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the_integrator [2015/05/25 19:29]
admin created
the_integrator [2015/05/25 20:06] (current)
admin
Line 15: Line 15:
 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