== The 2D Electrostatic Simulation Mode==
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=== 2D Quasi-Static Solution of TEM Line Structures ===
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At lower microwave frequencies (f < 10GHz), multi-conductor transmission line structures usually support either a dominant transverse electromagnetic (TEM) propagating mode or a dominant quasi-TEM propagating mode. These modes are almost non-dispersive, and their behavior can be regarded as frequency-independent. As a result, it is usually possible to perform a 2D electrostatic analysis of a transmission line structure and compute its characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub>. The "quasi-static approach" to modeling of a TEM transmission line involves two steps:
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<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<sub>a</sub>.</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>
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Then effective permittivity of the transmission line structure is then calculated from the equation:
<math> \epsilon_{eff} = \frac{C}{C_a} </math>
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and its characteristic impedance is given by:
<math> Z_0 = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
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where η<sub>0</sub> = 120π Ω is the intrinsic impedance of the free space.
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The guide wavelength of your transmission line at a given frequency f is then calculated from:
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<math> \lambda_g = \frac{\lambda_0}{\sqrt{\epsilon_{eff}}} = \frac{c}{f\sqrt{\epsilon_{eff}}} </math>
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and its propagation constant is given by:
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<math> \beta = k_0\sqrt{\epsilon_{eff}} = \frac{2\pi f}{c}\sqrt{\epsilon_{eff}} </math>
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where c is the speed of light in the free space.
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=== Using EM.Ferma to Simulate 2D Transmission Lines ===
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[[Image:Qsource16.png|thumb|400px|A field sensor and 2D solution plane defined for a microstrip line.]]
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 as described above, which [[EM.Ferma]]'s 2D Quasi-Static mode automatically performs to calculate ε<sub>eff</sub> and Z<sub>0</sub>.
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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.
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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.
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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.
[[Image:Qsource16.png|thumb|400px|Setting up a 2D solution plane for a microstrip line.]]