# Fundamental Physics/Electricity/Electric stabilization

## Electric stabilization

Voltage stabilizer provides table voltage over frequency of time

### Low frequency filter

 Configuration Formula RC Low frequency filter ${\frac {v_{o}}{v_{2}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{1+j\omega T}}$ $T=RC$ $\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}$ $v_{o}(\omega =0)=v_{i}$ $v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}$ $v_{o}(\omega =00)=0$ LR Low frequency filter ${\frac {v_{o}}{v_{2}}}={\frac {R}{R=j\omega L}}={\frac {1}{1+j\omega T}}$ $T={\frac {L}{R}}$ $\omega _{o}={\frac {1}{T}}={\frac {R}{L}}$ $v_{o}(\omega =0)=v_{i}$ $v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}$ $v_{o}(\omega =00)=0$ ### High frequency filter

 Configuration Formula CR High frequency filter ${\frac {v_{o}}{v_{2}}}={\frac {j\omega T}{1+j\omega T}}$ $T=RC$ $\omega _{o}={\frac {1}{T}}={\frac {1}{RC}}$ $v_{o}(\omega =0)=0$ $v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}$ $v_{o}(\omega =00)=v_{i}$ LR High frequency filter ${\frac {v_{o}}{v_{2}}}={\frac {j\omega T}{1+j\omega T}}$ $T={\frac {L}{R}}$ $\omega _{o}={\frac {1}{T}}={\frac {R}{L}}$ $v_{o}(\omega =0)=0$ $v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}$ $v_{o}(\omega =00)=v_{i}$ ### Band pass filter

 Configuration Formula  ${\frac {v_{o}}{v_{i}}}=({\frac {1}{1+j\omega T_{L}}})({\frac {j\omega T_{H}}{1+j\omega _{H}}})$ $T_{L}={\frac {L}{R}}$ $T_{H}=RC$ $\omega _{L}-\omega _{H}={\frac {R}{L}}-{\frac {1}{RC}}$   ${\frac {v_{o}}{v_{i}}}=({\frac {1}{1+j\omega T_{L}}})({\frac {j\omega T_{H}}{1+j\omega _{H}}})$ $T_{L}=RC$ $T_{H}={\frac {L}{R}}$ $\omega _{L}-\omega _{H}={\frac {1}{RC}}-{\frac {R}{L}}$ ### Resonance tuned selected band pass filter

 Configuration Formual ${\frac {v_{o}}{v_{i}}}={\frac {R}{R+j\omega L+{\frac {1}{j\omega C}}}}$ $\omega =\omega _{1}-\omega _{2}$ $v_{o}(\omega =0)=0$ $v_{o}(\omega =\omega _{o})=v_{i}$ $v_{o}(\omega =00)=0$ ${\frac {v_{o}}{v_{i}}}={\frac {j\omega C+{\frac {1}{j\omega L}}}{R+j\omega C+{\frac {1}{j\omega L}}}}$ $\omega =\omega _{1}-\omega _{2}$ $v_{o}(\omega =0)=0$ $v_{o}(\omega =\omega _{o})=v_{i}$ $v_{o}(\omega =00)=0$ ### Resonance tuned rejected band pass filter

 Configuration Formula LC-R ${\frac {v_{o}}{v_{i}}}={\frac {R}{R+j\omega L+{\frac {1}{j\omega C}}}}$ $\omega =\omega _{1}-\omega _{2}$ $v_{o}(\omega =0)=v_{i}$ $v_{o}(\omega =\omega _{o})=0$ $v_{o}(\omega =00)=v_{i}$ R-LC ${\frac {v_{o}}{v_{i}}}={\frac {j\omega C+{\frac {1}{j\omega L}}}{R+j\omega C+{\frac {1}{j\omega L}}}}$ $\omega =\omega _{1}-\omega _{2}$ $v_{o}(\omega =0)=v_{i}$ $v_{o}(\omega =\omega _{o})=0$ $v_{o}(\omega =00)=v_{i}$ 