Research Article The Nonlinear Distortions in the Oscillatory System of Generator on CFOA

Transcription

1 Active and Passive Electronic Components Volume 2012, Article ID , 6 pages doi: /2012/ Research Article The Nonlinear Distortions in the Oscillator Sstem of Generator on CFOA Yuri Konstantinovich Rbin National Research Tomsk Poltechnic Universit, Tomsk , Russia Correspondence should be addressed to Yuri Konstantinovich Rbin, rbin@tpu.ru Received 28 Januar 2012; Revised 18 March 2012; Accepted 23 March 2012 Academic Editor: Abhirup Lahiri Copright 2012 Yuri Konstantinovich Rbin. This is an open access article distributed under the Creative Commons Attribution License, hich permits unrestricted use, distribution, and reproduction in an medium, provided the original ork is properl cited. In recent ears, man articles came out here one could find the analsis of oscillator sstems of electric sinusoid signals generators ith amplifiers called CFOA current feedback operational amplifiers. As a rule, the analsis of such sstems is made b appling mathematical modeling methods on the basis of the amplifier linear model, hich does notallo estimating advantages and disadvantages of the sstems realied ith those amplifiers in comparison ith classical sstems. A nonlinear model of a current feedback operational amplifier (CFOA) is introduced in the paper; nonlinearit of current mirror is reflected in the form of current double limiting. The analsis of to knon oscillator sstems has been carried out ith the use of this nonlinear model. Dependence beteen current limiting level, output voltage amplitude, and maimum oscillation frequenc has been obtained. The paper shos that output current limiting under current output connection of capacitive load reduces frequenc range and output voltage amplitude considerabl and increases harmonic distortions in comparison ith classical oscillator sstems. The research done has found that the application of ne amplifiers does not give considerable advantages to the oscillator sstems ith CFOA. 1. Introduction In the end of the last centur a ne operational amplifier in the monolithic form appeared in the market of electronic components. Its distinctive features, in comparison ith traditional operational amplifiers, ere inverting input ith lo input resistance, additional output ith high output resistance, frequenc range etension, and ver fast large signal response. The amplifier as called a current feedback operational amplifier (CFOA). Tpicall, these amplifiers perform on the complementar bipolar technolog on heterogeneous smmetric p-n-p and n-p-n transistors. Man companies have developed the manufacture of the amplifiers. The eamples of the amplifiers are AD844, OPA622, and others. The description of the circuit technolog of the ne amplifiers is given in the materials of manufacturing companies [1, 2]. There is a detailed description of AD844 amplifier (Rbin [3]). Naturall, such amplifiers provoked great interest amidst developers of electronic devices, for eample, oscillator sstems (OSs) of electric signals generators. Man orks came out here different variants of OS of sinusoid oscillations ere given (Abuelma atti [4, 5], Abuelma atti and Al-Shahrani [6], Soliman [7, 8], and Martíne et al. [9].) There one could find the analsis of conditions of oscillation ecitation and establishing (Abuelma atti [4]), their advantages and disadvantages. Hoever, the analsis as done on the basis of linear models of CFOA, so it has limited use and does not allo disclosing all advantages and disadvantages. Taking into account the fact that OS is a basis of an electric signals generator, as periodic oscillation is ecited and established there, and OS determines their form and basic parameters, the author makes an attempt to anale OS on the basis of CFOA nonlinear model eemplified b to OSs. 2. Current Feedback Operational Amplifier Figure 1 shos a non-linear equivalent circuit CFOA amplifier of AD844 tpe. The circuit consists of to voltage folloers DA1 and DA2, current-controlled current suppl

2 2 Active and Passive Electronic Components V in1 DA1 I out 5 DA V in2 2 R in1 I in2 R in2 I R i C i VD 1 VD 2 Vout E 1 E Figure 2: Representations of CFOA of AD844 tpe at electric circuits ith numeric and corresponding letter smbols of outputs. I off2 Figure 1: Nonlinear equivalent circuit CFOA of AD844 tpe. done according to the current mirror (CM) circuit, RCcircuit imitating inertia, and double output voltage limiter. One amplifier input (V in1 ) is noninverting ith high input resistance (potential input); the other (V in2 ) is currentinverting ith lo input resistance (R in2 ). To represent different input resistances the circuit contains voltage folloer DA1. It is knon that the special feature of this amplifier is its to outputs: current output (I out )and potential output (U out ). A usual potential output ( )ismadeat the folloer DA2 output after the output voltage limiter on diodes VD1 and VD2 ith voltage sources E1 and E2. Currentoutput(I out ) has high output resistance Ri. It is important that the circuit has current limiter shon in CM (current mirror) block. Output current (I out )isequalto input current at inverting input due to the use of current mirror in the circuit, but it is limited b maimum current I = {I 1 if I 1 I ma ; I ma if I 1 > I ma ; I ma if I 1 < I ma }. That makes the circuit different from other knon models of CFOA (Thomas H. Lee). Limitation of current and voltage turns the equivalent circuit into a nonlinear one ith pieceise-linear elements. At the same time in the amplifier areas of linear amplification and restriction are formed. This allos analing the conditions of ecitation of oscillations in the oscillator. When the ecitation processes take place in the linear area of characteristic, restriction is used to determine the maimum amplitude and its dependence on frequenc of oscillations. Figure 2 gives a representation of the amplifier ith potential (3) and current (2) inputs and potential (6) and current (5) outputs. To build OS one can use the ne amplifier practicall in all knon OSs replacing VFOA voltage feedback operational amplifier b CFOA. The circuit analsis can be done b knon methods. Interesting are those OSs that can be realied onl ith CFOA and cannot be repeated ith usual amplifiers. 3. Analsis of Oscillator Sstems ith CFOA Figure 3 shos the first eample of OS generator circuit ith one amplifier. Specificall, Figure 3(a) shos a circuit of a knon OS ith Wien-Robinson bridge done ith an amplifier ith potential feedback VFOA; Figure 3(b) shos ne OS [4, 9]. One can see that the ne circuit uses current output connected ith output 5 of the microcircuit. It can also be observed that the circuits contain different numbers of passive elements. The classical circuit has 6 of them, and the ne one has onl 4. Certainl, the difference of to resistors is not essential. The point is different. To change oscillation frequenc one usuall uses to or even four adjustable elements (to resistors and/or to capacitors), for eample, doubled continuousl adjustable capacitor or doubled potentiometer. One or both capacitors should be isolated from the common ire. But continuousl adjustable capacitors ith mechanicall adjusted capacitance are bulk elements ith high stra capacitance per device case, hich influences significantl generation conditions and oscillation frequencies, especiall in lo capacitances. This draback applies equall to mechanic potentiometers also used to var frequencies. In the ne circuit both capacitors/potentiometers can be connected ith each other b one of the outputs ith common ire, and that could simplif their manufacture and application considerabl. Let us anale OS shon in Figure 3(b) to estimate conditions of sinusoid oscillation generation. With this aim in vie e put don the OS equation set ith ideal CFOA: V = I Z 2, V = I Z 1, V = V = V, I = I here Z 1 (s) = 1/sC 1, Z 2 (s) = R 2 /(1 sr 2 C 2 ), s = σ jω. Substituting currents I and I from the first and second equations into the fourth ith a glance at the third one, e obtain V [Z 1 (s) Z 2 (s)] = 0. After substituting circuit resistances e put don OS characteristic equation s 2 C 1 R 2 C 2 s(r 2 C 2 C 1 R 2 C 1 ) 1= 0. (1) Analing the obtained equation, e find conditions of phase and amplitude balance (the Barkhausen criterion) realiation: 1 ω =, R1 C 1 R 2 C 2 (2) R 2 C 2 C 1 R 2 C 1 = 0. The second condition, amplitude balance, does not differ from the condition obtained in [4]. So it is satisfied under R 2 = 2 and C 2 = 0.5C 1.Asonecansee,both oscillation frequenc and amplitude balance depend on the same elements:, C 1, R 2,andC 2. Therefore, there is a connection beteen oscillation frequenc and amplitude. In this case oscillation ould not be isochronous, as elements parameters instabilit ould be accompanied b simultaneous changing of oscillation amplitude and frequenc. One can eliminate the dependence of frequenc on the oscillation amplitude and at the same time appl frequenc

3 Active and Passive Electronic Components 3 C 1 VFOA CFOA R 2 C 2 R 4 R 3 C 2 R 2 C 1 (a) (b) Figure 3: Oscillation sstems circuits: (a) ith usual amplifier VFOA; (b) ith CFOA. driving elements ith equal parameters in enhanced OS shon in Figure 4. After similar transformations as for the circuit in Figure 3(b) e get the OS characteristic equation s 2 C 1 R 2 C 2 s [ R 2 C 2 C 1 β C 2 ] 1= 0. (3) Whence e find conditions of amplitude and phase balances: ω = 1 R1 C 1 C 2, R 2 C 2 C 1 β C 2 = 0. In this circuit the conditions for potential oscillation generation are satisfied under = R 2 = R, C 1 = C 2 = C, and β = 2. Then, oscillation frequenc is equal to ω = 1/RC. It is obvious that circuit β shouldbeanactivecircuit amplifier ith an amplification factor of to. OS ith such parameters is shon in Figure 4(b). It is formed b elements ith equal parameters of frequenc driving elements, hich is its advantage. Its amplitude balance, regardless of phase balance, is provided b resistance of additional resistors R 3 and R 4, beteen hich correlation R 4 = 2R 3 should be satisfied in stationar mode. The advantage of this circuit in comparison ith OS circuit in Figure 3(b) is in the fact that its oscillation is isochronous as being controlled b oscillation amplitude does not change its frequenc. Interesting is OS of to integrators, each of hich is realied ith CFOA [4]. Figure 5 eemplifies an OS ith to integrators: classical and ne circuits. To compare the circuits correctl, both of them are realied ith CFOA. The conditions of amplitude and phase balances for the first circuit are knon. It is not difficult to put the conditions don for the second circuit as ell on the basis of transfer function (4) of to frequenc-dependent active elements realied ith amplifiers DA1 and DA2: K 1 (s) = = Z 2(s) = R 2/(1sR 2 C 1 ) Z 2 (s) R 2 /(1sR 2 C 1 ) R 2 R 2 sr 2 C 1, K 2 (s) = Z C2(s) R 3 = 1 sr 3 C 2. Thus, in this circuit active linear frequenc-dependent elements, the first (under R 2 = = R) and the second, are integrators. OS characteristic equation and equations for amplitude and phase balances take the folloing form Q(s) = s 2 R 2 R 3 C 1 C 2 s[ R 2 ]R 3 C 2 R 2, R ω 2 1 = =, R 2 R 3 C 1 C 2 R1 R 3 C 1 C 2 R 2 = 0. Amplitude balance in the sstem is reached under equalit of resistances and R 2, hile phase balance and, consequentl, frequenc in this circuit does not depend on resistance R 2. That allos controlling oscillation amplitude ithout changing frequenc b changing resistance R 2.At the same time, changing resistance R 3, one can control oscillation frequenc ithout changing amplitude, though changing frequenc ould depend on resistor s resistance under comple la. Thus, the circuit gives the possibilit to control the conditions of oscillation ecitation and frequenc changing ith the help of resistors connected b the common ire. Let us compare OS for the realiation of their potential resources. Essentiall these schemes use different tpes of feedback. In the circuit shon in Figure 5(a) in each amplifier eternal voltage negative feedback is applied from the output of to (5) (6)

4 4 Active and Passive Electronic Components β CFOA CFOA1 CFOA2 C 2 R 2 R 3 R 4 C 1 C 2 R2 C 1 (a) (b) Figure 4: Enhanced oscillation sstemsith CFOA: (a) simplified, ith feedback circuit β; (b) fundamental, ith to CFOA, one of hich is used as circuit β. R 2 R 3 C 1 R 4 C 2 DA3 DA2 DA DA1 2 DA2 C 1 R 2 R 3 C 2 1 (a) (b) Figure 5: Oscillation sstems of to integrators ith CFOA: (a) classical and (b) ne circuits. an input, and in Figure 5(b) current feedback on input. It is knon that the input in the CFOA amplifiers is connected inside the circuit ith p-n-p and n-p-n emitters of the input transistors. In the latter case, on an resistance connected to the emitters the current feedback appears. Circuit 5b has less active and passive elements. It needs onl to amplifiers and five passive elements, but it is important to take into consideration that toda the difference of one amplifier in the monolithic form and to-three passive components hen making industrial generator is not essential. Moreover, in circuit 5a the additional amplifier makes it possible to get one more output. More important is OS comparison for non-linear distortions level. Lo non-linear distortions level approimates output voltage to sinusoid form. It is output voltage sinusoid form that becomes the objective of making sinusoid oscillation generators. Non-linear distortions reduction in the first circuit is reached b several factors: (i) introducing eternal voltage feedback from the output to the input ; (ii) Absence of in-phase distortions, as amplifiers inputs ork under quite lo signals in contrast to the ne circuit here both amplifiers inputs are under common-mode voltage equal to output voltage, hich ma cause distortions; It is knon that amplifiers of CFOA tpe have relativel lo common mode rejection ratio; (iii) reduction of influence of distortions of the input and output voltage folloer, as the are covered b local and common negative feedback. The point is that the folloers are output stage in the structure of usual amplifiers ith potential feedback, so in the first classical circuit their distortions influence on output voltage distortions is effectivel reduced b the eternal feedback; in the ne circuit the voltage folloers in the structure of CFOA are in the circuit of positive feedback and their distortions are not suppressed. To back this statement an eperiment as carried out here higher harmonic rates of the main blocks of generators-output integrators ere measured. For the eperiment amplifiers of AD844 tpe under suppl voltage ±10 V, resistors ith resistance 20 kω and capacitors ith capacitance nf ere chosen as amplifiers. Measurements ere taken under frequenc 200 H and output voltage amplitude 5 V. Generator GS-50 (THD < 120 db) and rejection filter ith rejection frequenc 200 H ere used in the eperiment. The results of the eperiment are given in Table 1. As one can see from Table 1, the classical integrator has the evident advantage of harmonic rate level. Its distortions are db less. Another important advantage of the OS ith CFOA mentioned in the materials of the compan manufacturer is its better frequenc qualities. These amplifiers, hen using

5 Active and Passive Electronic Components 5 Table 1: Comparison of integrators for higher harmonic level, db. Harmonic rate Integrator of DA1, R 4, C 2, Figure 5(a) Integrator of DA2, R 3, C 2,for Figure 5(b) K 2r K 3r K 4r Um (V) nf 1 nf 0.5 nf 0 potential output (output 6 in Figure 1), have ide range of amplified frequencies (up to 60 MH). Let us see hether e could realie this advantage of OS using current output. To appl CFOA ith current output (output 5) it is important to kno its output load capacit. The manufacturer of the amplifier [1] certifies maimum input current for inverting input not more than 5 ma. The same ould be maimum current for output. Eperimental measuring of maimum output current for output hen signal limit for current comes gives the folloing values: I ma = 2.5mA under suppl voltage ±10 V and I ma = 3.5mAunder±15 V. When connecting to the current output of outer elements current in them is limited eactl b these maimum values. Limit for current leads to limit for potential amplitude of integrator output voltage under given frequenc. Let us calculate the dependence of integrator output voltage amplitude on oscillation frequenc. The relation beteen these values ith a glance at oscillation sinusoid form is given b the knon equation I ma = 2πfCU m. This formula connects maimum current value, integrator output voltage amplitude, frequenc, and capacitance of capacitor. The minimum value of the capacitance of the integrator cannot be less than the capacitance of the output (transcapacitance), that is, it cannot be less than 4.5 pf for the amplifier AD844. This capacit is alas present and ill determine the error of output oscillation frequenc of the generator. Let us use the formula to estimate hether e could realie the amplifier potential frequenc properties in integrator circuit. According to the manufacturer [1] data one can get the voltage of 20 V peak-peak at the potential output under frequenc 20 MH. With the sinusoid form this voltage corresponds to double output voltage amplitude, that is, equal to 10 V. Let us put these values to the last formula and estimate potential value of the integrator capacitor capacitance under this frequenc and voltage amplitude ith the formula C = I ma /2πfU m. The value of the integrator capacitor capacitance is equal to 5.6 pf. The value is too small for frequenc driving capacitance and can be compared ith output stra capacitance of current output (4.5 pf), so it cannot be regarded as the integrator capacitance. Real potential values should be chosen ith a glance at the permissible error of oscillation frequenc in the limits of 1 2%, that is, in the limits of 500 pf. When reducing oscillation amplitude to the level of 5 V as ell, one could speak about maimum oscillation frequenc onl about 200 kh. Thus, it is not possible to realie maimum frequenc properties of the amplifier in the limits of OS ith CFOA ith current output under output oscillation f (MH) Figure 6: Dependence of maimum amplitude of the integrator output voltage on signal frequenc. Table 2: Comparison of circuits ith to integrators. Parameters Figure 5(a) Figure 5(b) Number of amplifiers 3 2 Number of passive elements 6 5 Outputs 0, 90, 180 0,90 Harmonic rate, db (85 90) (58 80) Frequenc range in OS ith CFOA, MH <1 <0,2 amplitude of some 5 V. Perhaps for this reason, the oscillation amplitude at frequencies above 1 MH in the orks [10, 11] is less than 1 V p-p. Figure 6 shos the dependences in diagrams. Using the diagrams and knoing the value of the integrator capacitor capacitance one can easil estimate maimum value of output voltage amplitude. Thus, the comparison of basic OS parameters ith to integrators is tabulated in Table 2. The main advantage of OS circuits ith CFOA mentioned b the authors of [3, 4, 6] is the possibilit to connect RC-elements of frequenc and oscillation amplitude control b the common ire. It is certainl an important advantage, but it is not crucial toda, as the time of bulk mechanical doubled capacitors and potentiometers for frequenc changing has passed. Toda frequenc is controlled b D/A converters and capacitors ith electronic changing, and the problem is not so pressing. 4. Conclusion The use of current feedback operational amplifiers (CFOAs) in oscillator sstems of generators instead of potential feedback amplifiers leads to (i) the increase of harmonic distortions, (ii) the reduction of generated frequenc range under equal oscillation amplitude.

6 6 Active and Passive Electronic Components Thus, oscillator sstem of electric signals generator ith CFOA does not have considerable advantages and in respect of harmonic level and frequenc properties even ields to knon oscillator sstems ith traditional amplifiers. References [1] Analog Devices: 60 MH, 2000 V/μs Monolitic Op Amp AD844, 2012, data sheets/ad844.pdf. [2] Burr Bron: Wide Bandidth Operational Amplifier OPA622, 2012, [3] Yu. K. Rbin, Electronic Devices for Analog Signal Processing, Springer, Dordrecht, The Netherlands, [4] M. T. Abuelma atti, Identification of a class of to CFOAbased sinusoidal RC oscillators, Analog Integrated Circuits and Signal Processing, vol. 65, no. 3, pp , [5] M. T. Abuelma atti, Ne to CFOA-based sinusoidal RC oscillators ith buffered outlet, Analog Integrated Circuits and Signal Processing, vol. 66, no. 3, pp , [6] M. T. Abuelma atti and S. M. Al-Shahrani, Novel CFOAbased sinusoidal oscillators, Electronics, vol. 85, no. 4, pp , [7] A. M. Soliman, Applications of the current feedback operational amplifiers, Analog Integrated Circuits and Signal Processing, vol. 11, no. 3, pp , [8] A. M. Soliman, Current feedback operational amplifier based oscillators, Analog Integrated Circuits and Signal Processing, vol. 23, no. 1, pp , [9] P.A.Martíne, S. Celma, and I. Gutiérre, Wien-tpe oscillators using CCII, Analog Integrated Circuits and Signal Processing, vol. 7, no. 2, pp , [10] A. M. Soliman, Generation of current conveor based oscillators using nodal admittance matri epansion, Analog Integrated Circuits and Signal Processing, vol. 65, no. 1, pp , [11] D. K. Srivastava and V. K. Singh, Single-capacitor-controlled oscillators using a single CFOA, in Proceedings of the International Conference on Circuits, Sstem and Simulation (IPCSIT 11), vol. 7, IACSIT Press, 2011.

7 Rotating Machiner Engineering The Scientific World Journal Distributed Sensor Netorks Sensors Control Science and Engineering Advances in Civil Engineering Submit our manuscripts at Electrical and Computer Engineering Robotics VLSI Design Advances in OptoElectronics Navigation and Observation Chemical Engineering Active and Passive Electronic Components Antennas and Propagation Aerospace Engineering Volume 2010 Modelling & Simulation in Engineering Shock and Vibration Advances in Acoustics and Vibration