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We present a passivity-preserving balanced truncation model reduction method for differential-algebraic equations arising in circuit simulation. This method is based on balancing the solutions of projected Lur'e equations. By making use of the special structure of circuit equations, we can reduce the numerical effort for balanced truncation significantly. It is shown that the property of reciprocity is also preserved in the reduced-order model. Network topological interpretations of certain circuit effects are given. The presented model reduction method is illustrated by numerical examples.