# FET and MOSFET Analysis

 Question 1
In the circuit below, the voltage $V_{L}$ is ____ $\_V$.
(rounded off to two decimal places) A 2 B 1.55 C 3.32 D 6.32
GATE EC 2023   Analog Circuits
Question 1 Explanation: We know,
\begin{aligned} I_{D} & \propto\left(\frac{W}{L}\right) \\ I_{1} & =1 \mathrm{~mA} \\ I_{2} & =\frac{10}{1} \times 1=10 \mathrm{~mA} \\ I_{3} & =10 \mathrm{~mA} \\ I_{4} & =7 \mathrm{~mA} \\ I_{5} & =5 \mathrm{~mA} \\ I_{0} & =I_{4}-I_{5}=7-5=2 \mathrm{~mA} \\ V_{L} & =2 \times 1=2 \mathrm{~V} \end{aligned}
 Question 2
For a MOS capacitor, $V_{f b}$ and $V_{t}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width $\left(W_{\text {dep }}\right)$ for varying gate voltage $\left(V_{g}\right)$ is best represented by A A B B C C D D
GATE EC 2023   Analog Circuits
Question 2 Explanation:
$\because$ We know $V_{G} \lt V_{F B}$ then accumulation mode.
$\therefore$ In accumulation mode $W_{d}=0$ because there is no depletion charge.
Now, $V_{F B} \lt V_{G} \lt V_{T} \Rightarrow$ then depletion and inversion mode.
$\therefore$ Depletion width is available.
$\therefore V_{G} \gt V_{T} \Rightarrow$ Strong inversion.
$\therefore$ Depletion width $W_{d} \Rightarrow$ Constant.
And $W_{d}=\sqrt{\frac{2 \epsilon\left|\phi_{S}\right|}{q N_{S}}}$ and $\left|\phi_{S}\right| \propto V_{G}$
But after strong inversion, $W_{d}$ remains constant.
$\therefore$ Correction option is (B).

 Question 3
Consider the circuit shown with an ideal long channel nMOSFET (enhancementmode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier. $v_i$ is the small-signal ac input voltage. $v_A$ and $v_B$ represent the small-signal voltages at the nodes A and B, respectively. The value of $\frac{v_A}{v_B}$ is ________ (rounded off to one decimal place). A -2 B 2 C -1 D 1
GATE EC 2022   Analog Circuits
Question 3 Explanation:
For ac analysis \begin{aligned} V_A &=-i_d\cdot 4k \\ V_B&=i_d\cdot 2k \\ \frac{V_A}{V_B}&=\frac{-4}{2} \\ \frac{V_A}{V_B}&=-2 \end{aligned}
 Question 4
Consider an ideal long channel nMOSFET (enhancement-mode) with gate length $10\mu m$ and width $100\mu m$. The product of electron mobility ($\mu _n$) and oxide capacitance per unit area ($C_{OX}$) is $\mu _n C_{OX}=1mA/V^2$. The threshold voltage of the transistor is 1 V. For a gate-to-source voltage $V_{GS}=[2-\sin (2t)]V$ and drain-tosource voltage $V_{DS}=1V$ (substrate connected to the source), the maximum value of the drain-to-source current is ________.
 A 40 mA B 20 mA C 15 mA D 5 mA
GATE EC 2022   Analog Circuits
Question 4 Explanation:
$\mu _n Co_x=1mA/V^2; W=100\mu m;L=10\mu m$
$V_T= \perp V; V_{GS}=[2-\sin 2t]V;V_{DS}=1V$ Let,
\begin{aligned} V_{GS} &=3V(max)\\ \Rightarrow V_{DS} &\lt V_{GS}-V_t\\ \because \; 1 &\lt (3-1) \end{aligned}
MOSFET in triode region
\begin{aligned} I_{Dmax}&=\mu _CO_x\left ( \frac{\omega }{L} \right )\left \{ \left ( V_{as \; max}-V_t \right )V_{DS}-\frac{1}{2}V_{DS}^2 \right \}\\ &=1 \times \left ( \frac{100}{10} \right )\left \{ (3-1) \times 1-\frac{1}{2} \times 1^2 \right \}mA\\ &=10(2-1/2)\\ &=15mA \end{aligned}
 Question 5
The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and -1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are ______ A $V_1=5 V, V_2=5 V$ B $V_1=5 V, V_2=4 V$ C $V_1=4 V, V_2=5 V$ D $V_1=4V, V_2=-5 V$
GATE EC 2022   Analog Circuits
Question 5 Explanation: There are 5 questions to complete.