MOSFET biasing: assume, solve, check the boundary

Từ vựng

English	Ý nghĩa
MOSFET	MOSFET: transistor trường hiệu kim loại-oxit-bán dẫn
saturation region	saturation region: vùng bão hòa
square-law model	square-law model: mô hình bình phương
threshold/ˈθreʃəʊld/	threshold: ngưỡng

English

The gate draws no DC current (megohm dividers allowed), and in the saturation region — the amplifier region, the opposite naming to the BJT — the square-law model gives $i_D = \tfrac{1}{2}k_n(W/L)(v_{GS} - V_t)^2$, with threshold $V_t$.
The region test is one comparison, $v_{DS} \ge v_{GS} - V_t$ — the boundary parabola on the characteristics plane. The model is an assumption; the check is what makes it legal.

Example

$V_{DD} = 10$ V, $\tfrac{1}{2}k_n(W/L) = 0.5$ mA/V², $V_t = 1.5$ V, $R_D = 3$ kΩ. Gate at 3 V: saturation gives $I_D = 1.125$ mA, $V_{DS} = 6.6$ V $\ge 1.5$ ✓ — stands. Gate at 5 V: saturation would need $V_{DS} = -8.4$ V — impossible; re-solve in triode: $v_{DS} = 1.00$ V, $i_D = 3.00$ mA, and the triode equation returns $0.5(2 \times 3.5 \times 1 - 1) = 3.0$ mA ✓.