# Quadrature Oscillators Using Operational Amplifiers

Authors: Jiun-Wei Horng
Journal: Active and Passive Electronic Components
 (2011)

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## Abstract

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.


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## Body

## 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

Figure1 shows the first proposed quadrature oscillator circuit. The characteristic equation of the circuit can be expressed as(1)s3C1C2C3R1R2R3R4R5+s2C3R3R4R5(C1R1+C2R2)+sC3R3R4R5+R1R2=0.Figure 1
The first proposed quadrature oscillator circuit.Ats=jω, by equating the real and imaginary parts with zero, the oscillation condition and oscillation frequency can be obtained as(2)R3R4R5=C1C2R12R22C3(C1R1+C2R2),(3)ωo=1C1C2R1R2.
From (2) and (3), the oscillation condition and oscillation frequency can be orthogonally controllable.From Figure1, the voltage transfer function from Vo2 to Vo1is(4)Vo2Vo1=-1sC3R4.
The phase difference, ϕ, between Vo2 and Vo1 is(5)ϕ=90°
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 Figure1 are all low and obtained as(6)SC1,C2,R1,R2ωo=-12.Figure2 shows the second proposed quadrature oscillator circuit. The characteristic equation of the circuit can be expressed as(7)s3C1C2C3C4C5R1R2R3+s2C3C4C5R3(C1R1+C2R2)+sC3C4C5R3+C1C2=0.Figure 2
The second proposed quadrature oscillator circuit.Ats=jω, by equating the real and imaginary parts with zero, the oscillation condition and oscillation frequency can be obtained as(8)R3=C12C22R1R2C3C4C5(C1R1+C2R2),(9)ωo=1C1C2R1R2.
From (8) and (9), the oscillation condition and oscillation frequency can be orthogonally controllable.From Figure2, the voltage transfer function from Vo2 to Vo1 is(10)Vo2Vo1=-1sC3R3.
The phase difference, ϕ, between Vo2 and Vo1 is(11)ϕ=90°
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 Figure2 are all low and obtained as(12)SC1,C2,R1,R2ωo=-12.


## 3. Experimental Results

The quadrature oscillator in Figure1 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.Figure 3
The experimental quadrature output waveforms of Figure1.Figure 4
Experimental results of the oscillation frequency of Figure1, which is obtained by varying the value of R; o o o, experimental results; —, ideal curve.The quadrature oscillator in Figure2 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.Figure 5
The experimental quadrature output waveforms of Figure2.Figure 6
Experimental results of the oscillation frequency of Figure2, which is obtained by varying the value of R; o o o, experimental results; —, ideal curve.


## 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 impedances and high current drive capability; (iv) simplicity and low cost; (v) the passive sensitivities are low.



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*Source: 320367-2011-09-21.xml*