error) can be decreased by
increasing load resistor Rm
placing a resistor equal to Rm at the top side of the potentiometer
using a symmetrical voltage supply
what is the output voltage of this sensor?
use Kirchhoff current law
solving this yields
error is zero at end of the wiper (α = 0, α = 1)
error is zero at central position (α = 0.5)
Vr (1-α)RT
αRT
Rm
vmVr
T
mr
T
mr
m
m
R
vV
R
vV
R
v
10
k
Vv r
m
11
12
15 Potentiometer – lead-wire resistance
3-wire circuit output voltage
assume k >> 1, hence loading error is negligible
output at α = 0
output at α = 1
circuit has two errors
reduced sensitivity
offset voltage
due to current
through Rw3
(1-α)RT
αRT
Rw1
Vr
vm
Rw2
Rw3
r
wwT
wm V
RRR
Rv
31
30
r
wwT
wTm V
RRR
RRv
31
31
1
10α
vm/Vr ideal output
real output
16 Potentiometer – lead-wire resistance
4-wire circuit output voltage
assume k >> 1, hence loading error is negligible
output at α = 0
output at α = 1
no offset voltage
sensitivity equal to 3-wire circuit
00 mv
r
wwT
Tm V
RRR
Rv
41
1
(1-α)RT
αRT
Rw1
Vr
vm
Rw2
Rw3
Rw4
1
10α
vm/Vr ideal output
real output
17 Potentiometer – construction
construction: wire wound around a coil
problem: wiper makes contact with 1 or 2 wires
results in uneven voltage steps
sensor has a variable resolution
resolution: smallest change in input
stimulus which can be sensed
consider average resolution when
computing displacement
construction: high-quality resistive film
theoretically an infinitesimal resolution
resolution limited by
noise in circuit
non-uniformity of material
18 Potentiometer
pro’s and con’s of potentiometers
(+) cheap
(+) simple concept
(+) no complicated processing circuits needed
(-) physical coupling to object needed
noticeable mechanical load
wear on the device
friction causes heating error
(-) excitation voltage causes heating error
(-) limited resolution
(-) substantial non-linearity error