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Saturation current
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Saturation current is a term used to describe a limit to the amount of current that can flow in an electronic circuit or device. As the voltage applied to a circuit is increased, the current flow will increase proportionately until the saturation current is achieved, at which point the excess current can no longer flow, and is instead converted into heat. This excess heat can cause overheating and even failure if a device's cooling capabilities are inadequate.

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Encyclopedia
Saturation current is a term used to describe a limit to the amount of current that can flow in an electronic circuit or device. As the voltage applied to a circuit is increased, the current flow will increase proportionately until the saturation current is achieved, at which point the excess current can no longer flow, and is instead converted into heat. This excess heat can cause overheating and even failure if a device's cooling capabilities are inadequate. The physical explanation for current saturation may be a fixed density of charge carriers (electrons) and a maximum possible value for their velocity, and has some conceptual parallels to the notion of mechanical friction.
To better comprehend the notion of current saturation, an analogy can be made to our everyday experience of water flowing through a faucet. As one opens the faucet, the flow of water increases, but only up to a certain maximum amount. That maximum might be described as the faucet's saturation flow, although such a term is not in use.
One of the most ubiquitous exploits of saturation current is in the incandescent light bulb.
In electronics, the heat generated by attempting to exceed a device's saturation current is leveraged in the design of a fuse, where that excess heat is used to melt a metallic conductor, thereby interrupting the current.
In transistors, velocity saturation usually occurs before the transistor itself goes into saturation. From a design point of view, this means that designed circuits will usually be slower than expected.
In an x-ray tube, saturation current is achieved when no more thermionic electrons can be directed from the filament to the disk anode of the x-ray tube. Increasing the milliamperes would only allow increased filament amperage.
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