Compensation of impedance meters when using an external front-end amplifier

310 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 2, APRIL 2002 Compensa ion o Impedance Me e s When Using an Ex e nal F on -End Ampli ie Josep M. To en s and Ramon Pallàs-A eny, Fellow, IEEE Abs ac —Fou - e minal impedance me e s based on pseudo-b idges yield unexpec ed unce ain ies when using high-con ac -impedance elec odes. Adding a on -end ampli ie o he impedance me e and ea anging he connec ion o he me e e minals o e come he con ac impedance p oblem. How- e e , because he compensa ion p o isions in he ins umen a e mean o compensa e only impedance esiduals o es ix u es, by ei he an open/sho o an open/sho /load co ec ion p ocedu e, he ex e nal on -end inc eases he inaccu acy o he measu e- men se up. This pape shows ha an open/sho /load co ec ion can also compensa e complica ed impedance esiduals such as hose om ex e nal ampli ie s. The pape de ails he co ec ion p ocedu e and p o ides he equa ions o calcula e he impedance unde es om he eadings o he impedance me e . Index Te ms—Impedance measu emen , pseudo-b idge, esidual impedance, . I. INTRODUCTION ELECTRICAL impedance measu emen s, including impedance spec oscopy, ha e been applied o ma e ial cha ac e iza ion o senso de elopmen and quali y con ol in se e al a eas anging om biological issue cha ac e iza ion [1] o cemen se ing s udies [2]. Common impedance mea- su emen s need imme sed elec odes when applied o ionic media [3] in o de o con e ionic cu en s in he elec oly e in o elec on cu en s in elec onic ci cui s. Elec ode con ac impedance is usually high, pa icula ly a low equencies. Because mos impedance me e s a e mainly in ended o cha ac e ize elec onic componen s o ci cui s whe e con ac impedances a e low, using high-impedance elec odes causes he ins umen o display inaccu a e esul s. Fig. 1 shows he basic wo king me hod o comme cial impedance me e s based upon pseudo-b idge echniques (au o-balance b idge ci cui ) such as he HP4192A [4]. The ins umen applies a es signal o equency and ampli ude (selec ed by he use ) o he impedance unde es ( ) h ough he high-cu en (HC) e minal, esul ing in a cu en h ough and a d op in ol age ( ) sensed a he high-po- en ial (HP) e minal ( ). Mos o lows h ough an in e nal e e ence esis o owa d a ol age-con olled ol age sou ce locked in phase o he es signal and connec ed o he low-cu en (LC) e - Manusc ip ecei ed Ap il 3, 2001; e ised Decembe 31, 2001. This wo k was suppo ed by he Spanish CICYT, unde P ojec TAP1999-0742. The au ho s a e wi h he Di isió d’Ins umen ació i Bioenginye ia, De- pa amen d’Enginye ia Elec ònica, Uni e si a Poli ècnica de Ca alunya, Ba celona, Spain (e-mail: [email p o ec ed]). Publishe I em Iden i ie S 0018-9456(02)04313-9. Fig. 1. Fou -wi e impedance measu emen using a pseudo-b idge when con ac impedances wi h he impedance unde es ( Z ) a e negligible. Fig. 2. Two-wi e impedance measu emen using a es ix u e modeled by i s ABCD pa ame e s. minal. The emaining cu en , , lows owa d a ze o de ec o (ZD) connec ed o he low-po en ial (LP) e minal. The ou pu o he ZD con ols he ampli ude and phase o in o de o achie e and a ze o ol age a he LP e minal. Then, and . Because is known, mea- su ing and yields he alue o he impedance unde es , . S ay capaci ance be ween he e minals o and g ound would no in luence he measu emen because e minals LP and LC a e a ze o po en ial and e minal HP is connec ed o a high-impedance ol me e . Ne e heless, he impedance unde es is ac ually connec ed o he impedance me e by passi e elemen s, such as po ex ensions and es ix u es, no shown in Fig. 1. In he simple wo-wi e connec ion, any inaccu acy a ibu able o passi e elemen s, such as esidual impedance o es ix u es, s ay impedance, o admi ance and connec ing lead pa asi ics, can be compensa ed by wo e e ence measu emen s a he es e minals, no mally an open-ci cui and a sho -ci cui impedance. Any passi e ne wo k connec ing an impedance me e o he impedance unde es by wo wi es (Fig. 2) can be ep esen ed by i s ansmission pa ame e s , , , and ([4], p. C-1). The inpu -ou pu ela ion is hen (1) whe e, by compa ing wi h Fig. 1, and , i and . 0018-9456/02$17.00 © 2002 IEEE TORRENTS AND PALLÀS-ARENY: COMPENSATION OF IMPEDANCE METERS 311 The esul o he measu ed impedance (me e eading) is . Hence, we ha e (2) The impedance unde es (e ec i e impedance, which includes pa asi ics and in luence ac o s such as empe a u e and e- quency) is . The e o e, can be calcula ed om i he ne wo k ansmission pa ame e s o a e de e - mined om independen measu emen s. An open-ci cui mea- su emen ( ) yields and a sho -ci cui mea- su emen ( ) yields . Then, i he measu ed ne wo k(whichincludes heins umen inpu po ex ensionand he es ix u e) is symme ic ( ), he ac ual impedance unde es canbecalcula ed om hemeasu edimpedance alue by (3) which ag ees wi h he exp ession gi en by [4, p. C-2]. Fo complica ed esiduals such as hose om cus om-made es ix u es and ex e nal ampli ie s, which may be asymme ic (), adding a hi d e e ence measu emen in ol ing an impedance close o he impedance unde es u he educes in- accu acies [6]. This p ocedu e is e med open/sho /load co ec- ion. The inal esul is hen (4) whe e is a s anda d o e e ence impedance and is i s measu ed alue. Equa ion (4) is he a anged exp ession gi en by [6]. This p ocedu e, howe e , is alid in p inciple only o wo-wi e measu emen s. Mo eo e , i in Fig. 1 we conside he con ac impedance () be ween he ins umen and he impedance unde es , we ob ain he equi alen ci cui in Fig. 3. The LC e minal is no longe a 0 V, which esul s in g oss measu emen e o s. An open/sho /load co ec ion, such as ha discussed abo e, would no sol e he p oblem because i only applies o wo-wi e mea- su emen s. Adding a on -end di e en ial ampli ie (DA) wi h high inpu impedance o he impedance me e and ea anging i s connec ions, as shown in Fig. 4, sol e he high-con ac impedance p oblem [5]. The ol age a he e minal HP is s ill he d op in ol age ac oss he impedance unde es because LC and LP a e sho ed and LP is a i ual g ound po en ial. The e o e, he i ual g ound a LC (LP, ze o de ec o ) yields in spi e o . Howe e , any s ay capaci ance be ween he e minals o and g ound would in luence he measu emen because is no i ually g ounded. Ne e heless, he on -end ampli ie adds i s own impedance esidualsand he ques iona ises abou how oco ec hem.This pape shows an e ec i e p ocedu e and p o ides he necessa y equa ions o educe inaccu acies esul ing om he on -end ampli ie needed o impedance measu emen s in ol ing high- con ac impedances, such as hose om imme sed elec odes. The p oposed p ocedu e ollows he same s eps han ha de- sc ibed o wo-wi e measu emen s. Fig. 3. Fou -wi e impedance measu emen using a pseudo-b idge when con ac (elec ode) impedances wi h he impedance unde es a e no negligible. Fig. 4. F on -end ampli ie (DA) and ea anged connec ions wi h he pseudo-b idge impedance me e in Fig. 3 as p oposed in [5]. Because e minals LC and LP a e sho ed, he elec ode impedance in se ies wi h he in e nal e e ence esis o ( R in Fig. 3) is a i ual g ound po en ial. II. METHOD Any ac i e ci cui be ween he ins umen and , such as he ampli ie shown in Fig. 4, can be desc ibed by i s ansmis- sionpa ame e s( ol agegain ,inpu impedance , and ou pu impedance ) as ollows (5) I he impedance me e wi h he added on -end is connec ed o he impedance unde es ( ) h ough a symme ic passi e ne wo k as in Fig. 5, we ha e (6), shown a he bo om o he page, whe e has been eplaced by ( because o symme y). Equa ion (6) leads o (7) The measu ed impedance alue is (8) Sol ing o yields (9) whe e (10) (11) (12) and is he impedance measu emen esul ob ained by he ins umen (me e eading). 312 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 2, APRIL 2002 Fig. 5. Se up o impedance measu emen when conside ing an ac i e on -end and addi ional passi e connec ing ne wo ks. The e o e,because depends on h eepa ame e s ( ), h ee independen measu emen s can, in p inciple, cha ac e ize he sys em made om he impedance me e , he on -end am- pli ie , and addi ional connec ions (po ex ension and es ix- u e) wi hou equi ing he knowledge o hei pa icula pa am- e e s. Th ee independen measu emen s yield h ee equa ions ha can be sol ed o , and . Because (9) depends on (which ob iously depends on ), esidual compensa ion in measu emen s in ol ing a la ge ange o impedance alues may no be possible wi h a single se o h ee e e ence impedance measu emen s. Ra he , one o he e e ence measu emen s mus be chosen close o he expec ed alue o he impedance unde es (“load” alue). III. EXPERIMENTAL RESULTS AND DISCUSSION The p oposed solu ion o esidual compensa ion has been es ed in he 10 Hz o 10 MHz equency ange on a sys em o med by an HP4192A impedance me e and a on -end am- pli ie like ha desc ibed in [5]. Residual impedances om he on -end, po ex ension, and es ix u es ha e been measu ed oge he wi h he ma e ial o componen unde es and he e- o e hey should be emo ed by he h ee- e e ence co ec ion p ocedu e. The i s impedance es ed was a 24 esis o di ec ly con- nec ed o he impedance me e . Cu e A in Fig. 6 shows he e- sul , which ag ees wi h he speci ied unce ain y o he ins u- men . The inc ease in impedance a ound 5 MHz is a ibu able o he pa asi ic induc ance o esis o leads. Nex , he 24 e- sis o was connec ed o ou equal impedances o 39 in se ies wi h4.0 F ha simula econ ac impedancessuchas hose om elec odes imme sed in an aqueous elec oly e. Cu e B shows he esul , indica ing ha he con ac impedances inc ease he measu emen e o well abo e ins umen speci ica ion, as ex- pec ed om Fig. 3. Then, he esis o wi h he added con ac impedances was connec ed o he impedance me e h ough he on -end am- pli ie and necessa y cables. Cu e C in Fig. 6 shows ha he accu acy imp o es as compa ed o cu e B, bu he e a e s ill esidual inaccu acies because o he unknown cha ac e is ics o he on -end ampli ie and he po ex ensions. Fig. 6. Resul s ob ained wi h he HP4192A impedance me e and he ac i e on end in [5] when measu ing a 24  esis o . (A) Di ec measu emen o he esis o . (B) Resul when he 24  esis o is connec ed o he impedance me e using ou impedances consis ing o a 39  esis o in se ies wi h a 4.0  F capaci o , which simula e elec ode con ac impedances. (C) Resul when he 24  esis o connec ed o he ou con ac impedances is connec ed o he impedance me e h ough a on -end ampli ie . (D) Calcula ed esul a e applying he esidual co ec ion p ocedu e o he impedance displayed by he ins umen . The nex s ep was o apply he p ocedu e o compensa ing esidual impedances desc ibed by (9). The alues we e he me e eadings a each equency (cu e C in Fig. 6). The h ee e e enceimpedances we e 1 , 120k , and 24 esis o s.The 1 esis o was close o he sho -ci cui impedance (a ue 0 impedance is impossible o achie e in p ac ice). The 120 k esis o was la ge enough as compa ed o he impedance unde es o be conside ed “open ci cui ;” he impedance me e would no wo k unde ac ual open-ci cui connec ion. The 24 e e - ence esis o was selec ed because i was known in ad ance o be close o he impedance unde es . Cu e D in Fig. 6 shows ha he calcula ed inal esul s a e e y close o hose o he di ec measu emen o he 24 esis o , meaning ha he p o- posed p ocedu e ac ually compensa es o esidual impedances in he equency ange conside ed. The p oposed compensa ion me hod is no exclusi e o any pa icula on -end ci cui , p o ided i can be desc ibed by ou ansmission pa ame e s as in Fig. 5. Hence, he gain and he inpu and ou pu impedance o he on -end ampli ie in Fig. 4 may be di e en om hose o he uni used he e. The bes e- sul sa e ob ained when he hi d e e encemeasu emen is close o he expec ed impedance esul . This esidual co ec ion me hod is pa icula ly con enien o impedance measu emen s in ol ing elec odes imme sed in elec oly es. We ha e measu ed a 0.9% NaCl saline solu ion in a me ac yla e cell (0.4 cm cell cons an ) using ou s ainless s eel elec odes wi h 0.94 cm con ac a ea. The heo e ical (6) TORRENTS AND PALLÀS-ARENY: COMPENSATION OF IMPEDANCE METERS 313 Fig. 7. Resul s om a measu emen cell wi h a 0.9% NaCl saline solu ion. (A) Impedance eading when using a on -end ampli ie bu no esidual impedance co ec ion. (B) Calcula ed impedance when using open/sho /load co ec ion. alue o he bulk impedance was abou 25 esis i e a oom empe a u e [7]. Acco ding o Geddes [1], he app oxima e equi alen elec ode impedance o s ainless s eel elec odes imme sed in saline wa e is abou 37 in se ies wi h 4.0 Fa 1 kHz. Anyway, he inal esul should no depend on elec ode impedance. Cu e A in Fig. 7 is he eading o he impedance me e when measu ing he cell ull o 0.9% saline using a on -end ampli- ie . Because o he high-con ac impedance o he elec odes, he e a e la ge esidual inaccu acies, mainly a low equency. Nex , he p ocedu e o co ec ing esidual impedances de- sc ibed by (9) was applied by measu ing he impedance o he “sho ci cui ” and “open ci cui ” cell and ha o a e e ence 25 esis o (wi h ohmic con ac , no wi h elec odes). The “sho ci cui ” cell was a cell ull o a sa u a ed saline solu ion. The “open ci cui ” cell was an emp y cell. Cu e B in Fig. 7 shows ha he open/sho /load co ec ion p ocedu e compensa es he impedance esiduals a low equencies, as needed. An appa en sho coming o he compensa ion p ocedu e de- sc ibed is he need o a e e ence measu emen close o he impedance unde es , which is unknown by de ini ion. How- e e , cu e C in Fig. 6 and cu e A in Fig. 7 p o ide a clue o he alue sough . Hence, he whole co ec ion p ocedu e is be e composedo wos eps. The i s s epis o measu e he un- known impedance by using he ex e nal on end wi hou any co ec ion in o de o ob ain a i s es ima e o i s alue. The second s ep is o measu e he “sho ci cui ” and “open ci cui ” impedances and a known impedance close o he abo ees ima e in he i s s ep. Equa ion (9) yields hen he closes es ima e o he impedance unde es . IV. CONCLUSION Some comme cial impedance me e s based on au o-bal- ancing echniques canno be di ec ly applied o impedance measu emen s in ionic media because o he high-con ac impedance o he elec odes in ol ed. Those impedance me e s, o e ing sepa a e cu en injec ion and ol age de- ec ion e minals ( ou -wi e measu emen s), can measu e he impedance o ionic media by adding a high-inpu impedance ex e nal p eampli ie . The esidual impedances o he con- nec ing cables and on -end ampli ie can hen be compensa ed by measu ing a leas h ee e e ence impedances. One o hese impedances mus be p e e ably close in alue o he unknown impedance. The on -end and he esidual co ec ion p ocedu e he e desc ibed open new applica ion ields o hese impedance me e s ha o he wise could no be applied o elec oly es. REFERENCES [1] L. A. Geddes, “Elec odes,” in P inciples o Applied Biomedical Ins u- men a ion, 3 d ed. New Yo k: Wiley, 1989, ch. 9. [2] B. J. Ch is ensen, R. T. Co e dale, R. A. Olson, S. J. Fo d, E. J. Ga - boczi, H. M. Hennings, and T. O. Mason, “Impedance spec oscopy o hyd a ing cemen -based ma e ials: Measu emen , in e p e a ion and ap- plica ion,” J. Ame . Ce am. Soc., ol. 77, no. 11, pp. 2789–2804, 1994. [3] J.R.Macdonald,ImpedanceSpec oscopy,EmphasizingSolidMa e ials and Sys ems, J. R. Macdonald, Ed. New Yo k: Wiley, 1987. [4] M. Honda, The Impedance Measu emen Handbook. A Guide o Measu emen Technology and Techniques. Tokyo, Japan: Yoko- gawa-Hewle -Packa d, 1989. [5] E. Ge sing, “Measu emen o elec ical impedance in o gans. Measu ing equipmen o esea ch and clinical applica ions,” Biomed. Tech., ol. 36, pp. 6–11, 1991. [6] “E ec i e Impedance Measu emen Using OPEN/SHORT/LOAD Co - ec ion,” Hewle Packa d, Applica ion No e 346-3, HP Li e a u e no. 5091-6553E. [7] A. S og yn, “Equa ions o calcula ing he dielec ic cons an o saline wa e ,” IEEE T ans Mic owa e Tech., ol. MTT-19, pp. 733–736, Aug. 1971. Josep M. To en s ecei ed he Enginye de Telecomunicació and Doc o En- ginye de Telecomunicació deg ees in 1989 and 1996 espec i ely, bo h om he Uni e si a Poli ècnica de Ca alunya, Ba celona, Spain. He is an Associa e P o esso o Elec onic Enginee ing a he Uni e si a Poli ècnica de Ca aluny, and he eaches cou ses in se e al a eas o elec onic ins umen a ion. F om 1998 o 1999, he was a Visi ing Schola a No hwes e n Uni e si y, E ans on, IL. His esea ch includes ins umen a ion me hods based on elec ical impedance measu emen s, mainly applied o soil, ce amic ma e- ials, and oils. Ramon Pallàs-A eny (F’98) ecei ed he Ingenie o Indus ial and Doc o Ingenie o Indus ial deg ees om he Uni e si a Poli ècnica de Ca alunya, Ba celona, Spain, in 1975 and 1982, espec i ely. He is a P o esso o elec onic enginee ing a he Uni e si a Poli ècnica de Ca alunya, and he eaches cou ses in medical and elec onic ins umen a ion. In 1989 and 1990, he was a Visi ing Fulb igh Schola and, in 1997 and 1998, he was an Hono a y Fellow a he Uni e si y o Wisconsin, Madison. In 2001, he was nomina ed P o esso Hono is Causa by he Facul y o Elec ical En- ginee ing o he Uni e si y o Cluj-Napoca, Romania. His esea ch includes ins umen a ion me hods and senso s based on elec ical impedance measu e- men s, senso in e aces, ECG and a e ial blood p essu e measu emen s, and elec omagne ic compa ibili y in elec onic sys ems. He is he au ho o se e al books on ins umen a ion in Spanish and Ca alan, he la es one being Senso s and In e aces, Sol ed P oblems (Ba celona, Spain: Edicions UPC, 1999). He is also coau ho (wi h John G. Webs e ) o Senso s and Signal Condi ioning (2nd ed., New Yo k: Wiley, 2001), and Analog Signal P ocessing (New Yo k: Wiley, 1999). D . Pallàs-A eny was a ecipien , wi h John G. Webs e , o he 1991 And ew R. Chi P ize Pape Awa d om he IEEE Ins umen a ion and Measu emen Socie y. He is a membe o he Biomedical Enginee ing Socie y and he In e - na ional Socie y o Measu emen and Con ol.