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

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Dr.-Eng. Hisham El-Sherif Mechatronics Engineering Department

ELCT903, Sensor Technology

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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

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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

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Dr.-Eng. Hisham El-Sherif Mechatronics Engineering Department

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Dr.-Eng. Hisham El-Sherif Mechatronics Engineering Department

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- 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

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-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

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-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

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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

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• 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

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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

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•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.

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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

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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

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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

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-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

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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

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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

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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

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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

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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

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Dr.-Eng. Hisham El-Sherif Mechatronics Engineering Department

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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

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