This paper proposes the concept of the topological equivalence between the commutation cells of a voltage source inverter (VSI) and a current source inverter (CSI) using duality and equivalent circuit transformation techniques. A switching resonance of CSI is analyzed and an effective three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> damper is derived from the dc-link <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> damper of VSIs based on the topological equivalence of the VSI and CSI commutation cells. Furthermore, a new three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> damper design framework utilizing the topological equivalence is proposed. Experimental results verify that the proposed three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> damper design for CSI significantly reduces the switching resonance and improves the CSI’s output waveform total harmonics distortions (THDs).