Technology
A continuum model constructed using the effective current density method: a two dimensional, interlaced, symmetric conducting grid
The two dimensional conducting grid illustrated in the figure consists of two interlaced networks called grid 1 and grid 2. This type of grid can be used to carry power and/or current and voltage signals across an integrated circuit or printed circuit board. The grid may also propagate unwanted signals or noise. Typically this type of grid will be much larger and will contain many more wiring elements than shown here. The grid is two dimensional in the sense that the short vertical conductors that connect the horizontal conductors at crossover points are assumed to have negligible impedance. This particular network is constructed using wires routed in orthogonal directions. Voltage and current flow in this type of grid is conveniently represented in a Cartesian coordinate system. Other types of grid with different geometry may be represented using a different set of basis vectors.
The type of network shown in the figure can be simulated using methods such as SPICE and SPICE derivatives as described in the prior art. In these methods the grid is deconstructed to form a connected network of short wiring elements. Each wire element is represented by a combination of resistance, capacitance and inductance models (RLC models) or, alternatively, by a transmission line model. These methods have the disadvantage that the simulation time grows with the wire density in the grid. A network with a large number of wire elements per unit area can often result in excessive numbers of RLC or transmission line components in the final netlist. The requirements for a full, dynamic, RLC simulation for a large network can often exceed the capability of available computing hardware.
A large netlist or part of a netlist can be replaced by continuum models derived using the effective current density method. The run time for the equivalent of a full RLC simulation using a continuum model remains constant as the number of wire elements per unit area grows. This means that the method can be used to reduce overall simulation times, particularly in systems containing large, dense wiring networks.