# Duty cycle

A duty cycle is the percent of time that an entity spends in an active state as a fraction of the total time under consideration.[1][2] The term is often used pertaining to electrical devices, e.g., switching power supplies. It is also sometimes used pertaining to living systems such as the firing of action potentials by neurons. In an electrical device, a 60% duty cycle means the power is on 60% of the time and off 40% of the time. The "on time" for a 60% duty cycle could be a fraction of a second – or for say, irrigation pumps, days – depending on how long the device's period is. Here one period is the length of time it takes for the device to go through a complete on/off cycle. The term "duty cycle" has no agreed meaning for aperiodic devices.[citation needed]

## Definition

The duty cycle $D$ is defined as the ratio between the pulse duration ($\tau$) and the period ($\Tau$) of a rectangular waveform

In a periodic event, duty cycle is the ratio of the duration of the event to the total period of a signal.

duty cycle $D = \frac{\tau}{\Tau} \,$[3]

where

$\tau$ is the duration that the function is active.
$\Tau$ is the period of the function.

## Examples

### Electronics and digital signal processing

In an ideal pulse train (one having rectangular pulses), the duty cycle is the pulse duration divided by the pulse period.[4] For example, a pulse train in which the pulse duration is 1 μs and the pulse period is 4 μs has a duty cycle of 25%. The pulse duration is normally calculated for positive pulses unless "negative duty cycle" is specified.

The duty cycle of a non-rectangular waveform, such as a sine or triangle wave, is defined as the fraction of the period the waveform spends above 0.[5]

In a continuously variable slope delta (CVSD) modulation converter, the mean proportion of binary "1" digits at the converter output in which each "1" indicates a run of a specified number of consecutive bits of the same polarity in the digital output signal.

### Electrical devices

Electrical motors typically use less than a 100% duty cycle. For example, if a motor runs for one out of 100 seconds, or 1/100 of the time, then, its duty cycle is 1/100, or 1 percent.[6]

In electronic music, music synthesizers vary the duty cycle of their audio-frequency oscillators to obtain a subtle effect on the tone colors. This technique is known as pulse-width modulation (PWM).

In the printer / copier industry, the duty cycle specification refers to the rated throughput (that is, printed pages) of a device per month.

In a welding power supply, the maximum duty cycle is defined as the percentage of time in a 10 minute period that it can be operated continuously before overheating.[7]

### Biological systems

The concept of duty cycles is also used to describe the activity of neurons and muscle fibers. In a neural network for example, a duty cycle specifically refers to the proportion of a cycle period in which a neuron remains active.[2]

## References

1. ^ "Definition: duty cycle", Institute for Telecommunication Sciences, Boulder, Colorado, accessed 2011-03-23; from Federal Standard 1037C, "Telecommunications: Glossary of Telecommunication Terms", 1996
2. ^ a b Harris-Warrick, Ronald; Nagy, Frédéric; Nusbaum, Michael (1992). Harris-Warrick, Ronald; Marder, Eve; Silverston, Alan et al., eds. Dynamic biological networks: the stomatogastric nervous system. Massachusetts: MIT Press. pp. 87–139. ISBN 0-262-08214-4.
3. ^ "555 timer", Doctronics, accessed 2011-03-23
4. ^ "Clock Positive Duty Cycle", Aubrax, accessed 2011-03-23
5. ^ MAX038 High-Frequency Function Generator Data Sheet 19-0266; Rev 7; 8/07, Maxim Integrated Products, Inc., accessed 2011-03-23
6. ^ "Electric Motors", Machine Design, accessed 2011-03-23
7. ^ "What does the term duty cycle mean?", ZENA, Inc. welding systems