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Circuits and Systems, 2011, 2, 65-73 doi:10.4236/cs.2011.22011 Published Online April 2011 (http://www.SciRP.org/journal/cs) Copyright © 2011 SciRes. CS Electronically-Controlled Current-Mode Second Order Sinusoidal Oscillators Using MO-OTAs and Grounded Capacitors Data Ram Bhaskar1, Kasim Karam Abdalla1, Raj Senani2 1Department of Electronics and Communication Engineering, Faculty of Engineering and Technology, Jamia Millia Islmia, New Delhi, India 2Division of Electronics and Communication Engineering, Netaji Subhas Institute of Technology, Delhi, India E-mail: senani@nsit.ac.in Received December 17, 2010; revised February 9, 2011; accepted February 21, 2011 Abstract Five new electronically-controllable second order current-mode sinusoidal oscillators using three multi- output operational transconductance amplifiers (MO-OTAs) and two grounded capacitors (GC) have been presented. Simulation results are included to confirm the theoretical analysis based upon CMOS OTAs im- plementable in 0.5 µm technology. Keywords: Oscillators, Analog Electronics, Current Mode Circuits, Operational Transconductance Amplifiers 1. Introduction Recently, Tsukutani, Sumi and Fukui [1] presented two current-mode OTA-C sinusoidal oscillators each of which employs three MO-OTAs and three grounded capacitors (GC) and provides three explicit current outputs. How- ever, whereas one of the circuits of [1] does not have in- dependent controllability of the condition of oscillation (CO) and the frequency of oscillation (FO) through dif- ferent transconductances (which is not only a desirable but also an expected property which one likes to see in any OTA-C oscillator), on the other hand, both the cir- cuits employ three GCs and hence, are not canonic. The main objective of this paper is to present five new current-mode electronically-controllable second order sinusoidal oscillators which use only three MO-OTAs like the circuits of [1] but in contrast to the circuits of [1], the proposed circuits use no more than two GCs and are capable of providing a non-interacting and independent control of both CO and FO and in addition also provide quadrature outputs which find numerous applications (for instance, in communications for quadrature mixers and single-sideband generators and in instrumentation for vector generator or selective voltmeters [2] etc.). 2. The Proposed Circuits The proposed circuits are shown in Figure 1. For an ideal MO-OTA with transconductance gm, the current output Io is given by Io = gm (V+ – V–), where V+ and V– are the input voltages at non-inverting input terminal and inverting input terminal respectively. Routine analysis yields, the condition of oscillation (CO) and the fre- quency of oscillation (FO) for all circuits as summarized in Table 1, which also shows the relevant modes of availability of quadrature outputs in all cases. From the expressions of FO given in Table 1, it can be easily de- duced that magnitude of all active and passive sensitivi- ties of FO, in all the five circuits, would be in the range of 0 to 1/2 and circuits thus, enjoy low sensitivity prop- erties. 3. Simulation Results To verify the validity of the proposed configurations, circuit simulation of the oscillators has been carried out using the CMOS MO-OTA circuit from [1] (presented here as Figure 2). In PSPICE simulation, implementa- tion was based upon a CMOS OTA in 0.5 µm technol- ogy. The aspect ratios of the MOSFETs were taken as shown in Table 2. The CMOS OTAs were biased with DC power supply voltages VDD = +2.5 V, VSS = −2.5 V. The generated waveforms, transient and the frequency spectrum for the proposed circuits obtained from simula- tions are shown in Figure 3, Figure 4 and Figure 5, D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 66 1 C m3 + - + + m1 + g - + + m2 + g - + + g 2 C + I02 I03 I01 (1) 1 C m3 + g - + + 2 C m2 + g - + + m1 + g -+ ++ I02 I03 I01 (2) 1 C m3 + g - + +2 C m2 + g -+ + m1 + g -+ + +I02 I03 I01 (3) 1 C m3 + g - + +2 C m1 + g - + + m2 + g - + +I03 I02 I01 (4) 1 Cm1 + g - + + 2 C m3 + g - + + m2 + g - + + +I02 I01 I03 (5) Figure 1. Proposed configurations. respectively. The element values used in the simulations along with the theoretical and practical output frequency and total harmonic distortions (THD) for the proposed circuits are summarized in Table 3. All the proposed oscillators have been checked for robustness using Monte-Carlo simulations, however, to conserve space, a sample result has been shown in Figure 6 for the oscil- lator (5) of Figure 1, which confirms that for 15% vari- ations in the value of gm3, the value of oscillation fre- quency remains close to its normal value of 1.1996 MHz and hence almost unaffected by change in gm3 (which should be the case since gm3 does not feature in the ex- pression of FO). In all cases, a very good correspondence between de- signed values and those observed from PSPICE simula- tions has been obtained. The simulation results, thus, confirm the workability of the proposed configurations. 4. Comparison with Other Previously Known OTA-Based Oscillators It is now useful to compare the proposed new circuits with some of the earlier proposed OTA-based oscillators. Recently, Kamat, Anand Mohan and Prabhu [3] presented a quadrature oscillator employing two MO-OTAs, two single output OTAs and two GCs. The circuit does not have independent controllability of CO and FO. It may also be recalled in this context that much earlier, in refer- ence [4], two minimum-component electronically-tunable sinusoidal oscillators using two OTAs and two GCs had been presented however, these circuits too did not have independent controllability of CO and FO. Furthermore, there is another class of OTA-based RC oscillators known earlier [5-9] which employ one or two OTAs along with a number of resistors and two capacitors. However, when these OTA-RC oscillators from [5-9] can be transformed into OTA-C oscillators, by simulating the resistors with OTAs, the resulting entirely-OTA-based oscillators will g m2 g m3 I o2 I o3 I o1 g m1 C2 C1 g m1 gm3 gm2 I o3 I o2 I o1 C2 C1 gm3 g m2 g m1 C1 C2 I o1 I o2 I o3 I o2 I o3 I o1 g m1 g m2 g m3 C1 C1 I o2 gm3 gm1 gm2 I o1 I o3 C1 C2 D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 67 VSS M1M2 3M4 M7M8 5M6 M9 M11 M 2 M1 M10 M VDD Ibias +Io -IoVin + Vin - Figure 2. MO-OTA. Table 1. Condition of oscillation and frequency of oscillation for the proposed circuits. Table 2. Aspect ratios of MOSFETs used in the MO-OTA implementation. MOSFET W(µm) L(µm) M1, M2 20 1.8 M3, M4, M5, M6, M9, M10 43 0.5 M7, M8, M11, M12 43 1.25 not remain as efficient and practically viable due to the requirement of an excessive number of OTAs. In comparison, the new circuits are free from above mentioned deficiencies of the circuits presented earlier in [3-9]. 5. Concluding Remarks Five new current-mode electronically controllable OTA-C sinusoidal oscillators have been presented. Like the recently proposed circuits of [1], the proposed circuits also employ only three MO-OTAs and grounded capaci- tors as preferred for IC fabrication [10] and [11]. How- ever, by contrast to the circuits presented in [1] both of which require three capacitors and hence are non-canonic, the proposed circuits require only two capacitors and hence, are canonic. All the proposed circuits enjoy the feature of independent controllability of oscillation fre- quency and condition of oscillation, which is not avail- able in one of the circuits presented in [1]. The new cir- cuits are also free from the drawbacks of the circuits pre- sented earlier in [3-9]. Also, all the proposed circuits pro- vide quadrature outputs as an additional feature not available in the circuits of [1]. The active and passivesen- sitivities of all the circuits are very low. The workability Circuit No. Condition of Oscillation (CO) Frequency of Oscillation (FO) Availability of Quadrature Outputs 1 (gm3 – gm1)≤ 0 12 12 1 2 mm gg CC 22 12 om o Is g I ssC , 212 332 omm om Is g g I sgsC 2 (gm2 – gm1) ≤ 0 23 12 1 2 mm g g CC 33 11 om o Is g I ssC , 33 21 om o Is g I ssC for gm1 = gm2 3 (gm1 – gm2) ≤ 0 23 12 1 2 mm g g CC 33 11 om o Is g I ssC , 33 21 om o Is g I ssC for gm1 = gm2 4 (C2 gm3 – C1 gm1)≤ 0 12 12 1 2 mm gg CC 11 21 om o Is g I ssC 5 (gm2 – gm3) ≤ 0 12 12 1 2 mm gg CC 121 331 omm om Is g g I sgsC , 11 21 om o Is g I ssC Ibias VSS +Io VDD – Io – in V in V D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 68 (a) (b) (c) (d) D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 69 (e) Figure 3. Output waveforms of (a) circuit 1 (b) circuit 2 (c) circuit 3 (d) circuit 4 (e) circuit 5. (a) (b) (c) D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 70 (d) (e) Figure 4. Output transient of (a) circuit 1 (b) circuit 2 (c) circuit 3 (d) circuit 4 (e) circuit 5. (a) (b) D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 71 (c) (d) (e) Figure 5. Frequency sp ectru m of (a) circuit 1 (b) circuit 2 (c) circu it 3 (d ) circuit 4 (e) circuit 5. of the proposed circuits has been demonstrated by SPICE simulation results. The transconductance of an OTA is temperature de- pendent this calls for appropriate temperature compensa- tion for which numbers of schemes are known in the literature [12-14]. However, the study of modified ver- sions of the proposed circuits incorporating temperature compensation would require considerable additional work; therefore, it was considered to be outside the scope of present work. Lastly, it may be mentioned that the D. R. BHASKAR ET AL. Copyright © 2011 SciRes. CS 72 Figure 6. Result of the Monte-Carlo Simulation of oscillator circuit (5) of Figure 1. Table 3. The values of the capacitors and transconductances for various oscillators. Circuit No. gm1 (mA/V) Ib1 (mA) gm2 (mA/V) Ib2 (mA) gm3 (mA/V) Ib3 (mA) C1 (nF) C2 (nF) FTheoretical (MHz) FPractical (MHz) THD 1 0.7954 2.8 0.7954 2.8 0.712 1.47 0.1 0.1 1.265918 1.277 2.6% 2 0.793 2.73 0.715 1.5 0.804 3.4 0.120.1 1.101566 1.1803 5.2% 3 0.7523 1.95 0.794 2.75 0.7718 2.26 0.070.071.732487 1.734 1.6% 4 0.7954 2.8 0.7046 1.4 0.788 2.6 0.110.111.083157 1.1514 2.3% 5 0.785 2.53 0.715 1.5 0.777 2.36 0.1 0.1 1.192361 1.1996 1% circuits proposed in this paper are inspired by the ideas contained in [15-19]. 6. References [1] T. Tsukutani, Y. Sumi and Y. Fukui, “Electronically Controlled Current-Mode Oscillators Using MO-OTAs and Grounded Capacitors,” Frequenz, Vol. 60, No. 11-12, 2006, pp. 220-223. doi:10.1515/FREQ.2006.60.11-12.220 [2] W. Tangsrirat, “ Current Differencing Transconductance Amplifier-Based Current-Mode Four-Phase Quadrature Oscillator,” Indian Journal of Engineering and Material Sciences, Vol. 14, No. 4, 2007, pp. 289-294. [3] D. V. Kamat, P. V. A. Mohan and K. G. Prabhu, “ Novel First-Order and Second-Order Current-Mode Filters Using Multiple-Output Operational Amplifiers,” Circuits Syst Signal Process, Vol. 29, No. 3, 2010, pp. 553-576. doi:10.1007/s00034-010-9163-y [4] M. T. Abuelma’atti, “New Minimum Componet Elec- tronically Tunable OTA-C Sinusoidal Oscillators,” Elec- tronics Letters, Vol. 25, No. 17,1989, pp. 1114-1115. doi:10.1049/el:19890747 [5] M. T. Abuelma’atti and M. H. Khan, “Grounded Capacitor Oscillators Using a Single Operationl Trans- conductance Amplifier,’’ Active and Passive Electronic Components, Vol. 19, No. 2, 1996, pp. 91-98. [6] Y. Tao and J. K. Fidler, “Generation of Second-Order Single-OTA RC Oscillators,” IEE Proceedings of Circuits Devices Systems, Vol. 145, No. 4, 1998, pp. 271-277. doi:10.1049/ip-cds:19981872 [7] Y. Tao and J. K. 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