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This paper presents the structure and operational principles of high-frequency electronically controllable sinusoidal oscillators employing current-feedback operational amplifiers (CFOAs) with externally accessible compensation node z as active components. The resonant circuits in the oscillators are connected to the terminal z, and for them in the selective network varactor diodes or varicaps as the variable capacitances are utilized, which are controlled by external DC voltage. Based on an analysis of the proposed circuit configurations, analytical expressions for the characteristic equation in a steady-state mode of operation and formulas for the basic electrical parameters have been obtained. In order to verify the functionality of the proposed electronic circuits and the effectiveness of the derived analytical expressions, an experimental and simulation study of sample electronic circuits with commercially available integrated circuit CFOAs AD844 in the frequency range up to about 10MHz is performed. The obtained results for the studied electronic circuits confirm the theoretical studies and hypotheses, and the comparative analysis shows that the maximum value for the relative error does not exceed 10%, which is acceptable considering the tolerances of the technological parameters of the used passive and active elements.