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== 2D Quasi-Static Solution of Modeling Transmission Lines Using EM.Ferma==

==2D Electrostatic Simulation Mode== EM.Ferma's electrostatic simulation engine features a 2D solution mode where the model is treated as a longitudinally infinite structure in the direction normal to specified "2D Solution Plane". More than one 2D solution plane may be defined. In that case, multiple 2D solutions are obtained. A 2D solution plane is defined based on a "Field Sensor" definition that already exists in the project. To explore EM.Ferma's 2D mode, right-click on "2D Solution Planes" in the navigation tree Navigation Tree and select "2D Domain Settings..."from the contextual menu. In the 2D Static Domain dialog, enable the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified Below". The user is then able to Add or Edit 2D Solution Plane definitions to the solution list. In the Add/Edit 2D Solution Plane dialog, you can choose a name other than the default name and select one of the available field sensor definitions in your project.  At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the respective field sensor planes. It is assumed that your structure is invariant along the direction normal to the 2D solution plane. Therefore, your computed field and potential profiles must be valid at all the planes perpendicular to the specified longitudinal direction.  === 2D Quasi-Static Solution of Transmission Lines === At lower microwave frequencies (f < 10GHz), it is usually possible to perform a 2D electrostatic analysis of a transmission line structure and compute its characteristics impedance Z₀ and effective permittivity &epsilon;_eff. This "quasi-static approach" involves two steps: <ol><li>First, you have remove all the dielectric materials from your structure and replace them with free space (or air). Obtain a 2D electrostatic solution of your "air-filled" transmission line structure and compute its capacitance per unit length C_a.</li><li>Next, obtain a 2D electrostatic solution of your actual transmission line structure with all of its dielectric parts and compute its true capacitance per unit length C.</li></ol> Then effective permittivity of the transmission line structure is then calculated from the equation:  and its characteristic impedance is given by: 

To perform a Transmission Line transmission line simulation,    first turn on Quasistatic simulation mode for a selected 2D Solution Plane, as shown in the figure at right. If an analysis is run with this option checked, the characteristic impedance (Z0) and Effective Epsilon will be computed for the corresponding 2D Solution Plane. This output can be found in appropriately-named text files in the project directory upon completion of the simulation. Fields and potentials at the selected 2D plane will still be computed. Many 2D quasistatic solutions can be obtained in the same analysis, if for example, your design contains many types of [[Transmission Lines|transmission lines]].