Tunable Quadrature Sinusoidal Oscillator Using Single-Ended OTAs

Montree Kumngern and Somyot Junnapiya Department of Telecommunications Engineering, Faculty of Engineering,

King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand E-mail: kkmontre@kmitl.ac.th, somyot@telecom.kmitl.ac.th

Abstract—This paper presents a new electronically tunable voltage-mode quadrature sinusoidal oscillator employing four single-ended operational transconductance amplifiers (OTAs) and two grounded capacitors. In general, the single-ended OTA configuration is simpler than the multiple-output OTA counterpart and the requirement of grounded capacitors is preferable for an integrated circuit fabrication process. Therefore, the proposed circuit provides a simple circuitry by using only single-ended OTA and highly suitable for integrated circuit (IC) implementation by using grounded capacitors. The condition of oscillation and the frequency of oscillation of the circuit can be set orthogonally. The circuit also offers an electronic control of the frequency of oscillation through adjusting the bias currents of OTAs. The theoretical results are verified by PSPICE simulators. From simulation results, it can be expressed that the proposed circuit agrees well with theory.

Keywords–quadrature sinusoidal oscillator (QSO), grounded capacitor, voltage-mode circuit, CMOS

I. INTRODUCTION

Quadrature sinusoidal oscillators (QSOs) have been found widely in communication and measurement systems. For example, it can be used to quadrature mixers and single-sideband generators in communication system, or to purposes in vector generators or selective voltmeters in measurement system [1], [2]. Therefore, many QSOs have been reposted in the literature [3]-[19]. In [3]-[10], current conveyor-based QSOs have been proposed. However, these oscillators suffer from the lack of electronic tunability. Although, QSOs in [11]-[13] offers an electronic control adjustable functions but they employ excessive number of active and/or passive components. Operational transconduc-tance amplifiers (OTAs) have exhibited some advantages in the circuit design. The OTA provides an electronic tunability, a wide tunable range, and powerful ability to generate various circuits. Moreover, OTA based circuits require no resistors and, therefore, are suitable for integrated circuit implementation [21]. Several QSOs using OTAs have been proposed already [14]-[19]. In [14], two oscillator circuits have been proposed. The first circuit employs two OTAs, three floating capacitors, one voltage follower (VF) and second one employs three OTAs, one floating capacitor, one grounded capacitor, one VF, The use of floating capacitor makes the circuits in [14] not ideal for IC implementation [20]. The OTA-based QSOs using grounded capacitors were presented in [15], [16]. However, these

structures suffer from the complexity. In [17], the QSO circuit enjoys temperature-insensitive, but this structure employs six OTAs, two grounded resistors and two grounded capacitors. The QSO realization in [18] uses four simple OTAs, but the circuit requires three capacitors. The current-mode QSO circuit using two multiple-output OTAs and two grounded capacitors has been proposed in [19]. However, the circuit suffers from the use of multiple-output OTAs. Compared with multiple-output OTA-based circuit, single-ended OTA-based circuit is simpler for implementation.

In this paper, a new electronically tunable voltage-mode QSO using four single-ended OTAs and two grounded capacitors is presented. The employment of grounded capacitors and no resistor makes the circuit ideal from the integrated circuit implementation. The oscillator provides two voltage sources with 90º phase difference. The frequency of oscillation and condition of oscillation can be set orthogonally. Also the frequency of oscillation can be electronically controlled. The proposed circuit has been simulated by using PSPICE simulators to confirm the presented theory.

II. PROPOSED CIRCUIT The circuit symbol of the OTA is shown in Fig. 1. Its

characteristic can be described by following equation,

)V(VgI 21mo −±= (1)

where Io is the output current, gm is the transconductance gain, V1 and V2 denote the non-inverting and inverting input voltage, respectively. Fig. 2 shows the addition/subtraction voltage. Assuming that OTA1 and OTA2 are identical, the voltage Vo can be expressed as [22]

321o VVVV +−= (2)

It is evident from (2) that the circuit in Fig. 2 can be obtained for addition and subtraction of voltage signals.

Figure 1. Circuit symbol of the OTA.

2012 Fourth International Conference on Computational Intelligence, Communication Systems and Networks

Unrecognized Copyright Information

DOI 10.1109/CICSyN.2012.24

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2012 Fourth International Conference on Computational Intelligence, Communication Systems and Networks

978-0-7695-4821-0/12 $26.00 © 2012 IEEE

DOI 10.1109/CICSyN.2012.24

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Figure 2. Addition/subtraction voltage circuit using OTAs.

Fig. 3 shows the proposed electronically tunable voltage-mode quadrature oscillator circuit. The circuit composes of an all-pass section and an integrator as shown as Fig. 3(a). The all-pass section and integrator are consisted of OTA1, OTA3, OTA4, C1 and OTA2, C2, respectively, as shown in Fig. 3(b). Note that the use of only grounded capacitor is suitable for integration point of view [20]. Also, the circuit employs only single-ended OTAs which provide a simple for realization. Using (1) and (2), the characteristic equation of proposed QSO in Fig. 3 can be obtained as

( ) 0gggCgCsCCs m2m1m21m12212 =+−+ . (3)

Therefore, the condition of oscillation and the frequency of oscillation can be obtained, respectively, as

m12m21 gCgC = (4)

21

m2m1o CC

ggω = . (5)

From (4), the condition of oscillation can be adjusted by C1 and C2 and/or gm1 and gm2. If letting gm1=gm2=gm, equation (5) can be simplify rewritten as

21mo CC

1gω = (6)

Then, the frequency of oscillation can be adjusted by gm through varying the biasing current. This implies that the circuit can work as electronically tunable. From the circuit in Fig. 3, OTA2 along with C2 form of the lossless integrator. The relationship between Vo1 and Vo2 can be expressed as

2

m2

o1

o2

sCg

VV −= (7)

where the phase difference is φ=-π/2. This guarantees that the proposed quadrature oscillator provides the quadrature outputs voltages, Vo1 and Vo2. It should be noted that the loads cannot be directly connected to Vo1 and Vo2. Then, the circuit needs the buffer circuits. The various passive and active sensitivities of the parameter ωo of this sinusoidal oscillator are

1m1

1m1

sCgsC-g

+

2

m2

sCg

−

Figure 3. Proposed quadrature sinusoidal oscillator, (a) block diagram;

(b) schemetic.

Figure 4. CMOS implementation of the single-ended OTA.

⎪⎭

⎪⎬⎫

−==

=

5.0SS

1S

o2

o1

om

ωC

ωC

ωg

. (8)

It can see that the sensitivities from (8) are not more that 1. The CMOS implementation of single-ended OTA is shown in Fig. 4. Assuming MOS transistors M1 and M2 are matched and operating in saturation, the transconductance gain (gm) can be expressed by

( ) abcoxm I W/LμCg = (9)

where Iabc is the bias current, μ is the carrier mobility, Cox is the gate oxide capacitance per unit area, W and L are the channel width and length, respectively.

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Figure 5. The simulated quadrature output waveforms.

Figure 6. Simulated results of the frequency of oscillation.

III. SIMULATION RESULTS The proposed circuit is verified through PSPICE

simulators using 0.5 μm CMOS process from MOSIS [23]. The power supplies are selected as VDD = −VSS = 3 V. The bias currents for OTA3 and OTA4 are fixed as 25μA. As an example design, the QSO was designed with C1=C2=50pF. The aspect ratios for OTA1, OTA2, OTA3, and OTA4 are W/L=2μm/2μm for M1 and M2 and W/L=40μm/2μm for M3 and M4. If the oscillator is not start, the aspect ratios of

transistors M1 and M2 for OTA2 should be needed to be larger than the aspect ratios of transistors M1 and M2 for OTA1 by (4). The adjustment the condition of oscillation by setting W/L of transistors makes the circuit easy for varying the frequency of oscillation (i.e., Iabc1=Iabc2=Iabc).

Fig. 5 represents the quadrature sinusoidal output waveforms of Fig. 3 (b) with Iabc1=Iabc2=50μA. This simulation result obtains a frequency of 244.6 kHz and total harmonic distortions about 0.65 % and 0.39 % for Vo1 and

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Vo2, respectively. Fig. 6 shows the simulation results of the proposed frequency of oscillation by varying the values of the bias currents Iabc (i.e., Iabc=Iabc1=Iabc2) versus capacitors C (i.e., C=C1=C2). This result is confirmed by (6) that the circuit can be operated as an electronically tunable.

IV. CONCLUSIONS In this paper, a new electronically tunable voltage-mode

quadrature sinusoidal oscillator is presented. The proposed circuit employs only four single-ended OTAs and two grounded capacitors. The circuit provides two voltage sources with 90º phase difference and electronic control of the frequency of oscillation. Also the condition of oscillation and the frequency of oscillation can be orthogonally controlled. The simulation results obtained were found to be in good agreement with the theory. It should be noted that the proposed quadrature sinusoidal oscillator is suitable for a high impedance load. If the low impedance load is applied, they need a voltage buffer at an output. Compared with [18], the proposed circuit using the number of OTAs is equal but lesser the used capacitor. Therefore, the proposed structure is more suitable for integrated circuit than the previous oscillators.

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