Linear Variable Differential Transformer
Linear Variable Differential Transformer (LVDT) are transducers most widely
used to translate linear motion to electrical signals, they can resolve very
small displacements as for their high resolution, high accuracy and good
stability.
-LVDT is considered as passive transducer, because the measured
displacement provides energy for “changing” the induced voltage.
-Even though……..
…………..An external power supply is used to energize the primary coil, which
in turn induces a steady voltage at the carrier frequency in the secondary coil
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
1
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
2
LVDT Operation
-The LVDT consists of an insulating, nonmagnetic form, which has a primary P1 in
the mid –segment and a secondary coil S1 and S2 symmetrically wound in the two
end segments.
-The housing is made of magnetized stainless steel in order to shield sensor from
outside fields .
-The primary coil is energized by an AC supply of voltage.
-This generates the mutual induction, an AC of the same frequency in the secondary
coil.
-The core is made of ferromagnetic material is inserted coaxially through the
cylindrical form without touching it.
-As the core moves, the reluctance of the flux path changes
The degree of flux linkage depends on the axial position of the core
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
3
Let the output of the secondary S1 be ES1 And that of S2 be ES2.
When the core is at its normal null position, equal voltages are induced in both
coils.
When the secondary coils outputs are connected in phase opposition, the
magnitude of the resultant voltage will be zero output ES1 will be equal to ES2.
As the moving core is displace, the mutual inductance between the fixed coils
changes.
The LVDT outputs a bipolar voltage proportional to displacement
The output signal describes both the magnitude and the direction of the core
motion.
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
4
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
5
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
6
- The two secondary coils are connected in series opposition.
- The potentials induced in the two secondary coil segments oppose each other.
The net induced voltage is zero when the core is centered between the two
secondary winding segments. This is called the null position
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
7
-When the core is displaced from the null position.
-A nonzero induced voltage will be generated
-The amplitude V0 of this induced voltage is proportional to the core
displacement x in the linear region
V0 May be used to measure the displacement
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
8
-The output signal from the differential transformer is normally not in phase with
the reference voltage.
-Inductance in the primary coil and leakage inductance in the secondary coil are
mainly responsible for this phase shift.
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
9
There is a midpoint in the core’s position where the voltage induced in each coil is
the same in amplitude and 180O out of phase producing a null output
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
10
• As the core moves from the null position, the output amplitude increases a
proportional amount over a linear range around the null.
• By measuring the output voltage amplitude, we can easily and accurately
determine the magnitude of the core displacement.
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
11
To determine the direction of the core displacement
• the secondary coils can be connected to a demodulation circuit.
• the diode bridges produce a positive or negative rectified sine wave, depending
on which side of the null position the core is located.
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
12
•A low pass filter is used to convert the rectified output into a smoothed signal
that tracks the core position.
•The cutoff frequency of the LPF is chosen to filter the high frequency in the
rectified wave but not the frequency components associated with the core
motion.
ELCT903,
Sensor
Technology
Dr.-Eng.
Hisham El-Sherif
•The
excitation
frequency is usually chosen to be at
least 10
times
from the
Mechatronics
Engineering
Department
expected frequency of the core.
13
From the above equivalent circuit
-Rp is the primary resistance and Lp is the
primary inductance
-The total resistance of the secondary coil
is Rs and Ls is the net leakage inductance
due to the magnetic flux leakage .
The magnetizing voltage in the primary coil
VP = Vref
jwL p
RP + jwL p
…………………………………………………..1
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
14
Suppose that the core length L is moved through a distance x from the null
position
Then
The induced voltage in one segment in the secondary coil would be
Va = V p k a
L
+x
2
………………………………………………….2
And the induced voltage in the other segment
Vb = V p kb
L
−x
2
………………………………………………….3
k a , kb are nonlinear functions of the position of the core
are complex functions of the frequency variable w
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
15
Due to the series opposition connection of the two secondary
segments, the net secondary voltage induced would be
Vs = Va − Vb = V p k a
L
L
+ x − kb
−x
2
2
-In the ideal case the two functions
………………………………….4
k a (⋅) and kb (⋅)
would be identical.
Then
At x=0 we have
Vs = 0
-Hence the null voltage would be zero in the ideal case
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
16
-Suppose that at, x=0 the magnitudes of
a slight phase difference.
k a (⋅) and kb (⋅) are equal, but there is
-Then
ka
L
L
- kb
2
2
o
Will have a small magnitude value, but its phase will be almost 90 with respect to
both
k a and kb . This is a quadrature error .
For small x, the Taylor series expansion of equation 4 for linearization
df
F ( x ) = F ( x) x =o +
dx
d2 f
x+ 2
dx
x =o
x =o
x2
+ ...
2Ι
For approximation
F ( x ) = F (o) x = o +
df
dx
x
x =o
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
17
F (o ) = k a
df
dx
X =0
L
= ka
2
dk a ( x) L
x=
+x
dx
2
x =o
Then
ka
L
+x
2
x =o
+ k a ( x) x =0 x
dk a ( x ) L
=
x
2
dx
L
L dk a L
x
+ x = ka +
2
2 dx 2
Similarly
kb
Substitute in equation 4
L
L dkb L
x
− x = kb +
2
2 dx 2
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
18
VS = VP k a
Assume the
∂k a L
∂kb L
L
L
x
x − kb
+
+
∂x 2
∂x 2
2
2
k a (⋅) = kb (⋅)
be denoted by
……………………….5
k0 (⋅)
Then
∂k 0 L
x
VS = 2V p
∂x 2
…………………………………………………6
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
19
Or
VS = V p kx
Where
………………………………………………..………….7
∂k0 L
k =2
∂x 2
……………………………………………………..8
In this case the net voltage is proportional to x is given by (substitute by Vp)
In equation 7
VS = Vref
jwL p
RP + jwL p
kx ………………………………………………9
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
20
And the output voltage to the load is given by
Vo = Vref
jwL p
RP + jwL p
RL + jwLL
kx …………………………10
(RL + Rs ) + jw(LL + Ls )
For small displacements, the amplitude of the net output voltage of the LVDT is
proportional to the displacement x
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
21
Signal Conditioning
Carrier
Frequency
Generator
DC
Power supply
Amplitude of the
resulting signal
provides the
transducer reading
Primary
Excitation
Displacement
LVDT
Amplitude
Modulated
Secondary
Output
Rectifier
Circuit
DC signal
Phase shift has to be
detected to determine the
direction
of motion
Dr.-Eng. Hisham
El-Sherif
Mechatronics Engineering Department
DC
Amplifier
Amplified
signal
Low-Pass
Filter
Measurement
High
frequency
noise are
eliminated
ELCT903, Sensor Technology
22
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
23
Advantages of LVDT
• Accuracy over the linear range.
• An analog output which don'
t require amplification.
• less sensitive to wide ranges of temperature.
Disadvantages of LVDT
• limited range of motion.
• Limited frequency response; the overall frequency response is limited by
inertial effects associated with the core’s mass and the choice of the primary
excitation frequency and the filter cutoff frequency.
Dr.-Eng. Hisham El-Sherif
Mechatronics Engineering Department
ELCT903, Sensor Technology
24