The influence of nonlinear characteristics on the performance of a very simple RC oscillator consisting of a third-order RC-ladder phase-shift network (quadrupole) and a nonlinear amplifier in the feedback path is studied. Proof for the existence of a periodic solution is given, and bounds for the nonlinear characteristic ensuring the existence of a unique periodic solution have been calculated. Bifurcation phenomena associated with the changes of slopes of chosen piecewise-linear characteristics are studied in detail both numerically and experimentally. A complete bifurcation diagram has been constructed revealing several interesting phenomena in the circuit, namely, creation of periodic orbits and symmetry-breaking bifurcation giving birth to two stable periodic orbits, which separately undergo period-doubling bifurcation leading to chaotic behavior. Two coexisting chaotic attractors born via period-doubling sequence finally merge together. Several periodic windows within the chaos range can be detected. >

Order and chaos in a third-order RC ladder network with nonlinear feedback

Two novel active RC oscillator circuits suitable for integration are given. The active building block used is the current conveyor. Both networks have the advantage of using earthed capacitors. One circuit is of a second order and uses two opposite polarity current conveyors and the other is a third-order oscillator with the advantage of using only one current conveyor.

Simple sinusoidal active RC oscillators

A comprehensive study for generation and design of grounded-capacitor variable-frequency RC-active oscillators using operational amplifiers (OAs) is reported. All the circuits derived are canonic, that is, the number of components (active as well as passive) in them is a minimum. First, a set of eight canonic circuits is found, each using one OA, two capacitors and six resistors. However, these circuits suffer from either a poor start-up property or a limited frequency range of variation. Thus, based on this set of eight circuits, another set of 12 variable-frequency oscillators is derived. This set provides easy tunability and a wider tuning range. Both the sets are shown to be complete. All the variable-frequency oscillators are single resistor controlled. Two of the circuits have their variable resistors grounded which makes them attractive candidates for voltage-controlled oscillators. Design equations for all the oscillator circuits are given. All the circuits have been laboratory tested. Experimental results are found to be in close agreement with the theoretical analysis. Representative test results are included in the article.

Erratum: Generation and design of canonic grounded capacitor variable frequency RC-active oscillators

A novel sinusoidal oscillator is presented which employs only one operational amplifier, two capacitors, and six resistors and has the facility of independent control of oscillation frequency through a single grounded resistor. The circuit may also be used as a very-low-frequency oscillator and as an economical voltage-controlled oscillator.

New canonic sinusoidal oscillator with independent frequency control through a single grounded resistor

A transconductance-amplifier-capacitor sinusoidal oscillator is introduced. The circuit requires only two operational transconductance amplifiers (OTAs) and two grounded capacitors. The frequency of oscillation is linearly tunable over a wide frequency range. >

A new minimum component active-C OTA-based linear voltage (current)-controlled sinusoidal oscillator

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.

R.S. Sidorowicz

Papers

An abundance of sinusoidal RC oscillators