C d v d t + v R = 0 {\displaystyle C{\frac {dv}{dt}}+{\frac {v}{R}}=0} d v d t = − 1 T v {\displaystyle {\frac {dv}{dt}}=-{\frac {1}{T}}v} T = R C {\displaystyle T=RC} ∫ d v v = − 1 T ∫ d t {\displaystyle \int {\frac {dv}{v}}=-{\frac {1}{T}}\int dt} L n v = − 1 T + c {\displaystyle Lnv=-{\frac {1}{T}}+c} v = e − 1 T t + c = A e − 1 T t {\displaystyle v=e^{-{\frac {1}{T}}t+c}=Ae^{-{\frac {1}{T}}t}}
v o v i = 1 j ω C R + 1 j ω C = 1 j ω R C + 1 = 1 1 + j ω T {\displaystyle {\frac {v_{o}}{v_{i}}}={\frac {\frac {1}{j\omega C}}{R+{\frac {1}{j\omega C}}}}={\frac {1}{j\omega RC+1}}={\frac {1}{1+j\omega T}}} T = R C {\displaystyle T=RC} ω o = 1 T = 1 R C = 2 π f {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {1}{RC}}=2\pi f} v o ( ω = 0 ) = v i {\displaystyle v_{o}(\omega =0)=v_{i}} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 00 ) = 0 {\displaystyle v_{o}(\omega =00)=0}
T = R C {\displaystyle T=RC} ω o = 1 T = 1 R C {\displaystyle \omega _{o}={\frac {1}{T}}={\frac {1}{RC}}} v o ( ω = 0 ) = 0 {\displaystyle v_{o}(\omega =0)=0} v o ( ω = ω o ) = v i 2 {\displaystyle v_{o}(\omega =\omega _{o})={\frac {v_{i}}{2}}} v o ( ω = 00 ) = v i {\displaystyle v_{o}(\omega =00)=v_{i}}
