Topic
Relaxation oscillator
About: Relaxation oscillator is a research topic. Over the lifetime, 1952 publications have been published within this topic receiving 22326 citations.
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01 Mar 1972
TL;DR: 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.
18 citations
TL;DR: Using a sigmoid interaction results in /spl sim/n/sup 2/, for relaxation oscillators in the sinusoidal and relaxation regimes, indicating that the form of the coupling is a controlling factor in the synchronization rate.
Abstract: Relaxation oscillators arise frequently in physics, electronics, mathematics, and biology. Their mathematical definitions possess a high degree of flexibility in the sense that through appropriate parameter choices relaxation oscillators can be made to exhibit qualitatively different kinds of oscillations. We study numerically four different classes of relaxation oscillators through their synchronization rates in one-dimensional chains with a Heaviside step function interaction and obtain the following results. Relaxation oscillators in the sinusoidal and relaxation regime both exhibit an average time to synchrony, /spl sim/n, where n is the chain length. Relaxation oscillators in the singular limit exhibit /spl sim/n/sup p/, where p is a numerically obtained value less than 0.5. Relaxation oscillators in the singular limit with parameters modified so that they resemble spike oscillations exhibit /spl sim/log(n) in chains and /spl sim/log(L) in two-dimensional square networks of length L. Finally, using a sigmoid interaction results in /spl sim/n/sup 2/, for relaxation oscillators in the sinusoidal and relaxation regimes, indicating that the form of the coupling is a controlling factor in the synchronization rate.
18 citations
TL;DR: In this paper, an inverse problem for relaxation oscillators modeled by the autonomous Lienard differential equation is considered, where exact expressions for the limit cycles in the phase plane (which correspond to periodic solutions) toward which all solutions converge, or from which they recede, as time tends to infinity.
18 citations
TL;DR: A 65-nm CMOS front-end relaxation oscillator-based interface circuit for resistive bridge sensors is presented and has demonstrated the best noise-energy figure-ofmerit and comparable linearity in the performance metrics even realized in the environment of nanometer CMOS technology.
Abstract: A 65-nm CMOS front-end relaxation oscillator- based interface circuit for resistive bridge sensors is presented. It converts the sensor ac input currents into the sawtooth frequencies through the use of the proposed direct current-sensing grounded integrator topology without resorting to any current mirror(s) for coupling or signal processing in current-mode circuit design. Validated by three test setups in experiments, the proposed work shows a sensitivity of 41.5 Hz/nA dedicated to the wide output frequency ranging from 1.3 kHz to 2.489 MHz in a current-to-frequency converter, a sensitivity of 44.43 Hz/( $\mu \Omega/\Omega $ ) basing on a center frequency of 1.177 MHz in a half-bridge sensing interface and the quarter-bridge temperature sensing interface using a commercial resistance temperature detector. In comparison with the prior-art works, it has demonstrated the best noise-energy figure-of-merit and comparable linearity in the performance metrics even realized in the environment of nanometer CMOS technology. The sensor interface dissipates only 168 $\mu \text{W}$ at a 1.2 V single supply. Therefore, it is very suitable for portable applications.
18 citations
TL;DR: In this paper, the operation and FM noise of millimeter-wave quantum well (QW) oscillators in a harmonic mode (relaxation oscillations) and a fundamental mode using post and cap waveguide mount structures were investigated.
Abstract: The operation and FM noise of millimeter-wave quantum well (QW) oscillators in a harmonic mode (relaxation oscillations) and a fundamental mode using post and cap waveguide mount structures are investigated. Harmonics up to the ninth harmonic was detected. State of the art results for QW oscillators registered were 84 μW (at 77 K physical temperature) and 60 μW at 90 GHz and 1 μW at 176 GHz (at 300 K physical temperature, respectively).
18 citations