The operating principle is based on the following … linear behaviour with d !! 7 0 0 0 0 1 2 0 0 (1 ) con 2 2 2 R kd R R x x A, k A h h R R R kd r 0 2 0 0 0 2 2 eing (1 ) 1 R N b

1

Inductive sensors

The operating principle is based on the

following relationship:

L=f(x)

M=g(x)

•High robusteness against influencing

quantities (environmental)

2

Basics

N

i

h1

h2

fmm = Ni = magnetic flux x reluctance= F x R [A-spire]

NiF

R[Weber]

The magnetomotive force is:

L variation based Inductive Sensors

3

N

i

h1

h2

R

NL

di

dNL

2

Where the reluctance is:

l: flux path

A: area of the section interested by the flux (path

cross section)

m0 : permeability in vacuum m0 = 4p x 10-7 Hm-1

mr : relative permeability

A

lR

rmm

0


4

•Usually the variation of N, l or m are used to

convert physical quantities into elctrical signal.

N variation


R

NL

di

dNL

2

A

lR

rmm

0

µ variation

5

Advantages:

•Robustness against environmental quantities

•Reduced load effects

•High responsivity

Drawbacks:

•Sensitivity to magnetic field: shielding;

•Side effects reduce the operating range.

•Must work below the Curie Temperature.

Materials:

•In Vacuum: low responsivity, high frequency

operation

•Ferromagnetic core: high responsivity, low

frequency operation (<20kHz).


6

d air gap

N

i

h1

h’’2

Aμ

d

Aμμ

h

Aμμ

h

A

l

μA

l

μR

rr 00

2

0

1

0

0

0

22211

h’2

h2=h’2+h’’2


Reluctance variation

A

lR

rmm

0

R

NL

di

dNL

2

7 Non linear behaviour with d !!

0

0

00

210

0

con )1(

222

R

kdxxRR

Aμk,

Aμμ

hhR

kdRR

r

0

2

0

0

0

22

eing

1)1(

R

NLb

x

L

xR

N

R

NL


Reluctance variation

R0 takes into account

flux path through the coil

and not through the air!

Aμ

d

Aμμ

h

Aμμ

h

A

l

μA

l

μR

rr 00

2

0

1

0

0

0

22211

dair gap

N

i

h1

h’’2

8


Reluctance variation in differential configuration

0

02

00r

210

02

R

)xd(ky con )y1(RR

Aμ

2k,

Aμμ

h2h2R

)xd(kRR

0

2

20

20

0

2

2

2

2

R

NL eingb

y1

L

)y1(R

N

R

NL

0

2

10

10

0

2

1

2

1

R

NL eingb

y1

L

)y1(R

N

R

NL

Standard advantages coming from the differential configuration

(influencing quantities compensation, high responsivity, ….)

9

Linear Variable Transducer

The core movement produces L1 and L2

variations which are then converted by suitable

bridges.


m variation

10

A primary coil and two secondary coils.

Linear Variable Differential Transformers

(LVDT)

The mutual inductance changes as a function

of the core position.

Core movement

M variation based Inductive Sensors

11

•Primary coil: sinusoidal excitation signal,

frequency ranging between [60 Hz and

20.000 Hz]

•The amplitude of the induced voltage on

the secondary coils depends on the core position.

eo

1

eo

2

eex

x

i

eo

1

eo

2

eex

LVDT


12

LVDT

e01

e02

eexc


NULL POSITION

e02

e01

eexc

In case the core is above the null position Max(e01)>Max(e02)

In case the core is below the null position Max(e02)>Max(e01)

This configuration allows for estimating the core position

by separately processing signals from the two coils!

13

LVDT

Secondary coils in differential configuration

e0 eexc


Advantages coming from the

differential configuration:

•influencing quantities compensation;

•high responsivity;

LVDT

e01

e02

e0


e01

e02

e01

e02

e0=e01-e02

CORE ABOVE NULL

LVDT

e01

e02

e0


e01

e02

e02

e01

e0=e01-e02

CORE BELOW NULL

17

LVDT

e01

e02

e0

e0


CORE BELOW NULL

CORE ABOVE NULL

18

LVDT

e01

e02

e0

e0


How do extract from e0 the core position?

CORE ABOVE NULL

CORE BELOW NULL

19

LVDT Modelling:

eex es1

es2

Ls/2

Ls/2

Rm

Rs/2

Rs/2

Rp

Lp

M1

M2

ip

is

M3 eo

2 1

3 2 1

3 2 1

02 2 2 2

0

ex p p p s

o m s

s s s sm s s p

s m s s s p

e i R sL i sM sM

e R i

R R L LR i s s sM i sM sM i

R R i s L M i s M M i


20

LVDT

eex

es1

es2

Ls/2

Ls/2

Rm

Rs/2

Rs/2

Rp

Lp

M1

M2

ip

is

M3 eo

Supposing Ls-M3 independent on

the core position, and assuming:

L2=Ls-M3

2 1

22

2 1 2 2

mo

ex p p p s p m p s m

s M M Re

e s M M L L s L R L R L R R R R

Assuming: 2

2 2 1pL L M M

2 1

2

2 2

mo


s M M Re

e s L L s L R L R L R R R R

-


21

The critical frequency nulling the phase lag is:

2

1

22

1

p

p

msp

cLL

)RR(Rf

2

210

LRL)RR(

)MM(R

e

e

ppms

m

ex

In this condition:

It can be demonstrated that under this condition the device

shows the maximum sensitivity.

If M1-M2=kx:

eo=eexk’’x


2 1

2

2 2

mo


s M M Re

e s L L s L R L R L R R R R

-

22

LVDT

As it can be observed the amplitude of eo

does NOT give information on the

displacement direction.

e0

eo=eexk’’x


23

LVDT

In case of a time changing displacement x:

the sensor output is a sinusoidal signal (driving signal) modulated by x.


24

LVDT

A rough demodulation producing the

output signal envelope:

• will give information on the

displacement amplitude;

•will NOT give information on the

displacement direction.


Two different x(t) produces similar outputs!!!

Differential LVDT output

Asynchronous

demodulation

Carrier

X(t)

Modulated

signal

Modulated

signal

26

The mean value of e0 allows to estimate the

absolute position of the core.

A phase sensitive demodulation will produce

information on both the amplitude and the

direction of the displacement.


27

LVDT

A phase sensitive demodulation will produce

information on both the amplitude and the

direction of the displacement.

.


Demodulating AM signals

Many sensors show an output signal which is

given by:

e0(t)=keexc(t)x(t)

Where:

k is a gain

eexc(t) is the excitation signal (carrier)

x(t) is the unknown quantity (modulating signal)

Es.: LVDT, ac bridges, etc;

eexc e0

x

e0 is a suppressed carrier AM signal!

AM modulation

Full carrier:

In this case the

modulated signal is

always phase locked to

the carrier independently

on the sign of the

modulating signal.

Suppressed carrier:

In this case the

modulated signal and the

carrier:

are in phase if the

modulating signal is

positive;

are in counterphase if the

modulating signal is

negative.

tcostcosAkV

e

)tcos(Ax

)tcos(Ve

ss

s

exc

000

0

00

2

e0(t)=keexc(t)x(t)

suppressed Carrier

AM modulation

In case of a LVDT in differential configuration:

e0(t)=keexc(t)x(t)

• The magnitude of e0 gives information on the core

displacement while its position as respect to “null”

(direction) cannot be estimated.

• The phase lag between e0 and eexc can produce

information on the displacement direction.

eexc

e0

e0

e0

eex es1

es2

Ls/2

Ls/2

Rm

Rs/2

Rs/2

Rp

Lp

M1

M2

ip

is

M3 eo

The Asynchronous demodulation will not produce

information on the displacement direction!

Carrier suppressed AM modulation

e0(t)

eref(t)

ed(t) em(t)

Synchronous demodulation

tcostcostcosAVkV

)tcos(tcostcosAVkV

e

tcostcosAkV

e

)tcos(Ve

sssr

ssr

m

ss

rref

00

0000

000

0

0

24

2

2

Two steps:

A low pass filter is required to

eliminate 20+s component.


1

2

Differential LVDT output

Asynchronous

demodulation

Snchronous

demodulation

Carrier

X(t)

Modulated

signal

Modulated

signal

The Synchronous demodulation can

be implemented by a

CARRIER AMPLIFIER


Dedicated electronics must be used to detect

the displacement direction!

Datasheet AD598

…LVDT conditioning …


Allegati/AD598.pdf

Linear Differential Voltage Transformers Analog Dialogue Analog Devices.htm

Allegati/Linear Differential Voltage Transformers Analog Dialogue Analog Devices.htm

39

LVDT


…another example…

The PO2211 is a differential microcoil inductive

sensor to measure the speed or position of a

gear PO2211 datasheet


Linear Differential Voltage Transformers Analog Dialogue Analog Devices.htm

Allegati/POD319.pdf

41

Advantages:

•Good resolution;

•Friction free operation;

•MTBF =2x106 h=228 years);

•Elctrical insulation between primary and secondary coils;

•Linearity and responsivity;

•High dynamic range.

Operating range 100mm;

25cm.

Power supply 1V, 24V;

50Hz, 20kHz.

Responsivity

(normalized to

power supply

voltage)

0.1V/cm;

40V/ mm.

Resolution Up to 0.1 mm

LVDT


42

LVDT

Behavior of the output signal as a function of the core position


43

Drawbacks

•Offset voltage in the null position due to

parasitic capacitance

•3° armonic distorsion due to the

ferromagnetic core saturation;

•Self heating of R.

LVDT


44

LVDT: rotational


The operating principle is based on the following … linear behaviour with d !! 7 0 0 0 0 1 2 0 0 (1 ) con 2 2 2 R kd R R x x A, k A h h R R R kd r 0 2 0 0 0 2 2 eing (1 ) 1 R N b

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