Time-domain Formulation of a Multi-layer Plane Circuit Coupled with Lumped-parameter Circuits using Maxwell Equations

Area of Science:

• Computational Electromagnetics
• Electrical Engineering
• Applied Physics

Background:

• Maxwell's equations govern electromagnetic phenomena.
• Accurate modeling of multi-layer circuits is crucial for electronic design.
• Existing methods may face computational challenges with complex geometries.

Purpose of the Study:

• To develop a numerical method for calculating electromagnetic phenomena in multi-layer plane circuits.
• To model the time-dependent wave propagation of potential and current density.
• To create an efficient algorithm for boundary conditions in multi-layer structures.

Main Methods:

• Utilizing Maxwell's equations as the foundation.
• Applying the finite-difference time-domain (FDTD) method to solve transport equations.
• Discretizing plane conductors into finite-volume elements.
• Developing a boundary calculation method for multi-layer planes, adapted from multi-transmission line techniques.

Main Results:

• A numerical method for potential and current density in 2D conductors is presented.
• The time development of electromagnetic phenomena is treated as wave propagation.
• A calculation method for multi-layer plane boundaries coupled with lumped-parameter circuits is formulated.
• An algorithm is introduced to reduce computational costs for 2D extensions.

Conclusions:

• The developed method enables accurate calculation of electromagnetic phenomena in multi-layer plane circuits.
• The approach effectively models wave propagation of potential, current density, and charge density.
• The introduced algorithm offers computational efficiency for complex circuit analysis.