Quadrature Sinusoidal Oscillators Using CDBAs: New Realizations

Abstract

Four new circuits of fully uncoupled quadrature sinusoidal oscillators, using two current differencing buffered amplifiers (CDBAs), four/five resistors and two capacitors have been presented. In contrast to all previously published CDBA-based, fully decoupled, quadrature sinusoidal oscillators in which one of the input terminals is left unutilized, the presented circuits are realized by utilizing the intrinsic current differencing property of CDBAs, thus utilizing all the four terminals of the CDBA. All these quadrature oscillator (QO) circuits have an inherent feature of amplitude control of output voltages without using external control circuitry. Out of the four proposed QO circuits, two circuits have the additional feature of generating low-frequency oscillations, thus making them capable of generating wide range of frequency waveforms. The proposed oscillator circuits also possess additional functionalities not available in other CDBA-based quadrature sinusoidal oscillator circuits presented previously. The workability of the proposed circuits has been confirmed through experimental results where CDBAs are implemented using commercially available current feedback operational amplifiers (AD844).

Appendix

Consider an exemplary Circuit 2 from Fig. 5 of [23] which is reproduced here in Fig. 17.

The CO and FO of this circuit are given by:

• CO: 2R₂ ≤ R₆ and FO: $\omega = \frac{1}{{\sqrt {R_{3} R_{9} C_{1} C_{10} } }}$

The modified version of this circuit as per the methodology of this paper will take the form as shown in Fig. 17.

Fig. 17

QO Circuit 2 from Fig. 5 of [23]

An analysis of this circuit reveals its CO and FO as:

• CO: 2R₂ ≤ R₆ and FO: $\omega = \sqrt {\frac{{R_{9} - R_{10} }}{{C_{1} C_{2} R_{3} R_{9} R_{10} }}}$

If we choose $R_{10} = \frac{{R_{9} }}{n}$, then $\omega = \sqrt {\frac{n - 1}{{C_{1} C_{2} R_{3} R_{9} }}}$, where n > 1. If we take n = 2, then $\omega = \sqrt {\frac{1}{{C_{1} C_{2} R_{3} R_{9} }}}$

From where it is clear that (i) the intended property of independent control of both CO and FO remains unaffected even in the modified circuit but now all the terminals of both the CDBAs are effectively utilized.

(ii) Also, as FO can be expressed as $\omega = \sqrt {\frac{\Delta R}{{C_{1} C_{2} R_{3} R_{9} R_{10} }}}$, where $\Delta R = R_{9} - R_{10} .$ From CO, and FO, it can be observed that the given QO circuit can be used to generate fully uncoupled amplitude adjustable low-frequency sinusoidal oscillation (LFO).

It is thus clear that as many as 12 QO circuits from Fig. 5 of [23] can be similarly modified at the cost of only one additional resistor (Fig. 18).

Fig. 18

Modified version of the QO circuit shown in Fig. 17

Figure 19 shows the modified version of the circuit 3 given in Fig. 2.

Fig. 19

Modified version of Circuit 3 of Fig. 2

An analysis of this circuit reveals its CO and FO as:

• CO: R₂ ≤ R₁ and FO: $\omega = \,\sqrt {\frac{{R_{4} \, - R_{5} }}{{C_{1} C_{2} R_{3} R_{4} R_{5} }}}$

For this circuit, we have produced a low-frequency output waveform of 2.47 Hz against a designed frequency of 2.7 Hz. The circuit parameters selected are as C₁ = C₂ = 100nF, R₁ = 10 kΩ, R₂ = 10 k Ω (100Ω in series with 22 kΩ pot), R₃ = 100 kΩ, R₄ = 10.25 kΩ and R₅ = 10.22 kΩ. Experimentally observed waveforms are shown in Fig. 20. The peak-to-peak output voltages V₀₁ and V₀₂ recorded are as 18.6 V and 2.95 V. The phase difference between V₀₁ and V₀₂ is 96.48^o.

Fig. 20

Experimental output waveforms of 2.47 Hz for Fig. 19

It is thus clear that as many as 12 QO circuits from Fig. 5 of [23] can be similarly modified as LFO QOs with the addition of only one extra resistor.