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Abstract

After briefly outlining the significant advantages offered by CFOA-based sinusoidal oscillators, a variety of prominent single-resistance-controlled oscillators (SRCO) have been described which include single CFOA-based SRCOs, two-CFOA-two-grounded-capacitor-based SRCOs, quadrature SRCOs, active-R SRCOs, SRCOs with explicit current output, and fully-uncoupled SRCOs. Also included are a variety of voltage-controlled oscillators (VCO) using CFOAs, employing FET-based VCOs as well as analog multiplier (AM)-based VCOs. Various characteristic features and advantages of all the discussed topologies have been highlighted and a number of ideas for further research have been pointed out.

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Notes

  1. 1.

    The circuit of Fig. 5.3a has also been derived independently in [24].

  2. 2.

    Many more variants of the 14 basic oscillators, obtained by using some transformations, terminal interchanges, etc., have been described in [78].

  3. 3.

    It is interesting to point out that although not explicitly mentioned in [10], this circuit can be considered to be derivable from a two-op-amp-GC SRCO published earlier in [18] by realizing the negative-impedance converter (NIC) therein by a CFOA without requiring any resistors and thereby simplifying the circuit as shown in Fig. 5.9.

  4. 4.

    In spite of the criticism of [30], the class of circuits described in this section is interesting and important in their own right.

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Appendix 1: Some Recent Contributions to CFOA-Based Oscillators

Appendix 1: Some Recent Contributions to CFOA-Based Oscillators

1.1 Quadrature Oscillators Using Two CFOAs and Four Passive Components

The Circuit 3 of Fig. 5.7 apart from employing two GCs also has the attractive feature of employing minimum number of total passive components namely, only two resistors and capacitors. However, very recently, Chen, Wang, Ku, and Hsieh [84] have presented two new circuits belonging to this class, which are shown in Fig. 5.44.

Fig. 5.44
figure 44

New CFOA-based quadrature oscillators proposed by Chen, Wang, Ku, and Hsieh [84]

Both of these circuits are characterized by the same CE which is given by

$$ {s}^2{C}_1{C}_2{R}_1{R}_2+s{C}_2\left({R}_1-{R}_2\right)+1=0 $$
(5.98)

so that the CO and FO are given by

$$ \mathrm{C}\mathrm{O}:{R}_1={R}_2\ \mathrm{and}\ \mathrm{F}\mathrm{O}:{\omega}_0=\sqrt{\frac{1}{C_1C{}_2R_1{R}_2}} $$
(5.99)

Hence, CO can be adjusted by R 1or R 2, whereas FO can be adjusted by C 1 or C 2. Furthermore, analysis reveals that the two outputs V 01 and V 02 are related by

$$ \frac{V_{01}(s)}{V_{02}(s)}=-\frac{1}{s{C}_2{R}_1} $$
(5.100)

Hence V 01 and V 02 are 90° apart in phase and hence, both the circuits are quadrature oscillators.

Using a CMOS CFOA biased with ±0.9 V, the circuits have been simulated in SPICE [84] with component values C 1 = C 2 = 3 pF, R 2 = 35 kΩ and R 1 adjusted 34.5 kΩ. In the CMOS CFOA, TSMC 0.18 CMOS process parameters were utilized. It was found that the oscillation frequency obtained from simulation f 0 = 1.52 MHz was quite close to the theoretical frequency 1.527 MHz.

1.2 New VLF Oscillators Using a Single CFOA

In the context of CFOA-based oscillators suitable for VLF generation for which circuit 1 of Fig. 5.7 appears to be suitable candidate, it is interesting to point out a circuit recently presented by Srivastava, Singh, and Senani [82] which is shown here in Fig. 5.45. This circuit, in addition to single-resistance-control of FO, also provides single resistance-control of CO but at the cost of one more capacitor but using only a single CFOA in contrast to the circuit 1 of Fig. 5.7. The CO and FO are found to be

Fig. 5.45
figure 45

VLF oscillator recently proposed by Srivastava, Singh, and Senani [82]

$$ \mathrm{C}\mathrm{O}:\frac{C_4-{C}_0}{C_3}=\frac{R_1}{R_0}+\frac{R_1}{R_2}\kern0.5em \mathrm{and}\kern0.5em \mathrm{F}\mathrm{O}:{\omega}_0=\sqrt{\frac{\left(\frac{R_4}{R_0}-1\right)}{C_0C{}_3R_1{R}_4}} $$
(5.101)

From the above equation, it can be seen that FO can be adjusted by varying R4 while ensuring (R 4/R 1) > 1, whereas the CO can also be independently adjusted by C 4 and/or R 2. From the expressions of the oscillation frequency (FO), it may be seen that keeping the difference term in the numerator of FO as small as possible, generation of VLF oscillations should be possible. Experimental results using AD844 have demonstrated that it has been possible to generate sinusoidal waveforms of frequency as low as 2 Hz.

1.3 Single CFOA-Based Oscillator Capable of Absorbing all Parasitic Impedances

Most of the investigations on CFOA oscillators have focused attention only on canonic realizations thereby it has been largely ignored that some noncanonic circuits may also possess some interesting features which may not be possible from the canonic realization. Recently, Srivastava, Singh, and Senani [83] presented a single CFOA noncanonic oscillator which is shown in Fig. 5.46, which has the interesting property that it can absorb all the parasitic impedances of the CFOA in the various external passive components employed. Analysis shows that CO and FO of this circuit are expressed as

Fig. 5.46
figure 46

CFOA-based oscillator capable of absorbing all parasitic impedances proposed by Srivastava, Singh, and Senani [83]

$$ \mathrm{C}\mathrm{O}:\frac{C_0}{R_3}+\frac{C_1+{C}_3}{R_0}=\frac{C_1}{R_4}\kern0.5em \mathrm{and}\kern0.5em \mathrm{F}\mathrm{O}:{\omega}_0=\sqrt{\frac{1}{R_0R{}_3C_0\left({C}_1+{C}_3\right)}} $$
(5.102)

Although this circuit does not provide control of FO, nevertheless the circuit can be adjusted to produce the oscillations by varying the resistor R 4 which does not feature in FO. Experimental results have shown that the error between the practically observed values of the oscillation frequencies and those calculated from the nonideal formula are indeed extremely small when theoretical values are determined by incorporating all parasitic impedances into external circuit elements [83].

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Senani, R., Bhaskar, D.R., Singh, V.K., Sharma, R.K. (2016). Realization of Sinusoidal Oscillators Using Current Feedback Op-Amps. In: Sinusoidal Oscillators and Waveform Generators using Modern Electronic Circuit Building Blocks. Springer, Cham. https://doi.org/10.1007/978-3-319-23712-1_5

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