Deck 1: MOS Field-Effect Transistors Mosfets

Question 1

Figure 5.1.1
(a) For the circuit shown in Fig. 5.1.1(a), show (neglecting $\lambda$ ) that
$$V=V_{t}+\sqrt{\frac{2 I}{k_{n}^{\prime}(W / L)}}$$
(b) The MOSFETs in the circuit of Fig. 5.1.1(b) [6 points] have $V_{t}=0.4 \mathrm{~V}, k_{n}^{\prime}=0.4 \mathrm{~mA} / \mathrm{V}^{2}$ , and $\lambda=0$ . Find $(W / L)_{1},(W / L)_{2}$ , and $(W / L)_{3}$ to obtain the reference voltages shown.

Answer 1

(a)


Figure 5.1.1(a)

Question 2

(a)


(b)
Figure 5.2.1
The MOSFETs in the circuits of Fig. 5.2.1 have $V_{t}=0.4 \mathrm{~V}, k_{n}^{\prime}=0.4 \mathrm{~mA} / \mathrm{V}^{2}, \lambda=0$ , and $L=$ $0.4 \mu \mathrm{m}$ .
(a) For the circuit in Fig. 5.2.1(a), find the values of $W$ and $R_{D}$ to operate the MOSFET at $I_{D}=$ $0.2 \mathrm{~mA}$ and $V_{D}=0.6 \mathrm{~V}$ .
(b) For the circuit in Fig. 5.2.1(b), find $W_{1}, W_{2}$ , and $W_{3}$ to obtain $V_{1}=0.5 \mathrm{~V}$ and $V_{2}=1.1 \mathrm{~V}$ .

Answer 2

Question 3

Figure 5.3.1
The MOSFET in Fig. 5.3.1 has $V_{t}=0.5 \mathrm{~V}, k_{n}^{\prime}=$ $0.4 \mathrm{~mA} / \mathrm{V}^{2}, V_{A}=10 \mathrm{~V}$ , and $W / L=10$ . Find the value of $R_{D}$ that results in
i. $V_{D}=0.1 \mathrm{~V}$
ii. $V_{D}=1.5 \mathrm{~V}$
In each case, find $I_{D}$ and the incremental drain-tosource resistance of the MOSFET.

Answer 3

Question 4

Figure 5.4.1
The MOSFET in the circuit of Fig. 5.4.1 has $V_{t}=$ $1 \mathrm{~V}$ and $k_{n}=2 \mathrm{~mA} / \mathrm{V}^{2}$ , and the Early effect can be neglected.
(a) Find the values of $R_{S}$ and $R_{D}$ that result in the MOSFET operating with an overdrive voltage of $0.5 \mathrm{~V}$ and a drain voltage of $1.5 \mathrm{~V}$ . What is the resulting $I_{D}$ value?
(b) If $R_{L}$ is reduced from $15 \mathrm{k} \Omega$ to $10 \mathrm{k} \Omega$ , what does $V_{D}$ become?
(c) If $R_{L}$ is disconnected, what does $V_{D}$ become?
(d) With $R_{L}$ disconnected, what is the largest $R_{D}$ that can be used while the MOSFET is remaining in saturation?

Question 5

Figure 5.5.1
The MOSFETs in the circuits of Fig. 5.5.1 have $k=1 \mathrm{~mA} / \mathrm{V}^{2},\left|V_{t}\right|=1 \mathrm{~V}$ , and $\lambda=0$ .
(a) For the circuit in Fig. 5.5.1(a), find the values of $R_{D}$ and $R_{S}$ that result in the MOSFET operating at the edge of the saturation region with $I_{D}=0.1 \mathrm{~mA}$ .
(b) For the circuit in Fig. 5.5.1(b), find $I_{D}$ and $R_{D}$ .
(c) For the circuit in Fig. 5.5.1(c), find $I_{D N}, I_{D P}$ , and $V_{O}$ . Also, find the drain-to-source incremental resistance of each of $Q_{N}$ and $Q_{P}$ .

Question 6

Figure 5.6.1
The transistors in the circuit of Fig. 5.6.1 have $k_{n}=k_{p}=2 \mathrm{~mA} / \mathrm{V}^{2}$ and $V_{t n}=-V_{t p}=0.4 \mathrm{~V}$ . Find $v_{O}$ for each of the following cases:
(a) $v_{I}=0 \mathrm{~V}$
(b) $v_{I}=+1 \mathrm{~V}$
(c) $v_{I}=-1 \mathrm{~V}$
(d) $v_{I}=+2 \mathrm{~V}$
(e) $v_{I}=-2 \mathrm{~V}$

Question 7

Figure 5.7.1
The MOSFETs in the circuit of Fig. 5.7.1 have $\mu_{n} C_{o x}=400 \mu \mathrm{A} / \mathrm{V}^{2}, V_{t}=0.4 \mathrm{~V}, \lambda=0, L=$ $0.4 \mu \mathrm{m}, W_{1}=2 \mu \mathrm{m}$ , and $W_{2}=W_{3}=10 \mu \mathrm{m}$ . Find $R$ to obtain a reference current $I_{\mathrm{REF}}$ of $40 \mu \mathrm{A}$ . Also, find the values of $V_{1}, I_{2}, V_{2}$ , and $V_{3}$ .