【正文】 x xxDxD D DxDx D i x D x Dx x xRsv sR C LRsRRv sR C s L C sR CR sL R sssC L L CRRssQL vR R Rs s QRRR R v R R R Rs s QssL L C???? ? ??? ? ?? ? ? ???? ?????? ? ? ? ??? ? ?????VelocitytoVoltage conversion ?To convert velocity to a voltage, use a resistive load Since this structure has pletely symmetrical I/O ports: 39。0 0 039。x x x Dx x D xL L R RR R R L Q? ? ??? ?? ? ? ? ??????Brute force approach: ? ?000111ixxxv sCsv R sLsC sC?? ? ?? ?? ?? ?002202 39。 20 0 039。39。2 39。39。0039。/ 11/111 / 1 /11/ 1 //1/ 1/ Q , 1 /xxDx x x x xi x Dx x x xx D x DxDxDxxx D x xxD x x D xxxx x x xxsCv sC C CssC R C L Cv C CsR C s L C ssC C C C CCCCCLCC C L CCC R C C LRss Q Q C CL L C RL Q? ? ??????? ? ? ? ??????? ? ? ??????? ?? ??? ? ? ? ? ?????D??????PositiontoVoltage conversion ?To sense position (., displacement), use a capacitive load Brute force approach: ? ? ? ?? ?239。0039。2239。0039。/1/xDi x Dv C Csv C CssQ????? ????????PositiontoVoltage conversion ?To shense position (., displacement), use a capacitive load ? ? ? ? ? ?39。 39。 39。 39。0 00N o te : Ca n w e sim il a r sh u t c u t t o the R c a seG e t D C r e sp o n c e C39。 s d o m ina teT h e n :1D C G a in , , ,ivs s Q Qvs???? ? ? ? ?2x22S i nce t hi s s t r uctu r e h a s c om pl e t e l y s y m m e t r i c a l I / O p ort: C exxeebmRLk???? ? ?VelocitytoVoltage conversion ?To convert velocity to a voltage, use a resitive load ? ?? ?039。39。0w ha t @ r e son a nc e : ( t o si m pl i f y t he a na l y si s) @ r e son a nc eT he n, ge ne r a t e t o of f r e son a nc e : , , w he r e Di x DxDi x D x Dv Rv R RvRRs Q Q Qv R R R R????? ? ? ???? ??? ?01p xpR R C? ?Problems With Purely Resistive Sensing ? ?? ? ? ?39。39。0 0Now, W e ge t : a pp r ox i m a t e l y1~ , ,1Di x Dpv Rs s Qsv R R ??? ? ?? ?Problems With Purely Resistive Sensing ?In general, the sensor output must be connected to the inputs of further signal conditioning circuits ? input Ri of these circuits can load RD These change w/ hookup ?not good Problem: need a sensing circuit that is immune to parasitics or loading Solu: use op amps. The TransR Amplifier Advantage ?The virtual ground provided by the ideal op amp eliminates the parasitic capacitance Cp and Ri ?The Zero output resistance of the (ideal) op amp can drive virtually anything ? ?? ?LDp I nte gr a ti on y ie l ds di spl a c e m e ntT o m a xi m i z e g a i n, m i ni m i z e f P r ob l e m : p a r a s t i c ca pac i t a ne C/ DC Gain : 1/R e m e dy : s up pre s s C Vi a u s e o f o p a m psD Pi pbx D Pi pbx D Pi pbC C CC C C CC C C C?? ? ????? ? ?Problems With PureC Position Sensing ?To sense position (., displacement), use a capacitive load ? ? ? ?39。 39。 39。 39。0 00/ 1 , , ,1/ xDi x Dv C Cs s Q Qv C C s ??? ? ? ? ??? ? ? ? ? ?00 0 22 2 21 1 1ix s xsvvv i R s ss C R s C v R C s?? ?? ? ? ? ? ? ? ?????The Op Amp Integrator Advantage ?The virtual ground provided by the ideal op amp eliminates the parasitic capacitance Cp ? ? 1 2 11 1 201 2 1 2 1 2121222I ssu e : Pa r a sit ic c a p a c it a n c e : A s b e f o r e , Cp r e d u c e s g a in so l n : u se o p a m p !p p pp p p DDppV C V C V CC C Cv v v V VC C C C C CCCVVC C C? ? ? ?? ?? ? ? ? ? ???? ? ????????Differential Position Sensing ?Example: ADXL50 BufferBootstrapped Position Sensing Includes capacitance from interconnects, bond pads, and Cgs of the op amp ?Bootstrap the ground lines around the interconnect and bond pads ?No voltage across Cp ?It’s effectively not there! Effect of Finite Op Amp Gain ? ? ? ? ? ?? ?000 0 0 0 0 0 000i000000p111Ge t Z : 1111 112Ex : 1 0 0 , C 2 2 0101Not n e g l i g i b l e c o m p a r e d /iiiii i p i p i pipii e ffpie ffvAv A v v A v v v A A vvAvAi v v sC v sC v sCi A ACvZCCiAsApA p F C f F???? ? ? ? ? ? ? ? ????? ? ? ? ? ???????? ? ? ?????????? ? ? ? ?f o f A DXL S O C ~ 1 0 0 fF? ? ? ? ? ?0 1 2 1 2 1 212000 121 A se e nni ngl y pe r f e c t di f f e r e nt i a l se ns or / a m pl i f i e r out put !but onl y whe n op a m p i s i de a lp p ppFFpFi i i v sC v sC v s C CCCv i vsC Cv CCvC? ? ? ? ? ?? ? ? ??? ? ? ?? ? ? ?? ? ? ?????IntegratorBased Diff. Position Sensing Can drive next stages Ri w/o interference to transfer function!