Efficient Balanced Truncation for RC and RLC Networks

An efficient balanced truncation for RC and RLC networks is presented in this paper. To accelerate the balanced truncation, sparse structures of original networks are considered. As a result, Lyapunov equations, the solutions of which are necessary for making the transformation matrices, are efficiently solved, and the reduced order models are efficiently obtained. It is proven that reciprocity of original networks is preserved while applying the proposed method. Passivity of the reduced RC networks is also guaranteed. In the illustrative examples, we will show that the proposed method is compatible with PRIMA in efficiency and is more accurate than PRIMA.