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What is the point of the body terminal in a MOSFET. If we assume Vsoure=0, Vdrain>0 then we will have a linearly changing voltage from drain to source. Then if Vgate>0 , depending on the difference between Vgate and the voltage on each point in the MOSFET below the gate, we might or might not have an inversion channel. So what is the actual purpose of the body being connected to source? Why we dont simply let it float? I know that if the body voltage is different than the source voltage, the threshold voltage will change, but what if the body terminal is left to float?

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If you look at the physical construction of a MOSFET, the electric field at the gate is between the gate and the body, not between the gate and the other terminals. (See https://en.wikipedia.org/wiki/MOSFET, for example).

So the device wouldn't work at all if the body were at an unknown floating voltage. For most applications, the simplest way to fix voltage on the body is to connect it internally to the source.

Four-terminal MOSFETs, with an independent connection to the body, are available but there are few applications for them.

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