Inductive sensors. The operating principle is based on the following relationship: L=f(x) M=g(x)

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Milo Boyd
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1 Inductive sensors The operating principle is based on the following relationship: L=f(x) M=g(x) High robusteness against influencing quantities (environmental) 1

2 L variation based Inductive Sensors Basics h 1 N i h The magnetomotive force is: fmm = Ni = magnetic flux x reluctance= F x [A-spire] Ni F [Weber]

3 L variation based Inductive Sensors h 1 N i L L d N di N h Where the reluctance is: m l m r A l: flux path A: area of the section interested by the flux (path cross section) m : permeability in vacuum m = 4p x 1-7 Hm -1 m r : relative permeability 3

4 L variation based Inductive Sensors L L d N di N m l m r A Usually the variation of N, l or m are used to convert physical quantities into elctrical signal. N variation µ variation 4

5 L variation based Inductive Sensors Advantages: obustness against environmental quantities educed 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 (<khz). 5

6 6 d air gap N i h 1 h A μ d A μ μ h A μ μ h A l μ A l μ r r h h =h +h L variation based Inductive Sensors eluctance variation A l m r m N L di d N L

7 7 Non linear behaviour with d!! 1 con ) (1 kd x x A μ k, A μ μ h h kd r eing 1 ) (1 N L b x L x N N L L variation based Inductive Sensors eluctance variation takes into account flux path through the coil and not through the air! A μ d A μ μ h A μ μ h A l μ A l μ r r d air gap N i h 1 h

8 L variation based Inductive Sensors eluctance variation in differential configuration L h1 μ being k( d r h μ A (1 y ) N L N, x ) con N (1 y ) k μ A k( d x ) y L 1 y L 1 being N 1 L N (1 y ) 1 N L1 1 y Standard advantages coming from the differential configuration (influencing quantities compensation, high responsivity,.) 8

9 L variation based Inductive Sensors Linear Variable Transducer m variation The core movement produces L1 and L variations which are then converted by suitable bridges. 9

10 Linear Variable Differential Transformers (LVDT) A primary coil and two secondary coils. Core movement The mutual inductance changes as a function of the core position. 1

11 LVDT e ex e ex x i e o 1 e o e o 1 e o Primary coil: sinusoidal excitation signal, frequency ranging between [6 Hz and. Hz] The amplitude of the induced voltage on the secondary coils depends on the core position. 11

12 LVDT e 1 e exc NULL POSITION e e exc e 1 e In case the core is above the null position Max(e 1 )>Max(e ) In case the core is below the null position Max(e )>Max(e 1 ) This configuration allows for estimating the core position by separately processing signals from the two coils! 1

13 LVDT Secondary coils in differential configuration e exc e Advantages coming from the differential configuration: influencing quantities compensation; high responsivity; 13

14 LVDT e 1 e e =e 1 -e COE ABOVE NULL e 1 e e 1 e e

15 LVDT e 1 e e =e 1 -e COE BELOW NULL e 1 e e e 1 e

16 LVDT e 1 e e COE ABOVE NULL e COE BELOW NULL 17

17 LVDT How do extract from e the core position? e 1 e e COE ABOVE NULL e COE BELOW NULL 18

18 Modelling: LVDT M 1 L s / s / i s i p e ex p L p e s1 L s / M 3 e o s / m M e s 1 e i sl i sm sm ex p p p s e o i m s L L i s s sm i sm sm i s s s s m s 3 s 1 p i s L M i s M M i s m s s 3 s 1 p 19

19 LVDT M 1 L s / s / i s i p e ex p e s1 M 3 e o m L p L s / s / M e s Supposing L s -M 3 independent on the core position, and assuming: L =L s -M 3 e s M o M1 m e s M M L L s L L L ex 1 p p p s p m p s m L L M M Assuming: p 1 e s M M e s L L s L L L o 1 m ex - p p p s p m p s m

20 e s M M e s L L s L L L o 1 m ex - p p p s p m p s m The critical frequency nulling the phase lag is: f c 1 p p ( L s L p m ) 1 e e ex In this condition: m( M1 M ) ( )L L s m p p If M 1 -M =kx: e o =e ex k x It can be demonstrated that under this condition the device shows the maximum sensitivity. 1

21 LVDT e o =e ex k x As it can be observed the amplitude of e o does NOT give information on the displacement direction. e

22 LVDT In case of a time changing displacement x: the sensor output is a sinusoidal signal (driving signal) modulated by x. 3

23 LVDT Two different x(t) produces similar outputs!!! A rough demodulation producing the output signal envelope: will give information on the displacement amplitude; will NOT give information on the displacement direction. 4

24 Carrier X(t) Modulated signal Differential LVDT output Modulated signal Asynchronous demodulation

25 A phase sensitive demodulation will produce information on both the amplitude and the direction of the displacement. The mean value of e allows to estimate the absolute position of the core. 6

26 LVDT A phase sensitive demodulation will produce information on both the amplitude and the direction of the displacement.. 7

27 Demodulating AM signals Many sensors show an output signal which is given by: e (t)=ke exc (t)x(t) Where: k is a gain e exc (t) is the excitation signal (carrier) x(t) is the unknown quantity (modulating signal) Es.: LVDT, ac bridges, etc; x e exc e e is a suppressed carrier AM signal!

28 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.

29 suppressed Carrier AM modulation e (t)=ke exc (t)x(t) e x e exc V cos( Acos( kv A s t ) cos t ) t cos s s t

30 Carrier suppressed AM modulation The Asynchronous demodulation will not produce information on the displacement direction! In case of a LVDT in differential configuration: M 1 L s / s / i s e (t)=ke exc (t)x(t) e exc e ex i p p L p e s1 L s / M 3 s / e o m M e e s e e The magnitude of e gives information on the core displacement while its position as respect to null (direction) cannot be estimated. The phase lag between e and e exc can produce information on the displacement direction.

31 Carrier suppressed AM modulation Synchronous demodulation e ref (t) e (t) e m (t) e d (t) Two steps: e e e ref m V r cos( t ) kv A cos kv AVr cos kv AVr cos s 4 t cos s t t cos s 1 t t cos t cos s s s cos( t s t ) A low pass filter is required to eliminate + s component.

32 Carrier X(t) Modulated signal Differential LVDT output Modulated signal Asynchronous demodulation Snchronous demodulation

33 Carrier suppressed AM modulation The Synchronous demodulation can be implemented by a CAIE AMPLIFIE

34 Demodulating AM signals Dedicated electronics must be used to detect the displacement direction! LVDT conditioning Datasheet AD598

35 LVDT 39

36 Demodulating AM signals another example The PO11 is a differential microcoil inductive sensor to measure the speed or position of a gear PO11 datasheet

37 LVDT Advantages: Good resolution; Friction free operation; MTBF =x1 6 h=8 years); Elctrical insulation between primary and secondary coils; Linearity and responsivity; High dynamic range. Operating range 1mm; 5cm. Power supply 1V, 4V; 5Hz, khz. esponsivity (normalized to power supply voltage) esolution.1v/cm; 4V/ mm. Up to.1 mm 41

38 LVDT Behavior of the output signal as a function of the core position 4

39 Drawbacks LVDT Offset voltage in the null position due to parasitic capacitance 3 armonic distorsion due to the ferromagnetic core saturation; Self heating of. 43

40 LVDT: rotational 44

Inductive sensors. The operating principle is based on the following relationship: L=f(x) M=g(x)

Inductive sensors. The operating principle is based on the following relationship: L=f(x) M=g(x) Inductive sensors The operating principle is based on the following relationship: L=f(x) M=g(x) High robusteness against influencing quantities (environmental) 1 L variation based Inductive Sensors Basics