Direct Conversation of Generalized Parameters of Multicomponent Two-Terminal Networks Using Capacitive Differentiator RC-Chains

Size: px

Start display at page:

Download "Direct Conversation of Generalized Parameters of Multicomponent Two-Terminal Networks Using Capacitive Differentiator RC-Chains"

Cody Richards
5 years ago
Views:

1 Mechaical Egieerig Research Vol. 4, No ISSN E-ISSN Pblishe by Caaia Ceer of Sciece a Ecaio Direc Coversaio of Geeralize Parameers of Mlicompoe Two-Termial Neworks Usig Capaciive Differeiaor RC-Chais Vlaimir I. Ivaov 1 & Vialij S. Tiov 1 1 Soh-Wes Sae Uiversiy, Deparme of Comper Sciece, rsk, Rssia Correspoece: Vlaimir I. Ivaov, Soh-Wes Sae Uiversiy, Deparme of Comper Sciece, rsk, Rssia. viva7@mail.r Receive: November 6, 01 Accepe: December, 01 Olie Pblishe: Jaary 6, 014 oi:10.559/mer.v41p6 URL: hp://x.oi.org/10.559/mer.v41p6 Absrac We prese a evice for irec coversio of geeralize parameers of passive mlicompoe wo-ermial eworks (TTN) wih exciaio of measrig circi (MC), comprisig a moel compoe a he wo-ermial ework beig ese, o applyig o he measrig circi volage plses which vary as he -h power of he ime a -fol sigal iffereiaio a measrig circi ip a op wih iffereiaors beig exece o RC-chais. eywors: mlicompoe wo-ermial ework, geeralize parameers, coversio of he parameers 1. Irocio Trasformaio of he parameers of bipolar elecrical circis is a ora brach of moer iformaio a measrig eqipme. Areas for applicaio of coverers: rasformaio parameers of physical processes sig parameric sesors, corol elemes a compoes elecroic eqipme. Coverers parameers mlieleme passive mlicompoe wo-ermial eworks (TTN) ca be cosrce sig he irec coversio a eqilibraio. Coverers wih balacig volage or crre TTN compesaig sigal are highly accrae, b have a low spee. Whe moiorig processes wih rapily chagig properies appropriae o se irec objec parameers beig ese. To cover he parameers of measrig circi (MC) io elecrical sigals as MC, i is avisable o se a volage ivier io oe arm which icles he measre wo-ermial, a i aoher-efesive chai. If he ac o he se volage plse, he shape of which has he form of a power fcio 10 m U, (1) where U m is he es lse amplie, is heir raio, a i a seay-se moe o compleio of he rasie process, he ivier op respose represes a oal of lses i he form of power fcios wih iices from o zero: m U! 1 m 1 m m...! U! U! U! 1! 1! 0!. () Each compoe of esio () coais iformaio o he correspoig geeralize MC parameer. Where 0, 1,,, are geeralize parameers of measrig circi rasfer fcio, wih is operaor image beig geerally expresse as p 0 1 b0 b1pbp.... () a a pa p... Whe a 0 0, geeralize parameers are efie by recrrece formla (Ivaov, Tiov, & Golbov, 010) 6

2 Mechaical Egieerig Research Vol. 4, No b0 b1 0a1 b 0a 1a1 b 0a 1a a1 0 1 (4) The vale of each op sigal compoe icles iformaio o oe or several elecrical parameers of he wo-ermial ework. The expoe of of he power lse ms correspo o he mber of N-compoes i he wo-ermial ework beig ese: N 1. Ths, for example, a exciaio of he measrig circi (MC) by cbic lses of volage, he MC op sigal becomes: 0Um U 1 m 6Um 6Um 0 Triple iffereiaio of sigal (5) allows o efie every -parameer. (5) 0 0 m 6 1 m 6 m U U U (6) m 6 1 m U U (7) 0 6 U 0 m. (8) Resls of eermiaio of -parameers irecly o formlas (5) (8) epe o amplie of fee-i lse. For he removal of his facor i is ecessary o a he seco chael of iffereiaors: 10 Um (9) 10 6 m U (10) 10 6 Um (11) a o raio he vales of sigals (5), (6), (7), (8) by sigals (1), (9), (10), (11) accorigly. Ths, formlas for he calclaio of -parameers will look like: (1) (1) : (14) 6 6. (15) I pblicaios (Ivaov, Tiov, & Perov, 011, 01) i was jsifie he meho of irec coversio of -parameers of he wo-ermial ework sig operaios of -fol iffereiaio of he es lse sigal a ivier op volage comprisig a sigle-compoe ework Z 0 a a wo-ermial ework (TTN) of he objec measre. Whe he rasie process i he measrig circi is complee, samplig of rasie vales of ivier ip a op sigals is performe, as well as all iffereiaor ops. The scheme of he coverer of parameers of he for-eleme wo-pole ework wih iffereiaio of sigals is give o Figre 1.

3 Mechaical Egieerig Research Vol. 4, No VIG Z TTN Sychroizaio Microcoroller Figre 1. Parameer coverer scheme wih iffereiaors I he aricle (Ivaov, Tiov, & Perov, 01) a meho a evice of irec rasformaio are cosiere wih iffereiaors o operaioal amplifiers (OpAmp). For seay work of mlisage iffereiaors he correcio of freqecy escripio of OpAmp is applie i area of high-freqecies.. Usig Passive RC-Secio for Differeiaio Sigal Differeiaig cascaes o acive compoes a operaig amplifiers i pariclar has rawbacks, sch as he eecy o sabiliy loss, complexiy of provisio of cascae ieiy, sabiliy, a rif elimiaio. I his aricle i is sggese o apply iffereiaors o he passive RC-chais cosisig of coesers a resisors. Use of passive circis is propose as mli-cascae iffereiaors comprisig i-series iffereiaig RC-chais. The scheme of coverer wih iffereiaig RC-chais is presee o Figre (Ivaov, Emelyaov, Tiov, & Soha, 011). VIG С1 С С Z0 R1 R R BS С4 С5 С6 Z(p) R4 R5 R6 TTN Sychroizaio Microcoroller Figre. Scheme of parameer coverer of wo-ermial ework wih iffereiaig RC-chais Each iffereiaor has hree iffereiaig RC-chais: R 1 C 1, R C, a R C i he firs oe a R 4 C 4, R 5 C 5, a R 6 C 6 i he seco. The firs iffereiaor ip receives a sigal from he volage lse geeraor (VIG) op powerig he measrig circi, a he seco iffereiaor ip receives volage from he wo-ermial ework (TTN). Bffer sage (BS) elimiaes he iflece of he seco iffereiaor ip circi o eace of he wo-ermial ework beig ese. Trasfer fcio of he oly oe iffereiaig RC-chais is expresse as: 8

4 Mechaical Egieerig Research Vol. 4, No prc p 1 prc To obai a -cascae iffereiaor havig rasfer fcio 1 RC, RC p p RC 1 prc i wol be goo o icle bffer cascaes bewee RC-chais complicaig he evice scheme. owever, a rasfer fcio close o he oe escribe above ca be provie sig oly passive RC circis. To slify aalyical expressios, i is reasoable o se each cascae s ime cosas o he same vales: R 1 C 1 = R C = R C = τ, sig iffere capaciace a resisace vales i each cascae. For example, if oe akes R C = RC = τ i he seco chai, he resisace is o be rece a capaciace icrease as mch as i he firs chai, a, coversely, resisace is o be icrease a capaciace rece by as mch as i he hir chai: C R C1 R1 mr C mc R m m, where m < 1. Le s efie rasfer fcios for he op of he firs, seco a hir cascaes of iffereiaors a heir geeralize parameers. Trasfer fcio for he firs RC-chai op is as follows 1RC Geeralize parameers of rasfer fcio (16) eqal he followig:, p p m p p. (16) 1 p m p m m p m Trasfer fcio for he seco RC-chai op is expresse as RC a is geeralize parameers eqal o he followig: m m 1 1. (17) p p p, (18) 1 p m p m m p m. (19) 1 Fially, he rasfer fcio for he hir RC-chai op ca be presee wih he formla a is -parameers eqal o p p, (0) 1 p m p m m p RC (1) Usig expressios for operaor image of cbic-form power lse (1) a geeralize parameers (17), (19), (1) of rasfer fcios 1RC (p), RC (p) a RC (p), we fi sigals a ops of he firs iffereiaor s hree cascaes: 11 Um 1m 1mm () 9

5 Mechaical Egieerig Research Vol. 4, No Um m () 1 Um 6. (4) Likewise, sig operaor image of volage o he wo-ermial ework beig ese (5), rasfer fcios 1RC (p), RC (p) a RC (p) a heir geeralize parameers (17), (19), (1), we fi sigals a ops of each of he seco iffereiaor s hree cascaes o compleio of he rasie process i he measrig circi: 1 U 1m 1mm 6U 1m 6 U (5) 0 m 1 m m 0 m 1 6 U 1 m 6 Um (6) 0 6 Um. (7) The op sigal raios of he hir iffereiaig cascaes (7) a (4), seco iffereiaig cascaes (6) a (), firs iffereiaig cascaes (5) a (), as well as volages o he wo-ermial ework a power lse a ime, respecively, eqal he followig: 0 (8) m (9) m 1m 1mm (0) (1) 10 Usig Eqaios (8) (1), oe ca calclae he vales of -parameers of he measrig circi: 0 () 1 m m1m 1 m m 1 m () (4) (5). Nmerical Simlaio To check a aeqacy for he coverer s heoreical moel parameers, he moelig of evices geeralize 40

6 Mechaical Egieerig Research Vol. 4, No parameers measreme for for-eleme RLC wo-pole eworks was exece. The scheme of oe of hem is represee by R 1, C 1, R, L 1 o Figre. Moelig is exece by meas of he MliSim program, a calclaio MahCa. R0 10 R1 C1 R L1 0 Figre. The scheme of for-eleme RCL wo-pole ework Parameers of elemes of he measrig scheme: R 0 = 1 kom, R 1 = 1.5 kom, R =.5 kom, C 1 = 5 F, L 1 = 4.5 m. The es sigal ha a form of a cbic lse of esio wih amplie U m = 10 V. Draio of a lse of ime 50 μs. Cosa of ime of RC of a chai τ = 5 μs, parameer m = 0.1. Trasfer fcio of a ivier of R 0 -Z has a appearace Is geeralize parameers are eqal R1 prrc 1 1 p RLC RCL p R1R0 pr1r0r R1R0C1 p R1R0LC 1 1. R 0 1 R 1 R0 R C R R R R R 1 0 R 0 C C L C Figre 4. Diagrams of volages i coverer parameers Figre 4 shows ime iagrams of volages o he ips a ops of each iffereiaig cascae. 41

7 Mechaical Egieerig Research Vol. 4, No Volage measreme imepoi i all corol pois = 00 μs. Resls of measremes: 10 = 5.1 V 0 =.9568 V 11 = V 1 = V 1 = 0.48 V = V 1 = 0.06 V = 0.06 V. Resls of calclaios of he geeralize parameers i formlas () (5): 0 = = 1.8 μs = 7.9 μs = μs. The receive vales of -parameers coicie wih he parameers of a measrig chai fo i formlas (4). 4. The Coclsios I is show ha i he evice for efiiio of geeralize parameers of mlicompoe passive wo-ermial eworks wih iffereiaig sigals, he measrig sysem ca be se iffereiaors, cosisig of series-coece passive RC-circis. Sle scheme o sable a ajsme-free compoes (capaciors a resisors) allows yo o measre he geeralize parameers of a wie class of objecs ha have a schema of replaceme RC-, RL- a RLC-wo-ermial evice. Receive he aalyical relaios for calclaio of he geeralize parameers for he oaliy of he measre vales of ip a op volages of he measrig circi a he ops of boh chaels iffereiaio. Refereces Ivaov, V. I., Emelyaov, S. G., Tiov, V. S., & Soha, M. Y. (011). Meho for efiiio of he parameers of mlicompoe wo-ermial eworks a meas for is lemeaio. Pae No. 444 RF, Izobre. Polez. Moeli, No.. Ivaov, V. I., Tiov, V. S., & Golbov, D. A. (010). The se of geeralize parameers of a measrig circi o ieify mlicompoe wo-ermial eworks. Dach. Sisemy, 8, Ivaov, V. I., Tiov, V. S., & Perov, A. S. (011). Meho a evice for measreme of he parameers of mlicompoe wo-ermial eworks. Pae No. 488 RF, Izobre. Polez. Moeli, No. 18. Ivaov, V. I., Tiov, V. S., & Perov, A. S. (01). Coversio of he parameers of mlicompoe wo-ermial eworks wih sigal iffereiaio. Measreme Techiqes, 55(9), hp://x.oi.org/ /s x Copyrighs Copyrigh for his aricle is reaie by he ahor(s), wih firs pblicaio righs grae o he joral. This is a ope-access aricle isribe er he erms a coiios of he Creaive Commos Aribio licese (hp://creaivecommos.org/liceses/by/.0/). 4

VARIATIONAL ITERATION METHOD: A COMPUTATIONAL TOOL FOR SOLVING COUPLED SYSTEM OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

VARIATIONAL ITERATION METHOD: A COMPUTATIONAL TOOL FOR SOLVING COUPLED SYSTEM OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Joral of Sciece a Ars Year 6 No. 336 pp. 43-48 6 ORIGINAL PAPER ARIATIONAL ITERATION METHOD: A COMPTATIONAL TOOL FOR SOLING COPLED SYSTEM OF NONLINEAR PARTIAL DIFFERENTIAL EQATIONS MORF OYEDNSI OLAYIOLA