Find $f_{T}$ for a MOSFET operating at $I_{D}=200 \mu \mathrm{A}$ and $V_{o v}=0.3 \mathrm{V}.$ The MOSFET has $C_{g s}=25 \mathrm{fF}$ and $C_{g d}=5 \mathrm{fF}.$

Given a depletion-type MOSFET with $I_{DSS}=6\text{ mA}$ and $V_P=-3\text{ V}$, determine the drain current at $V_{GS}=-1, 0, 1$ and $2\text{ V}$. In the positive $V_{GS}$ region, does the drain current increase at a significantly higher rate than for negative values? Does the $I_D$ curve become more and more vertical with increasing positive values of $V_{GS}$? Is there a linear or a nonlinear relationship between $I_D$ and $V_{GS}$? Explain.

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In an E-MOSFET, there is no drain current until $V_{\mathrm{GS}}$ (a) reaches $V_{\mathrm{GS}(\mathrm{th})}$, (b) is positive, (c) is negative, (d) equals $0 \mathrm{~V}$.

Consider the following systems in unknowns x and y :
(a) $\quad a x+b y=1$

$$c x+d y=0$$

(b) $a x+b y=0$

$$c x+d y=1$$

Suppose $D=a d-b c \neq 0$. Show that each system has the unique solution: (a) $x=d / D, y=-c / D$, (b) $x=-b / D, y=a / D$.

The value of $\lambda$ for a MOSFET is $0.02 \mathrm{~V}^{-1}$. (a) What is the value of $r_o$ at (i) $I_D=50 \mu \mathrm{A}$ and at (ii) $I_D=500 \mu \mathrm{A}$ ? (b) If $V_{D S}$ increases by $1 \mathrm{~V}$, what is the percentage increase in $I_D$ for the conditions given in part (a)?

Find $f_T$ for a MOSFET operating at $I_D=100 \mu \mathrm{A}$ and $V_{o v}=0.2 \mathrm{~V}$. The MOSFET has $C_{g r}=20 \mathrm{fF}$ and $C_{g d}=5 \mathrm{fF}$.

The drain current of a MOSFET in the triode region is expressed as $I_{D}=\mu_{n} C_{o x} \frac{W}{L}\left[\left(V_{G S}-V_{T H}\right) V_{D S}-\frac{1}{2} V_{D S}^{2}\right]$. Suppose the values of $\mu_{n} C_{o x}$ and W/L are unknown. Is it possible to determine these quantities by applying different values of $V_{G S}-V_{T H}$ and $V_{D S}$ and measuring $I_{D}$?

A MOSFET is to operate at $I_{D}=0.1 \mathrm{mA}$ and is to have $g_{m}=1 \mathrm{mA} / \mathrm{V} .$ If $k_{n}^{\prime}=50 \mu \mathrm{A} / \mathrm{V}^{2},$ find the required W/L ratio and the overdrive voltage.

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What do the abbreviations BJT, MOSFET, VLSI, IC, CVD, CMP, LELE, and DIP stand for?

An E-MOSFET has $R_{D S(o n)}=2 \Omega$ when $V_{G S(0 n)}=$ $3 \mathrm{~V}$ and $I_{D(o n)}=500 \mathrm{~mA}$. If it is biased in the ohmic region, what is the voltage across it for each of these drain currents:
a. $I_{D \text { (sat) }}=25 \mathrm{~mA}$
b. $I_{D(\text { sat })}=50 \mathrm{~mA} \quad$ d. $I_{D(\mathrm{sat})}=200 \mathrm{~mA}$ E-MOSFET in Fig. 12-50a if $V_{G S}=2.5 \mathrm{~V}$ ?
c. $I_{D(\text { sat })}=100 \mathrm{~mA}$

A D-MOSFET has an $I_\text{DSS}$ value of $20\text{ mA}$ and a $V_\text{GS(off)}$ value of $-5\text{ V}$. Calculate the drain current, $I_\text{D}$, for each of the following values of $V_\text{GS}$: a. $V_\text{GS}=-4\text{ V}$. b. $V_\text{GS}=-3\text{ V}$. c. $V_\text{GS}=-2\text{ V}$. d. $V_\text{GS}=-1\text{ V}$. e. $V_\text{GS}=+1\text{ V}$. f. $V_\text{GS}=+2\text{ V}$. g. $V_\text{GS}=+3\text{ V}$. h. $V_\text{GS}=+4\text{ V}$.

The datasheet for an E-MOSFET reveals that $I_{\mathrm{D}(\mathrm{on})}=10 \mathrm{~mA}$ at $V_{\mathrm{GS}}=-12 \mathrm{~V}$ and $V_{\mathrm{GS}(\text { (h) }}=-3 \mathrm{~V}$. Find $I_{\mathrm{D}}$ when $V_{\mathrm{GS}}=-6 \mathrm{~V}$.