单级放大器公式总结

Small signal network

$$i_d = g_m V_g - (g_m^* +{1 \over r_o})V_s + {1 \over r_o}V_d$$
其中
$$g_m^* = g_m + g_{mb}$$

General already knowns

若不考虑沟道调制效应，则 CS CG Stage 的增益公式都是

$$A_V = \pm \frac{R_D}{{1 \over g_m} + R_S} = \pm \frac{D , path}{S , path}$$

Common source Stage

$$G_m = \frac{g_m r_o}{R_s + g_m R_s r_o +r_o} \rightarrow g_m$$
$$R_{out} = R_s + g_m R_s r_o + r_o \rightarrow r_o$$
$$A_v = -G_m [R_{out} // R_D]$$
$$R_D = r_o;{1 \over g_m}//r_o;R_D$$

Source Foller

Voltage Buffer;
高 $R_{in}$；
中等高度 $R_{out}$;

计算电压增益时可以看作 ${1 \over g_m}$ 与 out 节点看到地的总电阻组成的分压器。

$$R_{out} = {1 \over g_m^*}//r_o//R_s$$

Common Gate Stage

Current Buffer;

$$G_m = - \frac{g_m r_o + 1}{R_s + g_m R_s r_o +r_o}$$
$$R_{out} = (R_s + g_m R_s r_o + r_o)//R_D$$
$$A_v = \frac{(g_m r_o + 1)R_D}{R_s + g_m R_s r_o +r_o +R_D}$$
$$R_{in} = \frac{R_D + r_o}{1+g_m r_o} \approx \frac{R_D}{g_m r_o} + {1 \over g_m}$$

Cascode

增大输出电阻；
屏蔽特性；

$$G_m \approx g_{m1}$$
$$R_{out} = r_{o1} + g_m r_{o1} r_{o2} + r_{o2} \approx g_m r_{o1} r_{o2}$$

telescopic

$$R_{out} = (r_{o1} + g_m r_{o1} r_{o2} + r_{o2})//(r_{o3} + g_m r_{o3} r_{o4} + r_{o4})$$
$$A_v \approx - g_{m1}[(g_m r_{o1} r_{o2})//(g_m r_{o3} r_{o4})]$$

Differential pair with active current mirror

$$V_{out} = V_X$$

X 经 $r_{o1}$ 流到节点 P 的电流较小，所以 P 点仍然可以看作虚地点。

$$A_{DM} = g_{m1,2} (r_{o2}//r_{o4})$$
$$A_{CM-DM} \approx - \frac{{1 \over 2}({1 \over g_{m3,4}}//r_{o3,4})}{{1 \over 2g_{m1,2}} + R_{SS}} \approx \frac{-1}{2g_{m3}R_{SS}}$$