【常用数学公式】总结

文章概览

三角函数

和差化积

sin(a)+sin(b) = 2sin[(a+b)/2]cos[(a-b)/2]

sin(a)-sin(b) = 2cos[(a+b)/2]sin[(a-b)/2]

cos(a)+cos(b) = 2cos[(a+b)/2]cos[(a-b)/2]

cos(a)-cos(b) = -2sin[(a+b)/2]sin[(a-b)/2]

tanA+tanB=sin(A+B)/cosAcosB

积化和差

sin(a)sin(b) = -1/2*[cos(a+b)-cos(a-b)]

cos(a)cos(b) = 1/2*[cos(a+b)+cos(a-b)]

sin(a)cos(b) = 1/2*[sin(a+b)+sin(a-b)]

cos(a)sin(b) = 1/2*[sin(a+b)-sin(a-b)]

滤波器

RC低通滤波器

$$H(j \omega)=\frac{U_{o}}{U}_{i}=\frac{X_{C}}{R+X_{C}}=\frac{\frac{1}{j \omega C}}{R+\frac{1}{j \omega C}}=\frac{1}{1 + R C j \omega}$$

截止频率

$$|H(j \omega)|=\sqrt{\frac{1}{1+(\omega RC)^{2}}}=\frac{\sqrt{2}}{2}\\ \omega_0 = \frac1{RC}\\ f_0 = \frac1{2 \pi R C}$$

RLC带通滤波器

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