6 Auocompensaive Sysem for Measuremen of he Capaciances Radioengineering ATOCOMPENSATIVE SYSTEM FOR MEASREMENT OF THE CAPACITANCES Marin KOLLÁR, Vikor ŠPÁNY, Tomáš GABAŠ Dep. of Elecronics and Mulimedia Telecommunicaions Park Komenského 3, 4 Košice niversiy of Technology Košice, Slovakia Dep. of Hybrid Microelecronics, Park Komenskeho, 4 Košice niversiy of Technology Košice, Slovakia conrol pulse [3] was firs derived by Kollar []. The auocompensaive sysem, in which he equivalen volage is se auomaically depending on he asymmery, was firs published in [4]. The goal of his paper is o show he possibiliy of measuremen of capaciances wih auocompensaive sysem wih flip-flop sensor and derivaion of formula for equivalen volage. Absrac A simple and successful design of an auocompensaive sysem wih flip-flop sensor for measuremen of capaciances is presened. The analysis of he sensor is based on he sae descripion wih he verical rise segmens of he conrol pulse. The heoreical resuls are compared wih measured daa and good agreemen is repored. Keywords Flip-flop sensor, equivalen volage, measuremen, capaciance.. Inroducion The main par of he auocompensaive sysem is flipflop sensor [], [3], [5]. The flip-flop sensor is par of a class of silicon sensors wih a digial oupu. Sandard flipflop consising of wo ransisors and wo resisors (Fig. is characerized wih wo sable saes. One of he auhors of he paen flip-flop sensor was Lian [] who showed ha flip-flop sensor can be used for measuremen of non-elecrical quaniy and derived formula for calculaion of equivalen volage of he flip-flop sensor conrolled by slowrise conrol pulse. The principle of measuremen is based on his ha measured non-elecrical quaniy will break he value symmery of he inverers relaive o he morphological symmery axis passing hrough poins K and Z. However i can be compensaed by a volage N = in such way ha by repeaed connecion o a source I( he 5% sae [] is resored, so ha he magniude of he measured non-elecrical quaniy will be refleced ino he volage, which we will call he equivalen volage. If needed, however, i is no necessary o sick o he cusom of using sensomeric elemens in Fig.. The formula for calculaion of equivalen volage of flip-flop sensor conrolled by verical rise segmens of he Fig. Flip-Flop sensor. Capaciances C and C represen parasiic capaciances of he ransisors T, T.. Sae descripion The flip-flop sensor can be described by sysem of differenial equaions [3] ( u u Ri( + ( R + R Q ( R + R C du N φ = ( d ( u u + Ri( + ( R + R Q ( R + R C du N φ = ( d where φ, φ are defined as and i + i β, φ = i + i β φ = (3 ( u V, i i ( u V i ies exp T = ES exp = (4 where β, β are curren gains, i ES, i ES are sauraion currens of bipolar ransisors and V T is hermal volage. 3. Formula for he equivalen volage In he case of conrol wih he verical rise segmens of he conrol pulse he currens passing hrough capaciors (C, C are no negligible compared o he ransisors currens of he flip-flop sensors. I is obvious ha unequal va- T
Radioengineering Auocompensaive Sysem for Measuremen of he Capaciances 7 Vol., No., June M. KOLLÁR, V. ŠPÁNY, T. GABAŠ lues of capaciances C, C will break he value symmery of he inverers of he flip-flop sensor bu can be compensaed by volage N =, wha was described above. In he case of value symmery i is no possible o decide abou he logical level of he oupu volage of he inverer R, T or R, T, afer connecion o a curren source. The reason is ha he occurrence of a logical one a he menioned oupu of he inverer has a saisical characer. Wih a sufficienly large number of connecions N o he curren source he probabiliy P(N /N of he occurrence of logical ones N a he inverer oupu is.5 (5% sae. In he case of value asymmery his similariy is broken, bu if N =, hen he 5% sae is resored and again i is no possible o decide abou he logical level of he oupu volage of he inverer R, T or R, T. Sysem of he differenial equaions (, ( was solved in []. In he case of value symmery soluion of he sysem (, ( wihou effec of a noise, has he form [] u = u (5 Le curren amplificaions coefficiens, he sauraion currens of he bipolar ransisors and resisors of he flipflop sensor are equal and le he soluion of he sysem (, (, in he case ha C C, is funcion (5, hen for equivalen volage we have: u C R C ( u = R I m φ( u, u (6 C C where I m is ampliude of curren conrol pulse, C = C + C R = R = R, φ = φ = φ, u = u = u and C = C. Eqn. (6 was derived hrough (, ( under condiion C/ C <<. Equivalen volage as a funcion of he volage u, calculaed by (6, secures a ransiion ino unsable sae S (Fig., wihou effec of a noise. The funcion (5 represens a separarix [3]. The separarix T (Fig. has a key role in he funcioning of he sensor. The separarix divides he sae plane ino wo regions conaining he aracors and. If he origin is locaed on he same side of he separarix as he poin, i means ha during each conrol pulse he flip-flop will go ino sae. A change of he equilibrium ino can be achieved by using he volage N in such way ha he origin lies on he same side of he separarix T as he poin. This principle was heoreically described in [3] and mahemaically was solved in []. Hence he decision abou a ransiion ino sae or is made in he origin of he sae plane as was described above. Bu here currens φ, φ are negligible compared o he capaciance currens and hen facor conaining φ(u,u in (6 can be negleced. Final formula for he equivalen volage is hen R C = (7 C I m This idea o assume a soluion of he sysem (, ( in he case of he value asymmery when N =, as funcion u = u was firs used in []. u [V].8.7.6.5.4.3.. Q= T...3.4.5.6.7.8 u [V] S Q= Fig. Sae rajecory T represens a ransiion o sae S. In Fig., Q =, Q = represen characerisics of firs and second inverer of he flip-flip sensor. Fig. 3 Auocompensaive sysem
8 Auocompensaive Sysem for Measuremen of he Capaciances Radioengineering 4. Auocompensaive sysem The auocompensaive sysem is shown in Fig. 3. R and R are he load resisors of he flip-flop and usually range from a few kω o ens of kωs. R k is small resisor is value is normally wo orders of magniude smaller han R and R. Volage u is aenuaed by he raio R /R k (R >>R k and is fed o flip-flop sensor. By adjusing u, he asymmery due o componens in he flip-flop can be compensaed, hus bringing he flip-flop sensor ino 5% sae []. The wo oupus of he flip-flop are conneced o comparaors and he comparaor oupus are conneced o he inegraor and reversible couner. The curren of he flip-flop is swiched on and off by a pulse generaor. I is obvious ha feedback is realized as analog, bu reversible couner conneced o he comparaors enables o represen measured capaciance in he digial form. u u u N NS N Fig. 4 Principle of auocompensaive sysem funcioning. Now suppose ha C > C. From (7, i is obvious ha >. Afer connecion of he curren generaor volage u N increases, bu if u N ( >, hen beginning wih his momen he siuaion sars o alernae which means he logical one will appear alernaely a he oupu of he firs inverer and hen second inverer. This fac is expressed by Fig. 4. From he Fig. 4 i follows ha he measured capaciance will be refleced ino he mean value NS of he symmerizing volage u N. The imporan parameer of he flip-flop sensor is offse volage. Le he offse volage depends on emperaure changes, mismaches in resisances and capaciances, mismaches in ransisor sauraion currens and curren gains. Assume ha he wo ransisors are subjeced o he same emperaure and ha he effec of mismaches in he ransisor sauraion currens and curren gains and of mismaches in he resisances of he flip-flop are negligible compared wih he effec of mismaches in he capaciances of he flip-flop sensor. The major cause of offse volage is hen due o mismaches in he capaciances of he flip-flop sensor. The offse volage can be compensaed by he addiion of a small DC volage, or by he addiion of a small capaciance, so ha C = C. In case of our experimen I m =.7 ma, R = 6.8 kω, R k = Ω, R =.8 kω, C i = nf, R i = kω, C = 387pF so ha offse volage OF was equal o 8.3 mv. The offse volage OF was measured indirecly proceeding : Firs, mean value of he volage u was measured (Fig. 3 using analog filer, Offse volage OF was calculaed using formula: R K OF =, ( RK + R where is mean value of he volage u and R K, R are resisors of he auocompensaive sysem (see Fig. 3. sing (7 for mismaches in he capaciances we have C =.86 pf. Now suppose ha measured capaciance C is in parallel conneced o capaciance C. The capaciance C can be calculaed using ` C C = C (8 RI m where ` is equivalen volage wih offse. The formula (8 was derived hrough (7 under condiion ha C = C + C. This idea o measure he capaciances wih compensaion of he offse was used in he experimen. In Fig. 5 measured equivalen volage wih compensaed effec of offse in he range from.5 pf o 3.5 pf is shown. The equivalen volage was measured indirecly proceeding : [mv] 4 35 5 ideal 5. Experimenal resuls 5 measured Resuls of heoreical consideraions were proved by a lab experimen. Experimenal circui was made by SMT. 5.5.5.5 3.5 C [pf] Fig. 5 Resul dependence beween he volage and C Mean value of u measured (Fig. 3 by analog filer. Equivalen volage ` wih offse compued using ( R R ` RK K + =,
Radioengineering Auocompensaive Sysem for Measuremen of he Capaciances 9 Vol., No., June M. KOLLÁR, V. ŠPÁNY, T. GABAŠ where is mean value of he volage u and R K, R are resisors of he auocompensaive sysem (Fig. 3. Equivalen volage wihou offse was calculaed as = ` - OF where OF is offse measured by proceeding. ( C [%] / C 3 5.5.5.5 3.5 C [pf] Fig. 6 The relaive error as a funcion of he capaciance C error wih and wihou dihering in he range from.5 o.6 pf as resul of simulaion in MATLAB is shown. In Fig. 9 he volage u as example of resul of he laboraory experimen wih effec of dihering can be seen. I is obvious ha in he case of our experimen he measuring range was o 3.5 pf. From (7, he measuring range can be changed by a value of he curren I m, resisor R and capaciance C respecively. The possibiliy o change he measuring range is no invesigaed in his paper. 4µs/div u ( In Fig. 6 absolue value of relaive error is ploed versus measured capaciance. i( 8 mv/div I m δ T/ δ Fig. 7 Curren conrol pulse Where ( C / C = ( C - C ` / C so ha C is measured capaciance by using capaciive bridge and capaciance C ` was calculaed by (8 under assumpion ha ` is equivalen volage wih offse and C is iniial difference of he capaciances of he flip-flop sensor. In he case of our experimen C =.86 pf. [µv] N /= dihering no dihering Fig. 9 The volage u as example of resul of he laboraory experimen wih effec of dihering. 6. Conclusions In he paper, possibiliy of capaciances measuremen wih auocompensaive flip-flop sensor is shown. Proposed mehod of capaciances measuremen enables o compensae offse of he flip-flop sensor. The validiy of he formula for he calculaion of equivalen volage was proved by laboraory experimen. The agreemen of real and measured value of he capaciance is good. From obained experimenal resuls i follows ha he inaccuracy of measured capaciance is less han 4.5%..5.6 C [pf] Fig. 8 Absolue error of he equivalen volage corresponding o parameer values by par 5. The sensor was conrolled by curren pulse according o Fig. 7, while δ = δ = ns, I m =.7 ma, T = µs. As described above, value of he measured capaciance is refleced ino he mean value of he symerizing volage u N and hen for absolue error we ge = - NS. The absolue error as funcion of he capaciance has a shape of he periodical riangular wave, which ampliude is N / (Fig. 4. Bu his error was negleced because a hermal noise of he pars of he flip-flop can be used for generaing a dihering signal, so ha hen he resul absolue error is smaller han µv (Fig. 8. In Fig. 8 absolue Fig. A phoography of he experimenal circui References [] LIAN, W. Inegraed silicon flip-flop sensor. Docoral Thesis. Delf: Technise niversie Delf, 99. [] KOLLAR, M. Auocompensaive sysem wih analog feedback. Diploma Thesis. Kosice: Technical niversiy of Kosice,. [3] SPANY, V., PIVKA, L. Dynamic properies of flip-flop sensors. Elecrical Engineering. 996, vol. 47, no. 7-8, p. 69-78.
3 Auocompensaive Sysem for Measuremen of he Capaciances Radioengineering [4] KALAKAJ, P., SPANY, V., SOLTYS, R. Flip-flop sensors wih feedback. In Proceedings of he Inernaional Conference Tesla III Millenium. Belegrade (Yugoslavia, 996, p. 45-49. [5] LEVICKY, D., MICHAELI, L., SPANY, V., PIVKA, L., KALA- KAJ, P. Auocompensaive sysem wih flip-flop sensor. In Proceedings of he Inernaional Conference. Napoli (Ialy, 996, p. 85-89. Abou auhors... Marin KOLLÁR was born in 974 in Spišská Nová Ves, Slovakia. This ime he is Ph.D. suden a he Deparmen of Elecronics and Mulimedia Communicaions. Vikor ŠPÁNY (Prof, Ing, DrSc, received his DrSc (DSc degree from he Slovak niversiy of Technology in Braislava, Czechoslovakia. Afer joing he niversiy of Technology in Kosice in 95 his reserach was devoed o pulse circuis and digial elecronics. The resuls of hese aciviies, published in local and inernaional journals, have been summarized in he book Bipolar Transisor in Pulse Circuis. He direced his furher aciviies oward numerical and graphical soluions of non-linear dynamical sysems. Among he mos imporan resuls were he algorihms for consrucion and uilizaion of boundary surfaces in flipflop circuis and oscillaory sysems. Currenly he is Professor Emerius of elecrical engineering a he Deparmen of Elecronics and Mulimedia Telecommunicaions. Tomáš GABAŠ (Ing. was born in 977 in Zvolen. He sared his Ph.D. sudy a he deparmen afer defending his diploma hesis "Thick films gas sensors" in. The opic of his nex work is oriened o hick films sensors. RADIOENGIERING REVIEWERS June, Volume, Number I. BALÁŽ, Slovak niv. of Technology, Braislava D. BIOLEK, Miliary Academy, Brno T. DOSTÁL, Brno niversiy of Technology, Brno P. GALAJDA, Technical niversiy, Košice Z. KOLKA, Brno niversiy of Technology, Brno J. KOLOCH, Brno niversiy of Technology, Brno I. KOPEČEK, Masaryk niversiy, Brno M. LAIPERT, Czech Technical niversiy, Praha O. OLACH, Slovak niv. of Technology, Braislava J. POSPÍŠIL, Brno niversiy of Technology, Brno J. PNČOCHÁŘ, Technical niversiy, Osrava M. SIGMND, Brno niversiy of Technology, Brno V. ŠPÁNY, Technical niversiy, Košice