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A generic model for second-order RC sinusoidal oscillators is derived. The model is based on treating an oscillator as a second-order passive network, with an arbitrary unknown structure, terminated at one port by a linear voltage-controlled negative resistor. A modified model which takes into account the fundamentally nonlinear characteristics of the negative resistor is also derived.

In this work we derive a general non-conservative model for any RC sinusoidal oscillator independent of its particular passive topology or the employed active devices. We consider an arbitrary unknown second-order passive RC network terminated at one port by a negative resistor and proceed to impose oscillation start-up and frequency constraints on a derived state-matrix.

The paper presents a systematic approach of synthesizing sinusoidal linear VCOs (i.e., an oscillator providing linear tuning law of the type f₀ ∝ V_C between the oscillation frequency f₀ and an external control voltage V_C). In view of recent interest on current feedback operational amplifier (CFOA)-based oscillators, the proposed methodology has been demonstrated by deriving a class of linear VCOs employing CFOAs and analog multipliers (AM). The workability of the new VCOs has been established by experimental results of the circuits implemented with commercially available AD844 type CFOAs and AD534 type AMs.

A new single-resistance-controlled-oscillator (SRCO) is presented which employs a single current feedback-operational amplifier (CFOA) along with four resistors but needs only a single external capacitor due to the incorporation of the CFOA-pole in the design. It provides independent control of the condition of oscillation and the frequency of oscillation through two separate resistors. To the best knowledge of the authors, this single-CFOA-based partially active-$R$ SRCO has not been reported explicitly in the technical literature earlier and hence is the fourth missing circuit of this class of SRCOs. Experimental results confirming the validity of the new proposition have been included and the comparative features of all the four circuits have been highlighted.

Prediction of dominant frequencies of two examples of current-feedback op amp (CFOA)-based Sprott's chaotic oscillators is presented through the use of simple Fourier analysis. In addition, two examples of CFOA-based Sprott's sinusoidal oscillators exhibiting periodic sinusoids are also demonstrated. In the Sprott's sinusoidal oscillators, the fundamental frequencies may be approximated by the prediction of the dominant frequencies.