the_integrator

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the_integrator [2015/05/25 19:29] admin created |
the_integrator [2015/05/25 20:06] (current) admin |
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which is the same current that flows into the capacitor. | which is the same current that flows into the capacitor. | ||

- | \[i=\frac{v_{IN}}{R}=C\frac{dV_C}{dt}\] | + | \[i=\frac{v_{IN}}{R}=C\frac{dv_C}{dt}\] |

+ | | ||

+ | Notice that $v_C=-v_{OUT}$. | ||

+ | | ||

+ | \[i=\frac{v_{IN}}{R}=-C\frac{dv_{OUT}}{dt}\] | ||

+ | | ||

+ | Now we just have to get the expression into the final form. | ||

+ | | ||

+ | \[\frac{-v_{IN}}{RC}dt=dv_{OUT}\] | ||

+ | | ||

+ | \[\frac{-1}{RC}\int_{t_0}^t{v_{IN}dt}=\int_{v_0}^v{dv_{OUT}}\] | ||

+ | | ||

+ | \[\frac{-1}{RC}\int_{t_0}^t{v_{IN}dt}+v_{0}=v_{OUT}\] |

the_integrator.txt · Last modified: 2015/05/25 20:06 by admin