Showing papers on "Relaxation oscillator published in 1987"

Asymptotic Methods for Relaxation Oscillations and Applications

Abstract: 1. Introduction.- 1.1 The Van der Pol oscillator.- 1.2 Mechanical prototypes of relaxation oscillators.- 1.3 Relaxation oscillations in physics and biology.- 1.4 Discontinuous approximations.- 1.5 Matched asymptotic expansions.- 1.6 Forced oscillations.- 1.7 Mutual entrainment.- 2 Free oscillation.- 2.1 Autonomous relaxation oscillation: definition and existence.- 2.1.1 A mathematical characterization of relaxation oscillations.- 2.1.2 Application of the Poincare-Bendixson theorem.- 2.1.3 Application of the extension theorem.- 2.1.4 Application of Tikhonov's theorem.- 2.1.5 The analytical method of Cartwright.- 2.2 Asymptotic solution of the Van der Pol equation.- 2.2.1 The physical plane.- 2.2.2 The phase plane.- 2.2.3 The Lienard plane.- 2.2.4 Approximations of amplitude and period.- 2.3 The Volterra-Lotka equations.- 2.3.1 Modeling prey-predator systems.- 2.3.2 Oscillations with both state variables having a large amplitude.- 2.3.3 Oscillations with one state variable having a large amplitude.- 2.3.4 The period for large amplitude oscillations by inverse Laplace asymptotics.- 2.4 Chemical oscillations.- 2.4.1 The Brusselator.- 2.4.2 The Belousov-Zhabotinskii reaction and the Oregonator.- 2.5 Bifurcation of the Van der Pol equation with a constant forcing term.- 2.5.1 Modeling nerve excitation the Bonhoeffer-Van der Pol equation.- 2.5.2 Canards.- 2.6 Stochastic and chaotic oscillations.- 2.6.1 Chaotic relaxation oscillations.- 2.6.2 Randomly perturbed oscillations.- 2.6.3 The Van der Pol oscillator with a random forcing term.- 2.6.4 Distinction between chaos and noise.- 3. Forced oscillation and mutual entrainment.- 3.1 Modeling coupled oscillations.- 3.1.1 Oscillations in the applied sciences.- 3.1.2 The system of differential equations and the method of analysis.- 3.2 A rigorous theory for weakly coupled oscillators.- 3.2.1 Validity of the discontinuous approximation.- 3.2.2 Construction of the asymptotic solution.- 3.2.3 Existence of a periodic solution.- 3.2.4 Formal extension to oscillators coupled with delay.- 3.3 Coupling of two oscillators.- 3.3.1 Piece-wise linear oscillators.- 3.3.2 Van der Pol oscillators.- 3.3.3 Entrainment with frequency ratio 1:3.- 3.3.4 Oscillators with different limit cycles.- Modeling biological oscillations.- 3.4.1 Entrainment with frequency ratio n:m.- 3.4.2 A chain of oscillators with decreasing autonomous frequency.- 3.4.3 A large population of coupled oscillators with widely different frequencies.- 3.4.4 A large population of coupled oscillators with frequencies having a Gaussian distribution.- 3.4.5 Periodic structures of coupled oscillators.- 3.4.6 Nonlinear phase diffusion equations.- 4. The Van der Pol oscillator with a sinusoidal forcing term.- 4.1 Qualitative methods of analysis.- 4.1.1 Global behavior and the Poincare mapping.- 4.1.2 The use of symbolic dynamics.- 4.1.3 Some remarks on the annulus mapping.- 4.2 Asymptotic solution of the Van der Pol equation with a moderate forcing term.- 4.2 Asymptotic solution of the Van der Pol equation with a large forcing term.- 4.2.1 Subharmonic solutions.- 4.2.2 Dips slices and chaotic solutions.- 4.3 Asymptotic solution of the Van der Pol equation with a large forcing term.- 4.3.1 Subharmonic solutions.- 4.3.2 Dips and slices.- 4.3.3 Irregular solutions.- Appendices.- A: Asymptotics of some special functions.- B: Asymptotic ordering and expansions.- C: Concepts of the theory of dynamical systems.- D: Stochastic differential equations and diffusion approximations.- Literature.- Author Index.

Start circuit for generation of pulse width modulated switching pulses for switch mode power supplies

Abstract: A start circuit for starting the generation of pulse width modulated switching pulses is disclosed for use in a DC/DC switching converter power supply. The starting circuit is responsive to the initiation of a DC voltage source and starts the operation of a pulse generator. The starting circuit also includes a relaxation oscillator connected to the DC voltage source for periodically generating a start pulse at a predetermined frequency. Ongoing power is coupled to the pulse generator once the generator begins operation. The relaxation oscillator is selectively disabled when the pulse generator is powered by the ongoing power supplied by the power supply during normal operation. The start circuit further includes a delay function for delaying the disabling of the relaxation oscillator for a preselected period after shutdown of the power supply and includes a rapid start function for reducing the time between restoration of input power and the operation of the start circuit.

Switching mode power supply start circuit.

Abstract: A start circuit (70) for a DC-DC switching converter (10) includes a relaxation oscillator (72-76) powered by a voltage input source (+VDC IN). The oscillator (72-76) generates start pulses which are coupled to a switch (16) and cause switch (16) to close during each pulse, thereby activating primary winding (12) of transformer (14). A secondary winding (34) generates a voltage which gradually charges a capacitor (78) coupled to a pulse generator (60). When sufficient energy has been stored in capacitor (78), the pulse generator (60) is activated and begins to modulate switch (16) to generate desired DC outputs across one or more capacitors (42, 50). Actuation of pulse generator (60) also causes start circuit (70) to shut off via a transformer (18) and elements (90-94). Thus, the primary winding and the secondary winding sides of transformer (14) are kept mutually isolated during start-up.

Low voltage driven oscillator circuit

Abstract: An ultra low voltage energized oscillator for providing a stepped-up alternating current voltage is provided. This oscillator utilizes a field effect transistor with a high impedance network including a capacitor coupling a feedback signal from a secondary output winding to a primary input winding of a transformer.

Linearization of voltage-controlled oscillators using switched capacitor feedback

Abstract: The voltage-frequency characteristics of any voltage-controlled oscillator can be linearized using a simple circuit containing a switched capacitor The oscillation frequency becomes insensitive to power supply or temperature variations, and is determined only by the values of a capacitor, resistor, and the control voltage with respect to a reference voltage

Origin of chaotic relaxation oscillations in an optically pumped molecular laser.

Abstract: We show that pump-induced modifications to the gain and dispersion profiles can induce a weak side-band modulation which acts as a driving term to sustain chaotic relaxation oscillations in a single-mode, resonant, optically pumped molecular laser Our study suggests that a careful two- or more-parameter unfolding of higher-codimension bifurcations should lead to a wealth of nonlinear dynamical behavior within easy access of current experiments

Active-R multiphase oscillators

Abstract: A multiphase active-R oscillator circuit is presented. The oscillator can produce m signals equal in amplitude and equally spaced in phase. The circuit uses one operational amplifier for each phase. Experimental results are included.

Particle analyzer for measuring the resistance and reactance of a particle

Abstract: A circuit (10) provides data needed to measure the electrical opacity of a particle (20), such as a blood cell passing through a Coulter type transducer (12). The circuit (10) includes a current source (22) for providing a conventional d.c. current through the sensing aperture (16) of the transducer (12), and an oscillator (24) for providing a high frequency current through the aperture (16). The oscillator (24) includes an active device (32) and a resonant circuit (34), and the aperture (16) is coupled in parallel with the resonant circuit (34). As a particle (20) passes through the aperture (16), the resistance of the aperture (16) increases, which increases the Q of the oscillator (24), whereby the oscillator (24) output signal (Fig. 3) is amplitude modulated in accordance with the increased Q. Multiple oscillators (F1, F2 ... FN) of different frequencies can be coupled in parallel with the transducer (12) through a coupling cirucit (54, 77 and 79), which connects each oscillator (F1, F2 ... FN) through a low impedance path and isolates each oscillater (F1, F2 ... FN) from signals having frequencies of the other oscillators.

Device including battery-activated oscillator

Abstract: A low duty cycle relaxation oscillator (12) periodically gates an ultrasonic frequency relaxation oscillator (13) into an on state. The ultrasonic frequency oscillations are supplied to an electric-compressional wave transducer (15) by way of a push-pull driver (14). The duty cycle and repetition rate of the relaxation oscillator (12) and the ultrasonic oscillation frequency are such that compressional waves derived by the transducer (15) incident on fleas in the region where the transducer (15) is located repels the fleas. All active elements in the oscillator (12,13) and driver (14) are CMOS devices which draw only leakage current while in quiescent bi-level states and through current from a battery (21) during transitions between the bi-level states. The drain from the battery (21) is reduced by connecting a high impedance (74) between the battery (21) and the CMOS devices (31,...36) during a relaxation oscillator transition.

Automatic voltage doubler switch

Abstract: An automatic voltage doubler switch includes a Triac having a gate electrode that is driven by a relaxation oscillator that includes a Diac switch. A capacitor, charged from a voltage that is indicative of the AC line voltage, triggers the Triac through the Diac switch to complete a conductive path for converting the power supply from a direct operating mode to a voltage doubler operating mode. A cutoff transistor senses the AC line voltage and functions to disable the relaxation oscillator when the AC line is at a particular level. A hysteresis circuit reduces the resistance in the base circuit of a line voltage detector transistor to keep it in conduction despite further drops in line voltage. A hysteresis inhibit transistor operates on power up of the power supply to override the effects of the hysteresis circuit.

Drift compensated digitally tuned voltage controlled oscillator

Abstract: A compensated digitally tuned voltage controlled oscillator includes a voltage controlled oscillator circuit that is driven by a digital to analog converter The digital to analog converter receives a digital input and converts it to a voltage to which the voltage controlled oscillator circuit will respond A feedback circuit is connected between a digital input circuit and the output of the voltage controlled oscillator circuit and includes a comparator having one input connected to receive the output of the voltage controlled oscillator circuit and a second input connected to receive the output of a reference oscillator which is also provided The output of the comparator is connected to influence the data that is applied to the digital to analog converter and to compensate for variations due to temperature and component aging

Regulated power supply for a solid state ignition system

Abstract: This invention relates to a blocking oscillating converter for transferring energy from a source of power, such as a vehicle battery, to a storage means, such as an energy storage capacitor in a capacitor discharge ignition system. A novel control and feedback circuit incorporated in the blocking oscillator allows the drive level to the switching transistor to be controlled in response to the peak current in said transistor as well as the output voltage of the blocking oscillator. Furthermore the control circuit allows the blocking oscillator to be turned off during the short period of time after each spark discharge that is needed for turnoff of a switching device used to control that discharge.

Electrical switching speed of the double-heterostructure optoelectronic switch

Abstract: The electrical switching speed of a new double-heterostructure optoelectronic switch (designated DOES) is measured in a relaxation oscillator circuit. A minimum value of capacitance was required to obtain oscillations. The turn-on speed was measured to be 100 ps. The turn-off speed was limited to the RC pull-up time.

Excess phase jitter cancellation method for SC relaxation oscillators

Abstract: A practical jitter cancellation method for relaxation SC oscillators is presented. Two versatile switched-capacitor (SC) oscillators using the proposed excess phase jitter suppression technique are described. The jitter and the dependence of the oscillation frequency on the saturation voltages of operational amplifiers (op-amp) or comparators are eliminated. Therefore, there is no oscillation frequency limitation, except the one determined by the Nyquist rate. Because the frequency of oscillation of the proposed SC oscillators depends on a capacitor ratio and a reference voltage, the oscillators have excellent stability and accuracy. Experimental results showed good agreement with theoretical ones.

Power supply start-up circuit with high frequency transformer

Abstract: A start-up circuit for a switch mode power supply comprises a relaxation oscillator including an RC charging circuit for developing a trigger voltage for firing a Sidac connected in series with the primary winding of a small ferrite core transformer The secondary winding of the transformer is resonated with a tuning capacitor and the voltage coupled to a rectifying circuit for developing a charge across a trigger capacitor When the trigger capacitor voltage achieves a trigger potential, an SCR is fired for starting a pulse width modulator in the switch mode power supply The relaxation oscillator is rendered ineffective by a feedback voltage supplied from the power supply when it starts

Method for measuring the ratio of a measurement-quantity-dependent capacitance and a reference capacitance and device for carrying out the method

Abstract: The measurement is carried out by converting the capacitance values into a signal oscillation and calculating the ratio of the frequency values. The two capacitances (C1, C2), for example of a capacitive force sensor, are alternately switched into the input circuit of a measurement-quantity converter (2) with a frequency (10 Hz) which is smaller by orders of magnitude than the centre frequency (16 kHz) of the signal oscillation. In this process, the frequency values (f1, f2) of the signal oscillations occurring in succession are measured by counting out the periods in a fixed time interval corresponding to the respective on-time (100 ms) of one capacitance. Using a relaxation oscillator with the capacitance to be measured as the frequency-determining quantity, in which in each case only a centre ramp section of the charging voltage across the capacitance is utilised for the measurement, this method can be used for achieving high measuring accuracies.

Bifurcations which destroy the out-of-phase mode in a pair of linearly coupled relaxation oscillators

Abstract: This paper presents two mechanisms, the Hopf bifurcation and the infinite period bifurcation, which lead to non-existence of the out-of-phase mode of oscillation in a pair of identical van der Pol relaxation oscillators with diffusive coupling in the displacements and velocities. We show that the out-of-phase mode is associated with a periodic solution in a two dimensional invariant out-of-phase manifold. Phase plane techniques are used to find the region of parameter space where this periodic solution exists and how it is destroyed at the boundaries of this region.

High frequency precision oscillator with synchronous capability

Abstract: A precision oscillator circuit with synchronous capability. The circuit receives a predetermined discharging voltage and a predetermined charging voltage for setting a precise discharging and charging rate. A comparator in the oscillator contains three transistors connected to each other at their emitters. A latch circuit is provided on two of the transistors for accelerating the speed with which they turn on. An overshoot correction circuit provides additional charging current when the timing capacitor has dropped below the valley voltage threshold. Synchronizing pulses are generated at the capacitor terminal to allow for a plurality of oscillators to operate synchronously when connected in parallel.

Relaxation quartz oscillators with crystal placed in feedback loop: Analysis and design

Abstract: Our purpose in this paper is to provide a complete theoretical analysis of relaxation quartz oscillators using integrated circuits as active elements and a crystal placed in feedback loop. The general theory of relaxation oscillations is a theoretical background for this analysis, which provides solutions for oscillating conditions, oscillation buildup and period, and a flicker-frequency noise level. The main results are the criteria for the design of an optimal quartz relaxation oscillator having high immunity to circuit and ambient parameter variations and a low phase noise level. The results are derived for oscillators using TTL gates, but they are of a general validity and can be easily modified for every circuit of this kind. The conclusions drawn are discussed and confirmed through experiments.

Coordinates input device

Abstract: PURPOSE:To improve the detection precision by providing a control circuit which selects automatically an additional capacity which sets the oscillation period of a relaxation oscillator due to additional capacitors to a value approximating 1/n of an induced noise period. CONSTITUTION:A measured output 19 due to a period measuring circuit 13 is inputted to an operating and selective control circuit 12. A capacity selecting signal which selects a prescribed capacity from external additional capacities, namely, plural additional capacities C1-C6 by which an oscillation reference point of relaxation oscillation at a period approximating the harmonic component period, which is the period, a 1/2 period, a 1/3 period - of a horizontal synchronizing signal 20 driving a CRT 9, is set to a relaxation oscillator 10 to which a CR constant is set preliminarily is outputted from the control circuit 12 to drive a switch circuit 17. Thus, the influence of induced noise is evaded automatically even in case of an input device provided with CRT display device different in horizontal synchronizing signal. Thus, input coordinates detection of touch operation is stabilized and the detection precision is improved.

Digital magnetic fluxmeter using unijunction transistor probe

Abstract: A simple circuit has been described which measures a magnetic field using the magnetic field dependent properties of a unijunction transistor. The transistor forms part of the relaxation oscillator circuit whose frequency changes with magnetic field.