Dual-Output All-Pass Filter Employing Fully-Differential Operational Amplifier and Current-Controlled Current Conveyor

Transcription

1 ELEO 11 7th International onference on Electrical and Electronics Engeerg, 1-4 December, Bursa, TURKEY Dual-Outut All-Pass Filter Emlog Full-Differential Oerational Amlifier and urrent-ontrolled urrent onveor iera Biolkova 1, Zdenek Kolka 1, and Dalibor Biolek 1 Det. of Radio Electronics, Brno Universit of Technolog, Purknova 118, Brno, ech Reublic biolkova@feec.vutbr.c, kolka@feec.vutbr.c Det. of EE/Microelectronics, Brno Universit of Technolog/Universit of Defence, Technicka 1/Kounicova 65, Brno, ech Reublic dalibor.biolek@unob.c Abstract First-order voltage-mode all-ass filter rovidg high ut and low ut imedances is described. The roosed filter emlos a full-differential oerational amlifier, a currentcontrolled current conveor II, and one caacitor, with the ossibilit of electronic control of natural frequenc. Two voltage uts are simultaneousl available for nonvertg and vertg transfer functions, with the ossibilit of utilig them as a differential ut. 1. Introduction Sce 1996, man active filters, emlog the non-vertg and vertg first-order all-ass filters, have been ublished [1-8]. The reason consists the imortance of these buildg blocks various alications, articularl for on-chi analog signal rocessg and generation. The required features of voltage-mode toologies clude high ut and low ut imedances, simlicit of circuit toolog, which redetermes low-ower oeration, low sensitivities to arameter variations, and articularl the absence of matchg conditions among the comonent arameters which would be necessar for the roer oeration. Some alications require electronic control of natural frequenc. Fulfillg the above requirements simultaneousl is a difficult task [8]. Man researchers searched for various circuit structures which emlo assorted tes of active elements, startg from conventional oerational amlifiers (OAms) [1-5], contug with commerciall available urrent-feedback OAms [6] and Oerational Transconductance Amlifiers [7-8], and utilig also modern buildg blocks, namel various tes of current conveors [9-15], Differential Difference Amlifier (DDA) [16], urrent Differencg Buffered Amlifier (DBA) [17-1], urrent Differencg Transconductance Amlifier (DTAs) [-7], oltage Differencg Differential Inut Buffered Amlifier (D-DIBA) [8] and others. In addition to the above-mentioned requirements, also economical versions of all-ass filters are needed, which clude both the non-vertg and vertg versions a sgle device. In [9], a full-differential OAm-based all-ass filter rovides both uts, enablg also differential voltage ut. However, the natural frequenc of this filter is determed b a fied resistor, and its direct electronic control is thus roblematic. In Section II of this aer, a full-differential OAm-based all-ass filter is roosed which also emlos a urrent- ontrolled urrent onveor II+ and one caacitor. Then the natural frequenc of the filter is determed b the conveor trsic resistance, which can be siml controlled via a bias current. The caacitor is of the floatg te. However, its one let is connected to low-imedance OAm ut, which elimates the corresondg arasitic imedance. The fluence of the imedance associated with the second let is analed Section III. Section I contas eerimental verification of the roosed circuit architecture via SPIE simulations, utilig a transistor-level model of II+ and behavioral model of commerciall available OAm.. Proosed all-ass filter The roosed all-ass filter emlog a full-differential OAm and a II+ is shown Fig. 1. I c II+ I = I Fig. 1. Proosed all-ass filter with high-imedance ut and two low-imedance uts and. Due to the negative feedback the circuit, the OAm differential ut voltage is close to ero, and the ut voltage aears at the termal of II+. The current I, flowg of the termal, is given b the voltage at the trsic resistance R of this termal, thus I. (1) R This current is conveed to the termal and then it flows through the caacitor, causg the voltage dro I c. () s ombg (1) and () ields. (3) sr 319

2 ELEO 11 7th International onference on Electrical and Electronics Engeerg, 1-4 December, Bursa, TURKEY The filter transfer function is then 1 sr 1 sr. (4) Note that R can be electronicall adjusted via the bias current I B accordg to the equation [3] R T (5) I B where T is the thermal voltage. Thus (4) reresents tical transfer functions of the non-vertg and vertg first-order all-ass filter with the natural frequenc 1 I (6) B R which is directl roortional to the bias current. The temerature deendence can be advantageousl utilied various temerature sensors such as temerature/hase shift converters or temerature/frequenc converters (when the allass cell is a art of susoidal oscillator). 3. Non-ideal case The theoretical small-signal behavior of the filter, described b Eq. (4), is affected b several non-idealities. Transfer function (4) can be fluenced b the followg real roerties of the active and assive elements: OAm ut and ut imedances, arasitic imedances of conveor termals, ESR (Equivalent Serial Resistance) and arasitic imedances of the caacitor, alha and beta factors of the current conveor, defed b the equations T R I, I I, (7) and the frequenc deendence of ke arameters, articularl the OAm ga and current conveor alha and beta factors. The above arameters were cluded the model of the filter Fig. 1, and the aroimate smbolic analsis of transfer function (4) was erformed via SNAP smbolic rogram [31]. Numerical values of the comonent arameters considered are from Section I. Domant sources of the imerfections the frequenc resonses with a given frequenc range, revealed via such an analsis, are dicated Fig. : alha and beta factors of the current conveor, and R and arasitic elements, which model the arasitic imedances of the termals of current conveor, OAm, and caacitor. Other arasitic imedances do not manifest themselves due to low-imedance OAm uts. Takg to account the above non-idealities, filter transfer function (4) is a more general form: R s R R 1 s R, (8) I R II+ I = Fig.. Simlified model for error analsis of filter from Fig. 1. where R is the resistance R modified b the fluence of OAm ut resistance R o : o R R R R. (9) Note that the low-frequenc ga (LFG) and the highfrequenc ga (HFG) are as follows: LFG R R, I HFG 1. (1) Their ratio, which is equal to one the ideal case, can serve as a rough measure of arasitic assband rile. Note that the high-frequenc ga has a tendenc to be higher than one, which can be elimated via selectg large caacitance >>. On the other hand, the low-frequenc ga has a tendenc to be smaller than one, articularl for < 1. This tendenc can be reduced via selectg small trsic resistance R << R. Note that the above conclusions ab the high-frequenc ga do not take the high-frequenc behavior of active elements to account. After a simle arrangement of Eq. (8) we obta R 1 s R 1 s R R. (11) R 1 s R 1 s The first term on the right side of (11) reresents the transfer function of ideal all-ass filter with the natural frequenc R. (1) R R The second term can be terreted as an additional error term. At the natural frequenc (1), its absolute value is err R 1 R. (13) 3

3 ELEO 11 7th International onference on Electrical and Electronics Engeerg, 1-4 December, Bursa, TURKEY This value (err) can serve for the estimation of a global error which is caused b the real fluences. Sce the beta factor is normall decled from its ideal value 1 b several er cent ots, it can be a domant error source comarison to R and, which normall differ b several decades from R and. For eamle, when ==.95, R /R = /=1-4, then err.35, LFG.95, HFG 1.1. (14) The first value means that the error term (11) is b 9 db less than the first term, which reresents the ideal all-ass filter with natural frequenc (1). This error is mal caused b the imerfection of the beta term, which is also resonsible for the decreased low-frequenc ga. The high-frequenc ga is almost ideal, sce it is not fluenced b the beta factor. At the natural frequenc (6) of ideal non-vertg allass filter with transfer function (4), the hase shift is eactl - 9. The imact of the real roerties can be also measured b comarg this frequenc with the frequenc, at which the same hase shift aears the non-ideal case. An analsis of Eq. (8) leads to the followg result: R R. (15) 1 It should be noted that there are several reasons for decreasg the frequenc of the -9 hase shift due to real fluences: Decreasg the alha and beta factors below 1, large arasitic caacitance, and the R /R ratio when it cannot be neglected. 4. Sice simulations In order to verif the feasibilit of the roosed all-ass filter, a PSPIE simulation of the structure Fig. 1 was erformed. The bias current I B = 5 A corresonds to the trsic resistance R = 58.6 for a temerature of 7 (see Eq. 5). For the caacitance = 6.16 nf, the theoretical natural frequenc from (6) is 1 kh. With regard to the low-voltage model of II, the lowvoltage full differential rail-rail OAm LT643-1 was also used the filter, together with its SPIE model from [33]. Its sul voltages were chosen the same as for the II. Table 1. Transistor models, adoted from [3]..model PX PNP +RB=37 IRB= RBM=4.55 R=5 RE=3 +IS=73.5E-18 EG=1.6 XTI=1.7 XTB=1.866 BF=11 +IKF=.359E-3 NF=1 AF=51.8 ISE=5.1E-16 NE=1.65 +BR=.4745 IKR=6.478E-3 NR=1 AR=9.96 IS= N= +TF=.61E-9 TR=.61E-8 JE=.18E-1 JE=.5 +MJE=.8 J=.164E-1 J=.8 MJ=.4 XJ=.37 +JS=1.3E-1 JS=.55 MJS=.35 F=.5.model NX NPN +RB=54.6 IRB= RBM=5 R=5 RE=1 +IS=11E-18 EG=1.6 XTI= XTB=1.538 BF= IKF=6.974E-3 NF=1 AF=159.4 ISE=36E-16 NE= BR=.758 IKR=.198E-3 NR=1 AR=1.73 IS= N= +TF=.45E-9 TR=.45E-8 JE=.14E-1 JE=.5 +MJE=.8 J=.983E-13 J=.5 MJ=.3 XJ=.34 +JS=.913E-1 JS=.64 MJS=.4 F=.5 In the first ste, a D analsis of the designed filter from Fig. 1 was erformed with the ut voltage swet with the range of -1 to +1, see Fig. 4. For =, the differential D ga is aroimatel 1.1 for both uts. Lear oeration is guaranteed aroimatel for abs( ) <.63. For larger ut voltages, the nonlearit of II becomes domant., [] [].5 1. Fig. 4. D analsis of roosed all-ass filter from Fig. 1. Fig. 3. Transistor-level model of II, adoted from [3]. The transistor-level modelg of the II was erformed accordg to [3], see Fig. 3. Sce onl the sgle-ut conveor is used Fig. 1, transistors Q14 and Q15 are omitted the model. As [3], the PNP and NPN transistors were modeled with the arameters of the PRN and NRN biolar transistors of ALA4 transistor arra from AT&T [3], see Table I. Smmetrical sul voltages of ±1.5 were used. The frequenc resonses of the filter from Fig. 1 are shown Fig. 5, demonstratg the natural frequenc control via the bias current. For I B = 5 A, the frequenc measured for -9 hase shift of the non-vertg cell is 9 kh, which is ca 8 er cent below its theoretical value. This decrease is due to the real roerties modeled b Eq. (15). The transient analsis confirmed the filter stabilit. For I B =5A and susoidal ecitation with a frequenc of 1 MH, the THD factor was.88% for an amlitude of 1 m and 5.48% for 1 m. 31

4 ELEO 11 7th International onference on Electrical and Electronics Engeerg, 1-4 December, Bursa, TURKEY 6 / [db] 7. References k 1k 1k 1M 1M frequenc [H] h() [deg] IB [ua]: 5, 1,, 5 IB [ua]: 5, 1,, k 1k 1k 1M 1M frequenc [H] Fig. 5. Simulated amlitude and hase frequenc resonses for various values of bias current I B. 5. onclusions The roosed first-order all-ass filter rovides both nonvertg and vertg uts simultaneousl. It can be also used for generatg a differential voltage ut with double voltage swg comarison with the sgle-ended solution. Due to the utiliation of full differential oerational amlifier, the filter toolog ehibits high-ut and low-ut imedances, which enables an eas cascade snthesis. The natural frequenc can be tuned electronicall via modifg the trsic resistance of the II termal. As a certa drawback can bee seen that the floatg caacitor with the caacitance is emloed. However, one of its lets is connected directl to the OAm low-imedance ut. The fluence of the arasitic imedance of the second let is analed Section III, with the conclusion that it causes a modification of the natural frequenc. This modification is negligible when the arasitic caacitance is much smaller than. If necessar, this henomenon can be easil comensated via a modification of. 6. Acknowledgment This work has been suorted b the roject Z.1.7/.3./.7 WIOMT of the oerational rogram Education for cometitiveness. This work has been also suorted b the ech Science Foundation under grants Nos. 1/9/168 and P1/1/1665, and b the research rogrammes of BUT No. MSM16353/513 and UD Brno No. MO FT43, ech Reublic. [1] J. E. B. Ponsonb, Active all-ass filter usg a differential oerational amlifier, Electronics Letters, vol., , [] R. Gen, Realiation of an all-ass transfer function usg oerational amlifiers, Proceedgs of the IEEE, vol. 56, , [3] P. Aronhime, and A. Budak, An oerational amlifier allass network, Proceedgs of the IEEE, vol. 57, , [4] A. M. Soliman, Realiation of oerational amlifier allass networks, Electronics Letters, vol. 9, , [5] T.. Donald, J.. David, and R. G. Jason, A high frequenc tegrable band-ass filter configuration, IEEE Transactions on ircuits and Sstems II, vol. 44, , [6] S. Kilc, and U. am, urrent-mode first-order allass filter emlog sgle current oerational amlifier, Analog Integrated ircuits and Signal Processg, vol. 41, , 4. [7] L. Acosta, A. J.R-Angulo, A. J. L-Martín, and R. G. arvajal, Low-voltage first-order full differential MOS all-ass filter with rogrammable ole-ero, Electronics Letters, vol. 45, , 9. [8] A. Ü. Kesk, K. Pal, and E. Hancioglu, Resistorless firstorder all-ass filter with electronic tung, International Journal of Electronics and ommunications (AEÜ), vol. 6, , 8. [9] A. M. Soliman, Inductorless Realiation of an All-Pass Transfer Function Usg the urrent onveor, IEEE Transactions on ircuit Theor, vol. T-,. 8-81, [1] A. M. Soliman, Another Realiation of an All-Pass or a Notch Filter Usg a urrent onveor, International Journal of Electronics, vol. 35, , [11] S. Maheshwari, and I. A. Khan, Novel first-order allass sections usg a sgle III, International Journal of Electronics, vol. 88, , 1. [1] M. A. Ibrahim, H. Kuntman, and O. icekoglu, Firstorder all-ass filter canonical the number of resistors and caacitors emlog a sgle DD, ircuits Sstems and Signal Processg, vol., , 3. [13] S. Maheshwari, New voltage and current-mode APS usg current controlled conveor, International Journal of Electronics, vol. 91, , 4. [14] J. W. Horng, urrent conveors based allass filters and quadrature oscillators emlog grounded caacitors and resistors, omuters and Electrical Engeerg, vol. 31,. 81 9, 5. [15] B. Met, O. icekoglu, and K. Pal, DD based all-ass filters usg mimum number of assive elements, Proc. of the MWSAS 7, , 7. [16] A. Toker, and S. Oogu, Novel all-ass filter section usg differential difference amlifier, International Journal of Electronics and ommunications (AEÜ), vol. 58, , 4. [17] A. Toker, S. Oogu, O. icekoglu, and. Acar, urrentmode allass filters usg current differencg buffered amlifier and a new high-q bandass filter configuration, IEEE Transactions on ircuits and Sstems-II: Analog and Digital Signal Processg, vol. 47, ,. 3

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