MOSFETS are some what confusing than the Bipolar Juntion Transistors BJT or simply transistors. MOSFETS (Metal Oxide Semiconductor Field Effect Transistors) are voltage controlled current source (VCCS) while BJT are current controlled current source. One of the well known relation for the transistor is Ic = B Ib. Where B is beta or Hfe current gain of the transistor and is usually >10 for high power transistors and >100 for small signal transistors.
So controlling the current flowing in the Base of the transistor one can control the output current flowing from the collector to emitter or from emiter to collector in case of NPN and PNP transistors.
High power transistors require more silicon space in comapre to the same space with the MOSFETS.
In case of Mosfets, they are of N channel and of P channel. Both have its own advantages and dis advantages. But the common of the Mosfets are that both the Mosfets only start conduction when the voltage in its GATE terminal exceeds some voltage level than that of the voltage level in source, which is called Vgs = Vth = Gate threshold voltage. Understanding this voltage level is very important for the design withe Mosfets. Vgs voltage from gate to source is position in the case of the N channel but for the P channel its in negative. But it is still easy to drive the gate of the Mosfets.
N channel have some advantages as they have electrons as their carrier and they have more mobility so the N channel mosfets have very low ON resistance called Rds than the P channel mosfet with same size of die or silicon and this reason need of more silicon space also make P channel mosfet more expensive.
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