Self-Induction Transducers
• Coil is activated by the supply and the current produces a magnetic flux which is
linked with the coil
• The level of flux linkage (self-inductance) can be varied by moving a
ferromagnetic object within the magnetic field
AC
Supply
vref
~
Inductance
Measuring
Circuit
Ferromagnetic
Target Object
x
(Measurand)
Self-Induction Proximity Sensor
Permanent Magnet Transducers
• A permanent magnet transducer uses a permanent magnet to generate the
magnetic field
• A relative motion between the magnetic field and an electrical conductor
induces a voltage
• This voltage is proportional to the speed at which the conductor crosses the
magnetic field
• Depending on the configuration either rectilinear speeds or angular speeds
can be measured
Rectilinear
Permanent
Magnet
Moving Coil
Output
vo
(Measurement)
Velocity v
(Measurand)
v0  v
DC Tachometer (Angular Velocity)
Commutator
Speed
Permanent
Magnet
-
S
N
h
Rotating
Coil
vo
Rotating
Coil
+
2r
• The rotor is directly connected to the rotating object.
• The output signal that is induced at the rotating coil is picked up using a
commutator device (consists of low resistance carbon brushes)
• Commutator is stationary but makes contact with the split slip rings
• Generated voltage is (Faraday’s Law)
v0  2nhrBSint
Example 3.5
A dc tachometer is shown below. The field windings are powered by dc voltage
vf. Angular speed ω and torque Ti are the input variables. The output voltage vo
of the armature circuit and the corresponding current io are the output variables.
Obtain a transfer-function model for this device. Discuss the assumptions
needed to “decouple” this result into a practical input-output model for a
tachometer. What are the corresponding design implications? In particular
discuss the significance of the mechanical time constant and the electrical time
constant of the tachometer.
if
+
Rf
La
Ra
io
+
Tg
+
Inertia
(Output Port)
vf
J, b
Lf
vg
Ti 
vo
Damping b
-
-
Ti 
(Input Port)
J
vg  K i f  i
vg  K i
Tg  K i f io
Tg  Kio
Vo  Ki  Ra  sLa I o
dio
vo  v g  Ra io  La
dt
d i
Ti  J
 bi  Tg
dt
KI o  Ti  b  sJ i
Vo   K  Ra  sLa b  sJ  / K
I   
 b  sJ  / K
 o 
 Ra  sLa  / K  i 
 

1/ K
 Ti 
Permanent Magnet AC Tachometer
• When the rotor is stationary or moving in a quasi-static manner the output
voltage will be constant
• As the rotor moves, an additional voltage, proportional to the speed of the rotor
will be induced
• The output is an amplitude modulated signal proportional to the rotor speed and
demodulation is necessary
• Direction is obtained from the phase angle
AC
Carrier Source
vref
Output
vo
~
Primary
Stator
PermanentMagnet
Rotor
Secondary
Stator
• For low frequency applications (~5Hz), supply with 60Hz is adequate
• Sensitivity is in the range 50 – 100mV/rad/s
AC Induction Tachometer
• Similar in construction to an induction motor. Rotor windings are shorted.
• The induced voltage in the rotor windings is a modulated signal of the supply.
Modulation is due to the speed of the rotor.
• The output voltage on the secondary is a result of primary and rotor windings
and is supply modulated by the speed
AC
Carrier Source
vref
Output
vo
~
Primary
Stator
Shorted
Rotor Coil
Secondary
Stator
• Main advantage of AC tachometers is that they have no slip rings or brushes
Eddy Current Transducers
• Conducting materials when subjected to a fluctuating magnetic field produce
Eddy currents
• When a target object is moved closer to the sensor the inductance of the active
coil changes
• The two coils on the probe head form two arms of an inductance bridge
• The output of the bridge is amplitude modulated signal
Coaxial
Cable
Output
vo
Calibrating
Unit
Compensating
Coil
Impedance Bridge
Demodulator
Low-Pass Filter
RF Signal
(100 MHz)
Radio Freq.
Converter
(Oscillator)
20 V DC
Supply
(Measurand)
x
Target Object
Conducting
Surface
Active
Coil
Impedance Bridge
C
R2
R1
Compensating
Coil
L
Bridge Output
(to Demodulator)
RF Generator
~
L + ΔL
Active
Coil
C
R1
R2
• The bridge is balanced when there is no object
• The change in inductance creates an imbalance in the circuit and results in the
output signal
• The modulated signal needs to be demodulated to determine the displacement
• For large displacements output is not linearly related to the displacement
• Typical diameter of the probe is about 2mm (large 75mm)
• The target object has to be slightly larger than the frontal area of the probe
• Output impedance is about 1 kΩ (medium impedance)
• Sensitivity is around 5V/mm
• Range .25mm – 30mm
• Suitable for high transient (100 kHz) measurements
• Applications include
• Displacement
• Fault detection
• Metal detection
• Braking