差动放大器偏置计算
差动放大器（差分对）是模拟集成电路的核心单元，广泛用于运算放大器的输入级。以下为其关键参数的计算公式。
一、偏置电流
尾电流源 $I_{EE}$ 分配：$I_{C1} = I_{C2} \approx \dfrac{I_{EE}}{2}$（静态平衡时）文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
二、差模电压增益
$A_d = \dfrac{v_{od}}{v_{id}} = g_m R_C$
其中跨导 $g_m = \dfrac{I_C}{V_T} = \dfrac{I_{EE}}{2V_T}$，$V_T \approx 26\text{mV}$（室温）。文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
三、共模电压增益
$A_{cm} \approx \dfrac{R_C}{2R_{EE}}$文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
$R_{EE}$ 为尾电流源的输出电阻（理想电流源 $R_{EE} \to \infty$，$A_{cm} \to 0$）。文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
四、共模抑制比
$CMRR = 20\log_{10}\left|\dfrac{A_d}{A_{cm}}\right| \text{ dB}$文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
理想差分放大器 $CMRR \to \infty$（$A_{cm}=0$），实际通常在 60-120dB。文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
五、输入偏置电流
$I_B = \dfrac{I_{B1} + I_{B2}}{2} = \dfrac{I_C}{\beta}$（$\beta$ 为晶体管电流增益）文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
六、频率响应
上限截止频率（-3dB）：$f_H = \dfrac{1}{2\pi R_C C_L}$（$C_L$ 为负载电容）文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
增益带宽积：$GBW = A_d \times f_H$文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html 文章源自公式库网-https://www.gongshiku.com/html/201910/chadongfangdaqipianzhidianya-dianliu-zengyi-pinshuaixiangyingzaixianyijianshengchengjisuanqi.html
