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=== Setting up a 2D Quasi-Static Solution of Transmission Lines Line Simulation ===

At 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), it is usually possible to perform a 2D electrostatic analysis of a transmission line structure and compute its . EM.Ferma computes the characteristics impedance Z₀ and effective permittivity &epsilon;_effof your TEM or quasi-TEM transmission line. This 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 &epsilon;_eff and Z₀.

<ol><li>First, you have remove all [[Image:Info_icon.png|40px]] Click here to learn more about the dielectric materials from your structure and replace them with free space (or air). Obtain a 2D electrostatic solution theory of your "air'''[[Electrostatic_and_Magnetostatic_Methods#2D_Quasi-filled" transmission line structure and compute its capacitance per unit length C_a.</li><li>Next, obtain a Static_Solution_of_Transmission_Lines | 2D electrostatic solution of your actual transmission line structure with all Quasi-Static Analysis of its dielectric parts and compute its true capacitance per unit length CTransmission Lines]]'''.</li></ol>

Then effective permittivity of the To perform a transmission line simulation, first draw your structure is then calculated from in the equation: <math> \epsilon_{eff} = \frac{C}{C_a} </math>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.

and its 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 is given by: Z<mathsub> Z_0 = \eta_0 \sqrt{ \frac{C_a}{C} } 0</mathsub>and effective permittivity &epsilon;_eff 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.

where &eta;₀ = 120&pi; &Omega; is the intrinsic impedance of the free space.  The guide wavelength of your transmission line at a given frequency f is then calculated from: <math> \lambda_g = \frac{\lambda_0}{\sqrt{\epsilon_{eff}}} = \frac{c}{f\sqrt{\epsilon_{eff}}} </math> and its propagation constant is given by: <math> \beta = k_0\sqrt{\epsilon_{eff}} = \frac{2\pi f}{c}\sqrt{\epsilon_{eff}} </math> where c is the speed of light in the free space.  EM.Ferma's 2D Quasi-Static mode automatically performs the two-step process described above and calculates &epsilon;_eff and Z₀. So you don't need to modify your structure in the first step.  === Setting up a Transmission Line Simulation === 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 Z₀ and effective permittivity &epsilon;_eff 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.