About theoretical and practical aspects of current mode RC oscillators design

Transcription

1 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN About theoretcal and practcal aspects of current mode RC oscllators desgn Luza rgorescu, Ioana Daconescu, heorghe Oproescu Abstract Ths paper addresses a group of constructve elements wth whch, (through adequate combnatons) one can generate current mode RC oscllator transfer functons. Obvously ths elements set s not unque. From the multtude of possble solutons only the solutons that accommodate the below condtons stand out: - the actve elements can be easly produced n monolthc technology, - each oscllator must have two resstors or two capactors connected to the mass. The latter requrement s very mportant for the oscllators wth varle frequency. It was made RC oscllators and ts transfer functons, and t was made a study of errors whch affects mantanng gan oscllatons and frequency oscllaton. The paper pont out the expermental results obtan through RC oscllators mplementaton wth PA 63 current conveyors showng that the current mode oscllators appears to be an nterestng approach from the perspectve of the smplcty/performance compromse. Keywords frequency, gan, oscllator. I. INTRODUCTION In ths paper we present an ntutve method for the creaton of a new current mode oscllator structure, based on the understandng of the way the oscllaton frequency s beng determned and the loop transfer rato s beng adjusted []. Ths method results n a new and elegant structure. Here are some of the features such a structure s ntended to acheve. The frequency tunng s to be done through the modfcaton of a sngle passve component, preferly a resstor. For hgh frequency usage the use of a varcap dode s accepted. For frequency tunng that s acheved through multple components, no precse parng of those s requred. The loop transfer control s done ndependently from the oscllaton frequency. Although there are multple structures that comply to ths requrement (at least wthn the boundares of an ntal approxmaton that gnores the sde effects), most of such oscllators have a certan dependency of the loop transfer tunng to the oscllaton frequency. A wde range of frequency varaton must be supported, Manuscrpt receved August 9, 8: Revsed verson receved October 4, 8. Ths work was supported n part by the loratores of Unversty "Dunarea de Jos" from alat. The paper auhors are:.luza rgorescu s Assocate Professor, Unversty "Dunarea de Jos" from alat, Romana, e-mal: lgrgorescu@ugal.ro.ioana Daconescu s Assocate Professor, Unversty "Dunarea de Jos" from alat, Romana, e-mal: daconescu@ugal.ro 3.heorghe Oproescu s Professor, Unversty "Dunarea de Jos" from alat, Romana, e-mal: goproescu@ugal.ro whch usually means more complcated crcutry needs to be put n place. It s desrle that all capactors have one end connected to the ground so that these oscllators can be mplemented wthn an ntegrated crcut. There should also be avalle a smple means of control for the oscllaton ampltude. Ths s vtal for an oscllator because a slght varaton of the oscllaton ampltude can lead to the oscllaton beng dstorted or even nterrupted. For RC oscllators t may seem surd to talk out obtanng a hgh degree of thermal stlty of the oscllaton frequency as long as none of them are very stle. We should on the other hand make sure that the oscllaton frequency s not dependant on any of the parameters of the actve components, snce these elements usually have a sgnfcant dependency to the envronmental temperature. The block schema of a RC oscllator s presented n fgure [], where by A we mean an deal current oscllator, whose gan s: = () Fg. The deal current oscllator For a lnear second order RC network, the current transfer functon can be descrbed as a s + a s+ a β () s = = bs + bs+ b Where s s the complex frequency value and a n (n=,,) are real numbers. In practce only stle networks are of nterest so the b n (n=,,) coeffcents must be postve real numbers. The Barkhausen oscllaton ntaton condton, applcle for any postve reacton oscllator s leadng to the followng equaton: as as a A = bs bs b () (3) Issue, Volume, 8 4

2 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN ( ) ( ) s a A b + s a A b + a A b = (4) For the crcut n fgure wth the closed reacton loop, the angular oscllaton frequency and the necessary gan for oscllaton mantanng ( ) have the below expressons = b b (5) b = (6) a The ove scopes wll be further called the oscllaton frequency and mantanng gan. Snce the gan n 6 must be fnte, the a can t be zero whle expresson (6) allows for a and a to be zero both smultaneously and each at a tme. II.FUNDAMENTAL BLOCKS FOR SECOND ORDER CMO-RC Dfferent shapes number of acceptle second order transfer functons for harmonc oscllators constructon wll be gven by restrctons towards the equaton () coeffcents n order to equatons (5) and (6) make physcal sense [4]. Based on the restrctons n the ove paragraph, we can dentfy four types of second order RC networks that can be used for the desgn of harmonc oscllators and correspondng them, second order RC oscllators. The most general type corresponds to the followng parameters: a ; a ; a. ven ths, the oscllaton frequency becomes b b = = S4 (7) b b Where we made the followng conventon S 4 = From equaton 7 one notces that, the oscllaton frequency s dependent by the S 4 factor, called the scale factor. To nvestgate the values that S4 factor can equals s a useful way to know the frequency tunng possbltes when rato b / b has a constant value. For these oscllators the mantanng gan s also gven by equaton 6. (8) III. CMO CONSTRUCTIONS The below paragraph proposes a set of constructve blocks that, by adequate desgn, wll produce the desred transfer ratos. Ths set s not by far unque, but from the multtude of possble solutons we chose one that comples wth the followng requrements[]: a) the passve components should be desgned easly and n a performng manner n monolthc technology. b) the oscllator should have ether two resstors or two capactors connected to the ground. The latter requrement has a great practcal mportance for varle frequency oscllators. For ths partcular reason a wde known network lke the Wen network may not be used for our purpose. A Actve Blocks The amplfers presented n fgure wll be used as actve elements[]. Fg. Actve blocks. a) deal current amplfer; b) deal current amplfer wth a sngle nput and two opposng outputs (SIDO). The amplfer n fgure.a s an deal current amplfer whose gan s = A (9) Where A can be both a negatve and a postve gan. The amplfer n fgure.b s an deal current amplfer wth a sngle nput and two opposng outputs (SIDO). Its behavor can be descrbed by where A s postve. = A () = A () B Passve Blocks Accordng to the last requrement prevously mentoned, the passve blocks taken nto consderaton wll be those from fgure 3. The crcut n fgure 3.a s a resstve current dvsor wth a transfer functon descrbed as R = = k R + R () Issue, Volume, 8 4

3 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN The crcut n fgure 3.b s a sngle secton CR network whose transfer functon s = + sc (3) R Accordng to relatons () and (3), the output current from the RC phase shftng crcut s R = (6) + scr The overall crcut output current s the sum of the ove two currents And thus the crcut transfer rato s = R + D (7) = A ( k) skrc + src (8) Fg. 3 The passve blocks. a) resstve current dvsor; b) sngle secton CR network; c) sngle secton RC network. IV. RC OSCILLATOR WITH THE CAPACITOR DE- PHASIN NETWORK AND SINLE SECTION RC NETWORK Wth the capactor de-phasng network(fgure 4), a sngle secton RC network(fgure 3b) and the ± A and A amplfers, one obtans the oscllator n fgure 5[6]. And fgure 3.c shows a sngle secton RC network wth the followng transfer functon o scr = (4) + sc R C Combned Blocks Ths category conssts of the smplest combnatons of actve elements and passve blocks of frst order transfer ratos. The structure that wll therefore result and satsfy prevous the restrctons be shown n fgure 4. The transfer rato s easly determned by usng the (9)-() relatons n combnaton wth one of the ()-(4) relatons. Fg. 5 RC oscllator a sngle secton RC network and capactor de-phasng network The loops transfer functon s obtaned by settng k = n equaton 8 and by multplyng the result wth the transfer functon of the sngle secton RC network whch looks lke:. Equaton 9 s thus obtaned + src sr C = AA s RRCC + s( RC + RC ) + (9) The expresson of the oscllaton sustanng gan s: Fg. 4 SIDO amplfer, a current dvsor and a sngle secton CR network. The crcut n fgure 4 conssts of a SIDO combned wth current dvsor (fgure 3.a) and a sngle secton CR network (fgure 3.b) and t wll be called de-phasng network wth current dvsor and grounded capactor. Accordng to relatons () and (), the output current of the R,R dvsor becomes D = ka (5) And the oscllaton frequency s: R C = + () R C = () RRCC The value of the sustanng gan remans constant f the raton of the resstors and capactors remans constant. For the case when R = R; C = C (practcal use case) one gets =. Issue, Volume, 8 4

4 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN The A amplfer n fgure 5 s not replacele because t has the role of separatng the networks. We can observe the oscllator would run smlarly should R and C would be nterchanged wth R and C. Then the transfer rato becomes: sr C = AA s RRCC + s RC + RC + ( ) () The oscllaton frequency remans the same and the oscllaton sustanng gan s: = + R C (3) R C The oscllator behavor s smlar to the one of a Wen network oscllator, but has the advantage of havng to ground resstors. Actually the ove nterchange s equvalent to the use of a sngle secton RC network. A The study of errors. Errors caused by the actual values of the conveyors mpedances. We wll contnue by computng the errors produced by the parameters whch are nvolved n the expressons of the oscllaton frequency sustanng gan. The estmaton of these errors was done for the oscllator n fgure 5. There were also taken nto account the resstances and capactors for the nputs/outputs of the ntegrated PA63 conveyors, opposte to the deal condtons (R X =; R Z = ; C Z =). Accordng to the catalogue nformaton, the nput resstance at nput X of the nverted current repeater has the typcal value R X = Ω,the capactor C Z =pf, and the output resstance R Z =3M Ω. For the schematcs n fgure 5, the output capactors of the (C X ) conveyors come n parallel wth C and C, whle the Rx resstance of SIDO comes n seres wth R. If one neglects the nput resstance of A, one gets the followng loop transfer rato ε M A MA M = [%] (7) M M Where by ε A we mean the relatve error n percentages, M stands for the errorless value of M and M A stands for the value of M affected by error A. For the estmaton of the nserted errors we wll take nto consderaton the worst case scenaro, meanng R =R = Ω, respectvely C =C =68pF (correspondng to the mnmal values of R and C used n the practcal mplementaton). We therefore obtan the numercal values of: ε mp = % and ε mp = 7, 6%. For the usual values R =R = Ω respectvely C =C =nf one obtans ε = % and ε =, 9%. mp mp. Errors due to the naccuracy of the conveyor current transfer To estmate these errors we wll consder the below expresson of the conveyor current transfer = ± δ (8) Where δ =, 5% s accordng to the catalogue data. We must take nto account the fact that a dfferental stage s made of two current conveyors. Consderng + = ( + δ ) respectvely = ( + δ ), the expresson of the transfer rato becomes: = ( + δ ) + δ δ + ( + ) scr AA sccrr s RC RC + The oscllaton frequency: (9) = + ( ) [ AA sr C C ]/ Z ( + X ) ( + Z )( + Z ) ( )( ) ( ) /{ s R R R C C C C + s R+ RX C+ CZ + C + CZ R + } The expresson of the loop gan becomes ( ) R + R C + C R C + C X = + Z Z + (4) (5) ( δ δ ) CR = + CC RR δ CR + The sustanng gan s: CR = + δ CR + (3) (3) Wth expressons 3 and 3 we can now calculate the relatve errors of the oscllaton frequency and the sustanng gan: Whle the expresson of the oscllaton frequency s: = (6) Z ( R R ) R ( C C )( C C ) X Z By () we mark here the parameters that are prone to errors. ε δ + δ δ = + δ (3) Issue, Volume, 8 43

5 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN ε δ = (33) + δ In the worst case scenaro ( δ =,5% respectvely δ =,5% ) one gets, 5% ε δ = respectvely ε δ = %. 3. Errors due to the mss-parng of the passve components We only consder the tolerance of the manufacturng process of the components and neglect the temperature dependency of the components values. Thus λ ( λ ); n( λ ); ( λ ); ( λ ) R = R ± R = R ± n C = C ± C = C ± n 3 n 4 where 4s the components tolerance (n percentages). We can say that the components tolerance has a small mpact on the sustanng gan expresson, because they only come n the shape of ratos R / R, whle these ratos have small values (%) for ntegrated mplementatons. The oscllaton frequency s, B Practcal Implementatons An oscllator as shown n fgure 5 has been mplemented n practce. On the prnted crcut we created, there was a ground plane created on the components sde, wth the purpose of protectng the assembly from external nterference. Wth the same purpose the entre crcut has also been nserted n a metal case. The crcut power source s a V CC =V SS =±V (E49), and the oscllatons vsualzaton was done by an E3-A osclloscope, whle the oscllaton frequency was done wth a BM56 (TESLA) frequency meter. For the created oscllator, the requred gan for the sustanng of a untary transfer raton n the loop was ensured by the frst dfferental stage, all the other actve stages havng a untary gan. One can t dscard the use of the current repeatng stage because we requre the RC de-phasng networks to be evaluated aganst ther current behavor. For the mplementaton of a SIDO stage we requre two PA63 current conveyors, whle for the mplementaton of a current repeater there was only one PA63 current conveyor requred[8]. Fgure 6a schematcally dsplays the confguraton of a SIDO, whle fgure 6b s showng the confguraton of a smple current repeater. = R R C C ( ± λ )( ± λ )( ± λ )( ± λ ) n n n n 3 4 (34) And the relatve error of the oscllaton frequency s: ε λ = ( ± λ )( ± λ )( ± λ )( ± λ ) 3 4 (35) Should we consder equal tolerances for all four components, the worst case scenaro s when they all are postve: For λ = λ = λ3 = λ4=% we get ε λ =,9%, for λ = λ = λ3 = λ4=5%, ε λ =9,% and for λ = λ = λ3 = λ4=% we get ε =7,35%. λ 4. Errors due to the oscllaton ampltude lmtaton crcut For a mnmal mplementaton the oscllaton ampltude lmtaton crcut s made of a resstance dvsor brdged by two ant-parallel coupled dodes (fgure 6a). Snce the lmtaton s done by a non-lnear crcut, mportant errors may appear both related to varatons from the nomnal oscllaton frequency, and the frequency specter of the resultng sgnal (we may get typcal harmonca dstortons of 3-5 %). The evaluaton of such errors s very complex and can only be approached by the use of a computer. One should also take nto account the fact that these latter errors can be used to compensate for the prevous ones. Fg. 6a) SIDO amplfer, b) The confguraton of a smple current repeater. Note: The collectors of the Y nput transstors we re connected to Vss for all CCII. From fgure 6a stands out the oscllaton lmtaton crcut, formed of the D and D dodes, whch are brdgng the R, R nput resstve dvsor. Wth an ntal approxmaton the SIDO gan s gven by ( R+ R) / R3. We should take notce that f for any gven reason the oscllaton ampltude may tend to grow, the D and D dodes wll tend to further open, thus decreasng the ntal value of R + R and so the entre transfer rato of the loop wll decrease. Issue, Volume, 8 44

6 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN To avod the latch-up phenomenon specfc to the PA63 current conveyor, we wll use (f requred) on the Z outputs of the conveyor, some 3.6V Zenner dodes (DZ3V6), n seres wth N448 fast dodes, as shown n the PA63 catalogue. Obvously the use of such dodes wll lead to a change n the loop transfer rato and also of the oscllaton ampltude. The conveyors polarzaton was done accordng to the catalogue schemas, by ensurng a polarzaton current of.6ma[8]. In order to mplement the RC de-phasng crcuts, we used % tolerance metal fol resstors, hgh precson capactors (-% precson) and hgh tolerance electrolytc capactors (-5% tolerance). The followng measurements have been performed: a) The oscllaton ampltude has been fxed to 8mV, also C =C =47nF and also R =R we re vared from to 96 KΩ. For resstor values hgher then KΩ, there was observed a slght drop n the oscllaton frequency. For values of R=R rangng from 5Ω to 96 KΩ(9:) we got a frequency varaton rangng from 7Hz to 5.7kHz (93:), wth a 5% precson. For values of R =R Ω, we notced an ncrease of errors up to out 55%. The expermental results are dsplayed n fgure 7. V. RC OSCILLATOR USIN A CR NETWORK WITH TWO SECTIONS The oscllator n fgure 9 s bult usng a CR net wth two sectons that are dfferentally coupled to the SIDO amplfer ( ± A) and to the smple amplfer +A [7]. The transfer rato for the loop s obtaned by multplyng the transfer loop of the double secton CR net wth the gans of the two current amplfers (A and A ). So, the expresson s: sr C = AA s RR CC + s( RC + RC + RC ) + Fg. 9 RC Oscllator usng a CR network wth two sectons (36) The sustanng gan expresson s (37) whle the oscllaton frequency s (38) R R C = + + (37) R R C = (38) RRCC Fg. 7 b) We contnued by settng R =R =KΩ and modfyng C =C rangng from,6pf to μf. For values of C =C rangng from nf to μf (:) we obtaned a frequency varaton from 6Hz to 6KHz (:) wth a 5% precson. For values of C =C =nf errors may grow up to 85%. Also for values of C =C >μf errors may grow up to 3% and are caused by the hgh tolerances of the electrolytc capactors. The expermental results are graphcally presented n fgure 8. Fg. 8 Expresson (37) shows that the value of the sustanng gan s constant f the ratos between the resstors and capactors reman constant, even f ther partcular values may be changed. The schematc n fgure 9 can be utlzed to buld varle frequency oscllators that can be brutally tuned by swtchng two equal resstors of fne tuned by the use of a varle capactor wth two dentcal sectons. In ths case, to mantan the oscllatons we need the followng condton to be true: A A = 3 (39) It s notced that transfer functon s dentcally wth a Wen net one whch s workng n current mode, but n comparson wth an oscllator wth Wen nets, the oscllator from fgure 9 has the advantage that both capactors are connected to the ground. Theoretcally speakng the A amplfer n fgure 9 could be elmnated f the SIDO amplfer offers suffcent gan, so that the requred sustanng gan to be obtaned. One can also note that theoretcally speakng the oscllator n fgure 9 works n a smlar way f the resstors and capactors can be nterchanged. Thus f R and C are nterchanged, as well as R and C, the transfer rato becomes: Issue, Volume, 8 45

7 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN AA sr C = s RRCC + s RC + RC + RC + ( ) (4) = ± δ (45) The oscllaton frequency s then gven by (38), and the sustanng gan s: C C R C C R = + + (4) The oscllator s behavor s agan equvalent to that of a Wen net oscllator, but n ths second case t has the advantage of havng two resstor connected to the ground. In fact the ove change s equvalent to the use of a double secton RC net. A The study of errors Errors due to the actual conveyor mpedances For the crcut n fgure 9, the output capactors (C Z ) of the SIDO(made out of two CCII) are put n parallel to the C and C capactors, the (R Z ) output resstor of the non-nvertng termnal of the SIDO s n parallel wth C, R and the output (R Z ) output resstor of the nvertng termnal of the SIDO s n parallel wth C. If R, R << R Z ther effect s neglected. The nput resstance of the A amplfer (R X ) s n seres wth R. In ths case the loop transfer rato becomes: = ( + Z) /{ ( + X) ( + Z)( + Z ) + AAsR C C s R R R C C C C + s R + R C + C + R C + C + R + R C + C + ( X)( Z) ( Z) ( X)( Z) } The sustanng gan s: R + R R + R C + C X X Z = + + R R C + CZ Whle the oscllaton frequency s: = R + R R C + C C + C ( ) ( )( X Z Z ) (44) (4) (43) For the estmaton of the nserted errors we wll take nto consderaton the worst case scenaro, meanng R =R = Ω, respectvely C =C =68pF (correspondng to the mnmal values of R and C used n the practcal mplementaton). We therefore obtan the numercal values of: ε mp = 3, 3% and mp ε = 7, 6%. For the usual values R =R = Ω respectvely C =C =nf one obtans ε mp =, 3% and ε mp =,9%. Errors due to the naccuracy of the conveyor current transfer To estmate these errors we wll consder the below expresson of the conveyor current transfer Where δ =, 5% s accordng to the catalogue data. We must take nto account the fact that a dfferental stage s made of two current conveyors. Consderng + = ( + δ ) respectvely = ( + δ ), the expresson of the transfer rato becomes: ( + δ ) + δ δ ( ) AA scr = sccrr s RC RC CR The oscllaton frequency: ( δ δ ) R C R + = + + CC RR δ R CR The sustanng gan s R C R + = + + δ R CR (46) (47) (48) Wth expressons 47 and 48 we can now calculate the relatve errors of the oscllaton frequency and the sustanng gan: ε δ + 3δ δ = + δ ε δ (49) = (5) + δ In the worst case scenaro ( δ =+,5% respectvely δ =,5% ) one gets ε δ =, 5% respectvely ε δ =, 49%. 3. Errors due to the mss-parng of the passve components. Identcally as n fgure Errors due to the oscllaton ampltude lmtaton crcut. Identcally as n fgure 5. VI. PRACTICAL IMPLEMENTATIONS An oscllator as n fgure 9 has been mplemented n practce. The followng measurements have been performed: The oscllaton ampltude has been fxed to 8mV. a) We fxated R =R =KΩ and tuned C =C between 36pF and μf. For capactor values under nf the loop gan needed to be dmnshed. For values of C =C between 5,65nF and μf (785:) we went through a frequency doman between 6Hz and 8,64 KHz ( 76:) wth a precson of approxmately 5%. We can demonstrate that for capactors values below nf, the errors rse up to out 67%. Also for large values of the Issue, Volume, 8 46

8 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN capactors, the errors also reach to 5%, but n ths case these errors can be blamed on the hgh tolerance of the electrolytc capactors beng used. skkrrcc + ( k )( k ) + ( + ) + ( ) + ( ) + + ( + ) + = AA A3 + s RC R C s RC R C s k k RC k k R C + s RC R C s RC R C The expresson of the scale factor s (5) S 4 = R C R C R C ( k) + ( k ) k + k R C (5) The mantanng gan s Fg. b) We fxated C =C =47nF and R =R have been modfed between Ω and 6,9KΩ. The oscllaton ampltude has been fxed at 8mV. For values of R =R >5KΩ the loop gan also needed to be changed and same for R =R <Ω. For values of R =R rangng from 5Ω to 6,9K Ω(83:) the obtaned frequences ranged from 55Hz to 5KHz ( 7: ) wth a 5% precson. When R =R Ω the errors grow up to %. R C + R C = R C k k k k ( ) + ( ) R C (53) The general expressons (5) to (53) are too complex to emphasze possble remarkle propertes of those oscllators. From a practce perspectve only the stuaton where the two current dvsors from the de-phasng crcuts have dentcal transfer ratos s of nterest, therefore k = k = k. ven ths, the scale factor becomes And the mantanng gan s S 4 k = (54) k = k ( k) (55) Fg. VII. THE CIRCUIT OF THE SECOND ORDER CURRENT MODE RC OSCILLATOR A wde varety of second order oscllators can be syntheszed just by usng the ove functonal blocks. We wll now present an oscllator whose reacton loop s characterzed by a complete second order transfer rato. The crcut n fgure s a cascade connecton of two de-phasng network wth current dvsor and grounded capactor, the lkes of the one n fgure 4[]. The transfer rato of the loop s obtaned from expresson (8) by multplcaton wth A 3 s gan Expresson (55) shows that n ths case the mantanng gan s ndependent of the R,R,C and C varatons. Ths means that the oscllator can be tuned by varyng one ore several components at a tme or smultaneously wthout havng to vary the loop gan. Fg. The second order current mode RC oscllator A Practcal Implementatons We used OrCad PSpce 9. to verfy the desgn. For ths we created a PA 63 Phototroncs current conveyor model, by usng the NS395 and NS394 transstors as actve elements Issue, Volume, 8 47

9 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN (see fgure 3). The snusodal oscllaton (see fgure 4) can be vsualzed at the measurng pont stuated between the collectors of the Q and Q6 transstors. One must note the stlty of the ampltude and oscllaton frequency. Fg.3 RC oscllator wth PA63 Fg. 4 The results of the numercal smulaton wth PSpce For the crcut n fgure the followng measurements have been performed: a) The followng components wth fxed values have been used: R =R =KΩ, C =56nF respectvely k =k =/, whle C has been vared wthn 68pF-μF (electrolytc). The oscllaton ampltude has been tuned to approxmately 8mV and remaned almost the same for the entre C value varaton. Also the loop gan needed no adjustments. For a varaton of C from,94nf to 7μF (out 65:) the frequency varaton ranged from 76Hz to 67Hz (8:) wth a precson under 5%. For a varaton of C from nf to μf(5:), the frequency vared from 8Hz to 73Hz (76:), wth a precson below 5%. We should note that for values of C nf errors may grow up to 7% even f the oscllaton frequency s n the order of tens of khz. Issue, Volume, 8 48

10 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN Fg. 5 The expermental results for R =R =KΩ, V m =8mV b) The followng components wth fxed values have been used: C =C = 47nF, R =KΩ and respectvely k =k =/, whle R wll vary from Ω to 96KΩ. The oscllaton frequency was ntally adjusted to 8mV and later dropped for R Ω. Also for R Ω the loop gan needed adjustments (gan ncrease). For a varaton of R rangng from 5Ω to 96KΩ (55:) the frequency range vared was 95Hz to 697Hz(73:) wth a precson hgher than 5%. For values of R Ω, errors rase up to 5% (R =Ω) and are caused by the ncrease n the nput mpedance module value on the X conveyor connecton, as the frequency ncreases. Fg. 6 The expermental results for C =C =47nF, V m =8mV c) The followng components wth fxed values have been used: R =R =KΩ, C =C =56 nf respectvely k =/ and k was vared. The oscllaton ampltude was mantaned at 8mV. One must menton that the loop gan needed adjustment for each change n the value of k. Snce for each two consecutve values (they change by out % each tme) t was requred for the gan to be readjusted, t can be supposed that a % varaton can lead to the oscllatons fadng out. The errors that occur (around 8%) could be due to / whch mpacts the scale factor formula. k Fg. 7 VIII. CONCLUSIONS From the expermental measurements we can conclude the followng related to the desgn of current mode oscllators by current conveyors:. Frst of all one must notce that the crcut presented here can work n a wde range of frequency just by modfyng a passve component and wthout the use of a complex AAC (automatc ampltude control) crcut. That s why ths oscllator s useful for the desgn of vobulated oscllators.. Crcuts may work n a wde range of frequences, should the components parng be better than -5 %, n order to have a reasonle precson. 3. We also experence a hgher precson of the oscllaton frequency wth the change of the resstors when the capactors are constant than wth the change of the capactors wth constant resstances. Ths s a consequence of the low tolerance of the resstors used (%) compared wth the one of the capactors (-%). 4. For low values of the capactors (<nf) even at tens of KHz frequency values errors can be qute large and ths can be explaned by the nductve behavor of the conveyors nput mpedances. 5. Also for small values of resstances (smaller than several hundreds ohms) errors can be qute sgnfcant and can be explaned by the growth wth the frequency of the conveyor nput mpedance value. 6. From a practcal perspectve the soluton has the dsadvantage of not ensurng the polarzaton stlty through negatve contnuous current reacton on the loop. As a fnal concluson, the conveyor based desgn of the current mode oscllators appears to be an nterestng approach from the perspectve of the smplcty/performance compromse. REFERENCES [] C.Toumazou, F.J. Ldgey and D.. Hagh, Analogue IC Desgn: the Current-Mode Approach, IEE Crcuts and Systems Seres, Peter Peregrnus Ltd.99. [] D. Frey, Current Mode Class AB second Order Flter, Electroncs Letters, Vol.3, No.3, pp.5-6, 994. [3] C. Toumazou, J.B. Huges and N.C. Batersby, Swtched-Current: An Analogue Technque for Dgtal Technology, IEE Crcuts and Systems Sere 5, Peter Peregrnus Ltd., 993. [4] R.Senan, New RC-Actve Oscllator Confguraton Employng Unty_an Amplfers, Electroncs Letters, Vol., No., pp , 985. [5] rgorescu L.,Practcal Aspects of RC Oscllators Desgn, nd Internatonal Conference on Electroncs, Computers and Artfcal Intellgence, ECAI 7, 9 th -3 th, Unversty of Ptest and IEEE Romana, Department of Electroncs, Communcatons and Computers Scence, pg. - 6, ISSN [6] rgorescu L., Nastac S.,The Current Mode RC Oscllators Synthess, 4 th IFAC Conference on Management and Control of Producton and Logstcs, Sbu, Romana, 7-3 September, 7, pg , ISBN [7] PA63, PA63A Professonal Audo Current Conveyor. Data sheet, Phototroncs Co. Regd., Manotck, Ontaro, Canada, 989. [8] Celma S., Carbosena A., Martnez P. A., Systematc eneraton of Cannonc RC-Actve Oscllators Usng CCII, ECCTD 93- Crcut Theory and Desgn, Elsever Scence Publshers B. V., pp [9] Sedra A., Smth K.C., A Second eneraton Current Conveyor and ts Applcatons, IEEE Transactons on Crcut Theory, February 97, pp Issue, Volume, 8 49

11 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SINAL PROCESSIN [] CCII Current-Conveyor Amplfer. Data sheet, LTP Electroncs Ltd., Oxford, UK, 993. [] rgorescu L., Nastac S.,Theoretcal and Practcal Aspects of Current Mode RC Oscllators, 4 th IFAC Conference on Management and Control of Producton and Logstcs, Sbu, Romana, 7-3 September, 7, pp , ISBN [] Chang C.M. Novel current-conveyor-bused. Sngle-resstancecontrolled/voltage-controlled oscllator employng grounded resstors and capactors, Electroncs Letters 3 rd February 994, vol. 3, no. 3, pp [3] Toumazou, C., Ldgey F.J. and Cheung PK, Current actuated analogue sgnal processng crcuts: Revew and recent developments. Procs 988 IEEE Int Symp Crcs and Systems (Portland, USA), pp , June 989. [4] Flanovsky, I. M., Stromsmoe, K. A., Fast ampltude control n a Twn-T Brdge RC Oscllator, Proceedngs of ISCAS 985, pp [5] Matthys, R. J., Crystal Oscllator Crcuts, John Wley & Sons, New York, 983. [6] Meyer-Ebrecht, D., Fast Ampltude Control of Harmonc Oscllatons, Proceedngs of IEEE, June 97, pp [7]Parzen, B., Desgn of Crystal and other Harmonc Oscllators, John Wley & Sons, 98. [8] Stuca, D., Crcute Integrate Analogce, Matrx ROM, Bucurest, 996. [9] Toumazou, C., Payne, A., Ldgey, J., Current Feedback Versus Voltage Feedback Amplfers Hstory, Insght and Relatonshp, 993, pp [] Wlson,., Usng Current Conveyors, Electroncs Letters & Wrless World, Aprl 986, pp Issue, Volume, 8 5