New Compact VM Four-Phase Oscillator Employing Only Single Z-Copy VDTA And All Grounded Passive Elements

ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013 1Abs ac —In his pape , a new compac ol age-mode ou - phase oscilla o employing single z-copy ol age di e encing ansconduc ance ampli ie (ZC-VDTA) and only g ounded passi e elemen s is in oduced. The use o only g ounded capaci o s and esis o s makes he p oposed ci cui ideal o in eg a ed ci cui implemen a ion. The condi ion o oscilla ion and he equency o oscilla ion a e independen ly adjus able. The passi e and ac i e sensi i i ies o he p oposed ci cui con igu a ion a e low. Expe imen al measu emen esul s using eadily a ailable Maxim In eg a ed ICs MAX435 a e gi en o p o e he heo y. Index Te ms—Analog signal p ocessing, ou -phase oscilla o , ol age-mode, z-copy ol age di e encing ansconduc ance ampli ie , ZC-VDTA. I. INTRODUCTION Sinusoidal oscilla o s a e linea elec ic ci cui s ha a e used in wide a ea o elec onics and ep esen an impo an uni in many adio ecei e s, elecommunica ion, ins umen a ion, con ol and da a moni o ing sys ems [1]– [3]. Recen ly he ol age-mode (VM) ou -phase oscilla o s, which a e special ype o mul iphase oscilla o s, ha e ecei ed conside able a en ion in he li e a u e [4]–[13]. In Table I he a ailable ci cui s a e lis ed and compa ed based on ele an c i e ions. The gi en su ey shows ha hese oscilla o s uc u es a e based on ope a ional ampli ie s (Op- Amps) [4], [7], di e en ial di e ence cu en con eyo s (DDCCs) [5], second-gene a ion cu en con eyo s (CCIIs) [6], [8], [9], di e en ial ou pu -cu en in e e bu e ed ampli ie (DO-CIBA) [10], ol age di e encing in e ing bu e ed ampli ie s (VDIBAs) [12], o dual-ou pu con olled gain cu en ollowe bu e ed ampli ie s (DO- Manusc ip ecei ed Janua y 30, 2013; accep ed May 21, 2013. Ing. No be He encsa , Ph.D. was suppo ed by he p ojec CZ.1.07/ 2.3.00/30.0039 o B no Uni e si y o Technology. Resea ch desc ibed in his pape was also in pa suppo ed by he p ojec SIX CZ.1.05/2.1.00/03.0072 om he ope a ional p og am Resea ch and De elopmen o Inno a ion, by he p ojec WICOMT CZ.1.07/2.3.00/20.0007 inanced om he ope a ional p og am Educa ion o compe i i eness, and Czech Science Founda ion p ojec s unde No. P102/11/P489 and P102/09/1681. CG-CFBAs) and cu en ampli ie (CA) [13]. In addi ion, he Complemen a y Me al–Oxide–Semiconduc o (CMOS)- RC based oscilla o s a e ecen ly also popula [11]. Conside ing he numbe o ac i e elemen s in abo e men ioned VM ou -phase oscilla o s i can be seen ha a leas wo ac i e building blocks (ABBs) a e equi ed o hei ealiza ion. Howe e , ou de ailed s udy showed ha used ABBs in [10] and [12] ep esen an in e connec ion o wo sub-ci cui s such as cu en in e e and di e en ial ou pu bu e ed ampli ie in case o [10] o ope a ional ansconduc ance ampli ie (OTA) [14] and uni y-gain in e ing ol age bu e in [12]. I should be also men ioned ha in [5] and [7] addi ional ol age ollowe s/in e e s a e needed. Hence, in hese ci cui s excessi e numbe o ABBs is used. F om he monoli hic in eg a ion poin o iew, ci cui s ha employ only g ounded passi e elemen s a e a ac i e. Only ci cui s in [6], [8], and [9] sa is y his c ucial c i e ion. Howe e , he oscilla o in [8] employs one addi ional capaci o (in o al h ee) ha signi ican ly inc eases he chip a ea in case o in eg a ion. In 2008, se o new ABB concep s ha e been in oduced [14] om hem ecen ly p obably he ol age di e encing ansconduc ance ampli ie (VDTA) ecei ed he mos o a en ion [15]–[19]. The VDTA belongs o new g oup o ABBs so-called ‘ ol age di e encing’ elemen s and i is a ‘ ol age’ coun e pa o he well-know cu en di e encing ansconduc ance ampli ie (CDTA) [14]. In his pape , o inc ease he uni e sali y o he con en ional VDTA, he “z-cu en copy” echnique is wi h ad an age used, which was p e iously in oduced o o he ci cui concep s [14]. In [15]–[19] VDTA-based VM and cu en -mode (CM) second- and ou -o de il e s, lossless g ounded & loa ing induc ance simula o s, and CM quad a u e oscilla o s we e published. Based on CM concep om [19], his pape p esen s he i s VM ou -phase quad a u e oscilla o using VDTA in he li e a u e and i s p ac ical ealiza ion including ampli ude gain con ol (AGC) ci cui . The p oposed ci cui employs only single z-copy VDTA. Hence, he numbe o ABBs agains [4]–[13] is educed. Mo eo e , i employs only g ounded capaci o s and New Compac VM Fou -Phase Oscilla o Employing Only Single Z-Copy VDTA and All G ounded Passi e Elemen s N. He encsa 1, R. So ne 2, J. Ko on1, J. Misu ec1, K. V ba1 1Depa men o Telecommunica ions, B no Uni e si y o Technology, Technicka 12, 616 00 B no, Czech Republic 2Depa men o Radio Elec onics, B no Uni e si y o Technology, Technicka 12, 616 00 B no, Czech Republic [email p o ec ed]z h p://dx.doi.o g/10.5755/j01.eee.19.10.5900 87 ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013 esis o s ha make he ci cui ideal o in eg a ed ci cui implemen a ion. Expe imen al measu emen esul s on equency o oscilla ion equal o 4 MHz wi h sa is ac o y o al ha monic dis o ion a e included o suppo he heo y. TABLE I. COMPARATIVE STUDY WITH PREVIOUSLY REPORTED VM FOUR-PHASE OSCILLATORS. Re . ABB ype No. o ABBs No. o g ounded R / C No. o loa ing R / C Resul s 0(Hz) THD (%) [4] Op-Amp 4 0 / 2 10 / 0 measu emen s 22.89 k < 0.1 [5] DDCC 4b 2 / 2 2 / 0 simula ions 500 k – [6] CCII 3 6 / 2 0 / 0 simula ions 10 k – [7] Op-Amp 5b 0 / 1 3 / 1 simula ions 10 k – [8] CCII 3 5 / 3 0 / 0 simula ions 1 M – [9] CCII 2 5 / 2 0 / 0 simula ions 1 M – [10] DO-CIBA 2 0 / 2 3 / 0 measu emen s 1 M 0.07 [11] –a – 0 / 0 4 / 2 simula ions 160.2 k < 2.5 [12] VDIBA 2 1 / 1 0 / 1 simula ions 8.5 M < 2.25 [13] DO-CG-CFBA+CA 3 0 / 2 3 / 0 simul. / meas. 978 k / 2.5 M < 1 / < 0.6 P op. ZC-VDTA 1 3 / 2 0 / 0 measu emen s 4 M 0.4 – 3.1 No es: – No men ioned o no applicable; aCMOS-RC ci cui ; bRe . [5] includes one ol age in e e and one ol age ollowe , [7] includes wo ol age in e e s and wo ol age ollowe s. (a) (b) Fig. 1. (a) Ci cui symbol and (b) beha io al model o ZC-VDTA. II. CIRCUIT DESCRIPTION The ci cui symbol and beha io al model o ZC-VDTA a e shown in Fig. 1(a) and Fig. 1(b), espec i ely. The ZC- VDTA essen ially consis s o wo balanced-ou pu OTAs, whe ein he di e ence o inpu ol ages V +and V –is ans e ed by he i s ansconduc ance gain gm1 o cu en a he e minals zand zc– (nega i e o z) and he ol age d op a he e minal zis ans e ed o cu en a he e minals x+ and x– (nega i e o x+) by second ansconduc ance gain gm2. In p ac ice bo h ansconduc ances gm1,2 can be simul aneously elec onically con olled by ei he ex e nal DC bias cu en s o ol ages. All six e minals exhibi high-impedance alues. Using s anda d no a ion, he e minals ela ionship o an ideal ZC- VDTA can be cha ac e ized by he ollowing hyb id ma ix 1 1 1 1 2 2 0 0. 0 0 0 0 z m m zc m m x m z x m I g g V I g g V I g V I g                                         (1) The p oposed ealiza ion o VM ou -phase oscilla o employing single ZC-VDTA, wo capaci o s, and h ee esis o s, all in g ounded o m, is shown in Fig. 2. Using (1), ou ine ci cui analysis yields he ollowing cha ac e is ic equa ion (CE). Fig. 2. P oposed VM ou -phase oscilla o . Fig. 3. Model o he ZC-VDTA including pa asi ic elemen s.   21 2 1 2 1 1 1 2 1 CE : 1 0. m m m s C C R sC g R g g R    (2) F om (2) he condi ion o oscilla ion (CO) and he equency o oscilla ion (FO) can be e alua ed as: 1 1 CO : 1, m g R  (3) 1 2 0 1 2 1 FO : . 2 m m g g C C   (4) F om (3) and (4) i is clea ha he CO can be con olled independen ly o FO by means o a ying he esis o R1and he FO can be adjus ed by he ansconduc ance gm2, espec i ely. Thus, he p oposed oscilla o is an SRCO and p o ides independen con ol o he CO and he FO. III. NON-IDEAL ANALYSIS Fo a comple e analysis, i is impo an o ake in o accoun pa asi ics o ac i e elemen shown in Fig. 3: Iz=  1gm1Vd,Izc–= –  2gm1Vd,Ix+=  1gm2Vz,Ix–= –  2gm2Vz, whe e Vd= (V +–V –),  iand  i ep esen ansconduc ance gains o he ZC-VDTA ha di e om 88 ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013 hei ideal alues by ansconduc ance acking e o s  1i and  2i(|  1i|, |  2i| « 1), whe e i= 1, 2. The pa asi ic esis ances R +,R –and pa asi ic capaci ances C +,C –appea be ween he high-impedance + and – inpu e minals o he ZC-VDTA and g ound, espec i ely, and hei ypical alues in case o ZC-VDTA implemen a ion by Maxim In eg a ed ICs MAX435 a e 800 kǁ 5 pF. The pa asi ic esis ances Rz,Rzc–and pa asi ic capaci ances Cz,Czc–appea be ween he high-impedance z and zc– auxilia y e minals o he ZC-VDTA and g ound, espec i ely, and hei ypical alues a e 3.48 kǁ 10 pF and 3.5 kǁ 5 pF, espec i ely. The pa asi ic esis ances Rx+,Rx–and pa asi ic capaci ances Cx+,Cx–appea be ween he high-impedance x+ and x– ou pu e minals o he ZC-VDTA and g ound, espec i ely, and hei ypical alues a e 3.5 kǁ 5 pF. Conside ing he e ec o a o emen ioned non-ideali ies on he p oposed oscilla o shown in Fig. 2, he ollowing use ul analysis can be p o ided: A he node 1 he pa asi ic esis ances R +,Rzand capaci ances C +,Cza e abso bed in o ex e nal esis o R1 and capaci o C1, espec i ely, as hey appea in shun wi h hem and in analysis below hey a e labeled as R1and C1. A he node 2 he pa asi ic capaci ances C –and Cx+a e abso bed in o ex e nal capaci o C2as i appea s in shun wi h hem and in u he analysis i is labeled as C2. Fu he mo e, i mus be also men ioned ha in he same node he pa asi ic esis ances R –and Rx+a e also in shun and in u he analysis labeled as R x. A nodes 3, 4 he pa asi ic esis ances Rzc–,Rx–a e abso bed in o ex e nal esis o s R2and R3, espec i ely, as hey appea in shun wi h hem and labeled as R2and R3. Thus, he non-ideal e ec s o pa asi ic impedance a 1s , 3 d, and 4 h nodes o he p oposed oscilla o a e educed, i no comple ely elimina ed. A he node 2 he pa asi ic capaci ance can also be abso bed in he ex e nal capaci o , bu he p esence o pa asi ic esis ance R x a his node would change he ype o he impedance, which should be o a pu ely capaci i e cha ac e . A possible solu ion is o make he ope a ing equency 0> 1/(2  R xC2). Taking in o accoun he a o emen ioned non-ideali ies, excep o he pa asi ic capaci ances Czc–and Cx–, he CE in (2) becomes  21 2 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 CE : 1 0, x x x m x m m m s C C R R s C R C R C R R g R R g g R g                       (5) which by neglec ing he pa asi ic esis ance R x u ns o a o m  21 2 1 2 1 1 1 1 1 1 1 2 CE : 1 0, m m m s C C R sC R g R g g                (6) ha only by non-ideal ansconduc ance gains  1and  1 di e s om he ideal CE in (2) and subsequen ly om he ideal CO and FO in (3) and (4). Hence, in p ac ice a p ecise design o he ZC-VDTA should be conside ed o alle ia e he non-ideal e ec s. IV. MEASUREMENT RESULTS In o de o con i m he heo e ical s udy, he beha io o he p oposed VM ou -phase oscilla o has been e i ied by expe imen al measu emen s. The comple e ci cui con igu a ion o he p oposed oscilla o supplemen ed by AGC ci cui including speci ic alues o passi e elemen s is shown in Fig. 4. In measu emen s he ZC-VDTA was implemen ed using comme cially a ailable ICs MAX435 by Maxim In eg a ed. The DC powe supply ol ages we e equal o ±5 V. Gene a ed ol ages in all nodes a e a ailable h ough addi ional ol age bu e s. Fo his pu pose ope a ional ampli ie LT1364 was used. The AGC ci cui con ains cascade diode double and BS250 FET ansis o . Expe imen al measu emen s we e ca ied ou using RIGOL DS1204B ou -channel oscilloscope and HP4395A ne wo k-spec um analyze . The spec um analyze equi es impedance ma ching (50 ). The e o e, he ol age bu e s LT1364 ha e been e y impo an . Measu emen esul s a e shown in Fig. 5–Fig. 7. Figu e 5 shows all ou ansien esponses oge he . Expe imen ally measu ed oscilla ion equency was 04 MHz, which ma ches well wi h heo y. The equency spec um o Vo2is depic ed in Fig. 6. Fig. 4. Comple e ci cui con igu a ion used o expe imen al es . Fig. 5. Measu emen esul s: ansien esponses a all ou ou pu s (Vo1- blue colo , Vo2- ed colo , Vo3- g een colo , Vo4- o ange colo ). THD alue ob ained om measu emen s o ou pu ampli udes Vo2a 04 MHz was 0.58 %. Tunabili y o 0 ia gm2and ou pu ol age le els and THD s. 0du ing he uning p ocess a e shown in Fig. 7. Ideal equency ange o FO uning was calcula ed om 2.18 o 14.49 MHz. Howe e , his calcula ion does no ake in o accoun he main eal ea u es o ac i e elemen s used. The e o e, 89 ELEKTRONIKA IR ELEKTROTECHNIKA,ISSN 1392-1215,VOL.19,NO.10,2013 expec ed ange o FO = {1.65 – 11} MHz was ob ained by mo e accu a e calcula ion, which includes mainly pa asi ic capaci ances and low alues o esis ance in high-impedance nodes (ou pu s o MAX435). Fig. 6. F equency spec um o Vo2. 1 10 0.4 20 1 10 20 0 (MHz) gm2 (mA/V) Ideal Calcula ed Measu ed (a) 1 10 0 0.5 1.0 1.5 2.0 2.5 0 1 2 3 4 5 Ou pu ol age (Vp-p) THD (%) 0 (MHz) Vo1,3 Vo2,4 THD_Vo1,3 THD_Vo2,4 (b) Fig. 7. (a) Tunabili y o 0 ia gm2, (b) ou pu ol age le els and THD s. 0 du ing he uning p ocess. Measu ed equency ange co esponds wi h expec ed calcula ions, since FO was in ange om 1.36 MHz– 10 MHz. Adjus men o FO was ealized by changes o ansconduc ance gm2 om 0.4 mA/V o 18.3 mA/V. Fo Vo1,3 ou pu ampli udes eached alues om 0.5 V o 1 V and o Vo2,4 om 1.1 V o 2.2 V, espec i ely. THD alues luc ua e be ween 0.4 %–1.4 % and 2.3 %–3.1 % o ou pu s Vo1,3 and Vo2,4, espec i ely. In addi ion, he ampli ude o Vo1,3 a e almos unchangeable in ange om 1.36 MHz o 7 MHz. In o e all, ob ained esul s ma ch e y well wi h heo y. V. 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