RC-controlled astable oscillator

An astable oscillator repeatedly switches its output between two levels. It has no stable output state, so it does not need a separate trigger for each transition. Its output is a continuous train of pulses that can provide a clock signal for a circuit.

RC control of the oscillation

An external resistor–capacitor (RC) network can set the oscillator’s running frequency. The capacitor charges and discharges through resistance, so its voltage changes over time. When that voltage reaches a switching level set by the circuit, the oscillator changes output state. The circuit then changes whether the capacitor is charging or discharging, allowing its voltage to move towards the next switching level. This cycle repeats.

The resistance and capacitance set the characteristic charging and discharging times. For a fixed circuit arrangement, increasing the relevant resistance or capacitance generally makes each cycle longer and lowers the frequency. Decreasing either generally makes the cycle shorter and raises the frequency. The exact relationship between frequency, resistance and capacitance depends on the circuit.

Clock pulse timing

A periodic clock signal repeats the same pulse pattern. One cycle is one complete repetition of that pattern. The period, $$T$$, is the time taken for one cycle, while the clock rate or frequency, $$f$$, is the number of cycles per second.

When the period is measured in seconds, the frequency is measured in hertz ($$\mathrm{Hz}$$). A frequency of $$1,\mathrm{Hz}$$ means one cycle per second. A shorter period therefore means a higher frequency.

Pulse width, mark and space

The pulse width is the duration of the pulse within one cycle. If the pulse is the high-level interval, its width is the mark time. The remaining low-level interval is the space time. Together, the mark and space make one complete cycle:

Duty cycle and mark-to-space ratio

The duty cycle is the fraction of the whole period for which the signal is at its high level:

Multiply this fraction by $$100$$ to express it as a percentage. The mark-to-space ratio is different: it compares the mark time directly with the space time, not with the whole period.

For example, suppose a signal is high for $$2,\mathrm{ms}$$ and low for $$3,\mathrm{ms}$$ in each cycle. Its period is $$5,\mathrm{ms}$$, or $$0.005,\mathrm{s}$$, so its frequency is $$1/(0.005,\mathrm{s}) = 200,\mathrm{Hz}$$. Its duty cycle is $$2/5 = 40%$$, while its mark-to-space ratio is $$2:3$$.