Keywords: Oscillators, Currentfeedbackoperational amplifiers, currentmode circuits, single element controlled oscillators, very lowfrequency oscillators
American Journal of Electrical and Electronic Engineering, 2015 3 (1),
pp 13.
DOI: 10.12691/ajeee311
Received December 19, 2014; Revised January 22, 2015; Accepted January 25, 2015
Copyright © 2015 Science and Education Publishing. All Rights Reserved.
1. Introduction
Very low frequency (VLF) oscillators (capable of generating frequencies < 20Hz) are required in many applications such as biomedical instrumentation, geophysical instrumentation and in some measurements in control system applications.
Owing to the wellknown advantages of current feedback opamps (CFOA) (for instance, see ^{[1, 2, 3, 4]}) and their wide spread acceptability as alternative building blocks, there have been numerous studies in recent literature on realizing sinusoidal oscillators using CFOAs, for instance, see ^{[5, 6, 7, 8]} and references cited therein. In ^{[8]}, Elwakil had reported a systematic method of designing VLF oscillators using CFOAs. The circuit of ^{[8]}, however, requires two CFOAs along with six resistors and two capacitors (one of which is floating).
The main object of this paper is to introduce a new CFOAbased VLF oscillator, which, by contrast to the circuit of ^{[8]}, requires no more than a single CFOA and employs both grounded capacitors, as preferred for integrated circuit implementation.
2. Proposed VLF oscillator using a single CFOA
CFOA is a four terminal building block which internally contains a plus type second generation current conveyor ^{[9]} and a voltage follower and is characterized by the following terminal equations
 (1) 
The symbolic notation of the CFOA and its equivalent circuit are shown in Figure 1.
Figure 1. Symbolic notation and the equivalent circuit of the CFOA
Figure 2. The proposed VLF oscillator
The proposed circuit configuration is shown in Figure 2. Using equation (1) for the CFOA, a straight forward analysis of the circuit gives the condition of oscillation as
 (2) 
whereas the frequency of oscillation is given by
 (3) 
From (2) and (3) it is seen that frequency of oscillation can be adjusted by varying R_{4} (while, ensuring ) whereas the condition of oscillation can also be independently adjusted by C_{4} and/or R_{2}, out of which using a variable resistance R_{2} is obviously more preferable. From equation (3), one can see that keeping the difference term in the numerator of FO as small as feasible, generation of VLF oscillations should be possible. It may be mentioned that while designing the circuit, the resistor values should be chosen such that they are much larger than the parasitic x port input impedance R_{x} (typically around 50Ω) but smaller than the parasitic z port resistance R_{p} (typically around 3MΩ) of the CFOA. Similarly, the external capacitors have to be chosen such that their values are larger than the parasitic output capacitance C_{p}_{ }(looking into the z terminal) of the CFOA (typically of the order of 45pF). This will ensure that the parasitic impedances of the CFOA will not have much effect on the realized frequency of oscillation.
3. Experimental Results
The workability of the proposed circuit has been checked by breadboarded versions of the circuit realized by using AD844 type of CFOAs biased with ±12V DC power supplies, taking R_{0}=R_{1}=1MΩ, C_{0}=C_{3}=100 nF, C_{4}=200 nF with the CO adjusted by variable resistance R_{2}_{ }(1MΩ fixed + 0.0.5M Ω variable). Figure 3 (a) shows the variation of FO with R_{4}, while typical waveform generated from this circuit is shown in Figure 3 (b). The experimental results, thus, confirm the practical workability of the new oscillator circuit.
4. Comparison with Previously Known Oscillators
A comparison of the proposed new oscillator with those previously published in literature ^{[5, 6, 7, 8, 10]} is now in order. This is shown in Table 1.
Figure 3. Experimental results of the proposed oscillator (a) variation of oscillation frequency with variable resistance R_{4} (b) a typical waveform generated by the circuit (1.984Hz, 2.5V pp)
Table 1. Comparison with relevant previously published oscillator circuits
From Table 1, it is seen that the proposed circuit is the only singleCFOA oscillator which possesses all the desirable features while using a reasonable number (only four) of the resistors.
5. Concluding Remarks
Anew CFOAbased VLF oscillator circuit configuration has been presented which employs only a single CFOA in contrast to an earlier CFOAbased VLF oscillator proposed by Elwakil ^{[8]} which requires two CFOAs. The workability of the new circuit has been confirmed by experimental results using AD844 type CFOAs and it has been found that the circuit can generate a sinusoidal waveforms of frequency as low as 2 Hz. Lastly, it must be mentioned that although a somewhat similar single CFOA oscillator has been reported earlier in ^{[10]}, however, the circuit described here has the advantage of providing independent control of CO also, which is not available in the quoted circuit of ^{[10]}.
Acknowledgements
This work was conducted partly at Analog Signal Processing Research Lab, NSIT, New Delhi and partly at Analog Signal Processing Research Lab, IET, Lucknow. Thanks are due to Prof. D R Bhaskar and Prof. A. K. Singh for their support.
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