Lecture9:Instrumentation 1
Induction
Faraday's law of induction: the induced
voltage, or electromotive force (e.m.f.), is
equal to the rate at which the magnetic flux
through the circuit changes.
Inductance = phenomena where an e.m.f. is
induced in it by a variation of current either in
the circuit or in a neighbouring circuit
Lecture9:Instrumentation 2
To increase inductance,
the conductor can be
formed into a loop or coil
Current through one loop
produces a magnetic field
that encircles the loop
As current increases, the
magnetic field expands
and cuts all the loops -
The current in each loop
affects all other loops
The field cutting the other
loop has the effect of
increasing the opposition
to a current change
Lecture9:Instrumentation 3
In magnetic circuit, reluctance ℜ is a measure of how
the circuit opposes the flow of magnetic flux
2
n
Inductance L=
ℜ
where n = number of loops or turns
l
ℜ=
µµ 0 A
With l = length
A = Area of cross-section
µ = core permeability
µ0 = 4π×10-7 Hm-1= free space permeability
Lecture9:Instrumentation 4
Variable reluctance sensor
Lecture9:Instrumentation 5
Also known as variable inductance transducer
or variable permeance transducer
If a permeable core moves through coil, the
inductance increases where the value of
inductance depends on the position of the core
Usually for displacement sensor
Often used in bridge circuit with an a-c
excitation voltage
Lecture9:Instrumentation 6
This variable-reluctance displacement sensor changes the inductance in a
coil in response to core motion.
Curtis Johnson
Process Control Instrumentation Technology, 8e] Copyright ©2006 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Lecture9:Instrumentation 7
Lecture9:Instrumentation 8
Example 1
The inductive transducer is to measure
displacement.Given: core permeability µc and armature
permeability µA = 100, air permeability µa =1, n = 500, R
= 2 cm, core radius r = 0.5cm, armature thickness is t =
0.5 cm. Determine reluctance ℜ and inductance L if
a) gap d = 0 b) gap d = 1 mm
Lecture9:Instrumentation 9
John P. Bentley
Principle of Measurement Systems, 4ed.
Lecture9:Instrumentation 10
Solution Example 1
Reluctance is given by:
l
ℜ=
µµ0 A
Total Reluctance within the system:
ℜtotal = ℜcore + ℜarmature + ℜgap
Core Reluctance:
l πR = π(2 × 10-2 )
ℜcore = =
µµ A µµ πr2 (100)(4π × 10−7)π(0.5×10−3)2
0 0
Lecture9:Instrumentation 11
Solution Example 1
π(2 × 10-2 )
=
(100)(4π × 10-7)π(0.5×10-3)2
= 6.37 × 106 H-1
Armature Reluctance:
l 2R
ℜarmature = =
µΑµΟ A µΑµΟ2rt
(2 × 10-2 )
=
(100)(4π × 10-7) (0.5×10-3)(0.5×10-3)
= 6.37 × 106 H-1
Lecture9:Instrumentation
12
Solution Example 1
Gap Reluctance:
l 2d
ℜgap = =
µ ΟΑ µΟπr2
(a) If d = 0,
ℜgap = 0
So,
ℜtotal = 6.37 × 106 + 6.37 × 106 = 12.73 × 106 H-1
Inductance,
L = n2/ℜ = (500)2/ 12.73 × 106 = 9.6mH
Lecture9:Instrumentation
13
Solution Example 1
(a) If d = 1mm,
2d 2(1 × 10-3 )
ℜgap = = = 2.03 × 107 H-1
µΟπr2 (4π × 10-7) π(0.5×10-2) 2
So,
ℜtotal = 6.37 × 106 + 6.37 × 106 + 2.03 × 107 = 3.30 × 107 H-1
Inductance,
L = n2/ℜ = (500)2/ 3.30 × 107 = 7.6mH
Lecture9:Instrumentation
14
Linear Variable Differential Transformer
• An LVDT transducer comprises a coil former or
bobbin onto which three coils are wound
• The first coil, the primary is excited with an a.c.
current, normally in the region of 1 to 10kHz at 0.5
to 10V rms
• The other two coils, the secondaries are wound
such that when a core is in the central linear
position, an equal voltage is induced into each coil
• The secondaries are connected in opposition so
that in the central position the outputs of the two
secondaries cancel each other out.
Lecture9:Instrumentation 15
FIGURE 5.6 The LVDT has a movable core with the three coils as shown.
Copyright ©2006 by Pearson Education, Inc.
Curtis Johnson
Upper Saddle River, New Jersey 07458
Process Control Instrumentation Technology, 8e] All rights reserved.
Lecture9:Instrumentation 16
Lecture9:Instrumentation 17
• The core (the moving part) assists the induction of current into Sec.
1 and Sec. 2
• The permeable core - a special magnetic material, connected to a
push rod (nonmagnetic) that connects core to the outside world
• Core in central, an equal voltage induced Sec.1 and Sec. 2
• As they are wired in opposition, the sum of the position sensor
secondary outputs cancel each other out resulting in a zero output
• As the core moves into Sec.1 (and out of Sec. 2), the sum of Sec.1
and Sec. 2 favours Sec.1, is in-phase with the excitation voltage
• As the core moves into Sec. 2 (and out of Sec.1) the sum favours
Sec. 2 (the out-of-phase voltage)
Lecture9:Instrumentation 18
LVDT
Lecture9:Instrumentation 19
• The output is an a.c. waveform
• The magnitude of the output of the transducer rises
regardless of the direction of movement from the electrical
zero position
Lecture9:Instrumentation 20
The LVDT secondary voltage amplitude for a series-opposition connection
varies linearly with displacement.
Copyright ©2006 by Pearson Education, Inc.
Curtis Johnson
Upper Saddle River, New Jersey 07458
Process Control Instrumentation Technology, 8e] All rights reserved.
Lecture9:Instrumentation 21
This simple circuit produces a bipolar dc voltage that varies with core
displacement.
Copyright ©2006 by Pearson Education, Inc.
Curtis Johnson
Upper Saddle River, New Jersey 07458
Process Control Instrumentation Technology, 8e] All rights reserved.
Lecture9:Instrumentation 22
Types:
• Linear Variable
Differential Transformer
(LVDT)
• Rotary Variable
Inductive Transformer
(RVIT)
Lecture9:Instrumentation 23
Common part of LVDT (inside)
Lecture9:Instrumentation 24
Inductive pressure transducer
Lecture9:Instrumentation 25
Examples of LVDT
Lecture9:Instrumentation 26
Inductive Sensors - LVDT
An LVDT is used as a sensitive displacement sensor: for example, in
a cardiac assist device or a basic research project to study
displacement produced by a contracting muscle.
LVDT
Linear Variable
Differential
Transformer
Taken from
http://www.pages.drexel.edu/~pyo22/mem351-2004/lecture04/pp062-073lvdt.pdf
Lecture9:Instrumentation 27
servo force balance
- suitable for high
pressure and high
accuracy
measurement
-Not suitable to for
varied pressure
measurement
Lecture9:Instrumentation 28
End of Lecture 9
Lecture9:Instrumentation 29
