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In this paper, we propose a novel model-order reduction (MOR) approach, second-order balanced truncation (BT) for passive-order reduction (SBPOR), which is the first second-order BT method proposed for passive reduction of RLCK circuits. By exploiting the special structure information in the circuit formulation, second-order Gramians are defined based on a symmetric first-order realization in descriptor from. As a result, SBPOR can perform the traditional balancing with passivity-preserving congruency transformation at the cost of solving one generalized Lyapunov equation. Owing to the second-order formulation, SBPOR also preserves the structure information inherent to RLCK circuits. We further propose, second-order Gramian approximation (SOGA) version of SBPOR , to mitigate high computational cost of solving Lyapunov equation. Experimental results demonstrate that SBPOR and SOGA are globally more accurate than the Krylov subspace based approaches.