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2-D Field Solver

The 2-D field solver in RF PCB Toolbox™ allows you to model and analyze the cross sections of multiconductor transmission lines in a multilayered dielectric above the ground plane such as a microstrip line. For more detailed information, see [1]

The four primary transmission line parameters are the resistance R, the inductance L, the conductance G and the capacitance C. You can obtain these parameters by applying a total charge on the conductor-to-dielectric interfaces and a polarization charge on the dielectric-to-dielectric interfaces and solving the created electrostatic field created. The 2-D field solver uses pulse approximation for the total charge σT and discretizes the contours of the conductor-to-dielectric and dielectric-to-dielectric interfaces using straight-line segments. The densities of the segments are controlled by the distribution of nodes along the contours. This figure shows the discretization for a single-conductor transmission line in a single-layered dielectric above the ground plane.

At any point p in the YZ plane and above the ground plane, the potential ϕ is due to the combination of σT and the image of σT about the ground plane.


where lj is the contour of jth interface in the YZ plane, dl' is the differential element of length at p' on lj, and p^' is the image of p' about the ground plane.

The electric field is then given by φ


The normal component of a displacement field is continuous across the dielectric-to-dielectric interface. You can derive the second integral by substituting the interface conditions for the displacement fields with Ep. You can solve the set of integral equations for a total charge σT using the methods of moments solver and as described in [2]. You can analyze the skin effect and the conductor and dielectric losses.



[1] Djordjevis, Antonije R., Miodrag B. Bazdar, Tapan K. Sarkar and Roger F. Harrington, Linpar for Windows: Matrix Parameters for Multiconductor Transmission Lines. Artech House, 1999

[2] Harringhton, R. F. Field Computation by Moment Methods. New York, Macmillan, 1968