Passivity Verification And Enforcement Of Maromodels In High-speed Interconnect Systems

With the continuous improvement of semiconductor technology, the Very LargeScale Integrated Circuits are going toward miniaturization, which brings about thechallenges of higher speed, higher density, lower supply voltages and larger currents.The previously negligible interconnect effects, such as signal reflections, crosstalkbetween signals and power/ground voltage fluctuation, have become the main factorsthat limit the system performance. Consequently, accurate modeling of high-speedinterconnects is very important. For high-speed interconnect systems, rationalmacromodeling has become a standard practice for generating the SPICE-compatibilityinterconnect models in time domain simulation. However, the passivity of initialmacromodels constructed by many methods can not be guaranteed, which may lead tounstable time-domain simulation. The dissertation presents some theoretical andnumerical results for macromodel technology of high-speed interconnect systems, andemphasizes on the passivity enfoecement probem in regular systems, delay systems andsingular systems. The major contributions of dissertation are outlined as follows:1. For the traditional quadratic pragramming method with inequality constraints, itcan be CPU expensive to solve the numerical optimization problem. For this, anefficient passivity enforcement method is presented in the dissertation. By perturbingresidual matrix of macromodels, the quadratic optimization question with equalityconstraint is constructed in the least square sense. It proves that the quadraticoptimization problem either with inequality constraints or with equality constraints hasthe same solution. So, a fast method to solve the optimization questions based on theLagrange multiplier is presented, which gives large savings for the CPU time andmemory requirement.2. Via the decomposition of the passivity enforcement method available, fourquadratic optimization methods with equality constraints are presented. The analysisshows that for the most cases, a significantly better performance is achieved by thepassivity compensation strategy based on the constraints constructed at discretefrequency sample and the objective function constructed in least square sense. Twoanalytical algorithms are given to solve the quadratic optimization problems. Theanalysis shows that the same solution is obtained by the pseudoinverse method andLagrange mehod. The analysis and simulation results show that the proposed analyticalmethod with the equality constraints is superior to the traditional methods applied in commercial tools (such as IDEM and EMTP).3. The transmission line macromodel based on the method of characteristic is aneffective modeling technology for electrically long interconnects, but this method canonly guarantee the causality except the passivity of the model. In this dissertation, thepassivity compensation algorithm based on the quadratic optimization method withequality constraint, which is introduced in linear macromodel, is extended to the delaymacromodels. There presents the residue matrix perturbation scheme and residueeigenvalue perturbation scheme. Compared with the residue matrix perturbation scheme,the residue eigenvalue perturbation scheme can significantly reduce the number of freevariables and eliminate the effect of the coupling term, which is caused by adding theconductance components at diagonal element of admittance matrix in order to ensurethe DC characteristics. Due to taking full advantage of the matrix sparsity, theperformence of the poposed mehod outperforms several existing methods.4. Many practical system can only be represented as the singular system modelinstead of the regular system model. For the macromodel in singular system, theexisting methods require system decomposition, which greatly increase thecomputational time. Therefore, a fast passivity compensation method is proposed.Directly perturbing the whole of state matrix, without expensive system decomposition,which can tremendously improve the efficiency of simulation compared with existingalgorithms. Finally, several examples are illustrateded to validate the efficiency of themehod.