In this study, a minimal equivalent circuit extraction scheme is provided for passive elements such as interconnects and packages. Instead of common poles, the non-common poles are used as the dominant poles of each frequency response when approximating those frequencies into a rational form. An illustration is given to show the relation between the electrical lengths of the interconnects/packages and the corresponding dominant poles. Finally, a three-port interconnect is used to validate the proposed approach. The circuit extracted by the proposed scheme has fewer components than the circuit from the conventional scheme, and decreases the computational load of the circuit simulation.