Third order low-pass filter using synthetic immittance elements with current conveyors

THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE THIRD ORDER LOW-PASS FILTER USING SYNTHETIC IMMITTANCE ELEMENTS WITH CURRENT CONVEYORS Pa el BRANDSTETTER1, Lukas KLEIN1 1Depa men o Elec onics, Facul y o Elec ical Enginee ing and Compu e Science, VSB-Technical Uni e si y o Os a a, 17. lis opadu 15, 708 33 Os a a, Czech Republic pa el.b ands [email p o ec ed], lukas.klein@ sb.cz Abs ac . The pape deals wi h a heo e ical p oposal o he esul ing ci cui o he equency il e using syn he ic immi ance elemen s o highe o de wi h cu en con eyo s. The ex pays pa icula a en ion o design p ocess o syn he ic immi ance elemen s, explains he p inciple o inc easing o o de , which is hen e lec ed o he equency il e o de . The ex hen deals less wi h he heo y o cu en con eyo s, which has al eady been discussed, in de ail, in p e ious pape s. Uni e sal cu en con eyo (UCC) is discussed mo e. This ac i e elemen is used o he heo e ical implemen a ion o he syn he ic elemen solu ion used in he equency il e . The heo e ical knowledge is hen demons a ed in he design o 3 d o de low-pass equency il e . The inal unc ionali y o he p oposed equency il e ci cui solu ion is alida ed by PSpice simula ion. Keywo ds Cu en con eyo , equency il e , low-pass il e , syn he ic immi ance elemen . 1. In oduc ion Me hod o he syn he ic elemen s is p ima ily based on he needs o classical induc o s subs i u ion by syn he ic equi alen s in elec onic ci cui s. I is no a new me hod, bu i s use in combina ion wi h new mode n ac i e componen s (cu en con eyo s), o he design and ealiza ion o equency il e s, is a ela i ely new idea [1], [2], [3], [4], [5], [6], [7], [8]. The basic ad an ages o using cu en con eyo s [1] include a wide equency ange, ease o in eg abili y o he esul ing ci cui solu ions, low supply ol age o ac i e elemen s and he possibili y o use o ba e y supply in esul ing ci cui , when i is used in he mobile de ices. Cu en con eyo s [1] can be basically ega ded as uni e sal elemen s, because ou basic unc ional block s uc u es can be ealized by combina ions o hese ac i e elemen s. Howe e , he basic disad an age is low comme cial a ailabili y o cu en con eyo s and comme cial una ailabili y o uni e sal cu en con eyo (UCC), which was selec ed o he ealiza ion o il e p oposed in his pape . Selec ion o UCC has i s impo an easons. This elemen seems o be e y p omising, especially in he design o ci cui solu ions wi h cu en con eyo s, because i could be used o he implemen a ion o all cu en con eyo s a ia ions. Uni e sal cu en con eyo cu en ly exis s only as a labo a o y sample and he wide ex ension ye o come. The pape ies o show i s impo ance and he ad an ages. 2. Syn he ic Immi ance Elemen s o Highe O de s Syn he ic dipoles wi h immi ance o highe o de [2] a e di ided in o ou g oups – DP, DS, EP, ES. They a e consis ing o se ial o pa allel elemen a y dipoles connec ions. Syn he ic elemen s DP, DS a e c ea ed by elemen a y D ype dipoles o o de 0 o ND,max. Syn he ic elemen s EP, ES a e c ea ed by elemen a y E ype dipoles o o de 0 o NE,max. The linea ci cui s heo y discusses ha s able equency il e s can be ealized, i he elemen a y dipoles o all o de s om he lowes (nd,min, ne,min) o highes (nd,max, ne,max) will be connec ed in he syn he ic elemen s. Mos o he alues o nd,min, ne,min equal o 0 o 1, alues o nd,max, ne,max se he o de o he syn he ic elemen . In he mos cases, hese alues also se he o de o equency il e ans e unc ion, espec i ely. As s a ed abo e, he e a e ou connec ions o syn he ic elemen s wi h immi ance o highe o de [2]: © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 89 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE  dipole DP ND,min ND,max consis s o a pa allel connec ion o syn he ic elemen a y dipoles o ype Dn o n = ND,min, ND,min + 1, ..., ND,max - 1, ND,max,  dipole DS ND,min ND,max consis s o a se ial connec ion o syn he ic elemen a y dipoles o ype Dn o n = ND,min, ND,min + 1, ..., ND,max - 1, ND,max,  dipole EP NE,min NE,max consis s o a pa allel connec ion o syn he ic elemen a y dipoles o ype En o n = NE,min, NE,min + 1, ..., NE,max - 1, NE,max,  dipole ES NE,min NE,max consis s o a se ial connec ion o syn he ic elemen a y dipoles o ype En o n = NE,min, NE,min + 1, ..., NE,max - 1, NE,max. 2.1. The Condi ions o Syn he ic Immi ance Elemen s Realiza ion I sui able syn he ic immi ance elemen s o highe o de should be designed, hen an app op ia e o m o inpu impedance, espec i ely inpu admi ance is sea ched [3]. The equi ed inpu impedance espec i ely inpu admi ance o m o syn he ic immi ance elemen s o DS and ES ype should be: VWV U IN YYY Y Z1  , WU WV IN YY YY Y . (1a, b) Inc ease o syn he ic elemen o de is done by epea edly eplace o admi ance YV wi h ci cui wi h inpu admi ance (1b). Inc ease o o de o syn he ic immi ance elemen can also be achie ed by eplacing he admi ance YU wi h ci cui wi h he inpu admi ance (2b). Fo syn he ic immi ance elemen s o DP and EP ype, i is equi ed inpu impedance espec i ely admi ance in o m:  WVU W IN YYY Y Z , U W VU IN Y Y YY Y . (2a, b) Admi ance YV is epea edly eplaced wi h ci cui wi h he inpu admi ance (2b), i we wan o inc ease o de o syn he ic immi ance elemen . 3. Uni e sal Cu en Con eyo Uni e sal cu en con eyo (see Fig. 1) was c ea ed on he base o he uni e sal elemen idea, which could easily implemen e e y cu en con eyo gene a ion o a ia ion in p ac ice. This elemen would allow a di e en applica ion use o cu en con eyo s and hei wide expansion. Uni e sal cu en con eyo has me hese equi emen s [4]. I can ealize all he known ypes o cu en con eyo s. I is he basic p inciple o i s e sa ili y. Implemen a ion o he a ious ypes o cu en con eyo s is p o ided by use o only ce ain inpu and ou pu e minals o uni e sal cu en con eyo , he emaining e minals a e p ope ly connec ed o g ounded. Ano he ad an age o he elemen is ha i con ains se e al inpu and ou pu e minals, which p o ides an oppo uni y o sum signals a he inpu o con eyo o o di ide he ou pu signals o mul iple loca ions [4]. The ac i e elemen is no cu en ly mass p oduced, and he e o e no widely a ailable. Fig. 1: Schema ic symbol o uni e sal cu en con eyo (UCC). Te minals Y1+, Y2-, Y3+ a e he ol age inpu s, X is he cu en inpu (see Fig. 1). Te minals Z 1+ and Z2+ a e cu en ou pu s wi h a posi i e ans e o cu en , Z1- and Z2- a e cu en ou pu s wi h a nega i e ans e o cu en om e minal X. The uni e sal cu en con eyo is gene ally desc ibed by equa ions [4]: 321 YYYX uuuu    , , 0 321  YYY iii XZZ iii    21 , . (3a, b, c, d) XZZ iii   21 4. Realiza ion o Syn he ic Immi ance Elemen s wi h Cu en Con eyo s I he app op ia e s uc u e o syn he ic immi ance dipoles o ype DP, DS, EP and ES ype is sea ched, hen he pa icula o m o inpu admi ance o impedance is p ima ily equi ed. I is e y di icul o ind he exac exp essions ha equal o he o mulas (1a, b) espec i ely (2a, b). We can mo e o en ind he exp essions app oaching hese o ms han exac o ms. They can be also used. Howe e , i is necessa y o heo e ically e i y hei sui abili y o use in equency il e s. The main a ge is o ge o ms o equa ions ha will be mos simila o he equa ions (1a, b) espec i ely (2a, b). The gene al ci cui ne wo k o sea ching o sui able ci cui s uc u es was used o implemen syn he ic immi ance elemen . The gene al ci cui ne wo k consis s o nine passi e elemen s (admi ances) and one gene al ou -po cu en con eyo [2]. Final © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 90 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE s uc u e is shown in Fig. 2. Fig. 2: De aul admi ance ne wo k o sea ch he syn he ic elemen solu ion. The syn he ic elemen sea ching p ocedu e is qui e simple. The selec ed admi ances a e emo ed om he gene al ci cui ne wo k. The esul ing ci cui s uc u e should consis o h ee admi ances and gene al ou -po cu en con eyo . Th ee admi ances a e enough o ealize he syn he ic immi ance elemen . Any o he gene al cu en con eyo e minals Y, X, Z1 o Z2 can be used as he inpu o he esul ing ci cui s uc u e [5]. The inpu admi ance o m is hen edi ed again by he sui able choice o he gene al cu en con eyo coe icien s a, b, c11, c22. I is inal change o he inpu admi ance. The inal inpu admi ance o he esul ing ci cui is hen deduc ed, i i equals (1a, b), (2a, b) o o ms close o hese equa ions. Se e al dozens o combina ions we e examined his way. Figu e 3 shows one o he ound s uc u es ha can be used o he ealiza ion o syn he ic elemen . The ci cui is sui able o implemen ing il e s o highe o de . Fig. 3: Ci cui s uc u e sui able o ealiza ion o syn he ic elemen . The inpu admi ance gene al o m o he ci cui shown in Fig. 3 has he o m: 22711771122 9722929222722272 1172117272727272 IN cYcYYcYY abYYacYYabYYacYYcYY acYYcYYabYYbYYaYYYY Y   . (4) The e he alues o he gene al cu en con eyo coe icien s om he possible combina ions we e chosen. Bes sui ed combina ion is a=-1, b=0, c11 =-1, c22=1. This combina ion o alues simpli ies he inpu admi ance gene al o m and b ings i o i s ideal o m. Gene al ci cui s uc u e is sui able o implemen he syn he ic immi ance elemen s DP o EP (1a, b). Selec ed coe icien s co espond o he in e ing cu en con eyo o second gene a ion ICCII+/-. A e his adjus men , he inpu admi ance o he ci cui is ans o med in o he o m: 2 7 92 IN 2Y Y YY Y , )2( 792 7 IN YYY Y Z . (5a, b) Ta ge ed selec ion o passi e elemen s and hei subs i u ion o gene al admi ance in he ci cui s uc u e c ea e he syn he ic immi ance elemen DP o second o de . The ci cui s uc u e is shown in Fig. 4. Fig. 4: Ci cui s uc u e o second o de syn he ic elemen DP. The esul ing inpu admi ance o syn he ic immi ance elemen shown in Fig. 4 has he o m: . (6) 2927 2 IN 2CpCCRpY  4.1. Syn he ic Immi ance Elemen O de Inc easing Inc easing o he syn he ic elemen o de will be demons a ed on he syn he ic elemen shown in Fig. 4. Inc easing o he syn he ic elemen o de is cascade, i.e. he e is a epea ed eplacemen o a passi e elemen o a whole ci cui s uc u e o iden ical syn he ic elemen in he s uc u e o syn he ic elemen . Inc easing o o de o syn he ic elemen in Fig. 4 o hi d o de shows Fig. 5. As can be seen om Fig. 5, he capaci o ma ked in Fig. 4 as C9 was eplaced by ci cui s uc u e o syn he ic elemen DP shown in Fig. 4. Fig. 5: Thi d o de syn he ic immi ance elemen DP. © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 91 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE The numbe o capaci o s in he s uc u e o a syn he ic elemen was inc eased. The esul is also inc easing o he syn he ic elemen o de . The inpu admi ance o he newly c ea ed syn he ic elemen o hi d o de has o m as ollows: . (7) 1211 2 32121 32CpCCRpCCCRRpYIN  The new inc easing o o de o syn he ic elemen would be made by eplacing he capaci o C3 o he whole syn he ic elemen s uc u e shown in Fig. 4. Fo ms o o he inpu admi ance caused by inc easing o he syn he ic immi ance elemen o de a e shown in Tab. 1. Tab.1: Inpu admi ance o ms. O de o Syn he ic Elemen Inpu Admi ance Fo m 4. YIN = p4R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2+ p2C1 5. YIN = p5R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C 1 6. YIN = p6R1R2R3R4 R5C1C2C3C4C5C6 + p52R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C1 7. p52R1R2R3R4C1C2C3C4C5 + p42R1R2R3C1C2C3C4 + p32R1R2C1C2C3 + p2R1C1C2 + p2C1 YIN = p7R1R2R3R4 R5R6C1C2C3C4C5C6C7+ p62R1R2R3R4 R5C1C2C3C4C5C6 + 5. F equency Fil e s Using Syn he ic Immi ance Elemen s The e was used syn he ic immi ance elemen DP shown in Fig. 5 o he ealiza ion o low-pass il e o hi d o de . Ci cui solu ion o hi d o de low-pass is shown in Fig. 6. FThi d o de low-pass using syn he ic elemen wi h cu en con eyo s. Two uni e sal cu en con eyo s we e used in he inal ci cui solu ion o ac i e equency il e . Wi h i s help, ICCII+/- was implemen ed. The e was also used passi e low-pass a he inpu o ac i e il e o smoo h he inal equency esponses a highe equencies. Resis o R ig. 6: he wi h capaci o C1. T ans e unc ion o ac i e hi d o de low-pass shown in Fig. 6 has o m as ollows: 1 was di ided in o wo pa s, and i c ea es passi e low- pass oge 1442 213221 2 432321 3 CRpCCRRpCCCRRRp KU Speci ic alues o passi e componen s we e calcula ed wi h gen 1 )( p. (8) e al design ela ions o ac i e hi d de low-pass [6]: o 432321 3 0 33 2 cCCCRRR  , (9) 3221 2 0 32 4 cCCRR  , (10) 21 0  Bu e wo h app oxima ion was chosen. The coe icien s o his app oxima ion o il e s o hi d o de ha e alues c 31 4 cCR. (11) esis o s (12), (13), (14) a e exp essed om equa ions (9), (10), (11): 31=c32=2, c33=1 [6]. As al eady men ioned in he p e ious ex , he alues o capaci o s a e chosen and alues o esis o s a e calcula ed. The alues o passi e elemen s o equency il e a e also based on he chosen alue o cu -o equency 1 MHz and he coe icien s o chosen app oxima ion. The o ms o calcula ion o alues o 20 31 14 c C R  , (12) 3310 32 2 c2 Cc R  , (13) 4320 3Cc  Values o esis o s a e calcula ed a e subs i u ing o speci ic alues. Op imiza ion in PSpice was also used o de e mine he ideal alues o passi e elemen s. The esul ing alues o he passi e elemen s we e de e mined R 33 c2 R. (14) 1=2,7 kΩ, R2=5,6 kΩ, R3=1,2 kΩ, C1=C2=C3=22 pF, C4=100 pF. The esul ing ampli ude equency esponse and phase esponse o a eal model o hi d o de low- pass is shown in Fig. 7. The e a e wo aces he e. Fi s ace is o ci cui solu ion o ac i e low-pass and second ace desc ibes he beha io o ci cui solu ion o ac i e low-pass using also passi e low-pass. As can be seen, use o passi e low-pass in he ci cui s uc u e o hi d o de ac i e low-pass changes he posi ion o cu -o equency. Howe e , his solu ion also gi es good esul s a highe equencies, whe e he gain inc ease is educed. Cu -o equency o he il e is de ined as a dec ease o magni ude abou 3 dB [6]. Cu -o equency in his case was chosen 1 MHz. The simula ed cha ac e is ic shown in Fig. 7 does no exac ly ma ch hose equi emen s. The selec ed cu -o equency o 1 MHz is de ined as a dec ease o ampli ude equency esponse abou 4,43 dB. Such a la ge de ia ion can be ole a ed. Some o © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 92 THEORETICAL AND APPLIED ELECTRICAL ENGINEERING NUMBER: 2 | 2012 | JUNE VOLUME: 10 | © 2012 IN ELECTRICAL AND ELECTRONIC ENGINEERING 93 ideal ope hange o cu -o equency o ac i e low-pass depends cula aces depending on he a iable ole ance o C2. he ac o s ha could cause he de ia ion a e he p ies o he used uni e sal cu en con eyo model and he passi e low-pass a he inpu o ac i e il e . Also, sensi i i y analysis was ca ying ou . The mos ly on capaci o C2. The ampli ude equency esponse and phase esponse shown in Fig. 8 desc ibe pa i c Fig. 7: Ampli ude equency esponse and phase esponse o hi d o de low-pass using syn he ic elemen wi h cu en con eyo s. Fig. 8: Mon e Ca lo analysis o ampli ude equency esponse and phase esponse o hi d o de low-pass wi h passi e il e . he inal ci cui solu ion. This y is a disad an age and ADVANCES 6. Conclusion The pape ies b ie ly desc ibe he ealiza ion o equency il e s wi h syn he ic immi ance elemen s o highe o de wi h cu en con eyo s. Applica ion use o syn he ic immi ance elemen s b ings a lo o ad an ages. One o he mos impo an ad an ages is he easy in eg abili y o is a e y impo an ac o especially in elec o- indus ial p oduc ion. I is ad an ageous o use uni e sal cu en con eyo in design. UCC is able o subs i u e all p e ious gene a ions o cu en con eyo s bu i s comme cial una ailabili THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 10 | NUMBER: 2 | 2012 | JUNE un sal cu en con eyo can be used only as a heo e ical elemen now. The desc ibed heo y and he inal ci cui solu ion o hi d o de low-pass indica e ha he desc ibed me hod p oduces ela i ely good esul s. The a icle desc ibes only one o o al h ee ound syn he ic elemen s. Despi e u he a emp s no o he elemen s we e ound. I can he e o e be assumed o ind ano he solu ion o syn he ic immi ance elemen s wi h cu en con eyo s is e y di icul . Howe e , o he solu ions o syn he ic immi ance elem i e en s can be ound wi h combina ions o di e en ypes o cu en con eyo s o wi h o he ac i e elemen s. SP2012/85, which was suppo ed by S uden G an Compe i ion o VSB-Technical Uni e si y o Os a a. u en c ions using Uni e sal Cu en Con eyo . In: Con e ence 3868-6. ISSN 0925-1030. DOI: 10.1007/s10470- onics. 2009, ol. 96, iss. 8, iwice: IEEE, ional ampli ie s. P aha: BEN, 2002. ISBN 80-7300-047-4. n s, Acknowledgemen s In he pape , he e a e he esul s o he p ojec Re e ences [1] SMITH, K. C. and A. S. SEDRA. The cu en con eyo : a new ci cui building block. IEEE P oceedings o he CAS. 1968, ol. 56, iss.1, ISSN 0018-9219. [2] SPONAR, R. and K. VRBA. Syn he ic dipole elemen s wi h highe -o de immi ances in equency il e s wi h c con eyo s. Elek o e ue [online]. 2004, ol 2004, no. 13. ISSN 1213-1539. A ailable a : h p://www.elek o e ue.cz/clanky/04013/index.h ml. [3] HORNG, J.-W., Ch.-L. HOU, Ch.-M. CHANG, H. YANG and W.-T SHYU. Highe -o de immi ance un cu en con eyo s. Jou nal Analog In eg a ed Ci cui s and Signal P ocessing. 2009, ol. 61, no. 2, pp. 205-209. ISSN 0925-1030. DOI: 10.1007/s10470-009-9298-6. [4] ZHANG, Q., Ch. WANG and Y. LENG. A No el Building Block: P oceedings o IEEE 8 h In e na ional Con e ence on ASIC. Changsha: IEEE, 2009, pp 1109-1112. ISBN 978-1-4244- [5] PSYCHALINOS, C. and G. SOULIOTIS. Low-Vol age Cu en Con olled Cu en Con eyo . Jou nal Analog In eg a ed Ci cui s and Signal P ocessing. 2010, ol. 63, no. 1, pp. 129-135. 009-9416-5. [6] KOTON, J., K. VRBA and HERENCSAR. Tuneable Fil e Using Vol age Con eyo s and Cu en Ac i e Elemen s. In e na ional Jou nal o Elec pp. 787-794. ISSN 0020-7217. [7] BRANDSTETTER, P. and L. KLEIN. Applica ions o Non- In e ing Posi i e Second Gene a ion Cu en Con eyo as a Comme cially A ailable Ve sa ile Ac i e Elemen . In: Con e ence P oceedings o In e na ional Con e ence on Signals and Elec onic Sys ems - ICSES´10. Gl 2010, pp. 157-160. ISBN 978-1-4244-5307-8. [8] PUNCOCHAR, J. His o y and p esen o ope a Abou Au ho s Pa el BRANDSTETTER was bo n in Os a a, Czech Republic, 1955. He ecei ed he M.Sc. and Ph.D. deg ees in Elec ical Enginee ing om B no Uni e si y o Technology, Czech Republic, in 1979 and 1987, espec i ely. He is cu en ly ull p o esso in Elec ical Machines, Appa a us and D i es and ice dean o Facul y o Elec ical Enginee ing and Compu e Science a VSB-Technical Uni e si y o Os a a. His cu en esea ch in e es s a e applied elec onics, mic ocompu e con ol sys ems and mode n con ol me hods o elec ical d i es. Lukas KLEIN was bo n in Uhe ske H adis e in 1984. He ob ained Bachelo ’s deg ee a B no Uni e si y o Technology in ield o Telein o ma ics in 2007 and hen he ob ained his Mas e ’s deg ee in ield o Mobile echnologies in 2009 a VSB-Technical Uni e si y o Os a a. He is cu en ly pu suing Ph.D. s udy a Depa men o Elec onics on Facul y o Elec ical Enginee ing and Compu e Science. His esea ch a ea includes applica ion o mode n ac i e eleme especially cu en con eyo s, in elec onic ci cui s. © 2012 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 94