Sensing, Compuing, Acuaing Sander Suik (s.suik@ue.nl) Deparmen of Elecrical Engineering Elecronic Sysems
INDUCTIE SENSOS (Chaper.5,.6,.0, 5.4)
3 Inducive sensors damping conrol wheel speed sensor (ABS) crankshaf posiion sensor pedal posiion sensor speedomeer (eddy curren)
4 Inducive sensors
5 Sensor classificaion ype / quaniy measured Quaniy Posiion, disance, displacemen Flow rae / Poin velociy Force Temperaure esisive agneoresisor Thermisor Srain gage TD S e n s o r Poeniomeer Capaciive Differenial capacior Capaciive srain gage Inducive and elecromagneic Thermisor Capacior Eddy currens DT oad cell + DT DT Hall effec agneosricion y p e Selfgeneraing DT agneosricion Thermal ranspor + hermocouple Piezoelecric sensor Pyroelecric sensor Thermocouple PN uncion Phooelecric sensor Diode Bipolar ransisor reacance variaion sensors (capaciive and inducive sensors) ypically require no physical conac eer minimal mechanical loading
6 agneic relucance elecrical circui may offer resisance o charge flow resisor: resisor dissipaes elecrical energy curren follows pah of leas resisance oal resisance o r magneic circui may offer relucance o magneic flu relucance: relucan circui sores magneic energy magneic flu follows pah of leas relucance oal relucance compued in similar way as resisance in elecrical circui o 3 4
7 agneic relucance relucance depends on physical properies of he device 0 l A l lengh of he device A cross-secional area μ 0 permeabiliy of free space (40-7 H/m) μ relaive permeabiliy of he maerial sof ferromagneic maerial (ypically 000 o 0000) permeabiliy of air (appro. ) opions o vary relucance modify lengh l (variable gap sensor) modify magneic permeabiliy μ (moving core sensor) modify cross-secional area A (no frequenly used)
8 agneic relucance relucance depends on physical properies of he device 0 l A sensor requires conversion of magneic signal o elecric signal Faraday s law relaes magneic relucance o elecric curren v N di d di d change in relucance changes oupu volage self-inducance and relucance are relaed: N device can also be used as sensor wihou changing relucance changing magneic field causes elecrons o move induces addiional (eddy) curren (eddy curren sensor)
9 ariable gap sensor core wha is he oupu volage (in erms of ) of a sensor wih N windings? l l core obec, obec, air l l core obec core0 A obec0 A air0 A oal core0 A obec0 A air0a oal core obec air relucance of core and obec are consan 0 relucance of he circui self-inducance of he circui l core N oal N k oupu volage of he sensor di v d l A core 0 0 N di k d 0 obec obec A A oal 0 0 air 0 0 k
0 ariable gap sensor oupu volage of he sensor v di d N k 0 highly non-linear relaion beween oupu and displacemen use of sensor limied o proimiy sensor di d
inear displacemen ransformer wo coils in series, moving obec increases relucance in one coil decreases relucance in oher coil v e circui is differenial volage divider impedance of coil is equal o Z N 0 l A N N A l 0 Z v e Z 0 /(-) changing l wih a relaive amoun Z N 0 A l Z 0 0 Z 0 /(+)
inear displacemen ransformer wo coils in series, moving obec increases relucance in one coil decreases relucance in oher coil v e circui is differenial volage divider oupu of he volage divider v o Z 0 / Z0 / ve ve Z / 0 linear relaion beween oupu volage and displacemen offse volage presen v e Z 0 /(-) displacemen () should be small sensor ofen no pracical Z 0 /(+)
3 uual inducance self-inducance induced volage due o change in own curren di v d muual inducance induced volage due o change in curren in neighboring circui di d di d v depends on relucance of he space beween he coils changing relucance beween coils alers muual inducance device usable as sensor wo coil soluion sill no pracical (large offse, small flucuaion) i v i v
4 inear ariable Differenial Transformer inear ariable Differenial Transformer (DT) wo secondary coils in series-opposiion linear relaion beween oupu volage and core displacemen operaion based on muual inducance v 0 v linear range
5 inear ariable Differenial Transformer assume sinusoidal eciaion of primary circui v ( ) sin oupu volage of secondary circui ( ) S sin S ω sensiiviy a frequency ω displacemen of he core from cener φ phase shif (in volage) from primary o secondary circui v S ω and φ depend on load of measuremen circui eciaion frequency ω phase shif can be compensaed
6 Signal condiioning for DT sensors oupu signal of DT is ampliude modulaed ac signal ( = 0 ) ( = 0 ) ( = - 0 ) ampliude indicaes magniude of displacemen phase indicaes direcion of displacemen v
7 inear ariable Differenial Transformer oupu volage (no load conneced o secondary winding) no curren in secondary circui (I = 0) o I I I I primary curren I independen of core posiion oupu volage o proporional o core posiion o k o k I k v i v 3
8 inear ariable Differenial Transformer oupu volage (no load conneced o secondary winding) o k sensiiviy o k k k k S sensiiviy increases wih increasing frequency phase shif oupu volage 90 ou of phase wih primary curren phase shif beween and 0 90 I k arcan consider phase shif when recovering posiion v i 3
9 inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) oupu volage curren hrough secondary winding define oal resisance in secondary windings as no volage source in secondary winding, hus holds I depends on I i v i 3 o I 3 ' 0 I I c 3 ' I I c c ' 3 ' I I c
0 inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) oupu volage o I I depends on I I c curren (I ) hrough primary winding ' 3 I I I I I I equal in boh epressions, hence v i 3 i
inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) oupu volage I equal in boh epressions, hence i v i 3 3 ' I I c o I c c I 3 ' 3 '
inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) o difference in muual inducance relaed o core posiion k oupu volage in erms of core posiion k o o = 0 when = (core in cener) i holds ha ' o changes linearly on boh sides of cener ' ' k ' k 3 ' 3 3 c 3 c i v 3 c 3 c i
3 inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) i holds ha hence sensiiviy sensiiviy increases wih (up-o some frequency) sensiiviy depends on eciaion frequency of primary circui c c o k 3 ' k 3 ' k S c c o c c o k k 3 ' 3 '
4 inear ariable Differenial Transformer oupu volage (load conneced o secondary winding) (in general) phase difference beween and 0 no phase shif when sensiiviy a frequency f n sensiiviy increases wih any oher frequency has lower sensiiviy for same 0 0 0 f f f c n c n c n c k k S c c f o n c c o k
5 inear ariable Differenial Transformer eample sensiiviy of an DT primary winding has a dc resisance of 67 Ω wo series-opposiion windings have a oal dc resisance of 800 Ω a khz primary winding has impedance of 90 Ω secondary windings have impedance of 4800 Ω sensiiviy (normalized o eciaion volage) is 70 (μ/)/μm calculae he following inducance of primary and secondary winding eciaion frequency ha yields zero phase shif beween primary and secondary volage wih load resisance of 0 kω normalized sensiiviy when he DT is ecied a 60 Hz and he load resisance is equal o 500 kω normalized sensiiviy when he DT is ecied a 60 Hz and he load resisance is equal o 0 kω
6 inear ariable Differenial Transformer eample sensiiviy of an DT calculae he inducance of primary and secondary winding primary winding Z f secondary winding 90 67 000Hz Z 45mH f ' 4800 800 Z 30mH f 000Hz calculae he eciaion frequency ha yields zero phase shif wih 0 kω load resisance 67800 0k 45mH30mH c fn 88Hz
7 inear ariable Differenial Transformer eample sensiiviy of an DT calculae he normalized sensiiviy when he DT is ecied a 60 Hz and he load resisance is equal o 500 kω secondary circui assumed open when load resisance is 500kΩ use sensiiviy is equal o S o f, a b a b f a khz, S = 70μ//μm k 700 0 m 6 fk 6 f m sensiiviy a 60Hz is hus equal o S f 70 67 khz 45mH 60rad.5 s / mrad 67 60rad 45mH 68. 000rad / / m.5 / m/ rad / s
8 inear ariable Differenial Transformer eample sensiiviy of an DT calculae he normalized sensiiviy when he DT is ecied a 60 Hz when he load resisance is equal o 0 kω secondary is loaded (no open) when load resisance is 0 kω we compued earlier S o.5 s / m rad 60rad 0k 67800 60Hz 45mH30mH 60Hz 800 45mH 67 30mH 53.3 c / / m k c
9 inear ariable Differenial Transformer assume sinusoidal eciaion of primary circui v ( ) sin oupu volage of secondary circui ( ) S sin S ω sensiiviy a frequency ω displacemen of he core from cener φ phase shif (in volage) from primary o secondary circui S ω and φ depend on load of measuremen circui eciaion frequency ω phase shif can be compensaed v
30 Signal condiioning for DT sensors oupu signal of DT is ampliude modulaed ac signal ( = 0 ) ( = 0 ) ( = - 0 ) ampliude indicaes magniude of displacemen phase indicaes direcion of displacemen v
3 Bridge recifier wih low-pass filering ~ - + ~ vou vou ~ - + ~ vou < 0 > 0 u u ampliude of recovered sign of no recovered
3 Signal condiioning for DT sensors oupu signal of DT is ampliude modulaed ac signal carrier amplifier and coheren deecor ac amplifier muliplier low-pass filer sensor oscillaor v
33 Phase-sensiive (synchronous) demodulaion ac amplifier muliplier low-pass filer sensor oscillaor eciaion volage of he sensor v ( ) cos f oupu of he sensor (assume no phase shif inpu/oupu volage) v e o e ( ) S ( ) v ( ) assume measured obec is moving ( ) X cos oupu volage hen equal o v ( ) S o X e cos e f f cos f e S X f f cos f f e cos e e e cos AcosB cosa B cosa B
34 Phase-sensiive (synchronous) demodulaion ac amplifier muliplier low-pass filer sensor () oscillaor oupu of he sensor (=inpu o deecor) v o ( ) S X f f cos f f e cos e (f) frequency specrum (double-sideband signal) e deecor mus recover ( ) X cos maimal displacemen of obec (X) frequency wih which obec changes direcion (f ) phase shif of moving obec (φ ) f f e -f f e +f f
35 Phase-sensiive (synchronous) demodulaion muliplier inpus signals have same phase (φ r = φ e ) oupu of he muliplier frequency of he signals are equal (ω r = ω e ) oupu of low-pass filer oupu of demodulaor equal o () (ecep for scaling facor) v r () v p () () v d () e e e e o r r r r S v S v v cos ) ( ) ( ) ( ) ( cos ) ( S v v v r e r e e r o r p cos cos ) ( ) ( ) ( ) ( S v e e r p cos ) ( ) ( ) ( ) ( ) ( S v PF v e r p d
36 Phase-sensiive (synchronous) demodulaion coheren deecor oupu sensor v p vd v d re ( ) S ( ) v e v r signal () does no have o be a sinusoid band-limied inpu signal X(f) sensor eciaion signal e (f) f m f sensor oupu signal o (f) f e f reference signal r (f) f e -f m f e f e +f m f muliplier oupu signal p (f) f r = f e f f -f m f m f r -f m f r f r +f m
37 Phase-sensiive (synchronous) demodulaion coheren deecor oupu sensor v p vd v d re ( ) S ( ) v e v r signal () does no have o be a sinusoid band-limied inpu signal X(f) muliplier oupu signal p (f) f m f PF frequency response f -f m f m f r -f m f r f r +f m H(f) deecor oupu v d (f) f m f c f f m f
38 Inerference oupu of sensor may conain inerference (e.g. from power line) sensor v e v r v p vd signal () and inerference signal band-limied inpu signal sensor oupu signal muliplier oupu signal deecor oupu inerference may be par of oupu signal aenuaion of inerference may be limied by PF response X(f) o (f) f m f if e -f m f e +f m f r -f i f r -f m f -f m f m f r +f m f r +f i v d (f) f m f r -f i f f f
39 Inerference ampliude response PF d p c ω c corner frequency oupu volage due o inerference v d i ri e i c sensor normal mode reecion raio (N) v d ( e) e e i i N 0log 0log 0log vd ( i ) c c reflecs capabiliy of filer o reec inerference approimaion valid when ω i << ω e v e v ( ) cos i i i v i v e i / v r v p ω e -ω i ω e +ω i vd ω
40 Inerference eample selec frequencies for coheren deecor measure 5 Hz signal wih ampliude error < SB for 8 bi ADC 40dB aenuaion for 50 Hz inerference a inpu of demodulaor which eciaion and corner frequencies should be used? ampliude error should be less han / 8 corner frequency should be 5Hz f c 8 N(50Hz) = 40dB, hence fe 50Hz 40dB 0log fe 5. 69kHz 56.4Hz 5Hz f c 56. 4Hz 8 8 eciaion frequency may be oo high for pracical circui use bandwidh filer in fron of coheren deecor use high-order PF filer
4 Phase-sensiive (synchronous) demodulaion muliplier a he cener of he PSD sensor v p vd analog mulipliers are epensive v e v r wo soluions for muliplier use (ani-)logarihmic amplifiers use symmerical square wave as reference ani-logarihmic amplifier addiion logarihmic amplifier v - + v - - + - + v m +
4 Phase-sensiive (synchronous) demodulaion muliplier a he cener of he PSD sensor v p vd analog mulipliers are epensive v e v r wo soluions for muliplier use (ani-)logarihmic amplifiers use symmerical square wave as reference PF wih gain amplifier compensae phase difference convoluion of v r and reference signal o square waves
43 Phase-sensiive (synchronous) demodulaion > 0 < 0 v d v d PF wih gain amplifier compensae phase difference convoluion of v r and reference signal o square waves
44 DT pro s and con s of DTs (+) non-conac sensor (no fricion) (+) infiniesimal resoluion (+) solid and robus consrucion (+) no hyseresis (mechanical and magneic) (+) oupu impedance is very low (-) sensiive o sray magneic fields (inerference) (-) comple signal processing required
45 oary ariable Differenial Transformer similar consrucion and operaion as DT o α i α o linear range oupu of (unloaded) DT o S linear relaion beween core roaion and oupu volage linear measuremen range limied o ±0 measuring full roaion is no possible
46 ariable ransformer muual inducance N i v i α v flu linked by secondary winding N i BS BS cos HS cos l B magneic flu densiy S secondary cross secion H magneic field srengh μ magneic permeabiliy of he core l lengh of primary winding S cos muual inducance is equal o N N S cos cos l muual inducance has relaion wih angle
47 ariable ransformer muual inducance N N S cos l cos v i α v wha is he volage on he secondary winding? consider open-circui siuaion volage on primary winding curren hrough primary winding i I p cos v p sin volage on secondary winding di v d si si p cos cos k cos cos ampliude of oupu volage depends on angle beween windings
48 esolver roor winding acs as primary winding wo saor windings a 90 ac as secondary windings cos(α) volage on primary winding v i sin i I cos p i induced volages on secondary windings K cos cos K cos sin p v i roor α α sin(α) saor oupu volage is produc of measured obec (α) eciaion volage (v i ) oupus differ by 90 phase difference v i
roaion α [rad] [] i [A] [] 49 esolver cos(α) ime [s] v i α sin(α) ime [s] ime [s] ime [s]
[] [] 50 esolver 90 80 70 90 80 70 ime [s] ime [s] 0 90 80 70 [] 0-0 [] 0-0 bridge recifier can be used o recover angle beween 0 α 90 phase sensiive deecor needed o recover angle in all quadrans
5 esolver how o supply v i o he roor? use brushes or slips (fricion, wear) brushless ransformer (preferred) v i α
5 esolver how o supply v i o he roor? use brushes or slips (fricion, wear) brushless ransformer (preferred) v i α roary ransformer v i α