电源网络S参数与芯片电源模型(Chip Power Module,CPM)级联可实现电源时域噪声仿真,完成电源完整性设计签核。当下部分仿真工具在AC阻抗优化过程中导出的S参数存在低频段无法覆盖的问题,影响时域纹波仿真精度,如果重新对S参数进行提取,...电源网络S参数与芯片电源模型(Chip Power Module,CPM)级联可实现电源时域噪声仿真,完成电源完整性设计签核。当下部分仿真工具在AC阻抗优化过程中导出的S参数存在低频段无法覆盖的问题,影响时域纹波仿真精度,如果重新对S参数进行提取,又会增加仿真时间降低仿真效率。针对AC阻抗优化过程中导出的S参数无法覆盖低频段的问题,提出了一种电源网络S参数低频段拓展方法,结合电压调节模块(Voltage Regulator Module,VRM)的R-L模型,推导出低频段的S参数可以借用抽取的S参数中最低频点处的S参数实现低频段S参数的拓展。仿真和实验结果表明,通过对低频段S参数进行拓展,电源时域纹波噪声仿真的精度提升31%。同时,低频段的S参数直接借用已抽取的S参数中低频点的数值无须重复提取,在8 GB内存的配置下,仿真时间节约14%左右,提高了仿真效率。展开更多
In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Un...In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.展开更多
This paper provides the static and dynamic pullin behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron...This paper provides the static and dynamic pullin behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron scales. For this purpose, the governing equation of motion and the boundary conditions are driven using a variational approach. This formulation includes the influences of fringing field and intermolecular forces such as Casimir and van der Waals forces. The differential quadrature （DQ） method is employed as a high-order approximation to discretize the governing nonlinear differential equation, yielding more accurate results with a Considerably smaller number of grid points. In addition, a powerful analytical method called parameter expansion method （PEM） is utilized to compute the dynamic solution and frequency-amplitude relationship. It is illustrated that the first two terms in series expansions are sufficient to produce an acceptable solution of the mentioned structure. Finally, the effects of basic parameters on static and dynamic pull-in insta- bility and natural frequency are studied.展开更多
文摘In this paper, the singular perturbation of initial value problem for nonlinear second order vector differential equationsis discussed, where r>0 is an arbitrary constant, e>0 is a small parameter, x, f,a and Under suitable assumptions, by using the method of many-parameter expansion and the technique of diagonalization, the existence oj the solution of perturbation problem is proved and its uniformly valid asymptotic expansion of higher order is derived.
文摘This paper provides the static and dynamic pullin behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron scales. For this purpose, the governing equation of motion and the boundary conditions are driven using a variational approach. This formulation includes the influences of fringing field and intermolecular forces such as Casimir and van der Waals forces. The differential quadrature （DQ） method is employed as a high-order approximation to discretize the governing nonlinear differential equation, yielding more accurate results with a Considerably smaller number of grid points. In addition, a powerful analytical method called parameter expansion method （PEM） is utilized to compute the dynamic solution and frequency-amplitude relationship. It is illustrated that the first two terms in series expansions are sufficient to produce an acceptable solution of the mentioned structure. Finally, the effects of basic parameters on static and dynamic pull-in insta- bility and natural frequency are studied.
