In very general terms this refers to how long it takes for some action (or duty) to occur. It especially pertains to duties that are repetitive. In engineering terms it is a percentage that expresses the amount of actual working time as compared to the total operating time of an intermittently working piece of equipment. This could be a motor that has to do some operation periodically, or a hard drive, or a person. In electronics it is the ratio of the “on” to “off” period of a circuit or a pulse waveform. A periodic (repetitive) waveform may not spend equal amounts of time above and below zero and this ratio can loosely be referred to as duty cycle. More specifically it has to do with square or pulse type waveforms. A square wave has a duty cycle ratio of 1:1; meaning it spends equal time in both states (hi and low). Pulse waveforms, by definition, are not square and therefore are defined by their pulse width or duty cycle. Duty cycle is also called Duty Factor and Duty Ratio, and in this context is literally the product of the pulse duration and the pulse repetition frequency (Duration x Frequency = Pulse Ratio).
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