Reduced Order Models of On-Chip Passive Components and Interconnects, Workbench and Test Structures [chapter]

Daniel Ioan, Gabriela Ciuprina
2008 Mathematics in Industry  
The models of passive components have to describe all relevant electromagnetic field effects at high frequency encountered inside these devices. These effects are quantified by the Maxwell equations of the electromagnetic field in full wave (FW) regime. Therefore, at the first level of approximation, the model of a passive device is defined by an electromagnetic (EM) field problem, formulated by Maxwell partial differential equations with appropriate boundary and initial conditions. This
more » ... itions. This problem defines a consistent I/O system which has a unique response, described by the output signals, for any input signal applied as terminal excitations. This system with distributed parameters has an infinite dimension state space, but a finite number of inputs and outputs related to the device terminals. The next level of approximation in the modeling process ( Fig. 1 ) results by applying a numerical method to discretize the continuous model defined above. This step associates a simpler ODE to the original PDE model, actually a system of DAE. It is an important step ahead, reducing the infinite dimensional state-space which is specific to distributed systems to a finite one. However, the size of the state-space is still too large for the designers needs. It has an order similar to the number of DOFs associated to the cells, finite elements used to discretize the computational domain. Fig. 1. Three levels of abstraction for a component model and its corresponding equations.
doi:10.1007/978-3-540-78841-6_20 fatcat:c3y7xu7u4zfchk6h3gryrnca6q