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

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Edmund Martin
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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 14

15 LVDT The output voltage e will follow the behaviour represented in the following plot: Why? 15

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

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

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

19 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

20 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

21 In case of m >> 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 Notes: If m If M 1 -M =kx: e o =e ex k x e e ex s( M M ) 1 sl p p A linear relationship between e and M 1 - M is evincible! In case of real m The critical frequency nulling the pahse lag is: e e ex f c In this condition: 1 p m( M1 M ) ( )L L s m p p p ( L s L p m ) If M 1 -M =kx: e o =e ex k x 1 It can be demonstrated that under this condition the device shows the maximum sensitivity. 1

22 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

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

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

25 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. 5

26 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

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

28 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!

29 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.

30 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

31 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.

32 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.

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

34 LVDT FILTEING: In case the modulation frequency is lower (ten times) than the carrier frequency, low cost C filter can be used! 34

35 Example: LVDT In case the maximum displacement frequency band is 1kHz and the LVDT excitation frequency is 1 khz The modulation process will furnish signals in the band [19. Hz, 1.Hz]. The filter must be designed in order to assure a residual ripple of 5%@19 khz f,17 s f

36 LVDT Such will show a gain of,68 and a phase lag of -47 which will affect too much the information on the displacement. Using a double cell C filter: f,37 s f 1 Such will show a gain of,94 and a phase lag of -6 which can be considered a good reproduction of the original information. The delay in time can be easily estimated by: t r p / 18 pf ms 36

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

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

39 LVDT 39

40 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 4

41 LVDT Behavior of the output signal as a function of the core position 41

42 Drawbacks LVDT Offset voltage in the null position due to parasitic capacitance 3 armonic distorsion due to the ferromagnetic core saturation; Self heating of. 4

43 LVDT: rotational 43

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