# NMOS Gate-Source voltage

My current understanding of the NMOS device is that if you apply a big enough potential difference to the gate relative to the p-type substrate $V_{GB}$, free electrons are going to appear near the surface of the substrate creating a channel that can potentially conduct a current if there is a non zero Drain-Source voltage. However, the equations that describe the mosfet like $V_{GS} > V_{T}$ are considering the difference between the gate voltage and the source voltage.

My question : Why those equations depend on $V_{GS}$ and not $V_{GB}$? Why the source voltage matters in creating this channel of electrons? Wouldn't it work if $V_{GB} > V_{T}$ and $V_{GS} = 0$ ? What I am missing?

For circuit design the source is usually the reference terminal. Consequently so called source-referenced transistor models were introduced to formulate the drain current as a function of voltages relative to the source terminal ($V_{GS}, V_{DS} V_{BS}$). In cases where the bulk source voltage $V_{BS}$ is zero the gate-source voltage $V_{GS}$ is equal to the gate-bulk voltage, so we actually see the effect of the gate-bulk voltage $V_{GB}$. For non-zero $V_{BS}$ the body-effect is used to model the behavior of the transistor. The body-effect describes a change of the threshold voltage $V_T$ and so the behavior of the transistor depending on $V_{GB}$ is obtained.
The threshold voltage $V_T$ with a backgate-bias voltage $V_{SB}$ is given by the following expression (see Wikipedia). $$V_T = V_{T0} + \gamma\left(\sqrt{|-2\phi_F + V_{SB}|}-\sqrt{|2\phi_F|} \right)$$ where $V_{T0}$ is the threshold voltage for $V_{BS} = 0$, $\gamma$ is the body-effect parameter and $2\phi_F$ is the surface-potential.