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Sensors and Actuators
Introduction to sensors
Sander Stuijk
([email protected])
Department of Electrical Engineering
Electronic Systems
2
INDUCTIVE SENSORS
(Chapter 3.4, 7.3)
3
Inductive sensors
4
Inductive sensors
damping control
wheel speed
sensor (ABS)
crankshaft
position sensor
pedal position sensor
speedometer
(eddy current)
5
Sensor classification – type / quantity measured
Quantity
Resistive
S
e
n
s
o
r
Position, distance,
displacement
Flow rate /
Point velocity
Force
Temperature
Magnetoresistor
Thermistor
Strain gage
RTD
Potentiometer
Capacitive
Differential capacitor
Inductive and
electromagnetic
Eddy currents
t
y
p
Selfe
generating
Thermistor
LVDT
Hall effect
Capacitive strain
gage
Capacitor
Load cell + LVDT
LVDT
Magnetostriction
LVDT
Magnetostriction
Thermal
transport +
thermocouple
Piezoelectric
sensor
Pyroelectric sensor
Thermocouple
PN junction
Photoelectric sensor
Diode
Bipolar transistor
 reactance variation sensors (capacitive and inductive sensors)
 typically require no physical contact
 exert minimal mechanical loading
6
Magnetic reluctance
 electrical circuit may offer resistance to charge flow
 resistor: R
Vr
 resistor dissipates electrical energy
 current follows path of least resistance
 total resistance Rtot  R1  R2
 magnetic circuit may offer reluctance to magnetic flux
 reluctance: 
 reluctant circuit stores magnetic energy
 magnetic flux follows path of least reluctance
 total reluctance computed in similar way as
resistance in electrical circuit
tot 
1 2 3


 4
2
2
2
R1
R2
vo
7
Magnetic reluctance
 reluctance depends on physical properties of the device





1 l
0 A
l – length of the device
A – cross-sectional area
μ0 – permeability of free space (4x10-7 H/m)
μ – relative permeability of the material
 “soft” ferromagnetic material (typically 1000 to 10000)
 permeability of air (approx. 1)
 options to vary reluctance
 modify length l (variable gap sensor)
 modify magnetic permeability μ (moving core sensor)
 modify cross-sectional area A (not frequently used)
8
Magnetic reluctance
 reluctance depends on physical properties of the device

1 l
0 A
 sensor requires conversion of magnetic signal to electric signal
 Faraday’s law relates magnetic reluctance to electric current
N 2 di
di
v
L
 dt
dt
 change in reluctance changes output voltage
N2
 self-inductance L and reluctance are related: L 

 device can also be used as sensor without changing reluctance
 changing magnetic field causes electrons to move
 induces additional (eddy) current (eddy current sensor)
9
Variable gap sensor
 what is the output voltage (in terms of x) of a sensor with N
windings?
core 
lcore
core0 A
, object 
lobject
object0 A
, air 
total  core  object  2  air
x

air 0 A     lcore  lobject  2 x

total
core0 A object0 A  air 0 A


 reluctance of core and object are constant
0 
lcore

lobject
core0 A object0 A
 reluctance of the circuit
total  0 
2x
air 0 A
 0  kx
 self-inductance of the circuit
N2
N2
L

total 0  kx
 output voltage of the sensor
di
N 2 di
vL 
dt 0  kx dt
10
Variable gap sensor
 output voltage of the sensor
di
N 2 di
vL 
dt 0  kx dt
 highly non-linear relation between output and displacement x
 use of sensor limited to proximity sensor
11
Linear displacement transformer
 two coils in series, moving object
 increases reluctance in one coil
 decreases reluctance in other coil
x
ve
 circuit is differential voltage divider
 impedance of coil is equal to
vo
Z  jL


N
N 2 0 A
N2

L
 j
  Z  j


l
1 l 


0 A 
2
Z0/(1-x)
ve
 changing l with a relative amount x
N 2 0 A jL0
Z0
Z  j


l 1  x  1  x  1  x 
Z0/(1+x) vo
12
Linear displacement transformer
 two coils in series, moving object
 increases reluctance in one coil
 decreases reluctance in other coil
x
ve
 circuit is differential voltage divider
 output of the voltage divider
vo 
vo
Z 0 / 1  x 
1 x
ve 
ve
Z 0 / 1  x   Z 0 / 1  x 
2
 linear relation between output voltage
and displacement
 offset voltage present
 displacement (x) should be small
 sensor often not practical
Z0/(1-x)
ve
Z0/(1+x) vo
13
Mutual inductance
 self-inductance
 induced voltage due to change in own current
vL
di
dt
 mutual inductance
 induced voltage due to change in current in neighboring circuit
v2  L2
di2
di
M 1
dt
dt
 depends on reluctance of the space between the coils
M
 changing reluctance between coils
alters mutual inductance
 device usable as sensor
 two coil solution still not practical
(large offset, small fluctuation)
v1
i2
i1
L1
v2
L2
Linear Variable Differential Transformer
14
 Linear Variable Differential Transformer (LVDT)
 two secondary coils in series-opposition
 linear relation between output voltage and core displacement
 operation based on mutual inductance
|v0|
M1
L2
v1
vo
L1
L’2
M2
x
x
linear range
Linear Variable Differential Transformer
15
 assume sinusoidal excitation of primary circuit
v1 (t )  V1 sint 
 output voltage of secondary circuit
vo (t )  S  x V1 sint   
 Sω – sensitivity at frequency ω
 x – displacement of the core from center
 φ – phase shift (in voltage) from primary to secondary circuit
M1
L2
v1
L1
L’2
M2
x
vo
 Sω and φ depend on
 load RL of measurement circuit
 excitation frequency ω
 phase shift can be compensated
Signal conditioning for LVDT sensors
16
 output signal of LVDT is amplitude modulated ac signal
vo (x = x0)
t
vo (x = 2x0)
t
amplitude indicates
magnitude of
displacement
phase indicates direction of
displacement
M1
L2
v1
L1
L’2
M2
x
vo (x = -2x0)
vo
t
Linear Variable Differential Transformer
17
 output voltage (no load connected to secondary winding)
 no current in secondary circuit (I2 = 0)
V1

jL1  R1   V  j M 2  M 1 V1
o
jL1  R1
Vo  I1  jM1  jM 2   jM 2  M1 I1 

M 2  M1   k x x
V1  I1 R1  jL1   I1 

jk x xV1


V

j

k
xI


o
x
1
jL1  R1


 primary current I1 independent of core position
 output voltage Vo proportional to core position
M1
R1
L2
v1
L2
vo
v1
L1
R2
M1
i1 L
1
M3
L’2
M2
L’2
M2
x
x
vo
R’2
18
Linear Variable Differential Transformer
 output voltage (no load connected to secondary winding)
Vo  jk x xI1 
jk x xV1
jL1  R1
 sensitivity
S
Vo V1
x

jk x

jL1  R1
kx
L1 
R1
j
kx

L1  j
R1

kx
L 
2
1

R12
2
 sensitivity increases with increasing frequency
 phase shift
 output voltage 90° out of phase
with primary current
v1
 phase shift between V1 and V0
  90  arctan
R2
M1
R1
L2
i1 L
1
M3
L1
R1
 consider phase shift when recovering position
L’2
M2
x
vo
R’2