Periodic steady-state analysis

The current through a capacitance of value C in time domain is ${\displaystyle i(t)=C{\frac {dv(t)}{dt}}}$, which becomes ${\displaystyle v(t)=v(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t_{0}+t}{i(t)dt}}$ . For this component operating in a periodic steady state circuit, its voltage will be ${\displaystyle v(t_{0}+T)=v(t_{0})}$ when T is equal to its fundamental period. Referring back to the original voltage function ${\displaystyle v(t)=v(t_{0})+{\frac {1}{C}}\int _{t_{0}}^{t_{0}+t}{i(t)dt}}$, it can be determined that the average current flowing through the capacitor is zero in periodic steady state.

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