Current differencing transconductance amplifier-based current-mode four-phase quadrature oscillator

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 14, August 2007, pp Current differencing transconductance amplifier-based current-mode four-phase quadrature oscillator Worapong Tangsrirat* Faculty of Engineering and Research Center for Communications and Information Technology (ReCCIT), King Mongkut s Institute of Technology Ladkrabang (KMITL), Chalongkrung Rd., Ladkrabang, Bangkok 10520, Thailand Received 25 October 2006; accepted 1 June 2007 A realization of a current-controlled current-mode four-phase quadrature oscillator based on current differencing transconductance amplifiers (CDTAs) is proposed. The proposed oscillator circuit employs only three CDTAs and two grounded capacitors, which can provide four high output impedance sinusoidal current outputs with four-phase difference. The oscillation condition and oscillation frequency can be controlled electronically and independently by the transconductance gain of the CDTA. PSPICE simulation and experimental results with the commercially available ICs are given to confirm the operation of the proposed oscillator. IPC Code: H03L The quadrature mode of operation is a well known of waveform generation in the field of sinusoidal oscillators. Generally, a quadrature sinusoidal oscillator provides output signals of identical frequency and amplitude but of different phase angle. It can be widely found in many applications such as, in telecommunications for quadrature mixers and singlesideband generators 1, or in instrumentations for vector generator or selective voltmeters 2. Therefore, a quadrature oscillator plays an important role in many communication, measurement and instrumentation systems 3-5. Recently, a new active element with two current inputs and two kinds of current output, namely the current differencing transconductance amplifier (CDTA), has been introduced 6. This device is a synthesis of the well-known advantages of the current differencing buffered amplifier (CDBA) and a transconductance amplifier to facilitate the implementation of current-mode analog signal processing. As a result, many applications and advantages in the design of various current-mode circuits using CDTAs as active elements have received considerable attention. They are universal biquad filters 7, an N th -order lowpass filter circuit 8, a current-mode universal 2 nd -order with one input and three outputs filter 9, and a current-mode KHN filter 10. These applications have also been * ktworapo@kmitl.ac.th proven that the CDTA is a versatile active building block for current-mode signal processing applications. Until now, there is only current-mode quadrature oscillator circuit based on CDTAs which has been reported elsewhere 11. However, it requires a large number of passive elements, i.e., four resistors and two capacitor, and cannot be tuned its oscillation frequency electronically. In this paper, a current-controlled current-mode four-phase quadrature oscillator circuit using only three CDTAs and two grounded capacitors is presented. The proposed oscillator can provide four output current signals of identical frequency and amplitude but of four-phase difference, all at high output impedance terminals. The proposed oscillator has the advantages of independent oscillation control by varying a transconductance gain (g m ) of the CDTA as well as independent frequency control through another g m -value. Sensitivity analysis has shown that the circuit exhibits low active and passive sensitivity performance. PSPICE simulations and experimental results demonstrating the performance of the proposed quadrature oscillator are also given. Current Differencing Transconductance Amplifier (CDTA) The circuit representation and the equivalent circuit of the CDTA are shown in Fig. 1. The terminal relation of the CDTA can be characterized by the following set of equations: 6-10.

2 290 INDIAN J. ENG. MATER. SCI., AUGUST 2007 Fig. 1 CDTA (a) circuit representation and (b) equivalent circuit v p = v n = 0, i z = i p - i n and i x = g m v z = g m Z z i z (1) where p and n are input terminals, z and x are output terminals, g m is the transconductance gain, and Z z is an external impedance connected at the terminal z. According to above equation and equivalent circuit of Fig. 1b, the current flowing out of the terminal z (i z ) is a difference between the currents through the terminals p and n (i p -i n ). The voltage drop at the terminal z is transferred to a current at the terminal x (i x ) by a transconductance gain (g m ), which is electronically controllable by an external bias current. These currents, which are copied to a general number of output current terminal x, are equal in magnitude but flow in opposite directions. Although there are several techniques to realize the CDTA, one possible implementation of the CDTA using commercially available ICs is given in Fig. 2. From the property of the CA3080 amplifier, the transconductance gain g m of the CDTA in this case is directly proportional to the external bias current I B, which can be written by I g B m = (2) 2VT where V T 26 mv at 27 ο C is the thermal voltage. Proposed Circuit Figure 3 shows the proposed current-mode fourphase quadrature oscillator circuit, which employs only three CDTAs and two grounded capacitors. The use of grounded capacitors is helpful for easing the elimination of various parasitic capacitance effects 12,13. By routine circuit analysis using Eq. (1), the characteristic equation of the proposed quadrature oscillator in Fig. 3 can be expressed as : Fig. 2 Possible implementation of the CDTA using commercially available ICs. Fig. 3 Proposed CDTA-based current-mode four-phase quadrature oscillator 2 g m gm g + m gm s + s = 0 C1 C1C 2 (3) The oscillation condition and the oscillation frequency (ω o ) can respectively be obtained as : g g (4) and m1 m3 ω gm1gm2 o = C1C (5) 2

3 TANGSRIRAT: CURRENT-MODE FOUR-PHASE QUADRATURE OSCILLATOR 291 From Eqs (4) and (5), it is clear that the transconductance gain g m3 controls the condition of oscillation without disturbing ω o, which is controlled electronically by g m2 without affecting the condition of oscillation. Therefore, both the condition of oscillation and the frequency of oscillation can be orthogonally adjusted. Additionally, owing to all the output currents i o1, i o2, i o3 and i o4 are obtained at high output impedances, the proposed oscillator circuit can be connected directly to the next stage 14,15. From the circuit of Fig. 3, the current transfer function from i o1 to i o2 is gm2 io2 io1 sc = (6) 2 The phase difference (φ) between i o1 and i o2 is equal to φ=90 (7) which results in two-quadrature outputs. Also, by based on the multiple-output CDTA, the circuit provides an inverted version of the output currents i o1 and i o2. Thus, the relations of all the output currents can be expressed as : i o1 = io3 and io2 = io4 (8) This means that the circuit can provide the fourquadrature current outputs. Sensitivity Analysis The incremental sensitivity study forms an important performance criterion of any active network. The relative sensitivity of a parameter F to a circuit parameter x i is defined by: F xi df S = (9) xi F dx i Using this definition, it is easy to show from Eq. (5) that the sensitivities of ω o to the variation in active and passive element values are given by: S ω o 1 1, = g m g m 2 2 (10) S ω g o3 = 0 (11) m and 1 S ω o C 1, C = (12) 2 2 Thus, the proposed oscillator circuit exhibits attractive performance with active and passive sensitivities less than 0.5 in magnitude. However, for equal-valued elements, the ω o -sensitivities with respect to g m1, g m2, C 1 and C 2 are equal to unity in magnitude. Simulation Results To verify the theoretical prediction, the proposed CDTA-based current-mode four-phase quadrature Fig. 4 Simulated output waveforms of the proposed current-mode quadrature oscillator

4 292 INDIAN J. ENG. MATER. SCI., AUGUST 2007 Fig. 5 Simulated frequency spectrums of the proposed current-mode quadrature oscillator oscillator of Fig. 3 has been simulated with PSPICE program and the simulation results have also been verified by experimentally tested. To realize the CDTA active element in both simulations and experiments, the CDTA was performed by using commercially available ICs, i.e., CFA AD844s and OTA CA3080s, as illustrated in Fig. 2. The DC supple voltages were taken as ±12V. As an example, the circuit was designed for the oscillation frequency of f o khz, at a room temperature of 27 C. For this purpose, the capacitor and bias current values were chosen as : C 1 = C 2 = 10 nf, g m1 = g m2 2 ma/v (I B1 = I B2 100 µa), and g m3 1.8 ma/v (I B3 90 µa), respectively. Note that the g m3 -value is chosen a bit less than the g m1 -value to ensure safe oscillation as mentioned above. Fig. 4 shows the simulated output currents of the proposed current-mode quadrature oscillator circuit in Fig. 3. It may be pointed out from the figure that four highoutput-impedance sinusoid current sources with four phase difference are available in the proposed circuit. Fig. 5 shows the simulated frequency spectrums of i o1, i o2, i o3 and i o4. The total harmonic distortion (THD) for the designed frequency has been analyzed, which can be measured that the THDs are 2.65% to 4.45% for all the four quadrature outputs. It was also observed that for low frequencies the THDs were found to decrease, whereas for high frequencies the THDs will be Fig. 6 Simulation results of the oscillation frequency of Fig. 3, which is obtained by varying the bias currents (I B = I B1 = I B2 ). increased. The simulation results of the oscillation frequency of Fig. 3 by varying the value of the bias currents (I B = I B1 = I B2 ) with C 1 = C 2 = 10 nf are shown in Fig. 6, which demonstrates the linear and independent current control of f o. In experiments, the proposed oscillator circuit of Fig. 3 was also set up in the laboratory with I B1 = I B2 100 µa, I B3 90 µa, and C 1 = C 2 = 10 nf. Fig. 7 represents the experiment results of the output waveforms obtained from the circuit, where the load resistors of R L = 1 kω were connected at each the output terminal. The oscillation frequencies obtained by experiments is f o khz with error of f o /f o 0.56%.

5 TANGSRIRAT: CURRENT-MODE FOUR-PHASE QUADRATURE OSCILLATOR 293

6 294 INDIAN J. ENG. MATER. SCI., AUGUST 2007 Fig. 7 Experimental results of the output waveforms of Fig.3: (a) i o1 and i o2,(b) i o1 and i o3, (c) i o1 and i o4 Conclusions The realization of a current-controlled currentmode four-phase quadrature oscillator employing only three CDTAs and two grounded capacitors has been presented. The proposed oscillator circuit provides independent current control of the oscillation condition and oscillation frequency. Also, the circuit is suitable for both monolithic integrated circuit (IC) and thin film fabrication due to including only grounded capacitors, and enjoys low active and passive sensitivities. Theoretical analysis has been confirmed with both PSPICE simulations and experimental results. Acknowledgment The author would like to thank Professor Wanlop Surakampontorn, Faculty of Engineering, King Mongkut s Institute of Technology Ladkrabang (KMITL), for his valuable suggestions. The author also expresses gratitude to Mr. Danucha Prasertsom for his help in performing experiments. References 1 Horowitz P & Hill W, The Art of Electronics, (Cambridge University Press, Cambridge. UK), 1991, Tietze U & Schenk C, Electronic Circuits: Design and Applications, (Springer, Berlin, Germany), 1991, Holzel R, IEEE Trans Instrum Meas, 42(3) (1993) Srisuchinwong B, Int J Electron, 87 (2000) Khan I A & Khwaja S, Int J Electron, 87 (2000) Biolek D, CDTA-Building block for current-mode analog signal processing, Proc ECCTD 03, vol. III, Krakow, Poland; Biolek D & Biolkova V, Universal biquads using CDTA elements for cascade filter design, Proc CSCC 2003, Corfu, Greece; 2003, ISBN (CD). 8 Bekri A T & Anday F, N th -order low-pass filter employing current differencing transconductance amplifiers, Proc European Conf Circuit Theory and Design, vol. 2, 2005, Biolek D & Biolkova V, CDTA-C current-mode universal 2 nd - order filter, Proc 5 th WSEAS Int Conf Applied Informatics and Communications, Malta, September 15-17; 2005, Keskin A U, Biolek D, Hancioglu E & Biolková V, Int J Electron Commun, 60 (2006) Keskin A U & Biolek D, IEE Proc Circuits Devices & Syst, 153 (2006) Bhusan M & Newcomb R W, Electron Lett, 3 (1967), Pal K & Singh R, Electron Lett, 18 (1982) Gunes E O & Anday F, Electron Lett, 32 (1996) Chang C M, Electron Lett, 29 (1993)