Research Article  Open Access
JiunWei Horng, "CurrentMode ThirdOrder Quadrature Oscillator Using CDTAs", Active and Passive Electronic Components, vol. 2009, Article ID 789171, 5 pages, 2009. https://doi.org/10.1155/2009/789171
CurrentMode ThirdOrder Quadrature Oscillator Using CDTAs
Abstract
This paper describes a currentmode thirdorder quadrature oscillator based on current differencing transconductance amplifiers (CDTAs). Outputs of two currentmode sinusoids with phase difference are available in the quadrature oscillator circuit. The oscillation condition and oscillation frequency are orthogonal controllable. The proposed circuit employs only grounded capacitors and is ideal for integration. Simulation results are included to confirm the theoretical analysis.
1. Introduction
Various new currentmode active building blocks have received considerable attentions owing to their larger dynamic range and wider bandwidth with respect to operational amplifierbased circuits. As a result, currentmode active components have been increasingly used to realize active filters, sinusoidal oscillators, and immittances.
Quadrature oscillator is used because the circuit provides two sinusoids with 90° phase difference, as, for example, in telecommunications for quadrature mixers and singlesideband generators or for measurement purposes in vector generators or selective voltmeters. Therefore, quadrature oscillators constitute an important unit in many communication and instrumentation systems [1–17]. Twointegrator loop technique was developed to realize quadrature oscillators by using operational amplifiers or transconductance elements in [1, 2]. Holzel [3] proposed a method for realizing quadrature oscillator consists of two allpass filters and an inverter using operational amplifiers. Keskin et al. [15, 17] proposed two quadrature oscillators that were designed out by the method in [3] using current differencing buffered amplifiers (CDBAs) or current differencing transconductance amplifiers (CDTAs). Ahmed et al. [4] proposed two quadrature oscillator circuits that were realized base on the allpass filters and the noninverting integrators as building blocks using operational transconductance amplifiers (OTAs). This method was also used in [16] to obtain a quadrature oscillator using CDBAs. Soliman [6] describes several quadrature oscillator circuits based on the modification of twointegrator loop technique using current conveyors. Because the highorder network has high accuracy and highquality factor, it gives good frequency response with low distortion [9–12]. Prommee and Dejhan [9] proposed two thirdorder quadrature oscillators using OTAs. Horng et al. [10, 11] proposed four voltagemode thirdorder quadrature oscillator circuits; each circuit uses three secondgeneration current conveyors (CCIIs). Maheshwari and Khan [12] proposed a currentmode thirdorder quadrature oscillator using four CCIIs.
In 2003, a new currentmode active element that is called current differencing transconductance amplifier (CDTA) was introduced [18]. Owing to the current conveying property, the CDTA is one of the modifications of the current conveyor (CC). Many applications in the design of active filter [19] and multiphase sinusoidal oscillator [20] using CDTAs as active elements have received considerable attention. A secondorder currentmode quadrature oscillator consists of two CDTAs, four resistors, and two capacitors was presented in [17]. However, the capacitors used in this circuit are connected to the input terminals of the CDTAs. Since the input terminals of CDTA have parasitic resistances [20], this quadrature oscillator is not ideal for highfrequency applications. In 2006, Biolek et al. proposed a secondorder currentmode quadrature oscillator based on twointegrator loop technique [21]. The main disadvantage of this oscillator is that there is no control on the condition of oscillation.
In this paper, a CDTAsbased currentmode thirdorder quadrature oscillator circuit is presented. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are orthogonal controllable. The proposed quadrature oscillator uses only grounded capacitors. The use of only grounded capacitors is especially interest from the fabrication point of view [22].
2. Proposed Circuit
The circuit symbol and the equivalent circuit of the CDTA are shown in Figure 1. The terminal characteristic of the CDTA can be described by the following equations [18]: where and are input terminals, and are output terminals, is the transconductance gain, and is external impedance connected at the terminal. According to the above equation and equivalent circuit of Figure 1(b), the current flowing out of the terminal is a difference between the currents through the terminals and . The voltage drop at the terminal is transferred to the currents at the terminal by the transconductance gain , which is electrically controllable by an external bias voltage. These currents that are copied to a general number of output current terminals are equal in magnitude but flow in opposite directions. A possible CMOSbased CDTA circuit realization is given in Figure 2 [17].
(a)
(b)
The CDTAsbased thirdorder quadrature oscillator is shown in Figure 3. The characteristic equation of the circuit in Figure 3 can be expressed as
The oscillation condition and oscillation frequency can be obtained as
From (3) and (4), the oscillation frequency can be controlled by or . The oscillation condition can be independently controlled by . From Figure 3, the current transfer function from to is Under sinusoidal steady state, (5) becomes The phase difference, , between and is ensuring the voltages I_{o2} and I_{o1} to be in quadrature.
The proposed quadrature oscillator employs only grounded capacitors. The use of grounded capacitors is particularly attractive for integrated circuit implementation [22]. From (6), the magnitude of and need not the same. For the applications need equal magnitude quadrature outputs, another amplifying circuits are needed.
3. Nonideal Effects
Taking the nonidealities of the CDTA into account, Figure 4 shows the simplified equivalent circuit that is used to represent the nonideal CDTA [20]. In the figure, and is the current tracking error from the terminal to the terminal of the CDTA, and is the current tracking error from the terminal to the terminal of the CDTA, and and is the output transconductance tracking error from the terminal to terminal of the CDTA. Moreover, there are parasitic resistances ( and ) at terminals and and parasitic resistances and capacitances (, and , ) from terminals and to ground. Reanalysing of the proposed quadrature oscillator in Figure 3 using the nonideal CDTA model and assuming that the operation oscillation frequencies, , are very much smaller than or and the parasitic resistances at the terminals are very much greater than the parasitic resistances at or terminals of CDTAs, the characteristic equation of Figure 3 becomes where
The modified oscillation condition and oscillation frequency are where , , , , , , and .
Because the values of and are slightly less than unity [23], the parasitic conductances () at the terminals of CDTAs are not zero and the capacitances , , and are greater than , , and , respectively. From (9) and (10), the oscillation condition and oscillation frequency are deviated from the ideal cases. Therefore, to compensate this effect, we can slightly adjust the or values. The oscillation condition still can be independently controlled by . The active and passive sensitivities of the quadrature oscillator are all low and obtained as
4. Simulation Results
The quadrature oscillators were simulated using HSPICE. The CMOS CDTA implementation is shown in Figure 2 (using 0.18 m MOSFET from TSMC). The aspect ratios of the MOS transistors were chosen as in Table 1. The multiple current outputs can be easily implemented by adding output branches. Figure 5 represents the currentmode quadrature sinusoidal output waveforms of Figure 3 with , , , and where was designed to be larger than the theoretical value to ensure that the oscillations will start. The bias voltages are , and . The power dissipation is 3.9486 mW. The results of the and total harmonic distortion analysis are summarized in Tables 2 and 3, respectively. Figure 6 shows the simulation results of the oscillation frequencies of Figure 3 by varying the value of the transconductance with , , and was varied with by (3) to ensures that the oscillations will start.



5. Conclusion
In this paper, a new currentmode thirdorder quadrature oscillator using three CDTA and three grounded capacitors is proposed. Outputs of two sinusoids with 90° phase difference are available in the proposed quadrature oscillator. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are orthogonal controllable. Simulation results verify the theoretical analysis.
Acknowledgments
The author would like to thank the reviewers for their suggestions. The National Science Council, China, supported this work under Grant no. NSC 982221E033054.
References
 A. S. Sedra and K. C. Smith, Microelectronic Circuits, Oxford University Press, New York, NY, USA, 4th edition, 1998.
 I. A. Khan and S. Khwaja, “An integrable gmC quadrature oscillator,” International Journal of Electronics, vol. 87, no. 11, pp. 1353–1357, 2000. View at: Publisher Site  Google Scholar
 R. Holzel, “Simple wideband sine wave quadrature oscillator,” IEEE Transactions on Instrumentation and Measurement, vol. 42, no. 3, pp. 758–760, 1993. View at: Publisher Site  Google Scholar
 M. T. Ahmed, I. A. Khan, and N. Minhaj, “On transconductanceC quadrature oscillators,” International Journal of Electronics, vol. 83, no. 2, pp. 201–207, 1997. View at: Google Scholar
 M. T. Abuelma'atti and H. A. Alzaher, “Comment on currentmode quadrature sinusoidal oscillator using single FTFN,” International Journal of Electronics, vol. 85, no. 2, pp. 177–180, 1998. View at: Google Scholar
 A. M. Soliman, “Synthesis of grounded capacitor and grounded resistor oscillators,” Journal of the Franklin Institute, vol. 336, no. 4, pp. 735–746, 1999. View at: Publisher Site  Google Scholar
 J.W. Horng, “Current differencing buffered amplifiers based single resistance controlled quadrature oscillator employing grounded capacitors,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E85A, no. 6, pp. 1416–1419, 2002. View at: Google Scholar
 J.W. Horng, “Currentmode quadrature oscillator with grounded capacitors and resistors using two DVCCs,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E86A, no. 8, pp. 2152–2154, 2003. View at: Google Scholar
 P. Prommee and K. Dejhan, “An integrable electroniccontrolled quadrature sinusoidal oscillator using CMOS operational transconductance amplifier,” International Journal of Electronics, vol. 89, no. 5, pp. 365–379, 2002. View at: Google Scholar
 J.W. Horng, C.L. Hou, C.M. Chang, W.Y. Chung, H.W. Tang, and Y.H. Wen, “Quadrature oscillators using CCIIs,” International Journal of Electronics, vol. 92, no. 1, pp. 21–31, 2005. View at: Publisher Site  Google Scholar
 J.W. Horng, C.L. Hou, C.M. Chang, S.W. Pan, J.Y. Shie, and Y.H. Wen, “Thirdorder quadrature oscillator with grounded capacitors using CCIIs,” WSEAS Transactions on Electronics, vol. 4, no. 1, pp. 20–22, 2007. View at: Google Scholar
 S. Maheshwari and I. A. Khan, “Current controlled third order quadrature oscillator,” IEE Proceedings: Circuits, Devices & Systems, vol. 152, no. 6, pp. 605–607, 2005. View at: Google Scholar
 J.W. Horng, C.L. Hou, C.M. Chang, H.P. Chou, C.T. Lin, and Y.H. Wen, “Quadrature oscillators with grounded capacitors and resistors using FDCCIIs,” ETRI Journal, vol. 28, no. 4, pp. 486–494, 2006. View at: Google Scholar
 J. W. Horng, C. L. Hou, C. M. Chang, S. T. Cheng, and H. Y. Su, “Current or/and voltagemode quadrature oscillators with grounded capacitors and resistors using FDCCIIs,” WSEAS Transactions on Circuits and Systems, vol. 7, no. 3, pp. 129–138, 2008. View at: Google Scholar
 A. U. Keskin, C. Aydin, E. Hancioglu, and C. Acar, “Quadrature oscillator using current differencing buffered amplifiers (CDBA),” Frequenz, vol. 60, no. 34, pp. 21–23, 2006. View at: Google Scholar
 W. Tangsrirat and S. Pisitchalermpong, “CDBAbased quadrature sinusoidal oscillator,” Frequenz, vol. 61, no. 34, pp. 102–104, 2007. View at: Google Scholar
 A. U. Keskin and D. Biolek, “Current mode quadrature oscillator using current differencing transconductance amplifiers (CDTA),” IEE Proceedings: Circuits, Devices & Systems, vol. 153, no. 3, pp. 214–218, 2006. View at: Publisher Site  Google Scholar
 D. Biolek, “CDTABuilding block for currentmode analog signal processing,” in Proceedings of the European Conference on Circuit Theory and Design (ECCTD '03), vol. 3, pp. 397–400, Krakow, Poland, September 2003. View at: Google Scholar
 A. U. Keskin, D. Biolek, E. Hancioglu, and V. Biolková, “Currentmode KHN filter employing current differencing transconductance amplifiers,” AEUInternational Journal of Electronics and Communications, vol. 60, no. 6, pp. 443–446, 2006. View at: Publisher Site  Google Scholar
 W. Tangsrirat and W. Tanjaroen, “Currentmode multiphase sinusoidal oscillator using current differencing transconductance amplifiers,” Circuits, Systems, and Signal Processing, vol. 27, no. 1, pp. 81–93, 2008. View at: Publisher Site  Google Scholar
 D. Biolek, V. Biolkova, and A. U. Keskin, “Current mode quadrature oscillator using two CDTAs and two grounded capacitors,” in Proceedings of the 5th International Conference on System Science and Simulation in Engineering (WSEAS '06), pp. 368–370, Tenerife, Spain, December 2006. View at: Google Scholar
 M. Bhusan and R. W. Newcomb, “Grounding of capacitors in integrated circuits,” Electronic Letters, vol. 3, no. 4, pp. 148–149, 1967. View at: Google Scholar
 A. Fabre, O. Saaid, and H. Barthelemy, “On the frequency limitations of the circuits based on second generation current conveyors,” Analog Integrated Circuits and Signal Processing, vol. 7, no. 2, pp. 113–129, 1995. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2009 JiunWei Horng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.