Low-Voltage Low-Power Differential Difference Current Conveyor Transconductance Amplifier and Its Application to a Versatile Analog Filter

Recei ed 5 June 2024, accep ed 16 June 2024, da e o publica ion 20 June 2024, da e o cu en e sion 12 July 2024. Digi al Objec Iden i ie 10.1109/ACCESS.2024.3417333 Low-Vol age Low-Powe Di e en ial Di e ence Cu en Con eyo T ansconduc ance Ampli ie and I s Applica ion o a Ve sa ile Analog Fil e MONTREE KUMNGERN 1, FABIAN KHATEB 2,3,4, AND TOMASZ KULEJ 5 1Depa men o Telecommunica ions Enginee ing, School o Enginee ing, King Mongku ’s Ins i u e o Technology Ladk abang, Bangkok 10520, Thailand 2Depa men o Mic oelec onics, B no Uni e si y o Technology, 601 90 B no, Czech Republic 3Facul y o Biomedical Enginee ing, Czech Technical Uni e si y in P ague, 272 01 Kladno, Czech Republic 4Depa men o Elec ical Enginee ing, Uni e si y o De ence, 662 10 B no, Czech Republic 5Depa men o Elec ical Enginee ing, Cze¸s ochowa Uni e si y o Technology, 42-201 Cze¸s ochowa, Poland Co esponding au ho s: Mon ee Kumnge n ([email p o ec ed]) and Fabian Kha eb (kha eb@ u b .cz) This wo k was suppo ed by he Uni e si y o De ence, B no, wi hin he O ganiza ion De elopmen P ojec VAROPS. ABSTRACT This pape p esen s a new low- ol age low-powe di e en ial di e ence cu en con eyo ansconduc ance ampli ie (DDCCTA). The p oposed DDCCTA u ilizes a mul iple-inpu ga e-d i en MOS ansis o (MIGD-MOST) ope a ing in he sub h eshold egion o achie e low supply ol age, minimum numbe o MOS di e en ial pai s and minimum powe consump ion. To show he ad an ages o he p oposed DDCCTA, i was used o ealize a e sa ile analog il e . The il e uses h ee DDCCTAs, wo g ounded capaci o s, and wo g ounded esis o s o ealize 65 ans e unc ions o low-pass, high-pass, band-pass, band-s op, and all-pass il e s by app op ia ely selec ing he inpu and ou pu e minals wi hou changing he il e opology. The il e also has he ad an ages o high-inpu impedance, which is ideal o ol age-mode ci cui s, independen con ol o he na u al equency and quali y ac o , and he abili y o elec onically une he na u al equency. The p oposed DDCCTA and e sa ile analog il e we e designed and simula ed using SPICE wi h TSMC 0.18 µm CMOS echnology o e i y he new ci cui s. The p oposed il e uses ±0.5 V o supply ol age and 103 µW o powe . INDEX TERMS Di e en ial di e ence cu en con eyo ansconduc ance ampli ie , analog il e , bulk- d i en MOS ansis o , low- ol age low-powe . I. INTRODUCTION The second-gene a ion cu en con eyo (CCII) was in o- duced in [1] and [2] as a e sa ile ac i e building block o ealizing analog ci cui s. CCII based ci cui s o e be e pe o mance in e ms o highe bandwid h, linea i y, and dynamic ange compa ed o ope a ional ampli ie (op-amp) based ci cui s [3],[4]. This ac i e elemen has h ee e minals ( he y-, x-, and z- e minal) and i s ideal cha ac e is ic can be gi en by Vy=Vxand Ix=Iz[2]. The CCII can be used in analog signal p ocessing, o example, o ealize The associa e edi o coo dina ing he e iew o his manusc ip and app o ing i o publica ion was Sai-Weng Sin . analog il e s [5],[6], signal gene a o s [7],[8], and p ecision ec i ie s [9],[10],[11]. Howe e , CCII based ci cui s lack he capabili y o elec onic uning. The ope a ional ansconduc ance ampli ie (OTA) is an ac i e building block ha o e s elec onic uning capabili y. I s ideal cha ac e is ics can be gi en by Io=gm(V+−V−) [12], whe e Iois he ou pu cu en , gmis he ansconduc- ance gain, V+and V−a e espec i ely he non-in e ing and in e ing inpu ol ages. The inpu ol age o his de ice can be con e ed o ou pu cu en using i s ansconduc ance gain, whe e ansconduc ance gain is an in insic cha ac e - is ic o he OTA ha can be gi en as he a io o he cu en ou pu o he inpu ol age. Typically, he ansconduc ance VOLUME 12, 2024 2024 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/ 92523 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e gain o an OTA can be con olled by a bias cu en / ol age. Thus, i he inpu ol age is ixed o an app op ia e alue, he ou pu cu en can be con olled by adjus ing he ansconduc- ance gain. The OTA also o e s mul iple ad an ages, such as easy implemen a ion o i s in e nal s uc u e ( he simple OTA s uc u e can be implemen ed using a bipola junc ion ansis o (BJT) o CMOS echnology). OTA-based ci cui s can educe he numbe o needed passi e esis o s, o elimi- na e hem a all, making hem sui able o implemen a ion in in eg a ed ci cui s (ICs). Based on he design o new ac i e elemen s o ana- log signal p ocessing [13], he ad an ages o he CCII and OTA can be inco po a ed in o a single ac i e building block, he so-called ‘‘cu en con eyo ansconduc ance ampli ie (CCTA)’’ [14]. The i s s age o he CCTA is a CCII cascaded by an OTA. The ad an ages o he CCTA can be con i med by applica ions in analog il e s and sinusoidal oscilla o s [15], [16],[17],[18]. Un o una ely, CCII is a single-end ac i e elemen - namely he e is a single e minal o he x-, y- , and z- e minals, which limi s he applica ions o holding he signal in di e en ial o ms and/o he addi ion and sub- ac ion o signals. To o e come hese limi a ions, ce ain ac i e elemen s ha e been p oposed, such as he di e en ial di e ence cu en con eyo (DDCC) [19], he di e en ial ol age cu en con eyo (DVCC) [20], and he ully di - e en ial second-gene a ion cu en con eyo (FDCCII) [21]. These ac i e building blocks can be used o ealize analog il e s [22],[23],[24], sinusoidal oscilla o s [25],[26], and ins umen a ion ampli ie s [27],[28]. Simila ly, o he con- en ional CCII, hese ac i e elemen s s ill lack an elec onic uning abili y. Based on he ealiza ion concep o new ac i e elemen s p esen ed in [13], new ac i e elemen s, such as he di e en ial di e ence cu en con eyo ansconduc ance ampli ie (DDCCTA) [29] and he ully di e en ial cu en con eyo ansconduc ance ampli ie (FDCCTA) [30], ha e been p oposed. The DDCCTA is he ocus o his wo k, whe e i was ealized by using DDCC a i s s age and cascaded by an OTA a he nex s age. The DDCCTA can be used o ealize analog ci cui s wi h an elec onic uning capabili y and o acili a e he ealiza ion o eedback addi- ional/sub ac ion ol age signals. Many applica ions o he DDCCTA/DVCCTA ha e been in oduced in [31],[32],[33], [34],[35],[36],[37], and [38]. Howe e , he p e ious DDCCTA s uc u es we e no designed o low supply ol age and low powe consump ion, i.e., he DDCCTA s uc u e in [29] uses ±1.25 V o supply ol age and consumes 1.8 mW o powe , he DVCCTA s uc u e in [36] uses ±1.4 V o supply ol age and consumes 4.4 mW o powe . Se e al DDCCTA applica ions in [31], [32],[33],[34], and [35] use CMOS implemen a ion o he DDCCTA in [29]. These used supply ol ages o ±3 V o [31],±2 V o [32] and [33],±1.5 V o [34] and [37], ±0.9 V o [35]. In his pape , a new low- ol age low-powe di e en- ial di e ence cu en con eyo ansconduc ance ampli ie (DDCCTA) is p oposed. The MOS di e en ial pai o he DDCCTA was ealized using he mul iple-inpu ga e-d i en MOS ansis o (MIGD-MOST) echnique; hence, a mini- mum numbe o MOS di e en ial pai s can be ob ained. The sou ce deg ada ion using wo MOSTs ope a ing in he iode egion was used o inc ease he linea i y o he ansconduc ance gain. The ci cui ope a ed wi h ±0.5 V o supply ol age and consumed 34.3 µW o powe . The p oposed DDCCTA was used o ealize a e sa ile analog il e . The il e employed h ee DDCCTAs, wo g ounded capaci o s, and wo g ounded esis o s. This il e showed ha he mul iple-inpu mul iple-ou pu o he DDCCTA can o e many ol age-mode ans e unc ions o low-pass il e (LPF), high-pass il e (HPF), band-pass il e (BPF), band- s op il e (BSF), and all-pass il e (APF) by app op ia ely selec ing inpu and ou pu e minals wi hou changing he il e opology. The na u al equency and quali y ac o o all il e s was able o be con olled elec onically and inde- penden ly. The p oposed DDCCTA and e sa ile analog il e we e designed and simula ed in SPICE wi h TSMC 0.18 µm CMOS echnology o alida e he new ci cui s. The e sa ile analog il e consumed 103 µW o powe . FIGURE 1. Con en ional DDCCTA: (a) in e nal block s uc u e, (b) elec ical symbol. II. CIRCUIT DESCRIPTION A. PROPOSED 1-V DDCCTA The con en ional DDCCTA is shown in Fig. 1- Fig. 1 (a) shows he concep o ealiza ion o he DDCCTA which consis s o a DDCC and a TA ( ansconduc ance ampli ie ), and Fig. 1 (b) shows he elec ical symbol o he DDCCTA. The po cha ac e is ics o Fig. 1 (b) can be gi en by [29] Vx=Vy1+Vy2−Vy3 Iz=Ix Io=gmVz   (1) whe e gmis he ansconduc ance gain o he DDCCTA. I should be no ed ha he DDCC and TA in Fig. 1(a) a e a single ou pu e minal (z- and o- e minals). The in e - ing inpu ol age e minal (–) o he TA is no used and is connec ed o he g ound. In his wo k, he in e ing inpu e minal o he TA was used as an addi ional inpu ol age, and he dual-ou pu z- e minals o he DDCC and plus/minus o- e minals o he TA we e a ailable and used as addi ional ou pu cu en s o he DDCCTA. Fig. 2shows he p oposed DDCCTA- Fig. 2(a) shows he CMOS implemen a ion and Fig. 1(b) shows he elec ical symbol. Compa ed o Fig. 1 (b), he in e ing inpu ol age e minal o TA in Fig. 2 (b) is a ailable and is connec ed o 92524 VOLUME 12, 2024 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e FIGURE 2. The p oposed DDCCTA, (a) CMOS implemen a ion, (b) elec ical symbol. FIGURE 3. MIGD MOST: (a) symbol, (b) implemen a ion o he MIGD MOST, (c) implemen a ion o RMOS. he z- e minal o he DDCC; he nonin e ing e minal o he TA is V1. The minus- ype ou pu e minal (o–) o he TA is ob ained using he c oss-coupled cu en mi o s. The ou pu cu en o he z- e minal o he DDCC is copied o he zc- e minal using he cu en mi o s echnique. The ideal cha ac e is ics o Fig. 2 (b) can be exp essed by Vx=Vy1−Vy2+Vy3 Iz=Ix Izc =Ix Io±= ±gm(Vz−V1)        (2) The CMOS ci cui in Fig. 2 (a) consis s o wo blocks. The i s one, composed o he ansis o s M1-M11, is a second- gene a ion di e en ial-di e ence cu en con eyo (DDCC) wi h a doubled z ou pu . The second block (M1-M19) is a linea ansconduc ance ampli ie (TA). The DDCC ci cui is based on an unbu e ed ope a ional ampli ie (M1-M6and M9) ope a ing in uni y-gain con igu a ion. I s inpu s age exploi s a di e en ial pai , M1, M2, biased by a lipped ol age ollowe consis ing o he ansis o s M1and M3. Such a con igu a ion can ope a e o VDD as low as VGS + VDSsa ; hus, i is especially sui able o LV designs. The ansis o s o he inpu pai a e loaded by he cu en sinks M4and M5, which de e mine he quiescen cu en s o M1 and M2. In o de o inc ease he numbe o inpu s (i.e., o ealize he di e en ial-di e ence unc ion), he ga e-d i en inpu ansis o s M1and M2we e eplaced by mul iple- inpu de ices, as shown in Fig. 3. The mul iple inpu s we e c ea ed by a capaci i e summing ci cui , connec ed o he ga e o a common MOS ansis o . In o de o p o ide p ope biasing o he ga e e minal o DC, each capaci o was bypassed by a la ge esis ance RMOS, ealized as an an i-pa allel connec ion o wo MOS ansis o s ope a ing in a cu o egion. Due o he ol age a enua ion in o- duced by he passi e elemen s, he common-mode inpu ange also inc eased. This achie ed an accep able ange o inpu signals, while using ga e-d i en ansis o s wi h lowe inpu noise and la ge ansconduc ances as hei bulk-d i en coun e pa s. The ou pu s age o he in e nal op-amp (M6, M9) ope a es in he so-called supe class AB [39], which imp o es i s powe e iciency. The ou pu signal o he i s s age con ols he ga e o M6. A he same ime, i is p o ided a he ga e o M9 ia he capaci o CB. The quiescen cu en o M9is well con olled by he biasing ansis o Mband he la ge esis ance RMOS is ealized as desc ibed p e iously. The capaci ance CBand he la ge esis ance RMOS c ea e a high-pass il e wi h a cu o equency o a ound 1 Hz. Fo equencies well-abo e his alue, he AC signal a he ga e o M9 ollows he one a he ga e o M6. In such a way, class AB ope a ion o he ou pu s age is achie ed. The capaci ance CC is used o a Mille equency compensa ion o he wo-s age in e nal ope a ional ampli ie . VOLUME 12, 2024 92525 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e Neglec ing he impac o he limi ed common-mode ejec- ion a io (CMRR) o he in e nal ope a ional ampli ie , he signal a he x- e minal can be exp essed as: Vx=KxVy1−Vy2+Vy3(3) whe e, assuming iden ical capaci ances CB, he ol age gain Kxcan be exp essed as: Kx= gm1,2 2( ds2|| ds5) (gm6+gm9) ( ds6+ ds9) 1+gm1,2 2( ds2|| ds5) (gm6+gm9) ( ds6+ ds9)(4) whe e he symbols used ha e hei usual meaning. No e ha he ansconduc ance o he inpu ansis o s M1and M2in he abo e o mula is di ided by 2 due o he inpu capaci i e di ide . Due o he wo-s age s uc u e, howe e , he alue o Kxis close o uni y, wi h a gain e o ypically less han 1%. The esis ance seen a he x- e minal is gi en by: x=1 gm1,2 2( ds2|| ds5) (gm6+gm9)(5) Since he ansis o s M7and M8(M10 and M11) a e con olled wi h he same ol ages as M6(M9), he cu en s a he z- and zc- e minals (neglec ing second o de e ec s) a e equal o he cu en a he x- e minal. Thus, he cu en Ixis con eyed o he e minals z and zc. The ou pu esis ances a he z- and zc- e minals a e iden ical and gi en by: z=1 ( ds7|| ds10)(6) The second block o he p oposed DDCCTA, namely he ansconduc ance ampli ie , can be conside ed as a cu en mi o s uc u e. I s inpu di e en ial s age exploi s he lin- ea iza ion p inciple p oposed by K ummenache and Joehl o ansis o s ope a ing in he s ong in e sion egion [40]. He e, he same p inciple is used o weakly in e ed de ices. The linea iza ion ansis o s M3and M4ope a e in a deep iode egion wi h VDS =0 a he ope a ing poin , ac ing as sou ce degene a i e esis o s. Con olling hese esis ances wi h he inpu di e en ial ol age o he ampli ie u he imp o es i s linea i y. Assuming ha he used cu en mi o s composed o o he ansis o s ha e a cu en gain equal o uni y, he ci cui ansconduc ance can be exp essed as: gm=4k 4k+1·Ise npUT (7) whe e npis he sub h eshold slope ac o o a p-channel ansis o , UTis he he mal po en ial, Ise is he biasing cu en and kis he a io o he aspec a ios o M3,4 o M1,2 gi en by: k=(W/L)3,4 (W/L)1,2 (8) The coe icien ka ec s ci cui linea i y. The op imum lin- ea i y is achie ed o k=0.5[41]. The cu en mi o s used in he s uc u e a e based on he so called sel -cascode ansis o s, which p o ide a la ge ou pu esis ance o he ci cui and consequen ly la ge DC Vo1=(sC2gm3+gm1gm2) (V2−V1)+sC2gm3(V7−V6) +gm1gm2V4+sC2gm1(V5−V3) D(s)(10) Vo2=sC1gm2(V2−V1)+gm2gm3(V6−V7)+(sC1gm2+gm2gm3)V4 +s2C1C2+sC2gm3(V5−V3) D(s)(11) Vo3=sC1gm2(V1−V2)+gm2gm3(V7−V6)+(sC1gm2+gm2gm3)V4 +gm2gm3(V5−V3) D(s)(12) Vo4=s2C1C2(V1−V2)+sC2gm3(V7−V6)+gm1gm2V4 +sC2gm1(V5−V3) D(s)(13) Vo5=s2C1C2(V1−V2)+s2C1C2+gm1gm2(V6−V7) +gm1gm2V4+sC2gm1(V5−V3) D(s)(14) Vo6=   s2C1C2gm3R1+sC1gm1gm2R1(V2−V1) +s2C1C2gm3R1(V7−V6)+sC1gm1gm2R1V4 +s2C1C2gm1R1(V5−V3)   D(s)(15) Vo7=(gm3R2)s2C1C2(V1−V2)+s2C1C2+gm2gm3(V6−V7) +gm1gm2V4+sC2gm1(V5−V3) D(s)(16) 92526 VOLUME 12, 2024 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e FIGURE 4. P oposed e sa ile analog il e using DDCCTAs. ol age gain o he ansconduc ance ampli ie , which can be app oxima ed as: A ∼ =gm[(gm8 ds8 ds8c)|| (gm14 ds14 ds14c)](9) In o de o ealize he unc ion o he DDCCTA desc ibed by (2), he ansconduc ance ampli ie is con olled by he di e ence o ol ages Vzand V1. B. PROPOSED VERSATILE ANALOG FILTER Fig. 4shows he p oposed e sa ile analog il e using DDCC- TAs as ac i e elemen s. The ci cui uses h ee DDCCTAs, wo g ounded capaci o s, and wo g ounded esis o s. I should be no ed ha he use o g ounded passi e componen s is p e e ed o in eg a ed ci cui s. Inpu s V1 o V7possess a high impedance le el, which is ideal o ol age mode ci - cui s, hence no addi ional bu e ci cui is needed. Using (2) and nodal analysis, he ou pu ol ages Vo1 o Vo7can be exp essed as (10)–(16), shown a he bo om o he p e ious page, whe e D(s)=s2C1C2+sC2gm3+gm1gm2. The ob aining a ian il e ing unc ion can be shown in Table 1. F om Table 1, he equi ed il e ing unc ions can be ob ained by app op ia e applying he inpu signals and selec ion o ou pu nodes, while he inpu s ha a e no used should be connec ed o g ound. Thanks o he DDCCTAs, he plus/minus inpu ol age e minals a e a ailable, he in e - ing inpu ol age is absen and many ou pu ol ages wi h di e en ypes o il e ing unc ions can be ob ained. Thus, om Table 1, he p oposed il e o e s 65 ans e unc ions, as bo h in e ing and non-in e ing ans e unc ions o LPF, HPF, BPF, BSF, and APF can be ob ained. No e ha he ou pu s Vo1 o Vo5p o ide a uni y ol age gain. I ol age gains o LPF, HPF, BPF, BSF, and APF a e equi ed, hey can be ob ained om he ou pu s Vo7o Vo6 o some il e ing unc ions. The na u al equency (ωo), bandwid h (ωoQ), and qual- i y ac o (Q) can be gi en by: ωo= gm1gm2 C1C2 (17) ωo Q=gm3 C1 (18) Q=1 gm3sC1gm1gm2 C2 (19) The na u al equency can be con olled elec onically by gm1 and gm2, he quali y ac o can be a ied elec onically by gm3 FIGURE 5. The DC ans e cha ac e is ics and i s e o s, (a) ol age swings o Vy1, Vy2 and Vx, (b) e o s o ol ages Vy1, Vy2 and Vx. when gm1=gm2and C1=C2. Thus, he na u al equency and quali y ac o can also be independen ly con olled. C. NON-IDEAL ANALYSIS A non-ideal DDCCTA can be cha ac e ized by: Vx=β1kkVy1+β2kVy2−β3kVy3 Iz=αkIx Izc =αkIx Io±= ±gmnk (Vz−V1)        (20) whe e βjk (j=1,2,3) and αk ep esen espec i ely he ol - age and cu en ans e gain o he k h DDCCTA and gmnk is he non-ideal ansconduc ance gain o he k h DDCCTA. Usually, he ans e gains o he DDCCTA de ia e om uni y by he ol age and cu en acking e o s. Mo e accu a ely, βjk =(1 −ε jk ) and αk=(1−εik ), whe e ε jk (ε jk ≪1) and εik (|εik |≪1), ep esen espec i ely he ol age and cu en acking e o s o he DDCCTA. The non-ideal ansconduc ance gmn o he DDCCTA a a equency nea he cu -o equency can be exp essed by [42] gmn (s)∼ =gm(1−µs)(21) whe e µ=1ωgm and ωgm deno es he i s pole equency o he gm. Taking in o accoun he non-ideali ies in (21) o he DDCCTA1, he DDCCTA2, and he DDCCTA3, he non-ideali ies can be ob ained as: Vx=β11Vy1−β21Vy2+β31Vy3 Iz=α1Ix Io±= ±gmn1(Vz−V1)   o DDCCTA1(22) VOLUME 12, 2024 92527 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e TABLE 1. Ob aining a ian il e ing unc ions o he p oposed e sa ile analog il e . 92528 VOLUME 12, 2024 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e FIGURE 6. The ansconduc ance cha ac e is ic wi h di e en se ing cu en s, (a) DC cha ac e is ic, (b) AC cha ac e is ic. FIGURE 7. The pa asi ic impedances a x-, z-, o- e minals o he DDCCTA. Vx=β12Vy1−β22Vy2+β32Vy3 Iz=α2Ix Io±= ±gmn2(Vz−V1)   o DDCCTA2(23) Vx=β13Vy1−β23Vy2+β33Vy3 Iz=α3Ix Io±= ±gmn3(Vz−V1)   o DDCCTA3(24) The denomina o o he p oposed e sa ile analog il e can be w i en as: D(s) =ns2C1C2β21β13α1α3+sC2gmn3β21β12α1+gmn1gmn2o (25) Using (21),(25) becomes: D(s)=ns2(C1C2β21β13α1α3+gm1gm2µ1µ3 −C2gm3β21β12α1µ2)+s(C2gm3β21β12α1 −gm1gm2µ3−gm1gm2µ1)+gm1gm2}(26) TABLE 2. T ansis o aspec a ios o he DDCCTA. o D(s)=ns2C1C2β21β13α1α3 1−C2gm3β21β12α1µ2−gm1gm2µ1µ3 C1C2β21β13α1α3 +sC2gm3β21β12α11−gm1gm2µ3+gm1gm2µ1 C2gm2β21β12α1 +gm1gm2}(27) The non-ideal e ec o he ansconduc ance o he DDCCTA can be made negligible by sa is ying he ollowing condi ion: C2gm3β21β12α1µ2−gm1gm2µ1µ3 C1C2β21β13α1α3≪1 gm1gm2µ3+gm1gm2µ1 C2gm3β21β12α1≪1)(28) The na u al equency, bandwid h, and quali y ac o can be ew i en as: ωo= gm1gm2 C1C2β21β13α1α3 (29) ωo Q=gm3β12 C1β13α3 (30) Q=1 gm3β12 sC1gm1gm2β13α3 C2β21α1 (31) The ol age and cu en acking e o s will sligh ly de ia e he na u al equency, bandwid h, and quali y ac o om he heo e ical alue. Howe e , since he il e has he abili y o elec onically une i s own equency, bandwid h and quali y ac o , any a ia ion in hese pa ame e s caused by PVT and MC can be co ec ed by he eadjus men o he se ing cu en . Conside ing he e ec o pa asi ic pa ame e s o he capaci o s C1and C2when Vo1and Vo3a e used in applica ions, he pa asi ic impedances o loads (o pa a- si ic impedances/capaci ances o he nex s age) will a ec he cha ac e is ics o he il e ing unc ions. Thus, a high impedance load is equi ed o connec he ou pu s Vo1and Vo3. I low impedance loads a e applied, bu e ci cui s a e needed. III. SIMULATION RESULTS To alida e he heo e ical analysis o he p oposed ci cui , he DDCCTA and he e sa ile analog il e we e simula ed in SPICE using 0.18 µm CMOS echnology om TSMC. The ansis o aspec a ios and capaci o alues a e gi en in VOLUME 12, 2024 92529 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e FIGURE 8. Simula ed magni ude and phase equency esponses o (a) LPF, (b) HPF, (c) BPF, (d) BSP, (e) APF. Table 2. These we e simila o he DDCC in [43], and he TA in [44]. The powe supplies we e gi en as VDD = −VSS = 0.5 V and IB=2.5 µA. Fig. 5 (a) shows he DC ans e cha ac e is ic be ween Vy1, Vy2 and Vxwhen he inpu s Vy1 and Vy2 we e swep om –280 mV o 280 mV, and Fig. 5 (b) shows he ol age e o s. The ol age e o s be ween Vy1and Vxwe e –2.15 mV a Vy1=0 mV, and -3.6 mV and 1.9 mV a Vy1=–280 mV and 280 mV, espec i ely. The ol age e o s be ween Vy2 and Vxwe e –2.15 mV a Vy2=0 mV, and –2.22 mV and –2.08 mV a Vy2=–280 mV and 280 mV, espec i ely. Mon e Ca lo analysis o he o se ol age a he x- e minal was in es iga ed. Based on he simula ion o 200 uns, he co esponding mean alue o o se ol age was ound o be –2.67 mV. Fig. 6shows he ansconduc ance cha ac e is ic wi h di e en se ing cu en s (Ise ). Fig. 6 (a) shows he anscon- duc ance cha ac e is ic e sus he DC inpu Vin o he TA, and Fig. 6 (b) shows he ansconduc ance cha ac e is ic e sus he inpu equency Vin o he TA. No e ha he inpu ol age ange shown in Fig. 6 (a) is su icien o he p oposed appli- ca ion, bu his ange can be ex ended by using bulk-d i en inpu ansis o s ins ead o ga e-d i en ansis o s i necessa y. Fig. 7shows he pa asi ic impedances a he x-, z-, o- e minals o he DDCCTA, which we e 2.67 k, 1.59 M, and 5.54 M, espec i ely. Fig. 8shows simula ed magni ude and phase equency esponses o he LPF, HPF, BPF, BSF, and APF when he p oposed il e in Fig. 4was gi en as C1=C2=0.37 nF, 92530 VOLUME 12, 2024 M. Kumnge n e al.: Low-Vol age Low-Powe DDCCTA and I s Applica ion o a Ve sa ile Analog Fil e FIGURE 9. Simula ed equency esponses o (a) LPF, (b) HPF, (c) BPF, (d) BSP, (e) APF wi h di e en biasing cu en Ise 3. TABLE 3. Compa ison o he p oposed il e ’s p ope ies wi h hose o some p e ious il e s. VOLUME 12, 2024 92531