Variable Inductance Transducers
• These motion transducers employ the principle of electromagnetic
induction
• Types of variable inductance transducers include
• Mutual induction transducers
• Self-induction transducers
• Permanent magnet transducers
• Variable inductance transducers that use a non-magnetized ferromagnetic
medium to alter the reluctance of the flux path are known as variable
reluctance transducers
• Some mutual induction transducers and most self-induction transducers
are variable reluctance type
• But permanent magnet transducers are not variable reluctance type
Mutual Induction Transducers and
Differential Transformers
vo
Secondary
Coil
Core
Primary
Coil
• An AC excitation in the primary winding
induces an AC voltage in the secondary
winding
• The amplitude of the induced voltage
depends on the flux linkage between the
two coils
vref
• In mutual induction transducers change in the flux is effected by either
ƒ
Moving a ferromagnetic material on the flux path – LVDT, RVDT, mutual
induction proximity probe
ƒ
Moving one coil with respect to the other – resolver, synchro-transformer
Linear Variable Differential Transformer
vo
(Measurement)
Primary
Coil
Insulating
Form
Ferromagnetic Core
Secondary
Coil Segment
vref
Secondary
Coil Segment
vo
Voltage
level
Housing
Core
Displacement
x
(Measurand)
Displacement x
Linear
Range
LVDT Operation
vo
Secondary
Coil
Core
Primary
Coil
vref
• When the core moves the reluctance of the flux path changes and the degree of
flux linkage depends on the core position
• Since the two secondary windings are connected in series opposition, when the
core is at the centre the output is zero (null position)
• In the linear operating range o/p voltage is proportional to the core displacement
• It provides magnitude as well as the direction. Direction can be obtained by
• Demodulating the signal or
• Phase angle of the o/p signal
• To measure transient motions accurately the reference signal frequency has to
be at least 10 times larger than the largest freq. component of the measurand
Example 3.3
An equivalent circuit for a differential transformer is shown below. The resistance
in the primary winding is denoted by Rp and the magnetizing inductance is
denoted by Lm. The resistance of the secondary winding is Rs. The net leakage
inductance, due to magnetic flux linkage, in the two segments is denoted by Ll.
The load resistance is RL and the load inductance is LL. Derive an expression for
the phase shift in the output signal.
Ll
Rp
Rs
+
RL
Core
vo
~
LL
vref
−
Lm
Load
~
Primary Circuit
Secondary Circuit
x
Measurand
Signal Conditioning
Rectification
Carrier
Frequency
Generator
Displacement
(Measurand)
DC
Power Supply
Primary
Excitation
Rectifier
LVDT
Secondary Circuit
Output
DC
Amplifier
Low-Pass
Filter
Measurement
• AC output from the LVDT is rectified to obtain a DC signal
• Phase shift of the LVDT output has to be checked separately to determine
the direction of motion
Demodulation
DC
Power Supply
Carrier
Frequency
Generator
Phase Shift
Displacement
(Measurand)
LVDT
Amplitude
Matching
Demodulator
DC
Amplifier
Low-Pass
Filter
Measurement
• Carrier frequency component is rejected from the output signal by
comparing it with a phase-shifted and amplitude adjusted version of the
reference signal
• Differential transformers with built in signal conditioning are commonly
available today
• DC differential transformers have built in oscillators to generate the carrier
signal. The supply voltage is usually 25V and output voltage is 5V.
Example 3.4
R
x(t)
C
Carrier
Signal
v1
vp sinωct
+
v2
v3 R1
_
Output
vo
_
R2
+
R1
R1
LVDT
Amplifier
Multiplier
Low-pass Filter
1. Write equations for the amplifier and filter circuits and, using them, give
expressions for the voltage signals v1, v2, v3, and vo
2. Suppose that the carrier frequency is ω c = 500 rad s and the filter resistance
R = 100 kΩ . If carrier component to be less than 5% through the filter,
estimate the required value of the filter capacitance C. Also, what is the
useful frequency range (measurement bandwidth) of the system in rad/s,
with these parameter values?
3. If the displacement x(t) is linearly increasing (i.e., speed is constant), sketch
the signals u(t), v1, v2, v3, and vo as functions of time.
Signals at various levels
v2
v1
x(t)
t
t
t
vo
v3
t
t
Advantages of LVDTs
• Essentially non-contacting with no frictional resistance.
Near ideal electromechanical energy conversion and
light weight core result in very small resistive forces.
Hysteresis is negligible
• Low output impedance ~100Ω
• Directional measurements are possible
• Available in small size 1cm long with 2mm displacement
• Simple and robust construction (inexpensive and
durable)
• Fine resolutions are possible (better than potentiometer)
Rotatory Variable Differential Transformer
Measurement
vo
vo
Primary
Coil
Secondary
Coil
Rotating
Ferromagnetic
Core
(Measurand)
−40°
40°
Linear
Range
Secondary
Coil
vref
Voltage
level
Rotation
Variable Inductance Devices
•
Induced voltage is generated through the rate of change of magnetic
flux
•
Displacement measurements are distorted by velocity; Velocity
measurements are distorted by acceleration
•
For the same displacement, the transducer reading will depend on the
velocity at that displacement
•
This error is proportional to
(cyclic velocity of the core)/(carrier frequency)
•
Error rates can be reduced by increasing carrier frequency
Mutual Induction Proximity Sensor
Secondary
Coil
~
vo
(Measurement)
Primary
Coil
Secondary
Coil
vref
Ferromagnetic
Target Object
x
(Measurand)
Output Voltage
vo
Proximity
x
Usage of Mutual Induction Proximity Sensor
• Generally used to measure
• Transverse displacements
• Small displacements (nonlinear)
• Presence or absence
• Mechanical loading is negligible (non contacting)
• Applications include
• Robotic Measurement and control of the gap between a
robotic welding torch head and the work surface
• Angular speed measurement at steady state, by counting
the number of rotations per unit time
• Level detection (e.g., in the filling)
• Bottling plant to check whether the lid is placed
Proximity Sensor Applications
Machine Tools
Plating Line
Resolver
• Mutual induction transducer for measuring angular displacements
Output
Rotor
~
θ
Stator
AC
Supply
vref
Output
Stator
• Rotor has the primary winding and is energized by the supply voltage
• Stator has two sets of windings placed 900 apart
Supply voltage
v ref = v a sin ωt
Induced Voltages
vo1 = avref cos θ
v o 2 = av ref sin θ
The induced quadrate signals are
vo2 = ava sin θ sin ωt
vo1 = ava cosθ sin ωt
Multiply each quadrature signal by vref to get
1
vm1 = vo1vref = ava cos θ sin ω t = ava 2 cos θ [1 − cos 2ω t ]
2
1
2
2
v m 2 = vo 2 vref = av a sin θ sin ωt = av a 2 sin θ [1 − cos 2ωt ]
2
2
2
Low pass filter to obtain
1
2
v f 1 = ava cos θ
2
vf 2 =
1
ava 2 sin θ
2
Advantages
• Fine resolution and high accuracy
• Low output impedance
• Small size (10mm diameter)
Limitations
• Nonlinear output signals
• Bandwidth limited by supply frequency
• Slip rings and brushes would be necessary if multiple rotations to be
measured (a brushless resolver can eliminate this)
Synchro Transformer
Rotor
Rotor
AC
~ Supply
vref
Transmitter
Output
Receiver
(Control Transformer)
• Two identical rotor stator pairs
• Each stator has three sets of windings 1200 apart
• Transmitter rotor is energized with supply voltage. This induces voltages in
the three stator windings
• Since the windings of the transmitter stator are connected to the receiver
stator windings, a voltage is induced in the receiver rotor.
• If the angle between the drive rotor and a stator winding is θt the resultant
magnetic field on the receiver stator will make the same angle with the
corresponding stator winding.
• If the receiver rotor is aligned with this magnetic filed the induced voltage will
be maximum
• If the receiver rotor is at 900 to this resultant magnetic field then the induced
voltage will be zero.
vo = avref cos(θ t − θ r )
• Synchros are operated near θ r = θ t + 90 o where the output voltage is zero
θ r = θ t + 90 o − θ
v o = av ref sin θ