Relaxation oscillator

[1][2][3][4] The circuit consists of a feedback loop containing a switching device such as a transistor, comparator, relay,[5] op amp, or a negative resistance device like a tunnel diode, that repetitively charges a capacitor or inductor through a resistance until it reaches a threshold level, then discharges it again.

[4][6] The period of the oscillator depends on the time constant of the capacitor or inductor circuit.

[2] The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform.

[7] Relaxation oscillators may be used for a wide range of frequencies, but as they are one of the oscillator types suited to low frequencies, below audio, they are typically used for applications such as blinking lights (turn signals) and electronic beepers, as well as voltage controlled oscillators (VCOs), inverters, switching power supplies, dual-slope analog to digital converters, and function generators.

[8][9][10][11] For example, geothermal geysers,[12][13] networks of firing nerve cells,[11] thermostat controlled heating systems,[14] coupled chemical reactions,[9] the beating human heart,[11][14] earthquakes,[12] the squeaking of chalk on a blackboard,[14] the cyclic populations of predator and prey animals, and gene activation systems[9] have been modeled as relaxation oscillators.

Relaxation oscillations are characterized by two alternating processes on different time scales: a long relaxation period during which the system approaches an equilibrium point, alternating with a short impulsive period in which the equilibrium point shifts.

[11] Relaxation oscillations are a type of limit cycle and are studied in nonlinear control theory.

[16] The first relaxation oscillator circuit, the astable multivibrator, was invented by Henri Abraham and Eugene Bloch using vacuum tubes during World War I.

[18][19][20] Van der Pol borrowed the term relaxation from mechanics; the discharge of the capacitor is analogous to the process of stress relaxation, the gradual disappearance of deformation and return to equilibrium in an inelastic medium.

[21] Relaxation oscillators can be divided into two classes[13] Before the advent of microelectronics, simple relaxation oscillators often used a negative resistance device with hysteresis such as a thyratron tube,[22] neon lamp,[22] or unijunction transistor, however today they are more often built with dedicated integrated circuits such as the 555 timer chip.

Relaxation oscillators are generally used to produce low frequency signals for such applications as blinking lights and electronic beepers.

During the vacuum tube era they were used as oscillators in electronic organs and horizontal deflection circuits and time bases for CRT oscilloscopes; one of the most common was the Miller integrator circuit invented by Alan Blumlein, which used vacuum tubes as a constant current source to produce a very linear ramp.

[22] They are also used in voltage controlled oscillators (VCOs),[23] inverters and switching power supplies, dual-slope analog to digital converters, and in function generators to produce square and triangle waves.

[24] However they have more phase noise[23] and poorer frequency stability than linear oscillators.

[2][23] This example can be implemented with a capacitive or resistive-capacitive integrating circuit driven respectively by a constant current or voltage source, and a threshold device with hysteresis (neon lamp, thyratron, diac, reverse-biased bipolar transistor,[25] or unijunction transistor) connected in parallel to the capacitor.

It then increases heavily its conductance in an avalanche-like manner because of the inherent positive feedback, which quickly discharges the capacitor.

The discharging duration can be extended by connecting an additional resistor in series to the threshold element.

A similar relaxation oscillator can be built with a 555 timer IC (acting in astable mode) that takes the place of the neon bulb above.

That is, when a chosen capacitor is charged to a design value, (e.g., 2/3 of the power supply voltage) comparators within the 555 timer flip a transistor switch that gradually discharges that capacitor through a chosen resistor (which determine the RC time constant) to ground.

The popular 555's comparator design permits accurate operation with any supply from 5 to 15 volts or even wider.

This section will analyze a similar implementation using a comparator as a discrete component.

The system is in unstable equilibrium if both of the inputs and the output of the comparator are at zero volts.

After a short time, the output of the comparator is the positive voltage rail,

The inverting input and the output of the comparator are linked by a series RC circuit.

is obtained using Ohm's law and the capacitor differential equation: Rearranging the

When Vss is not the inverse of Vdd we need to worry about asymmetric charge up and discharge times.

Taking this into account we end up with a formula of the form: Which reduces to the above result in the case that