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how do mosfets amplify current?

MIT 6.002 Circuits and Electronics, Spring 2007
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in case of mosfet,it is first stablised by dc source which controls the path of flow of carriers from source to drain,as it is the voltage controlled device.now if ac source is applied,it gets amplied on cost of that dc.
Even if I'm not sure to fully understand your thought, your question is a really good question. It opens a lot of consideration. I hope that my comment will be usefull for you. First of all, what is the most important difference between BJT and MOS? It depends on the "technology" they are made: BJT is based on junctions. So BJT mainly "deals" with current. Indeed, you speak about hfe, the current gain of a BJT. A MOSFET has an insulated gate and we can say that its job mainly depends on the "electrostatics" of a capacitor. The voltage applied to the gate determines the channel geometry and so the current you have between drain and source. So you can only speak about its transconductance gm (Id/Vgs). In this way, if you compare them you say: "the current gain of a MOSFET is infinite!" (indeed, at the stady state, the gate current is zero). But you also know that if you apply a signal to the gate, the input inductance decreases as the signal frequency increases. In this way you can analize the AC circuit, with the AC model of the MOSFET, and you can find some value for the current gain. Anyway, I think you cannot forget the main principle of the MOS funcion: with a modulation of the gate voltage you can obtain a current signal at the drain. This vision is really good for us. As Bob Pease (one of the most important analog designer of our century!) observed that we usually treat on voltage signals because we can see them (with an oscilloscope). A MOSFET fully cover this vision: it also looks at only a voltage signal at its input.
mosfets are voltage controlled devices ... so we consider the amplfication parameter as voltage and not current !

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Other answers:

partially true.This is why I sentenced "I'm not sure to fully understand akisandooja's thought", Anyway, if weconsider a common gate stage, you have a current-buffer. It doesn't amplify but allow you to interface a current-source and a current-load. What I mean is that, current amplification may depends on the circuit where a mosfet just represents the active element.
kashyap, i would like to point out that,by varying the arrangements like cga or cda,we can also make use of mosfets as current controlled current sources

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