Measurement of Capacitances Based on a Flip-Flop Sensor

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1 Sensors & Transducers ISSN by IFSA hp:// Measuremen of Capaciances Based on a Flip-Flop Sensor Marin KOLLÁR Deparmen of Theoreical Elecroechnics and Elecrical Measuremen, Technical Universiy of Košice, Park Komenskeho 3, 41 1 Kosice, Slovak Republic Phone: , Marin.Kollar@uke.sk Received: 4 Augus 23 /Acceped: 22 Sepember 23 / Published: 23 Sepember 23 Absrac: This paper deals wih a new ype of sysem for measuring capaciances wih he use of a flip-flop sensor conrolled by a so-called fas-rise curren conrol pulse. The heoreical consideraions are compared wih experimenal resuls, and good agreemen is repored. Copyrigh 23 IFSA. Keywords: Flip-flop sensor, Capaciances measuremen, Auo-compensaive sysem 1. Inroducion The circui in Fig.1 was inroduced in [1] as a flip-flop sensor. The flip-flop sensor is par of a class of silicon sensors wih a digial oupu. A sandard flip-flop consising from wo ransisors and wo resisors (see Fig.1) is characerized by wo sable saes, 1 and. One of he auhors of he paen flip-flop sensor was Lian [1], who showed ha a flip-flop sensor can be used for measuring non-elecrical quaniies and derived a formula for calculaing he equivalen volage of he flip-flop sensor conrolled by a slow-rise conrol pulse. The principle of measuremen is based on he measured non-elecrical quaniy breaking he value symmery of he inverers relaive o he morphological symmery axis passing hrough poins K and Z (see Fig.1). 1

2 i R1 K i R2 U N R 1 i 2 i 1 R 2 â 2 â 1 U() C 1 i 1 i 2 C 2 u 1 u 2 T 1 T 2 Z Fig. 1. Flip-flop sensor. However measured quaniy can be compensaed by a volage U N =U NE in such a way ha by repeaed connecion o source I() he 5% sae [1] is resored, so ha he magniude of he measured nonelecrical quaniy will be refleced in he volage U NE, which we will call he equivalen volage. However, i is no necessary o sick o he cusom of using sensorial elemens, as shown in Fig.1. I should be noed ha in curren conrol we also disinguish beween pulses wih a fas or slow-rise segmen of he conrol pulse (see Fig.2). I() I m ä 1 T/2 ä 2 Fig. 2. Curren conrol pulse. Conrol wih a fas-rise segmen of he conrol pulse is characerized by he raio I m /ä 1 being such ha he currens passing hrough he capaciors are no negligible compared o he ransisor currens of he flip-flop sensors. This noion should be undersood in is relaive sense. In pracice, his condiion is saisfied if ä 1,ä 2 <<R 1 C 1 and ä 1,ä 2 <<R 2 C 2 a he same ime. The goal of his paper is o show ha capaciors can be measured wih he use of a flip-flop sensor in he srucure of an auo-compensaive sysem [2,3]. 2. Equivalen Volage As described above, he asymmery of he flip-flop sensor can be compensaed by he equivalen volage U NE [1]. If we assume mismaches in he capaciances C 1,C 2, hen he formula for he equivalen volage has he form [2,3]: 2

3 U R C =, (1) 2C NE I m where I m is an ampliude of he curren conrol pulse, C1 = C + C, R=R 1 =R 2, C 2 =C and C / C << 1. The formula for calculaion of equivalen volage of flip-flop sensor conrolled by verical rise segmens of he conrol pulse was firs derived by Kollár [2,3]. 3. Auo-Compensaive Sysem An auo-compensaive sysem is shown in Fig.3. R 1 and R 2 are he load resisors of he flip-flop and usually range from a few k o ens of ks. R k is small resisor is value is normally wo orders of magniude smaller han R 1 and R 2. The 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 [1]. 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 digial form. Fig. 3. Auo-compensaive sysem. Now suppose ha C 1 >C 2. From he formula (1) i is obvious ha U NE >. Afer connecion of he curren generaor volage u N increases, bu if u N ( 1 )>U NE, 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. Fig.4 expresses his fac. From he Fig.4 i follows ha he measured capaciance will be refleced ino he mean value U NS of he symmerizing volage u N. 3

4 u 1 u 2 U NE ÄU N u N U NS 1 Fig.4. Principle of auo-compensaive sysem funcioning. The principle of he auo-compensaive sysem funcioning is in more deail described in references [2,3]. 4. Proposed Soluion Experimenal circui was made by surface monage echnology. Fig.5 shows an experimenal circui. The parameers were se as follows R=6.8k, R k =1, R =1.8 k, C i =1 nf, R i =1 k and C=53 pf. The flip-flop sensor was conrolled by a curren pulse according o Fig.2, while ä 1 =ä 2 =1ns, I m =.83 ma and T=1ìs. Flip-flop circui Fig. 5. A phoography of experimenal circui. An 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 is 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. An asymmery caused by mismaches in capaciances we will call a capaciive offse. A capaciive offse ÄC 1 can be compensaed by a small DC volage, or by a small capaciance o achieve C 1 =C 2. 4

5 Now suppose ha measured capaciance ÄC 2 is parallel conneced o capaciance C 1. The capaciance ÄC 2 can be calculaed using formula [2,3] ` 2U NEC C2 = C1, (2) RI m where U NE` is equivalen volage wih offse. The formula (2) was derived hrough (1) under he condiion ha C = C 1 + C2, where ÄC 1 represens a capaciive offse. The idea o measure he capaciances wih compensaion of he offse was used in he experimen. Firs mus be measured capaciive offse ÄC 1 and hen measured capaciance ÄC 2 can be calculaed using (2). As shown above, he principle of operaion is based on he measured capaciance breaking he value symmery of he flip-flop, bu he equivalen volage can compensae his. In his case, he asymmery will be refleced in he number of pulses read by he reversible couner. The capaciance will be equivalen o he mean number of he pulses read. In he pracical measuring, he number of pulses read was processed using microprocessor and measured capaciance was calculaed using formula (2) in Lab VIEW. 5. Merological Characerisics To use he sysem in an indusry applicaion is merological characerisics mus be known. In accordance wih norm IEC 77, Fig.6 shows achieved errors for he change inpu capaciance from.5 pf o 3.5 pf (up) and from 3.5 o.5 pf (down). Inpu capaciances were made from phone cable given disances [4] (see Fig.7), and measured by RLCG meer BM 59. 1,5 down 1,,5 error [%], -,5 up -1, -1,5,25,5,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 3,75 inpu capaciance [pf] Fig. 6. Achieved errors for he change inpu capaciance up and down in percens from measuring range (3 pf). 5

6 Fig. 7. Capaciances made from phone cable. From Fig.6 i follows ha maximal value of hyseresis is equal o 2,22 % for inpu capaciance 3,5 pf. The value of repeaabiliy is equal o,25% for inpu capaciance 2.75 pf. 6. Conclusions In his paper, a new mehod, based on a flip-flop sensor, for measuremen capaciances in range a few pf has been presened. Auo-compensaive sysem wih flip-flop sensor enables o se he equivalen volage auomaically. To measure a capaciance conneced o flip-flop, pulses from inverers are processed in reversible couner. A number of he pulses read represens a measured capaciance ÄC 2. Bu he flip-flop has a capaciive offse. To avoid incorrec measuremen, capaciive offse ÄC 1 mus be measured. Then capaciance ÄC 2 o be measured can be calculaed using formula (2) in Lab VIEW. Fig.8 shows phoography of measuring sysem. Measuring range can be changed wih he values of load resisors R, curren ampliude I m or capaciance C, respecively, bu i has no been invesigaed in his paper. Possibiliy o measure capaciances from range a few pf predeermines o use i in capaciive sensors. Auo-compensaive sysem Measured capaciance ÄC 2 Fig. 8. A phoography of measuring sysem. 6

7 Acknowledgemens Sensors & Transducers Magazine, Vol.35, Issue 8-9, Augus-Sepember 23, pp.1-7 The work presened in his paper was suppored by Gran of Minisry of Educaion and Academy of Science of Slovak republic VEGA under Gran No.1/93/2. References [1]. W Lian, Inegraed silicon flip-flop sensor, Ph.D. Thesis, Technical Universiy of Delf, The Neherlands, 199. [2]. M. Kollár, V. Špány, T. Gabaš, Auocompensaive sysem for measuremen of he capaciances, Radioengineering, Vol. 11, No. 2, 22, pp [3]. M. Kollár, Smar Sensors Based on a Flip-Flop Circuis, Ph.D. Thesis, Košice, Augus 22, p. 9. (In Slovak). [4]. M. Kollár, Formula for he Calculaion of he Equivalen volage of he Flip-Flop Sensor, Elecronics Leers, Vol. 2, 22, hp: 23 Copyrigh, Inernaional Frequency Sensor Associaion (IFSA). All righs reserved. (hp:// 7