Active Power Filter (APF) is an important power electronic device to compensate the load harmonic current so as to improve power quality of the system. Stability of voltage across the capacitor in DC side of APF is one of the key factors which determine the compensation effect. Therefore voltage ripple should be controlled within allowed range. This paper firstly deduced theoretical expressions of voltage ripple across the capacitor in DC side of APF caused by kth order harmonic current. Three-phase and single phase APF are considered respectively. Several simulations were carried out to verify the correctness of the expressions. Then voltage ripple caused by multi-order harmonic currents was deduced by superposition theorem. Corresponding simulations were also carried out to prove the theoretical results. Finally essential factors leading to voltage ripple were analyzed based on the above theoretical deductions and simulations. It was concluded that the ac components in the instantaneous power of AC side of APF were mostly responsible for the voltage ripple across the capacitor.