# Fundamental Physics/Electric stabilization

## Electric stabilization

Voltage stabilizer provides table voltage over frequency of time

### Low frequency filter

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

### High frequency filter

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

### Band pass filter

 Configuration Formula ${\displaystyle {\frac {v_{o}}{v_{i}}}=({\frac {1}{1+j\omega T_{L}}})({\frac {j\omega T_{H}}{1+j\omega _{H}}})}$ ${\displaystyle T_{L}={\frac {L}{R}}}$${\displaystyle T_{H}=RC}$ ${\displaystyle \omega _{L}-\omega _{H}={\frac {R}{L}}-{\frac {1}{RC}}}$ ${\displaystyle {\frac {v_{o}}{v_{i}}}=({\frac {1}{1+j\omega T_{L}}})({\frac {j\omega T_{H}}{1+j\omega _{H}}})}$ ${\displaystyle T_{L}=RC}$${\displaystyle T_{H}={\frac {L}{R}}}$ ${\displaystyle \omega _{L}-\omega _{H}={\frac {1}{RC}}-{\frac {R}{L}}}$

### Resonance tuned selected band pass filter

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

### Resonance tuned rejected band pass filter

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