Post on 14-Feb-2019
1Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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
2Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
3Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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
4Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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.
5Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
6Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
7Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
- 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
8Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
-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
9Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
-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.
10Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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
11Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
• 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.
12Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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.
13Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
•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.
•The excitation frequency is usually chosen to be at least 10 times from the expected frequency of the core.
14Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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
��
�
�
��
�
�
+=
pP
prefP jwLR
jwLVV …………………………………………………..1
15Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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
��
���
� += xL
kVV apa 2
And the induced voltage in the other segment
��
���
� −= xL
kVV bpb 2
………………………………………………….2
………………………………………………….3
are nonlinear functions of the position of the core
are complex functions of the frequency variable w
ba kk ,
16Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
Due to the series opposition connection of the two secondary segments, the net secondary voltage induced would be
��
�
���
���
� −−��
���
� +=−= xL
kxL
kVVVV bapbas 22
-In the ideal case the two functions would be identical.
Then
At x=0 we have
( ) ( )⋅⋅ ba kk and
0=sV-Hence the null voltage would be zero in the ideal case
………………………………….4
17Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
-Suppose that at, x=0 the magnitudes of are equal, but there is a slight phase difference.
-Then
( ) ( )⋅⋅ ba kk and
��
���
���
���
�
2 -
2L
kL
k ba
Will have a small magnitude value, but its phase will be almost 90o with respect to both . This is a quadrature error .
For small x, the Taylor series expansion of equation 4 for linearizationba kk and
( ) ...2
)(2
2
2
+Ι
++===
=
xdx
fdx
dxdf
xFxFoxox
ox
( ) xdxdf
oFxFox
ox=
=+= )(
For approximation
18Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
( )22 0
Lkx
LkoF a
Xa =��
�
� +==
xxkxL
dxxdk
xdxdf
xaox
a
ox��
�
�+�
�
���
� +==
==0
)(2
)(
xL
dxxdka �
�
���
�=2
)(
xL
dxdkL
kxL
k aaa �
�
���
�+=��
���
� +222
Similarly
xL
dxdkL
kxL
k bbb �
�
���
�+=��
���
� −222
Substitute in equation 4
Then
19Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
��
�
���
���
�
∂∂+�
�
���
�−��
���
�
∂∂+�
�
���
�= xL
xkL
kxL
xkL
kVV bb
aaPS 2222
……………………….5
Assume the be denoted by ( ) ( )⋅=⋅ ba kk ( ) 0 ⋅k
Then
xL
xk
VV pS ��
���
�
∂∂=
22 0
…………………………………………………6
20Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
Or
kxVV pS = ………………………………………………..………….7
Where
��
���
�
∂∂=
22 0 L
xk
k ……………………………………………………..8
In this case the net voltage is proportional to x is given by (substitute by Vp)
In equation 7
kxjwLR
jwLVV
pP
prefS �
�
�
�
��
�
�
+= ………………………………………………9
21Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
And the output voltage to the load is given by
( ) ( ) kxLLjwRR
jwLRjwLR
jwLVV
sLsL
LL
pP
prefo ��
�
����
�
++++
��
�
�
��
�
�
+= …………………………10
For small displacements, the amplitude of the net output voltage of the LVDT is proportional to the displacement x
22Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
Carrier Frequency Generator
DCPower supply
LVDTRectifierCircuit
DC Amplifier
Low-PassFilter
Displacement
Primary Excitation
SecondaryOutput
Measurement
Signal Conditioning
Amplitude Modulated
DC signalAmplified signal High
frequency noise are eliminated
Amplitude of the resulting signal provides the transducer reading
Phase shift has to be detected to determine the direction of motion
23Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
24Dr.-Eng. Hisham El-SherifMechatronics Engineering Department
ELCT903, Sensor Technology
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.