# Body effect

Increasingly complex equations have been devised to account for body effect in MOS transistors. A source to body voltage is modeled as increasing threshold voltage and thus decreasing current.

A simple symmetry argument makes this unnecessary: Consider the current through an nMOS transistor with source at ground (Id0). Split this transistor into 2 transistors of length k and 1-k in series. The current is unchanged. Designate the drain d and the node s:

          Ids/(1-k) = Is0/k = Id0/1
          k = Is0/Id0
          Ids = Id0 - Is0

The body effect is saying that the relevant current is between Vd and Vs on the IV curve.

This observation is independent of the shape of the IV curve (it applies to the linear response of a resistor). Of course, a dual effect applies to pMOS transistors. It may have implications regarding appropriate transistor models. For example, gate voltage should not be referenced to source (Vg-Vs is not a useful factor).

It appears that conventional body effect compensation generates too large a current for series transistors. For the level-2 SPICE model that inspired this analysis, it was about 25% high. This produces an unrealisticly fast model of NAND gate fall time.