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Feedback is an event that occurs when the output of a system is used as input back into the system as part of a chain of cause and effect. This alters variables in the system, therefore resulting in different output and consequently different feedback as well, which can either be good or bad. In the case of a system which requires knowledge of the output in order to improve or deliver on a specific output, then feedback is essential and good. But for a system that does not require feedback, such as an audio system, then feedback is often bad. Take for example a microphone and speaker system, when the sound from the speakers (output) is picked up by the microphone (input) it creates a negative feedback that produces a very high pitched sound.
Feedback is basically the concept of taking output and using it as input, either to further drive the system or produce a desired output. A good example is feedback used in an assembly line, when an output does not meet the minimum quality or quantity set by the system, it adjusts itself either to ramp up the production speed or even automatically stop if there are major deviations in the output.
In electronics, feedback is often used to get a desired result from a circuit. The simplest example would be an operational amplifier which uses feedback to vary the characteristic output of the op-amp, hence changing its "operation." The output of the op-amp is basically fed back into one of its two inputs, and depending on the configuration of the feedback loop, the feedback can control the gain of the op-amp or make it act as a kind of signal conditioner, filtering out signal distortions from the system. In this case, feedback is used as a purely quantitative element with predefined mathematical equations.