Question 11.3: MOSFET Q-Point Calculation Determine the Q point for the MOS......

Known Quantities: MOSFET drain resistance; drain and gate supply voltages; MOSFET equations.
Find: MOSFET quiescent drain current i_{DQ} and quiescent drain-source voltage  v_{DSQ} .

Schematics, Diagrams, Circuits, and Given Data: V_{GG} = 2.4  V ; V_{DD} = 10  V; V_{T} = 1.4  V ; K = 48.5 mA/V²; R_{D} = 100  \Omega .

Assumptions: Use the MOSFET equations 11.2 through 11.4 as needed.

i_D  =  0 \quad\text{Cutoff region}        (11.2)

i_D  =  K[2(v_{GS} − V_T )v_{DS}  −   v^2_{DS} ] \quad Triode or ohmic region       (11.4)

Analysis: The gate supply V_{GG} ensures that v_{GSQ}  =  V_{GG} = 2.4  V . Thus, v_{GSQ} \gt V_T . We assume that the MOSFET is in the saturation region, and we proceed to use equation 11.3 to calculate the drain current:

\begin{aligned} i_D  &=  K(v_{GS}  −  V_T )^2\left(1  +  \frac{v_{DS}}{V_A}\right) \\ &\cong  K(v_{GS}  −  V_T )^2 \end{aligned} \quad Saturation region       (11.3)

i_{DQ}  =  K(v_{GS}  −  V_T )^2  =  48.5(2.4  −  1.4)  =  48.5  mA  

Applying KVL to the drain loop, we can calculate the quiescent drain-to-source voltage as:

v_{DSQ}  =  V_{DD}  −  R_D i_{DQ}  =  10  −  100 \times 48.5 \times 10^{−3}  =  5.15  V   

Now we can verify the assumption that the MOSFET was operating in the saturation region. Recall that the conditions required for operation in region 2 (saturation) were v_{GS} \gt V_T and v_{GD} \lt V_T . The first condition is clearly satisfied. The second can be verified by recognizing that v_{GD}  =  v_{GS}  +  v_{SD}  =  v_{GS}  –  v_{DS}  =  – 2.75  V . Clearly, the condition v_{GD} \gt V_T is also satisfied, and the MOSFET is indeed operating in the saturation region .