Lesson 5. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Transcription

1 Lessn 5 Thermmechancal Measurements r Energy Systems (MEN) Measurements r Mechancal Systems and Prductn (MME) A.Y Zaccara (n ) Del Prete

2 We wll nw analyze mre n depth each ne the unctnal blcks the general measurement chan X TANSDUCE,, I SIGNAL CONDITIONE ISUALIZE x In the ndustry and n mst mdern measurement applcatns, the measurement chan s electrc and the nrmatn passes thrugh the derent stages as ltage sgnal r as a current! Despte the enrmus technlgcal adancements the last 30 years, the man electrcal sualzer nstruments can stll be ncluded n nly three classes:. The galanmeter 2. The scllscpe 3. The dgtal ltmeter The analg OSCILLOSCOPE

3 Analg scllscpe s the lder type and can nstantaneusly dsplay n the screen the waerm the nput sgnal! The perdc nput sgnal s cmbned n the lurescent screen wth an nternal sawtth (sweep) sgnal! A trgger synchrnzes the tw sgnals!

4 Acceleratn and cllmatn the electrn beam! ertcal delectn the beam by the hrzntal plates!

5 Sawtth (sweep) and snusdal sgnal cmbnatn n the CT screen!

6 Dgtal OSCILLOSCOPE The dgtal scllscpe des the same tasks as the analg scpe (and much mre) but t s actually a dgtal ltmeter that samples the nput sgnal and dsplays t n a GA screen!

7 We wll nw study the mst mprtant sgnal manpulatn crcuts used n measurement nstruments : X TANSD d dt dt, SIGN, I MANIP A A/D ISUAL FFT x In mdern and cmplex ndustry measurement system, the sgnal utputted by the transducer s almst always an electrcal sgnal r r whch, mst the tme, we need t enhance the nrmatn cntent (the ntensty the measurand)! e It s always pssble t measure a ltage wth an ampermeter and a current wth a ltmeter

8 The recter dde : a) The SC dde wrks here as a hal-wae recter! b) The Gretz brdge wth 4 SC ddes wrks here as a ull- wae recter!

9 The lw-pass C crcut Let s study the tw electrc crcuts nput (ltage) sgnal: X C utput (ltage) sgnal: X C the current s and the utput ltage: X C X X C C X C but X C s the capacte reactance, therere the utput/nput rat s : jc jc Cnsderng c C the utput/nput rat s als: j

10 We can calculate the mdulus the preus cmplex unctn : G the gan! 2 And the phase delay: arctg c We recgnze the requency respnse a smple st rder electrc sgnal manpulatn stage! r ω = 0 G = ω ꝏ G = 0 ω = ω c G 2 The C crcut s a lw-pass lter (ne ple Butterwrth lter) wth a 3 db cut- requency: c 2C Nte that r jc whch s c C the utput sgnal s als the ntegral the nput sgnal: t j t

11 The hgh-pass C crcut The tw electrc crcuts equatns nw are: nput (ltage) sgnal: utput (ltage) sgnal: X C whch nw result n : wth the same ntatns: The utput/nput rat s : It s als a st rder electrc sgnal manpulatn stage wth a gan : X C C j X C C c j j C j C j X C 2 c c G

12 c 2C Fr we get jc G r jc C r t j t the utput sgnal s the derate the nput sgnal! c j s an ntegratn peratr we cnsder, r example, a snusdal sgnal ( t) sent e jt and we derate and ntegrate t : j s a derate peratr d ( t) dt de dt jt j e jt j ( t) jt jt ( t) dt e dt e ( t) j j

13 The peratnal ampler OA : Ideal OA characterstcs : We wll nt study the nner electrnc crcuts the OA but the mprtant peratnal eatures t er r the measurements! Amplcatn A (0 7 ) Input mpedance Z (0 0 ) Otput mpedance Z 0 (00 ) Band wdth BW ꝏ Oset ltage 0

14 The pen lp OA can amply a ltage sgnal A ( ) but NOT er ts supply ltages! I we hae cc = ±0 and A = Then 0 0 and The real pen-lp requency respnse cure s determned by the Gan Bandwdth Prduct (GBP) s the maxmum nput sgnal the OA can handle! The OA ges nt saturatn r: MAX 7 2 MAX 20 lg A r 20 lg ut n n db

15 The Operatnal Ampler CAN NOT be used as an ampler n the pen lp cnguratn! Therere, we must cnnect tw resstrs at the termnals as shwed n the gure, realzng the nertng peratnal Ampler cnguratn: At the rtual earth summng junctn we hae: nput sgnal: utput sgnal: 0 The current at the rtual earth pnt s: And because we hae 0 whch s the statc characterstc cure the dece and ges als the GAIN the ampler: G whch s negate!

16 T get a pste sgnal amplcatn we hae t swtch t the nn-nertng peratnal ampler cnguratn: Because the hgh nput mpedance the OA dece, there s rtually n current enterng the + termnal the OA and we hae nw: and S, the utput sgnal can be wrtten as where and In the end we hae: And the statc characterstc cure nw s: wth a pste GAIN! Bth cnguratns hae much lwer amplcatn than hweer the amplcatn can be desgned by chsng the tw resstance alues! Een the nn-nertng cnguratn may seem preerable, the nertng cnguratn has mprtant applcatns

17 The ltage summng OA : Here we wsh t sum tw ltages a and b Frm the nertng OA characterstc cure, we hae: wth b b a a b a I we desgn the crcut nputs wth the tw resstance alues beng equal: We can smply the abe equatn and we btan : whch s the sum the tw nput ltages! Nte that summng tw ltages means physcally t sum the tw nput currents! b a b a

18 The acte lw-pass lter (ntegratr) : The gan the nertng OA s: wth Therere Z and Z X C jc j C j C j c the utput sgnal s the electrc ntegral the nput sgnal! I we wsh t amply the utput, then we hae t put an extra resstance n the eedback arm and the extra gan wll be : G The acte hgh-pass lter (derate) : Z The gan s stll: Z wth Z X C and Z jc s j C j jc the electrc c derate! Z Z

19 Cnsder nw that the OA accepts TWO ltages at the nput termnals + = 2 and - = bth reerred t earth, and amples ts derence: A2 But ths s true n the IDEAL case! In the realty, there are TWO slghtly derent amplcatns at the nputs: A A 2 2 Ths stuatn can be eectely descrbed by the derental nput : d 2 and the cmmn mde nput : whch s the mean dstance rm the earth reerence the tw nput ltages. c 2 2 Fr an deal OA we wuld hae A A2 A and the OA wuld amply nly the derental nput, cmpletely elmnatng the cmmn mde nput! A A2 Ths stuatn can be eectely descrbed by the derental amplcatn : Ad whch perates n d and by the cmmn mde amplcatn : A whch perates n 2 c A2A c T mnmze ths prblem the OA must be desgned wth a hgh A d and a ery small A c whch means A A 2 The rat between the tw amplcatns s an mprtant qualty parameter the OA, the Cmmn Mde A ejectn at : d CM ten expressed n lgarthmc scale Ac A CM 20lg alues range rm 60 db up t 20 Db r hgh qualty OA A d c

20 The Instrumentatn Ampler IA : The mst emplyed ampler n measurements s desgned wth tw stages:. A ery hgh nput mpedance stage (0 0 Ω) 2. A derental amplcatn stage It has generally a ery hgh Cmmn Mde ejectn at (> 00 db) whch makes t sutable t amply latng sgnals ( 2 ) The (derental) GAIN s : G

21 The Carrer AC Ampler : The Carrer Ampler s an AC ampler whch des NOT amply DC sgnals r cmpnents! It s desgned n the sgnal mdulatn and demdulatn prncple rad transmssn! The lw requency ( s ) sgnal s mdulated by the carrer requency ( c ) whch s the nly requency the ampler s able t amply! A phase senste demdulatr and a lw pass-lter return an ampled lw requency sgnal!

22 The Wheatstne Brdge : Tw resstances r and r are cnnected n parallel and a galanmeter G s cnnected n a brdge cnguratn acrss the tw resstances n the pnts A and B We me nw the pnt A and B n the resstances s t hae zer current thugh the galanmeter, whch means als: A B In ths stuatn we dented 4 resstances :, 2, 3, 4 r whch we can wrte the llwng equatns: I CA CB 4I2 AD BD 2I 3I 2 Makng the rat the tw equatns, we get: 4 r 3 24 the brdge equlbrum equatn! 2 3

23 N current thrugh the brdge means als the galanmeter wth a mllltmeter! A B 0 therere, n practcal applcatn, we can substtute The Wheatstne Brdge s a zer methd electrc netwrk used r resstance measurements: I x s unknwn, we equlbrate the brdge by peratng n 2 and, knwng the alues 2, 3, 4, we get: 24 x 3 Hweer, ths s NOT the man use the Wheatstne Brdge We mght hae a resstance that changes slghtly ts alue Δ r physcal reasns It s pssble t read ths small change drectly n the ltmeter ndcatr but, t d s, we need t knw the brdge graduatn cure (r statc characterstc equatn): ( ) I we cnsder r smplcty a brdge wth 4 equal resstances: and a aratn Δ nly n the resstance, we get: AB

24 The cmplete Wheatstne Brdge characterstc cure : e 4 whch s clearly NON lnear! E 2 Hweer, the aratn s really ery small: 0.0 Then, the denmnatr the graduatn cure can be apprxmated wth 2 and the characterstc equatn has been lnearzed! E 4 e Lnearzed Wheatstne Brdge characterstc cure!

25 Same result the nly resstance wth a small aratn Δ 2 wuld hae been 2 n the secnd arm the brdge: E e 2 4 negate because 2 s n the negate term the equlbrum equatn: In the case smultaeus small aratns all 4 resstances the Wheatstne Brdge, we wuld get: E 4 e The Full Wheatstne Brdge characterstc cure! ( nte the sgn alternatns ery mprtant prperty )