Wide-band Macromodel Technology and Passivity Compensation
|School||Xi'an University of Electronic Science and Technology|
|Course||Circuits and Systems|
|Keywords||vector fitting macromodel passivity compensation matrix perturbation theory Hamiltonian matrices interconnect simulation|
With the trend of the modern electronic systems toward higher speed, higher density, lower power, lower supply voltages and larger current, the previously negligible effects of interconnect, such as delay, reflections, crosstalk and power/ground bounce have been highlighted. Interconnects can exist at various levels of hierarchy such as on-chip, packages, multichip modules, printed circuit boards and backplanes, which have become the main factors affecting the signal quality. High-speed interconnects are always characterized by S-parameters. Macromodel technology has become the de facto standard of including S-parameters in time domain simulation. The initial macromodels, which are construnted by vector fitting, can not be guaranteed to be passive. It is well known that non-passive macromodel leads to unstable transient simulations. Based on extensively summarization of the relative reaearch results, the thesis systematically analyzes the entire process of macromodel technology, and focuses on the probem of passivity. The new ideas of dissertation are mainly listed as follows:1. Presently, delayed rational macromodels fitting the raw data in the least squares sense, which are realized by pseudoinverse. This method ignores the special sparse structure of macromodels,which is dependent on the number of ports. For muti-port systems, the efficiency of the method is very low. With this consideration, an efficient delayed rational macromodeling technique is presented in this paper. By the detailed analysis of the structure of the delayed rational macromodels, the high-order pseudoinverse could be simplified to low-order pseudoinverse through QR decomposition. This procedure can greatly improve the efficiency.2. In traditional convex optimization based method, the number of free variables is large which will lead to demanding computations. With this consideration, a fast convex optimization method is proposed in this paper. The initial value of the energy matrix is determined before optimization with only some degrees of freedom. The procedure can reduce 60% of the number of free variables, which can greatly improve the efficiency of the method.3. Based on systematically analyzing the differences between equality constraint and conventional inequality constraint, an efficient algebraic method for the passivity enforcement of macromodels is presented. The method is based on quadratic programming with equality constraint. Compared with the general quadratic programming based method, where the passivity violations are compensated via numerical optimization, the presented analytical method is based on the solution of sparse linear equations. With the special sparse structure of macromodels, the passivity compensation is equivalent to the solution of some small size linear equations. This gives large savings for CPU time and memory requirement.4. An efficient least squares based method for the passivity enforcement of delayed rational macromodels is presented. The least-squares objective function and the impulse-energy objective function are described and compared. A new formulation for the objective function of impulse-energy type is also derived, which shows that least-squares objective function and impulse-energy objective function are mathematically equivalent. This confirms two important conclusions. Firstly, for both types of objective function based methods, equality constraint and inequality constraint yield the same results. Secondly, the algorithms of passivity compensation for these two objective functions based methods are interchangeable.