linear variable differential transformer - guceee.guc.edu.eg/courses/electronics/elct903 sensor...

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



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



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.



- 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



-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



-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.



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



• 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.



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.



•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.



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



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 ,



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



-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



( )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



��

�

��

��

�

∂∂+�

�

��

�−��

��

�

∂∂+�

�

��

�= 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



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



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



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



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.

linear variable differential transformer - guceee.guc.edu.eg/courses/electronics/elct903 sensor...

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