Pearson–Anson effect
The Pearson–Anson effect, discovered in 1922 by Stephen Oswald Pearson[1] and Horatio Saint George Anson,[2][3] is the phenomenon of an oscillating electric voltage produced by a neon bulb connected across a capacitor, when a direct current is applied through a resistor.
[7] It has been used in low frequency applications such as blinking warning lights,[9] stroboscopes,[9] tone generators in electronic organs[8][10] and other electronic music circuits,[11] and in time base generators and deflection circuits of early cathode-ray tube oscilloscopes.
The gas in the bulb ionizes, starting a glow discharge, and its resistance drops to a low value.
Below this voltage, the current provides insufficient energy to keep the gas ionized, so the bulb switches back to its high resistance, nonconductive state (point a).
Hysteresis is due to the bulb's negative resistance, the fall in voltage with increasing current after breakdown,[7][14] which is a property of all gas-discharge lamps.
[17] The detailed cycle is illustrated by the hysteresis loop abcd on the current-voltage diagram at right:[4][7][10] The circuit thus functions as a low-frequency relaxation oscillator, the capacitor voltage oscillating between the breakdown and extinction voltages of the bulb in a sawtooth wave.
The slope of the load line is equal to R. The possible DC operating points of the circuit are at the intersection of the load line and the neon lamp's IV curve (black) In order for the circuit to be unstable and oscillate, the load line must intersect the IV curve in its negative resistance region, between b and d, where the voltage declines with increasing current.
If the load line crosses the IV curve where it has positive resistance, outside the shaded region, this represents a stable operating point, so the circuit will not oscillate: Small neon bulbs will typically oscillate with values of R between 500kΩ and 20MΩ.
[7] If C is not small, it may be necessary to add a resistor in series with the neon bulb, to limit current through it to prevent damage when the capacitor discharges.
[6][7][10][18] During the charging period, the bulb has high resistance and can be considered an open circuit, so the rest of the oscillator constitutes an RC circuit with the capacitor voltage approaching VS exponentially, with time constant RC.
If v(t) is the output voltage across the capacitor so the differential equation of the circuit is The general solution is Applying boundary conditions
[7][8][10] The breakdown and extinction voltages of neon lamps may vary between similar parts;[17] manufacturers usually specify only wide ranges for these parameters.
Even if the external frequency is different from the natural frequency of the oscillator, the peaks of the applied signal can exceed the breakdown threshold of the bulb, discharging the capacitor prematurely, so that the period of the oscillator becomes locked to the applied signal.
[19] When the periodic and quasiperiodic regimes overlap, the behavior of the circuit may become aperiodic, meaning that the pattern of the oscillations never repeats.
