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== Modeling Transmission Lines Using EM.FermaThe 2D Electrostatic Simulation Mode==
[[Image:Qsource16.png|thumb|400px|Setting up a 2D solution plane for a microstrip line.]]
EM.Ferma's electrostatic simulation engine features a 2D solution mode where your physical 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 your project.
===To explore EM.Ferma's 2D Electrostatic Simulation Mode===mode, right-click on '''2D Solution Planes''' in the "Computational Domain" section of the navigation tree and select '''2D Domain Settings...''' from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified Below". This would enable you to add new 2D Solution Plane definitions to the list or edit the existing ones. 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.
You can also use EM.Ferma's electrostatic simulation engine features to perform a quasi-static analysis of multi-conductor transmission line structures, which usually provides good results at lower microwave frequencies (f < 10GHz). For that purpose, check the box labeled "Perform 2D Quasi-Static Simulation" when defining the 2D solution mode where your physical model is treated as a longitudinally infinite structure in plane. EM.Ferma computes the direction normal characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of your TEM or quasi-TEM transmission line. The results are written to specified two output data files named "2D Solution Planesolution_plane_Z0.DAT" and "solution_plane_EpsEff. More than one DAT", respectively, where "solution_plane" is the default name of your 2D solution plane may . At the end of a quasi-static analysis, the electric field components and scalar potential at the selected 2D planes will still be computed and can be definedvisualized. In that the caseof a parametric sweep, the data files will contain multiple 2D solutions are obtaineddata entries listed against the corresponding variable samples. A 2D solution plane is defined based on a "Field Sensor" definition that already exists Such data files can be plotted in your projectEM.Grid.
To explore EM[[Image:Info_icon.Ferma's 2D mode, right-click on '''2D Solution Planes''' in png|40px]] Click here to learn more about the "Computational Domain" section theory of the navigation tree and select '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.Cube#2D_Quasi-Static_Solution_of_Transmission_Lines | 2D Domain Settings...Quasi-Static Analysis of Transmission Lines]]''' from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified Below". This would enable you to add new 2D Solution Plane definitions to the list or edit the existing ones. 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 [[Image:Info_icon.png|40px]] Click here to learn more about the end theory of a 2D electrostatic analysis'''[[Modeling_Lumped_Elements, you can view the electric field _Circuits_%26_Devices_in_EM.Cube##Modeling_Transmission_Lines_Using_EM.Ferma | Modeling Transmission Lines Using EM.Ferma]]'''. The quantities ε<sub>eff</sub> and potential results on the respective field sensor planesZ<sub>0</sub> are two of EM. It is assumed that your structure is invariant along the direction normal Ferma's standard output [[parameters]]. You can use them to the 2D solution planeoptimize a transmission line structure. ThereforeTwo possible objectives are "Z<sub>0</sub> == 50" or "sqrt(ε<sub>eff</sub>) == 1.5". [[Image:Info_icon.png|40px]] Click here for a discussion of '''[[Parametric_Modeling, your computed field and potential profiles must be valid _Sweep_%26_Optimization#Optimization | Optimization in EM.Cube]]'''. For a step-by-step demonstration (including transmission line [[optimization]]), take a look at all the planes perpendicular to the specified longitudinal directionthis video on our YouTube channel: [http://www.youtube.com/watch?v=Iiu9rQf1QI4 EM. CUBE Microstrip Optimization]
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=== Setting up a 2D Quasi-Static Transmission Line Simulation ===
You can use EM.Ferma to perform a quasi-static analysis of multi-conductor transmission line structures, which usually provides good results at lower microwave frequencies (f < 10GHz). EM.Ferma computes the characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of your TEM or quasi-TEM transmission line. The "quasi-static approach" involves two steps, in which the capacitance of your transmission line structure is calculated once "As Is" and then with all the dielectric material replaced with air. EM.Ferma's 2D Quasi-Static mode automatically performs the two-step process and calculates ε<sub>eff</sub> and Z<sub>0</sub>.
[[Image:Info_icon.png|40px]] Click here to learn more about the theory of '''[[Electrostatic_and_Magnetostatic_Methods#2D_Quasi-Static_Solution_of_Transmission_Lines | 2D Quasi-Static Analysis of Transmission Lines]]'''.
To perform a transmission line simulation, first draw your structure in the project workspace just like a typical 3D structure. Define a "Field Sensor" observable in the navigation tree so as to capture the cross section of your structure as your desired transmission line profile.
Next, define a "2D Solution Plane" in the navigation tree based on your existing field sensor. When defining the 2D plane, check the box labeled "Perform 2D Quasi-Static Simulation". If an analysis is run with this option checked, the characteristic impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> will be computed for the corresponding 2D Solution Plane. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively, where "solution_plane" is the default name of your 2D plane.
Many 2D quasi-static solutions can be obtained in the same analysis, for example, when your design contains many types of [[Transmission Lines|transmission lines]]. At the end of a quasi-static analysis, the electric field components and scalar potential at the selected 2D planes will still be computed and can be visualized. In the case of a parametric sweep, the data files will contain multiple data entries listed against the corresponding variable samples. Such data files can be plotted in EM.Grid.
=== Optimizing a Transmission Line ===
In an [[optimization]] simulation, the values of one or more [[variables]] are varied over their specified ranges, and a design objective is tested at each simulation run. A design objective is typically a logical expression that sets an expression equal to a target value. EM.Ferma currently offers two standard outputs: ε<sub>eff</sub> and Z<sub>0</sub>. Two possible objectives are "Z<sub>0</sub> == 50" or "sqrt(ε<sub>eff</sub>) == 1.5". To define an objective, click the "Objectives" button of the Simulate Toolbar, or select the "Objectives" item of the Simulate Menu, or simply use the keyboard shortcut "Ctrl+J". In the Objectives Dialog, you can add new objective or edit the existing objectives.
For a step-by-step demonstration (including transmission line [[optimization]]), take a look at this video on our YouTube channel: [http://www.youtube.com/watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization]
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