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雙二階濾波器
時(shí)間:2022-10-20 人氣: 來源:山東合運(yùn)電氣有限公司
{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{1}*s+p_{0}}{s^{2}+e_{1}*s+e_{0}}}}{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{1}*s+p_{0}}{s^{2}+e_{1}*s+e_{0}}}}
或
{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{1}*s+p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{1}*s+p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}
分子二項(xiàng)式中系數(shù){\displaystyle p_{2}}p_{2},{\displaystyle p_{1}}p_{1}決定濾波器的類型:
雙二階低通濾波器
{\displaystyle G(s)={\frac{p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}{\displaystyle G(s)={\frac{p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}
其衰減函數(shù)為\。
{\displaystyle A(\Omega)=G(j*\omega)*G(-j*\omega)={\frac{Q^{2}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}{\displaystyle A(\Omega)=G(j*\omega)*G(-j*\omega)={\frac{Q^{2}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}
其中{\displaystyle\Omega={\frac{\omega}{\omega _{0}}}}{\displaystyle\Omega={\frac{\omega}{\omega _{0}}}}
無源雙二階低通濾波器
無源雙二階低通濾波器由電阻、電容和電感元件組成[3]
{\displaystyle p_{0}={\frac{1}{LC}}}{\displaystyle p_{0}={\frac{1}{LC}}}
{\displaystyle\omega _{0}={\sqrt{\frac{1}{LC}}}}{\displaystyle\omega _{0}={\sqrt{\frac{1}{LC}}}}
{\displaystyle Q=R*{\sqrt{C/L}}}{\displaystyle Q=R*{\sqrt{C/L}}}
有源雙二階低通濾波器
有源雙二階低通濾波器由運(yùn)算放大器、電容、電感和電阻構(gòu)成。
雙二階高通濾波器
雙二階高通濾波器的傳遞函數(shù)為
{\displaystyle G(s)={\frac{s^{2}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}{\displaystyle G(s)={\frac{s^{2}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}
雙二階高通濾波片的頻率響應(yīng):
{\displaystyle A(\Omega)={\frac{-Q^{2}*\Omega^{4}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}{\displaystyle A(\Omega)={\frac{-Q^{2}*\Omega^{4}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}
{\displaystyle p_{2}=1}{\displaystyle p_{2}=1}
{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}
{\displaystyle Q=R*{\sqrt{C/L}}}{\displaystyle Q=R*{\sqrt{C/L}}}
雙二階帶通濾波器
雙二階帶通濾波器的傳遞函數(shù)為。
{\displaystyle G(s)={\frac{p_{1}*s}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}{\displaystyle G(s)={\frac{p_{1}*s}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}
{\displaystyle A(\Omega)={\frac{\Omega^{2}*Q^{2}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}{\displaystyle A(\Omega)={\frac{\Omega^{2}*Q^{2}}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}
相角:
{\displaystyle\theta:=90-180*arctan({\frac{\omega*\omega _{0}}{(Q*(\omega _{0}^{2}-\omega^{2})}})/\pi}{\displaystyle\theta:=90-180*arctan({\frac{\omega*\omega _{0}}{(Q*(\omega _{0}^{2}-\omega^{2})}})/\pi}
{\displaystyle p_{1}={\frac{1}{CR}}}{\displaystyle p_{1}={\frac{1}{CR}}}
{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}
{\displaystyle Q=R*{\sqrt{C/L}}}{\displaystyle Q=R*{\sqrt{C/L}}}
雙二階帶阻濾波器
雙二階帶阻濾波器的傳遞函數(shù)為<refnname=rs>Rolf Schaumann,H.Xiao,M.E.van Valkenburg,p225</ref>
{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}{\displaystyle G(s)={\frac{p_{2}*s^{2}+p_{0}}{s^{2}+{\frac{\omega _{0}}{Q}}*s+\omega _{0}^{2}}}}
其頻率響應(yīng)
{\displaystyle A(\Omega)={\frac{Q^{2}*(\Omega^{4}-2*\Omega^{2}+1)}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}{\displaystyle A(\Omega)={\frac{Q^{2}*(\Omega^{4}-2*\Omega^{2}+1)}{(\Omega^{4}*Q^{2}-2*\Omega^{2}*Q^{2}+\Omega^{2}+Q^{2})}}}
相角:
{\displaystyle theta:=180*arctan({\frac{\Omega}{(Q*(\Omega^{2}-1)}})/\pi}{\displaystyle theta:=180*arctan({\frac{\Omega}{(Q*(\Omega^{2}-1)}})/\pi}
無源雙二階帶阻濾波器
無源雙二階帶阻濾波器
雙二階帶阻濾波器的頻率響應(yīng)
雙二階帶阻濾波器的頻率響應(yīng)
雙二階帶阻濾波器的相角
雙二階帶阻濾波器的相角
{\displaystyle p_{2}=1}{\displaystyle p_{2}=1}
{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}{\displaystyle\omega={\frac{1}{\sqrt{LC}}}}
{\displaystyle Q=R*{\sqrt{C/L}}}{\displaystyle Q=R*{\sqrt{C/L}}}
關(guān)于雙二階濾波器,小編為大家就分享這些。歡迎聯(lián)系我們合運(yùn)電氣有限公司,以獲取更多相關(guān)知識(shí)。