[[Image:Splash-static.jpg|right|720px]]<strong><font color="#2603c4" size="4">Electrostatic, Magnetostatic & Thermal Solvers For DC And Low Frequency Simulations</font></strong><table><tr><td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.FermaTempo]] is [[image:prop-ico.png | link=EM.CubeTerrano]] [[image:planar-ico.png |link=EM.CUBEPicasso]]'s 3D static solver[[image:metal-ico. It features two distinct electrostatic and magnetostatic simulation engines that can be used to solve a variety of static and lowpng | link=EM.Libera]] [[image:po-frequency electromagnetic problemsico. Both simulation engines are based on finite difference solutions of Poissonpng | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] 's equation for electric and magnetic potentials''[[EM. Cube#EM.Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''
With [[Image:Back_icon.png|30px]] '''[[EM.Ferma, you can explore the electric fields due Cube | Back to volume charge distributions or fixed-potential perfect conductors, and magnetic fields due to wire or volume current sources and permanent magnets. Your structure may include dielectric or magnetic (permeable) material blocks. You can also use EM.FermaCube Main Page]]'s 2D quasi-static mode to compute the characteristic impedance (Z0) and effective permittivity of transmission line structures with complex cross section profiles.''==Product Overview==
== Methods Of Electrostatics & Magnetostatics= EM.Ferma in a Nutshell ===
EM.Ferma solves is a 3D static solver. It features two distinct electrostatic and magnetostatic simulation engines and a steady-state thermal simulation engine that can be used to solve a variety of static and low-frequency electromagnetic and thermal problems. The thermal solver includes both conduction and convection heat transfer mechanisms. All the three simulation engines are based on finite difference solutions of Poisson 's equation for the electric scalar potential subject to specified boundary conditions:and magnetic potentials and temperature.
<math>\Delta\PhiWith EM.Ferma, you can explore the electric fields due to volume charge distributions or fixed-potential perfect conductors, and magnetic fields due to wire or volume current sources and permanent magnets. Your structure may include dielectric or magnetic (\mathbf{r}permeable) = \nabla^2 \Phi(\mathbf{r}) = material blocks. Using the thermal simulator, you can solve for the steady-state temperature distribution of structures that include perfect thermal conductors, insulators and volume heat sources. You can also use EM.Ferma's 2D quasi-\frac{\rhostatic mode to compute the characteristic impedance (\mathbf{r}Z0)}{\epsilon}</math>and effective permittivity of transmission line structures with complex cross section profiles.
[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Electrostatic & Magnetostatic Field Analysis | Theory of Electrostatic and Magnetostatic Methods]]'''.
where Φ(<b>r</b>) is [[Image:Info_icon.png|30px]] Click here to learn more about the electric scalar potential, ρ(<b>r</b>) is the volume charge density, and ε = ε<sub>r</sub> ε<sub>0</sub> is the permittivity '''[[Steady-State_Thermal_Analysis | Theory of the mediumSteady-State Heat Transfer Methods]]'''.
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[[Image:Magnet lines1.png|thumb|left|400px| Vector plot of magnetic field distribution in a cylindrical permanent magnet.]]
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The electric field boundary conditions at === EM.Ferma as the interface between two material media are:Static Module of EM.Cube ===
<math> \hat{\mathbf{n}} EM. [ \mathbf{D_2(r)} Ferma is the low- \mathbf{D_1(r)} frequency '''Static Module''' of '''[[EM.Cube] = \rho_s (\mathbf{r}) </math>]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Ferma shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD]] with all of [[EM.Cube]]'s other computational modules.
[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.
<math> \hat{\mathbf{n}} \times [ \mathbf{E_2(r)} - \mathbf{E_1(r)} ] = 0 </math>== Advantages & Limitations of EM.Ferma's Static Simulator ===
EM.Ferma computes the electric and magnetic fields independent of each other based on electrostatic and magnetostatic approximations, respectively. As a result, any "electromagnetic" coupling effects or wave retardation effects are ignored in the simulation process. In exchange, static or quasi-static solutions are computationally much more efficient than the full-wave solutions of Maxwell's equations. Therefore, for low-frequency electromagnetic modeling problems or for simulation of sub-wavelength devices, EM.Ferma offers a faster alternative to [[EM.Cube]]'s full-wave modules like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]]. EM.Ferma currently provides a fixed-cell brick volume mesh generator. To model highly irregular geometries or curved objects, you may have to use very small cell sizes, which may lead to a large computational problem.
where <mathtable> \hat{\mathbf{n}} </mathtr> is the unit normal vector at the interface pointing from medium 1 towards medium 2,<btd>D[[Image:Ferma L8 Fig title.png|thumb|left|400px| Vector plot of electric field distribution in a coplanar waveguide (rCPW)transmission line.]]</btd> = ε<b>E(r)</btr> is the electric flux density, <b>E(r)</btable> is the electric field vector, and ρ<sub>s</sub> is the surface charge density at the interface.
== EM.Ferma Features at a Glance ==
In a source-free region, ρ(<b>r</b>) = 0, and Poisson's equation reduces to the familiar Laplace equation: == Physical Structure Definition ===
<mathul>\Delta\Phi <li> Perfect electric conductor(\mathbf{r}PEC) = \nabla^2 \Phisolids and surfaces (\mathbf{r}Electrostatics) = 0</mathli> <li> Dielectric objects (Electrostatics)</li> <li> Magnetic (permeable) objects (Magnetostatics)</li> <li> Perfect thermal conductor (PTC) solids and surfaces (Thermal)</li> <li> Insulator objects (Thermal)</li></ul>
=== Sources ===
Keep in mind that in the absence of an electric charge source, you need to specify a non<ul> <li> Fixed-zero potential somewhere in your structure, PEC for example, on a perfect electric conductor maintaining equi-potential metal objects (PECElectrostatics)</li> <li> Volume charge sources (Electrostatics)</li> <li> Volume current sources (Magnetostatics)</li> <li> Wire current sources (Magnetostatics)</li> <li> Permanent magnets (Magnetostatics)</li> <li> Fixed-temperature PTC for maintaining iso-thermal objects (Thermal)</li> <li> Volume heat sources (Thermal). Otherwise, you will get a trivial zero solution of the Laplace equation. </li></ul>
=== Mesh generation ===
Once the electric scalar potential is computed, the electric field can easily be computed via the equation below: <ul> <li> Fixed-size brick cells</li></ul>
<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r})</math>== 3D Electrostatic & Magnetostatic Simulation ===
<ul>
<li>
Finite difference solution of Laplace and Poisson equations for the electric scalar potential with Dirichlet and Neumann domain boundary conditions </li>
<li>
Finite difference solution of Laplace and Poisson equations for the magnetic vector potential with Dirichlet domain boundary conditions </li>
<li>
Calculation of electric scalar potential and electric field</li>
<li>
Calculation of magnetic vector potential and magnetic field</li>
<li>
Calculation of electric flux over user defined flux boxes and capacitance</li>
<li>
Calculation of magnetic flux over user defined flux surfaces and inductance</li>
<li>
Calculation of electric and magnetic energies, Ohmic power loss and resistance</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
</ul>
EM.Ferma also solves the Poisson equation for the magnetic vector potential subject to specified boundary conditions:=== 2D Quasi-Static Simulation ===
<mathul>\Delta \mathbf{A} (\mathbf{r}) = \nabla^2 \mathbf{A}(\mathbf{r}) = - \mu \mathbf{J}(\mathbf{r}) <li> 2D Finite difference solution of cross section of transmission line structures</li> <li> 3D domain solution as well as 2D solution of a longitudinally infinite version of the structure defined on a 2D plane </li> <li> Calculation of electric potential and electric field distribution</li> <li> Parametric sweep of transmission line's geometric and material parameters</li> <li> Optimization of transmission line's parameters for impedance design</li></mathul>
=== Steady-State Thermal Simulation ===
where <bul>A(r) </bli> is Finite difference solution of Laplace and Poisson equations for the magnetic vector potential, temperature with Dirichlet and Neumann domain boundary conditions <b/li>J(r) </bli> is the volume current density, Calculation of temperature and μ = μheat flux density<sub/li>r <li> Calculation of thermal energy density on field sensor planes</subli> μ <subli>0 Calculation of thermal flux over user defined flux boxes</subli> is the permeability of the medium. The magnetic Poisson equation is vectorial in nature and involves a system of three scalar differential equations corresponding to the three components <li> Calculation of thermal energy<b/li>A(r)</bul>.
=== Data Generation & Visualization ===
The <ul> <li> Electric and magnetic field boundary conditions at the interface between two material media are:intensity and vector plots on planes</li> <li> Electric and magnetic potential intensity plots on planes</li> <li> Temperature and heat flux intensity and vector plots on planes</li> <li> Electric and magnetic energy density, dissipated power density and thermal energy density plots on planes</li> <li> Animation of field and potential plots after parametric sweeps</li> <li> Graphs of characteristic impedance and effective permittivity of transmission line structures vs. sweep variables</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
<math> \hat{\mathbf{n}} == Building the Physical Structure in EM. [ \mathbf{B_2(r)} - \mathbf{B_1(r)} ] Ferma == 0 </math>
=== Variety of Physical Objects in EM.Ferma ===
<math> \hat{\mathbf{n}} \times [ \mathbf{H_2The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the boundary of the computational domain. As soon as you introduce a dielectric object next to a charge source or a magnetic (rpermeable)} - \mathbf{H_1material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson equation subject to the domain boundary conditions as well as material interface boundary conditions. The simplest thermal problem involves one or more thermal plates held at fixed temperatures. Once you introduce material blocks, you have to enforce conductive and convective boundary conditions at the interface between different materials and air. EM.Ferma uses the Finite Difference (rFD)} ] = \mathbf{J_s(r)} </math>technique to find a numerical solution of your static boundary value problem.
[[EM.Ferma]] offers the following types of physical objects:
where <math> \hat{\mathbf{n}} </math> is the unit normal vector at the interface pointing from medium 1 towards medium 2,| class="wikitable"<b>B|-! scope="col"| Icon! scope="col"| Physical Object Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Notes & Restrictions|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Fixed-Potential PEC |Fixed-Potential Perfect Electric Conductor (rPEC)<]]| style="width:300px;" | Modeling perfect metals with a fixed voltage| style="width:100px;" | Solid and surface objects| style="width:250px;" | Can be considered an electric source if the fixed voltage is nonzero |-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric/b> Magnetic Material]]| style= "width:300px;" | Modeling any homogeneous or inhomogeneous material| style="width:100px;" | Solid objects| style="width:250px;" | non-source material|-| style="width:30px;" | [[File:aniso_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices &muOther Physical Object Types#Volume Charge |Volume Charge]]| style="width:300px;<b>H" | Modeling volume charge sources with a fixed charge density or an expression in the global coordinates (rx,y,z)</b> is | style="width:100px;" | Solid objects| style="width:250px;" | Acts as an electric source|-| style="width:30px;" | [[File:voxel_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Current |Volume Current]]| style="width:300px;" | Modeling volume current sources with a fixed volume current density vector or expressions in the global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a magnetic flux densitysource|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, <b>HSources, Devices & Other Physical Object Types#Permanent Magnet |Permanent Magnet]]| style="width:300px;" | Modeling permanent magnet sources with a fixed magnetization vector or expressions in the global coordinates (rx,y,z)</b> is the | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a magnetic field vectorsource|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Current |Wire Current]]| style="width:300px;" | Modeling wire current sources| style="width:100px;" | Line and <b>J<sub>polyline objects| style="width:250px;" | Acts as a magnetic source|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's</sub></b> Materials, Sources, Devices & Other Physical Object Types#Fixed-Temperature PTC |Fixed-Temperature Perfect Thermal Conductor (PTC)]]| style="width:300px;" | Modeling isothermal surfaces with a fixed temperature| style="width:100px;" | Solid and surface objects| style="width:250px;" | Can be considered a thermal source if the fixed temperature is different than the surface current ambient temperature (shares the same navigation tree node as PEC object)|-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Insulator Material]]| style="width:300px;" | Modeling any homogeneous or inhomogeneous material| style="width:100px;" | Solid objects| style="width:250px;" | non-source material (shares the same navigation tree node as dielectric material)|-| style="width:30px;" | [[File:aniso_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Heat Source |Volume Heat Source]]| style="width:300px;" | Modeling volume heat sources with a fixed heat density at or an expression in the interfaceglobal coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a thermal source (shares the same navigation tree node as volume charge)|-| style="width:30px;" | [[File:Virt_group_icon. png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:100px;" | All types of objects| style="width:250px;" | None|}
Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].
Once the magnetic vector potential is computed, the magnetic field can easily be computed via the equation below: === Grouping Objects by Material or Source Type ===
<math> \mathbf{H(r)} = \frac{1}{\mu} \nabla \times \mathbf{A} (\mathbf{r})</math>Your physical structure in EM.Ferma is typically made up of some kind of source object either in the free space or in the presence of one or more material objects. EM.Ferma's electrostatic and magnetostatic or thermal simulation engines then discretize the entire computational domain including these source and material objects and solve the Laplace or Poisson equations to find the electric or magnetic fields or temperature everywhere in the computational domain.
== A Note on Material All the geometric objects in the project workspace are organized together into object groups which share the same properties including color and Source Types electric or magnetic parameters. It is recommended that you first create object groups, and then draw new objects under the active group. To create a new object group, right-click on its category name in the "Physical Structure" section of the navigation tree and select one of the "Insert New Group..." items from the contextual menu. However, if you start a new EM.Ferma ==project from scratch, and start drawing a new object without having previously defined any object groups, a new default "Fixed-Potential PEC" object group with a zero voltage is created and added to the navigation tree to hold your new geometric object.
In [[EM.Cube]]'s other modules, material types are specified under the "Physical Structure" section of the Navigation Tree, and sources are organized under It is important to note that there is a separate "Sources" section. In those modules, the physical structure one-to-one correspondence between electrostatic and its various material types typically represent all the CAD objects you draw in your project. Sources are virtual thermal simulation entities that might be associated with certain physical objects and provide the excitation of your boundary value problem. :
{| class="wikitable"
|-
! scope="col"| Electrostatic Item
! scope="col"| Corresponding Thermal Item
|-
| style="width:200px;" | Electric Scalar Potential
| style="width:200px;" | Temperature
|-
| style="width:200px;" | Electric Field
| style="width:200px;" | Heat Flux Density
|-
| style="width:200px;" | Perfect Electric Conductor
| style="width:200px;" | Perfect Thermal Conductor
|-
| style="width:200px;" | Dielectric Material
| style="width:200px;" | Insulator Material
|-
| style="width:200px;" | Volume Charge
| style="width:200px;" | Volume Heat Source
|}
In [[EM.Cube]]'s Static Module, materials {{Note|Electrostatic and sources are all listed under thermal solvers share the "Physical Structure" section of same material categories on the Navigation Tree, and there is no separate "Sources" sectionnavigation tree. For example, you can define default zero-potential perfect electric conductors (This means that PEC) in your project to model metal objects. You can also define fixed-potential PEC are treated as PTC objects with a nonzero voltage, which can effectively act dielectric objects are treated as a voltage source for your boundary value problem. In this case, you will solve the Lapalce equation subject to the specified nonzero potential boundary values. Both types of PEC insulator objects are defined from the same PEC node of the Navigation Tree by assigning different voltage values. Charge and current sources volume charges are defined treated as CAD objects that you must draw in volume heat sources when the project workspacethermal solver is enabled.}}
== Defining Once a new object group node has been created in the Physical Structure navigation tree, it becomes and remains the "Active" object group, which is always listed in EMbold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active object group. There is only one object group that is active at any time. Any group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.Ferma ==
The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the computational domain boundary[[Image:Info_icon. As soon as you introduce a dielectric object next png|30px]] Click here to a charge source learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic PoissonModules | Moving Objects among Different Groups]]'''s equation subject to the domain boundary conditions as well as material interface boundary conditions. EM.Ferma used the Finite Difference technique for numerical solution of your static boundary value problem.
For static analysis, the model can be excited with any number of Voltage Sources, Charge Sources, or Current Sources<table><tr><td> [[Image:STAT MAN1. For Quasistatic analysis, only Voltage Sources are of practical usepng|thumb|left|480px|EM.Ferma's navigation tree.]] </td></tr></table>
=== A Note on Material and Source Types in EM.Ferma ===
=== Fixed-Potential PEC Objects===In [[EM.Cube]]'s other modules, material types are categorized under the "Physical Structure" section of the navigation tree, and sources are organized under a separate "Sources" section. In those modules, all the geometric objects you draw in your project workspace typically represent material bodies. All of [[EM.Cube]] modules except for EM.Ferma require at least one excitation source to be selected from the "Sources" section of the navigation tree before you can run a simulation.
A perfect electric conductor (PEC) is a material with ε<sub>r</sub> = 1 In EM.Ferma, materials and σ = ∞. Under sources are all lumped together and listed under the static condition, every point on a PEC object has "Physical Structure" section of the same electric potentialnavigation tree. By defaultIn other words, this there is a no separate "Sources" section. For example, you can define default zero -potential, assuming the perfect electric conductors (PEC object is "grounded") in your project to model metal objects. You can also define fixed-potential PEC objects with a nonzero voltage value , which can effectively act as a voltage source for a PEC groupyour boundary value problem. In that this case, you will solve the Lapalce equation subject to the specified nonzero potential boundary values. Both types of PEC objects are defined from the same PEC object is effective turned into a node of the navigation tree by assigning different voltage sourcevalues. For exampleCharge and current sources are also defined as geometric objects, tow parallel PEC plates, one with a zero potential and you have to draw them in the project workspace just like other with a nonzero potential represent a simple air-filled capacitormaterial objects.
To add a new Fixed-Potential PEC group to a project, right-click on "Fixed-Potential PEC Objects" on the Navigation Tree, and select "Insert New PEC..." From the PEC dialog, you can change the default red color and set a value for the "Voltage" in Volts== EM. Ferma's Computational Domain ==
{{Note| You can define any solid or surface object as a fixed-potential PEC object.}} ===The Domain Box===
In EM.Ferma, the Poisson or Laplace equations are solved subject to boundary conditions using the Finite Difference technique. As a result, you need to specify a finite computational domain and then specify the domain boundary conditions. EM.Ferma's computational domain defines where the domain boundary condition will be specified. A default domain box is always placed in the project workspace as soon as you draw your first object. The domain can be seen as a blue cubic wireframe that surrounds all of the CAD objects in the project workspace.
=== Dielectric/Magnetic Materials === To modify the domain settings, click the Domain button of the Simulate Toolbar or right-click on "3D Static Domain" entry in the Navigation Tree and select "Domain Settings..." from the contextual menu. In the Domain Settings Dialog, the computational domain can be defined in two different ways: Default and Custom. The default type places an enclosing box with a specified offset from the largest bounding box of your project's CAD objects. The default offset value is 20 project units, but you can change this value arbitrarily. The custom type defines a fixed domain box by specifying the coordinates of its two opposite corners labeled Min and Max in the world coordinate system.
In electromagnetic analysis, a general dielectric material is represented by four constitutive material [[parameters]]: relative permittivity ε<subtable>r</subtr>, relative permeability μ<sub>r</sub>, electric conductivity σ and magnetic conductivity σ<sub>m</subtd>[[Image:Qsource5. In png|thumb|left|480px|EM.Ferma, you can define dielectric materials for electrostatic analysis and magnetic (permeable) materials for magnetostatic analysis from the same section of the Navigation Tree titled "Dielectric/Magnetic Materials"'s Domain Settings dialog. For a dielectric material, you specify the relative permittivity ε]] <sub/td>r</subtr> and electric conductivity σ. For a magnetic material, you specify the relative permeability μ<sub>r</subtable>.
To add a new dielectric or magnetic material group to a project, right-click on "Dielectric/Magnetic Materials" on the Navigation Tree, and select "Insert New Dielectric..." From the Dielectric Dialog, you can change the default green color of a material group or set the values of the material [[parameters]]. ===Domain Boundary Conditions===
{{Note| You can define any solid object *EM.Ferma allows you to specify the electric potential boundary conditions on the domain box. Two options are available. The Dirichlet boundary condition is the default option and is specified as a dielectric or magnetic material objectfixed potential value on the surface of the domain walls. By default, this value is 0 Volts. The Neumann boundary condition specifies the normal derivative of the electric scalar potential on the surface of the domain walls. This is equivalent to a constant normal electric field component on the domain walls and its value is specified in V/m.}}
*The magnetostatic simulation engine always assumes Dirichlet domain boundary conditions and sets the values of the magnetic vector potential to zero on all the domain walls.
=== Volume Charge Sources === *EM.Ferma provides two options for thermal boundary conditions on the domain box. The Dirichlet boundary condition is the default option and is specified as a fixed temperature value on the surface of the domain walls. By default, this value is 0°C. The Neumann boundary condition specifies the normal derivative of the temperature on the surface of the domain walls. This is equivalent to a constant heat flux passing through the domain walls and its value is specified in W/m<sup>2</sup>. A zero heat flux means a perfectly insulated domain box and is known as the adiabatic boundary condition.
You can define volume charge sources with a specified charge density in C/m<sup>3</sup> confined to certain region of your project. You use [[EM.Cube]]'s [[Solid Objects|solid objects]] to define volume charge sources. All the charge sources belonging to the same group have the same color and same charge density value. The charge density can be positive or negative. To add a new charge source group to a projectmodify the boundary conditions, right-click on "Volume ChargesBoundary Conditions" on in the Navigation Treenavigation tree, and select "Insert New Charge SourceBoundary Conditions..." From from the Charge Source contextual menu to open the Boundary Conditions Dialog. When you switch from the electrostatic-magnetostatic solver to the thermal solver in EM.Ferma's Run Simulation dialog, it automatically checks the box labeled '''Treat as a Thermal Structure''' in the Boundary Conditions dialog. Conversely, if you can change check this box in the default purple color Boundary Conditions dialog, the solver type is set to the thermal solver in the Simulation Run dialog. In the "Global Thermal Properties" section of the source group or Boundary Conditions dialog, you can set the values of the Charge Densityambient temperature in °C, thermal conductivity of the environment in W/(m.K) and the convective coefficient in W/(m<sup>2</sup>.K). You can also disable the enforcement of the convective boundary condition on the surface of solid insulator objects.
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<td> [[Image:fermbc.png|thumb|left|480px|EM.Ferma's Boundary Conditions dialog.]] </td>
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=== Volume Current Sources =EM.Ferma's Simulation Data & Observables ==
You can define volume current sources with a specified current density in A/m<sup>2</sup> confined to certain region At the end of your projectan electrostatic simulation, the electric field vector and electric scalar potential values are computed at all the mesh grid points of the entire computational domain. Note that current density is a vectorial quantity At the end of an magnetostatic simulation, the magnetic field vector and has a magnitude and unit direction magnetic vectorpotential values are computed at all the grid nodes. You use [[EM.Cube]]'s [[Solid Objects|solid objects]] to define volume current sources. All At the volume current sources belonging to end of a thermal simulation, the same group have the same color temperature and same current density magnitude and unit heat flux vectorare computed at all the mesh grid points of the entire computational domain.
To add Besides the electric and magnetic fields and temperature, EM.Ferma can compute a new volume number of field integral quantities such as voltage, current source group to a project, right-click on "Volume Currents" on the Navigation Treeflux, and select "Insert New Current Source.energy, etc.." From the Volume Current Source DialogThe field components, you potential values and field integrals are written into output data files and can change be visualized on the default brown color of the source group screen or set graphed in Data Manager only if you define a field sensor or a field integral observable. In the values absence of any observable defined in the navigation tree, the Current Density magnitude static simulation will be carried out and unit direction vector components. The default direction vector is z-directedcompleted, but no output simulation data will be generated.
EM.Ferma offers the following types of output simulation data:
{| class="wikitable"|-! scope="col"| Icon! scope= Wire Current Sources "col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Ferma allows you to define idealized wire current sources. You can use this source type to model filament currents or coils. Wire currents are defined using only line Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and polyline objects. You also need to define a current value I in Amperes magnetic field components, electric scalar potential and magnitude of magnetic vector potential on a wire radius r in the project units. The line or polyline object is then approximated as a volume current with a current density planar cross section of J the computational domain |-| style= I/(&pi"width:30px;r<sup>2</sup>) flowing along the line or polyline side's direction" | [[File:fieldsensor_icon. All the wire current sources belonging to the same group have the same color, same current value png]]| style="width:150px;" | Electric and same wire radius. The direction Magnetic Energy and Dissipated Power Density Maps | style="width:150px;" | [[Glossary of the current can be reversed in wire current sourcesEM.  To add a new wire current source group to a project, rightCube's Simulation Observables & Graph Types#Near-click on Field_Sensor_Observable |Near-Field Sensor]] | style="Wire Currentswidth:450px;" | Computing electric and magnetic energy densities and dissipated power density on a planar cross section of the Navigation Tree, and select computational domain |-| style="Insert New Current Source..width:30px;" | [[File:fieldsensor_icon.png]]| style=" From the Wire Current Source Dialog, you can change the default brown color of the source group or set the values of the Current width:150px;" | Temperature and Wire Radius. There is also a check box for Heat Flux Distribution Maps| style="Reverse Current Directionwidth:150px;". Note that this will reverse the direction | [[Glossary of all the wire currents belonging to the same groupEM. When you draw a line or polyline object under a wire current group in the Navigation Tree, you will notice that direction arrows are placed on the drawn CAD object. You can draw any curve object in the project workspace Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing temperature and convert it to heat flux components on a polyline using planar cross section of the computational domain |-| style="width:30px;" | [[EMFile:fieldsensor_icon.Cubepng]]'s Polygonize Tool. | style="width:150px;" | Thermal Energy Density Maps {{Note| If you draw [style="width:150px;" | [[Curve ObjectsGlossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]]] under | style="width:450px;" | Computing thermal energy density on a wire current group, they will be permanently converted to polyline objects before running planar cross section of the simulation engine.}} computational domain |-| style=== Permanent Magnets=== A permanent magnet is typically a ferromagnetic material with a fixed inherent magnetization vector"width:30px;" | [[File:field_integ_icon. As a result, it can be used as a source in an magnetostatic problem. When a permeable material has a permanent magnetization, the following relationship holds: png]]  <math> \mathbf{B(r)} | style= {\mu} (\mathbf{H(r)} + \mathbf{M(r)} ) </math>"width:150px;" | Field Integral Quantities  where <b>M(r)</b> is the magnetization vector| style="width:150px;" | [[Glossary of EM. In SI units systemCube's Simulation Observables & Graph Types#Static_Field_Integral_Observable | Static Field Integral]] | style="width:450px;" | Computing line, surface and volume integrals of the electric and magnetic field <b>H</b> fields and magnetization <b>M</b> both have the same units of A/m. heat flux |}
It can be shown that for magnetostatic analysis, Click on each category to learn more details about it in the effect [[Glossary of the permanent magnetization can be modeled as an equivalent volume current source:EM.Cube's Simulation Observables & Graph Types]].
<table><mathtr> \mathbf{J_{eq}(r)} = \nabla \times \mathbf{M(r)} <td> [[Image:Ferma L1 Fig15.png|thumb|left|640px|Electric field distribution of a spherical charge on a horizontal field sensor plane.]] </td></tr> <tr> <td> [[Image:Ferma L1 Fig16.png|thumb|left|640px|Electric scalar potential distribution of a spherical charge on a horizontal field sensor plane.]] </td></tr></mathtable>
The table below list the different types of field integrals and their definitions:
If the magnetization vector is uniform and constant inside the volume, then its curl is zero everywhere inside the volume except on its boundary surface. In this case, the permanent magnetic can be effectively modeled by an equivalent surface current density on the surface of the permanent magnetic object: Â Â <math> \mathbf{J_{s,eq}(r)} = \mathbf{M(r)} \times \hat{\mathbf{n}} </math>Â Â where <math> \hat{\mathbf{n}} </math> is the unit outward normal vector at the surface of the permanent magnet object. Note that the volume of the permanent magnet still acts as a permeable material in the magnetostatic analysis. Â To add a new permanent magnet source group to a project, right-click on "Permanent Magnets" on the Navigation Tree, and select "Insert New Permanent Magnet Source..." From the Permanent Magnet Source Dialog, you can change the default purple color of the source group or set the values of the relative permeability, Magnetization magnitude and unit direction vector components. The default direction vector is z-directed. Â Â {| borderclass="0wikitable"
|-
| valign! scope="topcol"|Field Integral[[File:vsource.png|thumb|left|250px|EM.Ferma's Voltage Source Dialog]]| valign! scope="bottomcol"|Definition[[File:qsource.png|thumb|left|250px|EM.Ferma's Charge Source Dialog]]| valign! scope="topcol"|[[Output Data File:isource.png|thumb|left|250px|EM.Ferma's Current Source Dialog]]
|-
! scope="row"| Voltage
| <math> V = - \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| voltage.DAT
|-
! scope="row"| Current
| <math> I = \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| current.DAT
|-
! scope="row"| Conduction Current
| <math> I_{cond} = \int\int_S \mathbf{J(r)} . \mathbf{ds} = \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| conduction_current.DAT
|-
! scope="row"| Electric Flux
| <math> \Phi_E = \int\int_{S_o} \mathbf{D(r)} . \mathbf{ds} = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} </math>
| flux_E.DAT
|-
! scope="row"| Magnetic Flux
| <math> \Phi_H = \int\int_S \mathbf{B(r)} . \mathbf{ds} = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} </math>
| flux_H.DAT
|-
! scope="row"| Electric Energy
| <math> W_E = \frac{1}{2} \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv </math>
| energy_E.DAT
|-
! scope="row"| Magnetic Energy
| <math> W_H = \frac{1}{2} \int\int\int_V \mu \vert \mathbf{H(r)} \vert ^2 dv </math>
| energy_H.DAT
|-
! scope="row"| Ohmic Power Loss
| <math> P_{ohmic} = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| ohmic.DAT
|-
! scope="row"| Capacitance
| <math> C = \Phi_E/V = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} / \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| capacitance.DAT
|-
! scope="row"| Capacitance (Alternative)
| <math> C = 2W_E/V^2 = 2 \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv / \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2</math>
| capacitance.DAT
|-
! scope="row"| Self-Inductance
| <math> L = \Phi_H/I = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| inductance.DAT
|-
! scope="row"| Self-Inductance (Alternative)
| <math> L = 2W_M/I^2 = 2 \int \int \int_V \mu \vert \mathbf{H(r)} \vert ^2 dv / \left( \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} \right)^2</math>
| inductance.DAT
|-
! scope="row"| Mutual Inductance
| <math> M = \Phi_H^{\prime}/I = \int\int_{S^{\prime}} \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| mutual_inductance.DAT
|-
! scope="row"| Resistance
| <math> R = V/I_{cond} = - \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| resistance.DAT
|-
! scope="row"| Resistance (Alternative 1)
| <math> R = V^2/P_{ohmic} = \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2 / \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| resistance.DAT
|-
! scope="row"| Resistance (Alternative 2)
| <math> R = P_{ohmic}/I_{cond}^2 = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv / \left( \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} \right)^2</math>
| resistance.DAT
|-
! scope="row"| Thermal Flux
| <math> \Phi_T = \int\int_{S_o} \mathbf{q(r)} . \mathbf{ds} </math>
| flux_T.DAT
|-
! scope="row"| Thermal Energy
| <math> W_T = Q = \int \int \int_V \rho_V c_p \left( T\mathbf{(r)} - T_{env} \right) dv </math>
| energy_T.DAT
|}
<table>
<tr>
<td>
[[Image:Qsource13.png|thumb|left|480px|Defining the capacitance observable in the field integral dialog.]]
</td>
</tr>
<tr>
<tr>
<td>
[[Image:Qsource11.png|thumb|left|480px|The electric flux box for calculation of charge around a capacitor.]]
</td>
</tr>
<tr>
<td>
[[Image:Qsource12.png|thumb|left|480px|A line defining the voltage path for calculation of voltage between capacitor plates.]]
</td>
</tr>
</table>
== Computational Domain and Boundary Conditions Discretizing the Physical Structure in EM.Ferma ==
[[Image:fermbc.png|thumb|200px|Boundary Condition Dialog]]In EM.Ferma, the Poisson or Laplace equations are solved subject to boundary conditions using the Finite Difference technique. As a result, you need to specify a finite computational domain and then specify the domain boundary conditions. EM.Ferma's computational domain defines where the domain boundary condition will be specified. A default domain box is always placed in the project workspace as soon as you draw your first object. The domain can be seen as a blue cubic wireframe that surrounds all of the CAD objects in the project workspace.   [[Image:qsource2.png|thumb|200px|The blue wireframe around the CAD objects defines the extents of the computational domain. The specified boundary conditions are applied on the domain walls. ]] To modify the domain settings, click the Domain button of the Simulate Toolbar or right-click on "3D Static Domain" entry in the Navigation Tree and select "Domain Settings..." from the contextual menu. In the Domain Settings Dialog, the computational domain can be defined in two different ways: Default and Custom. The default type places an enclosing box with a specified offset from the largest bounding box of your project's CAD objects. The default offset value is 20 project units, but you can change this value arbitrarily. The custom type defines a fixed domain box by specifying the coordinates of its two opposite corners labeled Min and Max in the world coordinate system.   EM.Ferma allows you to specify the electric potential boundary conditions on the domain box. Two options are available. The Dirichlet boundary condition is the default option and is specified as a fixed potential value on the surface of the domain walls. By default, this value is 0 Volts. The Neumann boundary condition specifies the normal derivative of the electric scalar potential on the surface of the domain walls. This is equivalent to the normal electric field component on the domain walls and its value is specified in V/m. The magnetostatic simulation engine always assumes Dirichlet domain boundary conditions and sets the values of the magnetic vector potential to zero on all the domain walls. To modify the boundary conditions, right-click on "Boundary Conditions" in the Navigation Tree, and select "Boundary Conditions..." from the contextual menu to open the Boundary Conditions Dialog.  === The Static Mesh===
The Finite Difference technique discretizes the computational domain using a 3D rectangular grid. EM.Ferma generates a fixed-cell mesh. This means that the extents of the mesh cells along the principal axes are fixed: Δx, Δy, Δz. By default, the mesh cell size is set to one unit project along all the three directions (with Δx = Δy = Δz). To modify the cell size, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static Mesh" in the Navigation Tree, and select "Mesh Settings..." from the contextual menu to open the Mesh Settings Dialog.
{{Note|To obtain accurate results, it is highly recommended to use a square mesh as much as possible.}}
== Observables in EM[[Image:Info_icon.png|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators | Working with Mesh Generator]]'''.Ferma ==
=== Field Sensors ===[[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's Fixed-Cell Brick Mesh Generator]]'''.
Just like other <table><tr> <td> [[EMImage:Qsource4.Cubepng|thumb|350px|EM.CUBE]] Modules, EM.Ferma has a Field Sensor observable, which plots 3D visualizations of electric and magnetic field components on a specified plane. However, unlike the other modules, EM.Ferma field sensors have two additional plots for electric scalar potential and magnitude of the magnetic vector potential. These are called the "EPot" and "HPot" nodes on the Navigation Tree. To define a Field Sensor, right-click on "Field Sensors" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Field Sensor 's Mesh Settings dialog allows the user to select the direction of the sensor (X, Y, Z), visualization type, and whether E-field output or H-field output will be shown during a sweep analysis. ]] </td></tr></table>
The E-fields <table><tr> <td> [[Image:Qsource2.png|thumb|360px|Geometry of a spherical charge source and Hthe enclosing domain box.]] </td><td> [[Image:Qsource3.png|thumb|360px|Fixed-fields are computed at each cel mesh node within the specified 2D Field Sensor plane. In other words, the resolution of the Field Sensor is controlled by the mesh resolutionspherical charge object.]] </td></tr></table>
== Running Static Simulations in EM.Ferma ==
=== Field Integrals EM.Ferma's Simulation Modes ===
It is often needed to compute integrals of the electric or magnetic fields to define other related quantities[[EM. The following table shows some of widely used field integralsFerma]] currently offers three different simulation modes as follows:
{| class="wikitable"
|-
! scope="col"| QuantitySimulation Mode! scope="col"| Field IntegralUsage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions
|-
! scope| style="rowwidth:120px;"| Voltage[[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]| integralstyle="width:270px;" | Simulates the physical structure "As Is"| style="width:100px;" | Single run| style="width:200px;" | N/A| style="width:150px;" | None
|-
! scope| style="rowwidth:120px;"| Current[[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| integralstyle="width:270px;" | Varies the value(s) of one or more project variables| style="width:100px;" | Multiple runs| style="width:200px;" | N/A| style="width:150px;" | None
|-
! scope| style="rowwidth:120px;"| Electric Flux[[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | integralOptimization]]|-! scopestyle="rowwidth:270px;"| Magnetic FluxOptimizes the value(s) of one or more project variables to achieve a design goal | integral|-! scopestyle="rowwidth:100px;"| Electric EnergyMultiple runs | integral|-! scopestyle="rowwidth:200px;"| CapacitanceN/A| integral|-! scopestyle="rowwidth:150px;"| Inductance| integralNone
|}
=== Transmission Line Characteristics Running an Electrostatic, Magnetostatic or Thermal Analysis ===
In [[EM.Ferma's quasistatic mode, transmission-line [[parameters]] Z0 has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and EpsEff are computedThermal. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in addition to output due to the Field Sensor, which is required to define the 2D solution planepresence of electric sources (volume charges and fixed-potential PEC blocks) and dielectric material media. Text files corresponding The magnetostatic engine solves the magnetic form of Poisson's equation for magnetic vector potential subject to these observables will be placed magnetic field boundary conditions, in the projectpresence of magnetic sources (wire and volume currents and permanent magnetic blocks) and magnetic material media. The thermal engine solves the thermal form of Poisson's working directory after each analysisequation for steady-state temperature subject to thermal boundary conditions, in the presence of heat sources (volume sources and fixed-temperature PTC blocks) and insulator material media.
== 2D Solution Planes in EMTo run a static simulation, first you have to open the Run Dialog.Ferma ==This is done by clicking the "Run" button of the Simulate Toolbar, or by selecting the "Run" item of the Simulate Menu, or simply using the keyboard shortcut "Ctrl+R". There are two available options for the simulation engine: '''Electrostatic-Magnetostatic Solver''' and '''Steady-State Thermal Solver'''. Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation.
<table><tr> <td> [[Image:qstaticFerma L1 Fig11.png|thumb|300pxleft|600px|Setting up a Transmission Line simulation.]]EM.Ferma features a 2D solution mode where the model is treated as a longitudinally infinite structure at a list of specified 2D Solution Planes. The 2D planes are defined by a Field Sensor definition that already exists in the project's Simulation Run dialog.]] </td></tr></table>
To explore In EM.Fermayou don's 2D mode, right-click on "2D Solution Planes" in t have to choose between the navigation tree electrostatic or magnetostatic simulation engines. The program looks at the types of sources and select "2D Domain Settingsmaterial objects present in your project workspace and then it determines whether an electrostatic analysis or a magnetostatic analysis or possibly both should be performed.When there are only electric sources present, you will get nonzero electric fields and zero magnetic fields.When there are only magnetic sources present, you will get nonzero magnetic fields and zero electric fields.". In On the 2D Static Domain dialogother hand, enable since the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified Below"electrostatic and thermal solvers share the same navigation resources, you can run only one of the two engines at a time. The user is then able to Add or Edit 2D Solution Plane definitions to By default, the solution listelectrostatic solver is enabled.
=== Setting up An "Analysis" is the simplest simulation mode of EM.Ferma. It is a Transmission Line Simulation ===single-shot finite difference solution of your static problem. The physical structure of your project workspace is first discretized using a fixed-cell mesh and the Poisson equation is solved numerically everywhere in the computational domain. The field and potential values at each mesh node are computed, and the specified observables are written into data files. The other available simulation modes, parametric sweep and optimization, involve multiple runs of the static solvers.
To perform a 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]]. ===Static Simulation Engine Settings===
Quasistatic analysis EM.Ferma offers two different types of linear system solver for solving the matrix equations that result from discretization of Poisson's equation: an iterative solver based on the stabilized Bi-Conjugate Gradient (BiCG) method and a Gauss-Seidel solver. The default solver type is BiCG. You can only be performed with specify some numerical parameters related to the BiCG solver. To do that, you need to open the Simulation Engine Settings Dialog by clicking the "Settings" button located next to the "Select Engine" drop-down list. From this dialog you can set the maximum number of BiCG iterations, which has a Dirichlet boundary condition with 0V default value of 10,000. You can also set a value for "Convergence Error". The default value for electrostatic analysis is 0.001. For magnetostatic analysis, the specified on value of convergence error is reduced by a factor 1000 automatically. Therefore, the boundariesdefault convergence error in this case is 10<sup>-6</sup>.
{{Note|The value of convergence error affect the accuracy of your simulation results. For a step-by-step demonstration (including transmission line [[optimization]])most practical scenarios, take a look at this video on our YouTube channel: [http://wwwthe default values are adequate.youtube.com/watch?v=Iiu9rQf1QI4 EMYou can reduce the convergence error for better accuracy at the expense of longer computation time.CUBE Microstrip Optimization]}}
== Simulation Modes ==<table><tr> <td> [[Image:Qsource7.png|thumb|left|480px|EM.Ferma's Static Engine Settings dialog.]]</td></tr></table>
EM.Ferma currently offers Analysis, Parametric Sweep, and [[Optimization]] simulation modes. More information about these simulation modes can be found on the [[Optimization]] page.== The 2D Quasi-Static Simulation Mode==
{{Note|All of these EM.Ferma's electrostatic simulation modes are subject 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 mode being disabled or enabledPlane". Before starting A 2D solution plane is defined based on a simulation"Field Sensor" definition that already exists in your project. To explore EM.Ferma's 2D mode, you may wish to review right-click on '''2D Solution Planes''' in the current state "Computational Domain" section of this settings in the navigation tree and select '''2D Domain Settings...''' from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Reduce the 3D Domain to a 2D Solution Plane". The first field sensor observable in the navigation tree is used for the definition of the 2D solution plane.}}
== Simulation Examples At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the field sensor plane. 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. A 2D structure of this type can be considered to represent a transmission line of infinite length. EM.Ferma also performs a quasi-static analysis of the transmission line structure, and usually provides good results at lower microwave frequencies (f < 10GHz). It computes the characteristics impedance Z<sub>0</ Gallery ==sub> and effective permittivity ε<sub>eff</sub> of the multi-conductor TEM or quasi-TEM transmission line. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively.
{| border="0"<table>|-| valign="top"|<tr> <td> [[FileImage:ScreenCapture1Qsource14.png|thumb|left|350px450px|Classic Example: Two oppositely charged spheresThe 2D static domain dialog.]]</td></tr> </table> [[Image:Info_icon.png| valign="top"30px]] Click here to learn more about the theory of '''[[Electrostatic_%26_Magnetostatic_Field_Analysis#2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures |2D Quasi-Static Analysis of Transmission Lines]]'''. <table><tr> <td> [[FileImage:iarrayQsource16.png|thumb|left|350px480px|H-Field from array of current loopsA field sensor and 2D solution plane defined for a microstrip line.]]|-</td>|}</tr>{| border="0"</table>|-| valign="top"|<table><tr> <td> [[FileImage:ustripQsource17.png|thumb|left|350px480px|Potential near Electric field distribution of the microstrip conductor from a quasistatic simulationline on the 2D solution plane.]]</td>| valign="top"|</tr> <tr> <td> [[FileImage:ustrip2Qsource18.png|thumb|left|350px480px|Electric field near scalar potential distribution of the microstrip conductor from a quasistatic simulation. This Field Sensor's view mode has been set to Vector modeline on the 2D solution plane.]]</td>|-</tr>|}</table> <br />
== Version History ==<hr>
* First available in [[EMImage:Top_icon.Cubepng|30px]] '''[[EM.CUBEFerma#Product_Overview | Back to the Top of the Page]] 14.2'''
== More Resources ==[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''
* [http[Image://en.wikipedia.org/wiki/Electrostatics Wikipedia: ElectrostaticsBack_icon.png|30px]]* '''[http://www[EM.youtube.com/watch?v=Iiu9rQf1QI4 YouTube: Cube | Back to EM.Ferma Optimization Example.Cube Main Page]* [http://www.emagtech.com/content/emferma More about EM.Ferma.]'''