Quadrature Oscillators Using Operational Amplifiers

Hindawi Publishing Corporation Active and Passive Electronic Components Volume 2011, Article ID 320367, 4 pages doi:10.1155/2011/320367 Research Article Quadrature Oscillators Using Operational Amplifiers Jiun-Wei Horng Department of Electronic Engineering, Chung Yuan Christian University, Chung-Li 32023, Taiwan Correspondence should be addressed to Jiun-Wei Horng, Received 19 May 2011; Accepted 2 July 2011 Academic Editor: Ahmed M. Soliman Copyright © 2011 Jiun-Wei 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. Two new quadrature oscillator circuits using operational amplifiers are presented. Outputs of two sinusoidal signals with 90◦ phase difference are available in each circuit configuration. Both proposed quadrature oscillators are based on third-order characteristic equations. The oscillation conditions and oscillation frequencies of the proposed quadrature oscillators are orthogonally controllable. The circuits are implemented using the widely available operational amplifiers which results in low output impedance and high current drive capability. Experimental results are included. 1. Introduction Quadrature oscillator is used because the circuit provides two sinusoids with 90◦ phase difference, as, for example, in telecommunications for quadrature mixers and single-sideband generators or for measurement purposes in vector generators or selective voltmeters. Therefore, quadrature oscillators constitute an important unit in many communication and instrumentation systems [1–7]. Recently, several multiphase oscillators based on operational amplifiers were proposed [6–11]. Two-integrator loop technique was developed to realize quadrature oscillators using operational amplifiers [6]. In 1993 [7], Holzel proposed a new method for realizing quadrature oscillator, which consists of two all-pass filters and one inverter using operational amplifiers. Several multiphase oscillators using operational amplifiers were proposed in [8–11]. However, the quadrature output voltages cannot be obtained from [8– 10]. The multiphase sinusoidal oscillator in [11] was constructed by cascading several first-order all-pass networks and unity-gain inverting networks. However, the block diagram of the quadrature oscillators in [11] was the same with [7]. In this paper, two new quadrature oscillator circuits using operational amplifiers are proposed. Outputs of two sinusoidal signals with 90◦ phase difference are available in each proposed circuit configuration. Both proposed quadrature oscillators are based on third-order characteristic equations. The oscillation conditions and oscillation frequencies of the proposed quadrature oscillators are orthogonally controllable. The circuits are implemented using the widely available operational amplifiers which results in low output impedance, high current drive capability (enabling the systems to drive a variety of loads), simplicity, and low cost. 2. Circuit Description Figure 1 shows the first proposed quadrature oscillator circuit. The characteristic equation of the circuit can be expressed as s3 C1 C2 C3 R1 R2 R3 R4 R5 + s2 C3 R3 R4 R5 (C1 R1 + C2 R2 ) + sC3 R3 R4 R5 + R1 R2 = 0. (1) At s = jω, by equating the real and imaginary parts with zero, the oscillation condition and oscillation frequency can be obtained as R3 R4 R5 = C1 C2 R1 2 R2 2 , C3 (C1 R1 + C2 R2 ) ωo =  1 . C1 C2 R1 R2 (2) (3) From (2) and (3), the oscillation condition and oscillation frequency can be orthogonally controllable. 2 Active and Passive Electronic Components From Figure 1, the voltage transfer function from Vo2 to Vo1 is Vo2 1 =− . Vo1 sC3 R4 R5 φ = 90 s C1 C2 C3 C4 C5 R1 R2 R3 + s C3 C4 C5 R3 (C1 R1 + C2 R2 ) (5) C1 2 C2 2 R1 R2 , C3 C4 C5 (C1 R1 + C2 R2 ) ωo =  1 . C1 C2 R1 R2 (7) (8) (9) (10) The phase difference, φ, between Vo2 and Vo1 is φ = 90◦ (11) ensuring the voltage Vo2 and Vo1 to be in quadrature. Because the output impedance of the operational amplifier is very small, the two output terminals, Vo1 and Vo2 , can be directly connected to the next stage, respectively. The passive sensitivities of the quadrature oscillator in Figure 2 are all low and obtained as 1 SωC1o ,C2 ,R1 ,R2 = − . 2 (12) Vo1 − + + Figure 1: The first proposed quadrature oscillator circuit. C3 Vo2 R3 R1 Vo1 − + C4 − From (8) and (9), the oscillation condition and oscillation frequency can be orthogonally controllable. From Figure 2, the voltage transfer function from Vo2 to Vo1 is Vo2 1 =− . Vo1 sC3 R3 R3 C1 At s = jω, by equating the real and imaginary parts with zero, the oscillation condition and oscillation frequency can be obtained as R3 = C2 − (6) 2 + sC3 C4 C5 R3 + C1 C2 = 0. R2 C1 Figure 2 shows the second proposed quadrature oscillator circuit. The characteristic equation of the circuit can be expressed as 3 + R1 ensuring the voltage Vo2 and Vo1 to be in quadrature. Because the output impedance of the operational amplifier is very small, the two output terminals, Vo1 and Vo2 , can be directly connected to the next stage, respectively. The passive sensitivities of the quadrature oscillator in Figure 1 are all low and obtained as 1 SωC1o ,C2 ,R1 ,R2 = − . 2 R4 − (4) The phase difference, φ, between Vo2 and Vo1 is ◦ C3 Vo2 C5 R2 + C2 − + Figure 2: The second proposed quadrature oscillator circuit. 3. Experimental Results The quadrature oscillator in Figure 1 was constructed using LF351s. Figure 3 represents the quadrature sinusoidal output waveforms of Figure 1 with C1 = C2 = C3 = 1 nF, R1 = R2 = R4 = R5 = 10 kΩ, R3 = 4.563 kΩ, and the power supply ±10 V. Figure 4 shows the experimental results of the oscillation frequency of Figure 1 by varying the value of R (R = R1 = R2 = R4 = R5 ) with C1 = C2 = C3 = 1 nF, and R3 was varied with R by (2) to ensure the oscillations will start. The quadrature oscillator in Figure 2 was constructed using LF351s. Figure 5 represents the quadrature sinusoidal output waveforms of Figure 2 with C1 = C2 = C3 = C4 = C5 = 1 nF, R1 = R2 = 10 kΩ, R3 = 4.767 kΩ, and the power supply ±10 V. Figure 6 shows the experimental results of the oscillation frequency of Figure 2 by varying the value of R (R = R1 = R2 ) with C1 = C2 = C3 = C4 = C5 = 1 nF, and R3 was varied with R by (8) to ensure the oscillations will start. 4. Conclusions Two new quadrature oscillator circuits based on operational amplifiers are presented. The proposed quadrature oscillators provide the following advantages: (i) two sinusoidal output signals of 90◦ phase difference are obtained simultaneously in each configuration; (ii) the oscillation conditions and oscillation frequencies are orthogonally controllable; (iii) the output terminals have the advantages of low output Active and Passive Electronic Components Tek stop 3 Tek stop T T T T (...truncated)