An abundance of sinusoidal RC oscillators

TLDR: In this article, a general form of this function is introduced for RC oscillators of the second order, and expressions for the required maintenance gain and the oscillation frequency are derived.

Abstract: It is assumed that a sinusoidal RC oscillator consists of a linear, passive or active RC network and an amplifier. The properties of such an oscillator are primarily dependent on its open-loop voltage transfer function. A general form of this function is introduced for RC oscillators of the second order, and expressions for the required maintenance gain and the oscillation frequency are derived. It is shown that there exist four distinct types of 2nd-order oscillators. A set of basic building elements for the oscillators is proposed. This consists of some simple RC networks, a voltage divider, a buffer and two amplifiers. The theory and the building elements are used to develop 18 novel oscillator circuits. All these oscillators have either two earthed tuning capacitances or two earthed resistances. It is shown that six of them can be tuned by varying only one capacitance or resistance. Eight of the oscillators are tunable by varying a voltage parameter; in four of these, the voltage-tuning range can be very wide. 14 additional 2nd-order oscillators are suggested. A general 3rd-order RC oscillator is also considered, and it is shown that there exist 15 distinct kinds of this oscillator. The procedure used in the development of the 2nd-order oscillators can also be applied to the design of those of the third order. It is thought that this will lead to a very large number of different oscillator circuits.