模拟集成电路(6)----单级放大器（共源共栅级 Cascode Stage）

模拟集成电路(6)----单级放大器（共源共栅级 Cascode Stage）

大信号分析

对M1
$$\begin{gathered} V_x\ge V_{in}-V_{TH1}{V}_x=V_B-V_{GS2} \\ {V}_B\ge V_{in}-V_{TH1}+V_{GS2} \end{gathered}$$
对M2
$$\begin{array}{rl}& V_{out}\ge V_B-V_{TH2}\\ & V_{out}\ge V_{in}-V_{TH1}+V_{GS2}-V_{TH2}\\ & V_{out}\ge V_{OD1}+V_{OD2}\end{array}$$

输入输出电阻

$\begin{array}{rl}& \mathrm{When}{V}_{in}<V_{TH1},{\mathrm{M}}_1\mathrm{and}{\mathrm{M}}_2\mathrm{are}\mathrm{off},V_{out}=V_{DD},V_x=V_B-V_{TH2}\end{array}$

$\begin{array}{rl}& \mathrm{When}{V}_{\mathrm{in}}>V_{\mathrm{TH}1},V_{\mathrm{out}}\mathrm{drops},\\ & -V_{GS2}\text{increases, resulting in a drop of }{V}_X\end{array}$

$$\begin{gathered} R_{out}=[1+(g_{m2}+g_{mb2})r_{O2}]r_{O1}+r_{O2} \\ =r_{O1}+r_{O2}+(g_{m2}+g_{mb2})r_{O2}{r}_{O1} \end{gathered}$$
$if{g}_m{r}_O>>1,\mathrm{then}{R}_{out}\approx (g_{m2}+g_{mb2})r_{O2}{r}_{O1}\approx g_{m2}{r}_{O2}{r}_{O1}$

$$\begin{array}{rl}& R_{out}\approx (g_{m3}+g_{mb3})r_{O3}{R}_S\approx \underline{g_{m3}{r}_{O3}{R}_S}\\ & R_S\approx g_{m2}{r}_{O2}{r}_{O1}\\ & \to R_{out}\approx g_{m3}{r}_{O3}\cdot g_{m2}{r}_{O2}\cdot r_{o1}\end{array}$$

小信号分析

增益

$$A_{\nu }=-g_{m1}{R}_D$$
如若是电流源负载

$$A_v=-G_m{r}_{out}$$

$$G_m\approx g_{m1}$$

$$A_{\nu }\approx -g_{m1}\cdot g_{m2}{r}_{o2}{r}_{o1}=-g_{m1}{r}_{o1}\cdot g_{m2}{r}_{o2}$$

可以结合课本3.21去理解

$$\begin{gathered} g_m=\sqrt{2I_{\mathrm{D}}{\mu }_{\mathrm{n}}{C}_{\mathrm{ox}}\frac{W}{L}} \\ {r}_{\mathrm{o}}=\frac{1}{\lambda I_{\mathrm{D}}} \\ {A}_{\mathrm{int}}=g_m{r}_{\mathrm{o}} \end{gathered}$$

$$\begin{gathered} g_{m1}=\frac{g_{\mathrm{m}}}{2} \\ {r}_{\mathrm{ol}}=4r_{\mathrm{o}} \\ {A}_{\mathrm{intl}}=2A_{\mathrm{int}} \end{gathered}$$

$$\begin{gathered} g_{m2}=g_m \\ {r}_{o2}=A_{\mathrm{int}}{r}_{\mathrm{o}} \\ {A}_{\mathrm{int}2}=A_{\mathrm{int}}^2 \end{gathered}$$
用PMOS cascode电流源作负载

$$\begin{array}{rl}{r}_{outn}& \approx g_{m2}{r}_{o2}\cdot r_{o1}\\ r_{outp}& \approx g_{m3}{r}_{o3}\cdot r_{o4}\end{array}$$

$$\begin{array}{rl}{A}_{\nu }& \approx -g_{m1}\cdot (r_{outn}\parallel r_{outp})\\ & \approx -g_{m1}\cdot (g_{m3}{r}_{o3}\cdot r_{o4}\parallel g_{m2}{r}_{o2}\cdot r_{o1})\end{array}$$

$$V_{out\max }\le V_{DD}-V_{OD3}-V_{OD4}$$

$$V_{out,min}\ge V_{OD1}+V_{OD2}$$