Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with Index at Most One Satoru Iwata, Mizuyo Takamatsu, and Caren Tischendorf Abstract Commercial packages for transient circuit simulation are often based on the modified nodal analysis (MNA) which allows an automatic setup of model equa- tions and requires a nearly minimal number of variables. However, it may lead to differential-algebraic equations (DAEs) with higher index. Here, we present a hy- brid analysis for nonlinear time-varying circuits leading to DAEs with index at most one. This hybrid analysis is based merely on the network topology, which possi- bly leads to an automatic setup of the hybrid equations from netlists. Moreover, we prove that the minimum index of the DAE arising from the hybrid analysis never ex- ceeds the index from MNA. As a positive side effect, the number of equations from the hybrid analysis is always no greater than that one from MNA. This suggests that the hybrid analysis is superior to MNA in numerical accuracy and computational effort. 1 Introduction When modelling electric circuits for transient simulation, one has to regard Kirch- hoff’s laws for the network and the constitutive equations for the different types of network elements. They are originally based on the branch voltages and the branch Satoru Iwata Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan, e-mail: iwata@kurims.kyoto-u.ac.jp Mizuyo Takamatsu Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan, e-mail: mizuyo takamatsu@mist.i.u-tokyo.ac.jp Caren Tischendorf Mathematical Institute, University of Cologne, Weyertal 86-90 50931 K¨ oln, Germany, e-mail: tischendorf@math.uni-koeln.de 1