Given the availability of NMOS and PMOS transistors that are matched and have $k_{n}=k_{p}=$ $5 \mathrm{~mA} / \mathrm{V}^{2}$ and $V_{A n}=-V_{A p}=5 \mathrm{~V}$, give circuits for the following amplifiers. In each case, find the output resistance and the voltage gain. In all cases, operate each transistor at a dc bias current of $100 \mu \mathrm{A}$ and give the value of $\left|V_{O V}\right|$ at which each transistor is operating.
(a) An NMOS common-source amplifier with a PMOS current-source load.
(b) An NMOS common-source amplifier with an NMOS cascode stage and a single-transistor PMOS current-source load.
(c) An NMOS common-source amplifier with an NMOS cascode stage and a cascode PMOS current-source load.

Question

Given the availability of NMOS and PMOS transistors that are matched and have $k_{n}=k_{p}=$ $5 \mathrm{~mA} / \mathrm{V}^{2}$ and $V_{A n}=-V_{A p}=5 \mathrm{~V}$, give circuits for the following amplifiers. In each case, find the output resistance and the voltage gain. In all cases, operate each transistor at a dc bias current of $100 \mu \mathrm{A}$ and give the value of $\left|V_{O V}\right|$ at which each transistor is operating.
(a) An NMOS common-source amplifier with a PMOS current-source load.
(b) An NMOS common-source amplifier with an NMOS cascode stage and a single-transistor PMOS current-source load. 
(c) An NMOS common-source amplifier with an NMOS cascode stage and a cascode PMOS current-source load.

Quizplus · Accepted Answer

The Answer is For each transistor,

\begin{aligned}k_{n} & =k_{p}=5 \mathrm{~mA} / \mathrm{V}^{2} \V_{A n} & =-V_{A p}=5 \mathrm{~V} \I_{D} & =100 \mu \mathrm{A}\end{aligned}

\begin{aligned}I_{D} & =\frac{1}{2} k\left|V_{O V} ight|^{2} \0.1 & =\frac{1}{2} imes 5 imes\left|V_{O V} ight|^{2} \\Rightarrow\left|V_{O V} ight| & =0.2 \mathrm{~V} \g_{m} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.1}{0.2}=1 \mathrm{~mA} / \mathrm{V} \r_{O} & =\frac{\left|V_{A} ight|}{I_{D}}=\frac{5}{0.1}=50 \mathrm{k} \Omega\end{aligned}

(a)
$For each transistor, \begin{aligned} k_{n} & =k_{p}=5 \mathrm{~mA} / \mathrm{V}^{2} \ V_{A n} & =-V_{A p}=5 \mathrm{~V} \ I_{D} & =100 \mu \mathrm{A} \end{aligned} \begin{aligned} I_{D} & =\frac{1}{2} k\left|V_{O V} ight|^{2} \ 0.1 & =\frac{1}{2} imes 5 imes\left|V_{O V} ight|^{2} \ \Rightarrow\left|V_{O V} ight| & =0.2 \mathrm{~V} \ g_{m} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.1}{0.2}=1 \mathrm{~mA} / \mathrm{V} \ r_{O} & =\frac{\left|V_{A} ight|}{I_{D}}=\frac{5}{0.1}=50 \mathrm{k} \Omega \end{aligned} (a) Figure 8.2.1 See Figure 8.2.1. \begin{aligned} & R_{o}=r_{o n}\left\|r_{o p}=50 ight\| 50=25 \mathrm{k} \Omega \ & A_{V}=-g_{m} R_{O}=-1 imes 25=-25 \mathrm{~V} / \mathrm{V} \end{aligned} (b) Figure 8.2.2 \begin{aligned} R_{O 2} & \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} \ & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} & =r_{o 3}=50 \mathrm{k} \Omega \ R_{O} & =R_{O 2}\left\|R_{O 3}=50 ight\| 2500=49 \mathrm{k} \Omega \ A_{v} & =-g_{m 1} R_{O}=-1 imes 49=-49 \mathrm{~V} / \mathrm{V} \end{aligned} (c) Figure 8.2.3 \begin{aligned} R_{o 2} \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} \simeq\left(g_{m 3} r_{o 3} ight) r_{o 4} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O}=R_{O 2} \| R_{O 3} & =2500 \| 2500=1250 \mathrm{k} \Omega \ A_{v}=-g_{m 1} R_{O} & =-1 imes 1250=-1250 \mathrm{~V} / \mathrm{V} \end{aligned}$
Figure 8.2.1
See Figure 8.2.1.

\begin{aligned}& R_{o}=r_{o n}\left\|r_{o p}=50 ight\| 50=25 \mathrm{k} \Omega \& A_{V}=-g_{m} R_{O}=-1 imes 25=-25 \mathrm{~V} / \mathrm{V}\end{aligned}

(b)
$For each transistor, \begin{aligned} k_{n} & =k_{p}=5 \mathrm{~mA} / \mathrm{V}^{2} \ V_{A n} & =-V_{A p}=5 \mathrm{~V} \ I_{D} & =100 \mu \mathrm{A} \end{aligned} \begin{aligned} I_{D} & =\frac{1}{2} k\left|V_{O V} ight|^{2} \ 0.1 & =\frac{1}{2} imes 5 imes\left|V_{O V} ight|^{2} \ \Rightarrow\left|V_{O V} ight| & =0.2 \mathrm{~V} \ g_{m} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.1}{0.2}=1 \mathrm{~mA} / \mathrm{V} \ r_{O} & =\frac{\left|V_{A} ight|}{I_{D}}=\frac{5}{0.1}=50 \mathrm{k} \Omega \end{aligned} (a) Figure 8.2.1 See Figure 8.2.1. \begin{aligned} & R_{o}=r_{o n}\left\|r_{o p}=50 ight\| 50=25 \mathrm{k} \Omega \ & A_{V}=-g_{m} R_{O}=-1 imes 25=-25 \mathrm{~V} / \mathrm{V} \end{aligned} (b) Figure 8.2.2 \begin{aligned} R_{O 2} & \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} \ & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} & =r_{o 3}=50 \mathrm{k} \Omega \ R_{O} & =R_{O 2}\left\|R_{O 3}=50 ight\| 2500=49 \mathrm{k} \Omega \ A_{v} & =-g_{m 1} R_{O}=-1 imes 49=-49 \mathrm{~V} / \mathrm{V} \end{aligned} (c) Figure 8.2.3 \begin{aligned} R_{o 2} \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} \simeq\left(g_{m 3} r_{o 3} ight) r_{o 4} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O}=R_{O 2} \| R_{O 3} & =2500 \| 2500=1250 \mathrm{k} \Omega \ A_{v}=-g_{m 1} R_{O} & =-1 imes 1250=-1250 \mathrm{~V} / \mathrm{V} \end{aligned}$

Figure 8.2.2

\begin{aligned}R_{O 2} & \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} \& =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \R_{O 3} & =r_{o 3}=50 \mathrm{k} \Omega \R_{O} & =R_{O 2}\left\|R_{O 3}=50 ight\| 2500=49 \mathrm{k} \Omega \A_{v} & =-g_{m 1} R_{O}=-1 imes 49=-49 \mathrm{~V} / \mathrm{V}\end{aligned}

(c)
$For each transistor, \begin{aligned} k_{n} & =k_{p}=5 \mathrm{~mA} / \mathrm{V}^{2} \ V_{A n} & =-V_{A p}=5 \mathrm{~V} \ I_{D} & =100 \mu \mathrm{A} \end{aligned} \begin{aligned} I_{D} & =\frac{1}{2} k\left|V_{O V} ight|^{2} \ 0.1 & =\frac{1}{2} imes 5 imes\left|V_{O V} ight|^{2} \ \Rightarrow\left|V_{O V} ight| & =0.2 \mathrm{~V} \ g_{m} & =\frac{2 I_{D}}{\left|V_{O V} ight|}=\frac{2 imes 0.1}{0.2}=1 \mathrm{~mA} / \mathrm{V} \ r_{O} & =\frac{\left|V_{A} ight|}{I_{D}}=\frac{5}{0.1}=50 \mathrm{k} \Omega \end{aligned} (a) Figure 8.2.1 See Figure 8.2.1. \begin{aligned} & R_{o}=r_{o n}\left\|r_{o p}=50 ight\| 50=25 \mathrm{k} \Omega \ & A_{V}=-g_{m} R_{O}=-1 imes 25=-25 \mathrm{~V} / \mathrm{V} \end{aligned} (b) Figure 8.2.2 \begin{aligned} R_{O 2} & \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} \ & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} & =r_{o 3}=50 \mathrm{k} \Omega \ R_{O} & =R_{O 2}\left\|R_{O 3}=50 ight\| 2500=49 \mathrm{k} \Omega \ A_{v} & =-g_{m 1} R_{O}=-1 imes 49=-49 \mathrm{~V} / \mathrm{V} \end{aligned} (c) Figure 8.2.3 \begin{aligned} R_{o 2} \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O 3} \simeq\left(g_{m 3} r_{o 3} ight) r_{o 4} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \ R_{O}=R_{O 2} \| R_{O 3} & =2500 \| 2500=1250 \mathrm{k} \Omega \ A_{v}=-g_{m 1} R_{O} & =-1 imes 1250=-1250 \mathrm{~V} / \mathrm{V} \end{aligned}$

Figure 8.2.3

\begin{aligned}R_{o 2} \simeq\left(g_{m 2} r_{o 2} ight) r_{o 1} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \R_{O 3} \simeq\left(g_{m 3} r_{o 3} ight) r_{o 4} & =(1 imes 50) imes 50=2500 \mathrm{k} \Omega \R_{O}=R_{O 2} \| R_{O 3} & =2500 \| 2500=1250 \mathrm{k} \Omega \A_{v}=-g_{m 1} R_{O} & =-1 imes 1250=-1250 \mathrm{~V} / \mathrm{V}\end{aligned}

Given the Availability of NMOS and PMOS Transistors That Are kn=kp=k_{n}=k_{p}=kn​=kp​=

Given the Availability of NMOS and PMOS Transistors That Are $k_{n}=k_{p}=$