Drain-to-gate feedback bias

Drain-to-gate feedback bias is a single-resistor MOSFET biasing scheme: connect a large resistor $R_G$ from the drain back to the gate. It does two jobs at once — it forces the device into saturation automatically, and it provides Negative feedback that stabilises the bias point.

It guarantees saturation

Because the gate draws no current (Gate oxide), no current flows through $R_G$ in DC, so there is no voltage drop across it and the gate sits at the same DC potential as the drain:

$V_G=V_D\Rightarrow V_{GD}=0$

The saturation condition is $V_{DS}\ge V_{OV}=V_{GS}-V_t$. With $V_{GD}=0$ we have $V_{DS}=V_{GS}$, and since $V_t>0$, $V_{DS}=V_{GS}>V_{GS}-V_t=V_{OV}$ is automatically satisfied whenever the device conducts. So a drain-to-gate connected MOSFET is always saturated when on — the same reasoning as the Diode-connected MOSFET, just with a large resistor in the gate path instead of a short. You never have to worry about it slipping into triode.

Drain-to-gate $R_G$ guarantees saturation and gives negative-feedback bias stabilisation.

The negative-feedback loop

Trace what happens if $I_D$ drifts up (a low-$V_t$ part, a temperature rise):

$I_D\uparrow \Rightarrow \text{drop across }{R}_D\uparrow \Rightarrow V_D\downarrow \Rightarrow V_G\downarrow \Rightarrow V_{GS}\downarrow \Rightarrow I_D\downarrow$

The rising current pulls the drain (and therefore the gate) down, which reduces $V_{GS}$, which pushes the current back down. A self-correcting loop — exactly the negative-feedback bias-stabilisation idea behind MOSFET biasing, implemented with one resistor. The BJT analogue is collector-to-base feedback bias, which works by the identical mechanism (a resistor from collector to base). The trade-off, as with any feedback bias, is that $R_G$ also feeds signal from drain to gate, which lowers the AC input resistance via the Miller effect — but for biasing purposes the guaranteed saturation plus stabilisation with a single component is attractive.