[[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 & Quasi-Statics = 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.
<table>
<tr>
<td> [[Image:fermbc.png|thumb|left|480px|EM.Ferma's Boundary Conditions dialog.]] </td>
</tr>
</table>
=== 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.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and magnetic field components, electric scalar potential and magnitude of magnetic vector potential on a planar cross section of the computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Electric and Magnetic Energy and Dissipated Power Density Maps | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and magnetic energy densities and dissipated power density on a planar cross section of the computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Temperature and Heat Flux Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing temperature and heat flux components on a planar cross section of the computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Thermal Energy Density Maps | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing thermal energy density on a planar cross section of the computational domain |-| style="width:30px;" | [[File:field_integ_icon.png]]| style="width:150px;" | Field Integral Quantities| style="width:150px;" | [[Glossary of EM.Cube'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 fields and heat flux |}
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 and polyline objects. You also need Click on each category to define a current value I in Amperes and a wire radius r learn more details about it in the project units[[Glossary of EM. The line or polyline object is then approximated as a volume current with a current density of J = I/(πr<sup>2</sup>) flowing along the line or polyline sideCube's direction. All the wire current sources belonging to the same group have the same color, same current value and same wire radius. The direction of the current can be reversed in wire current sourcesSimulation Observables & Graph Types]].
To add <table><tr> <td> [[Image:Ferma L1 Fig15.png|thumb|left|640px|Electric field distribution of a new wire current source group to spherical charge on a project, right-click on "Wire Currents" on the Navigation Tree, and select "Insert New Current Sourcehorizontal field sensor plane.]] </td></tr> <tr> <td> [[Image:Ferma L1 Fig16.." From the Wire Current Source Dialog, you can change the default brown color png|thumb|left|640px|Electric scalar potential distribution of the source group or set the values of the Current and Wire Radius. There is also a check box for "Reverse Current Direction". Note that this will reverse the direction of all the wire currents belonging to the same group. 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 spherical charge on the drawn CAD object. You can draw any curve object in the project workspace and convert it to a polyline using [[EMhorizontal field sensor plane.Cube]]'s Polygonize Tool. </td></tr></table>
{{Note| If you draw [[[Curve Objects]]] under a wire current group, they will be permanently converted to polyline objects before running The table below list the simulation engine.}} different types of field integrals and their definitions:
{| class="wikitable"
|-
! scope="col"| Field Integral
! scope="col"| Definition
! scope="col"| Output Data File
|-
! 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
|}
=== Permanent Magnets===<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>
A permanent magnet is typically a ferromagnetic material with a fixed inherent magnetization vector. As a result, it can be used as a source == Discretizing the Physical Structure in an magnetostatic problemEM. When a permeable material has a permanent magnetization, the following relationship holds: Ferma ==
===The Static Mesh===
<math> \mathbf{BThe 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 (r)} with Δx = {\mu} (\mathbf{H(rΔy = 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. + \mathbf{M(r){Note|To obtain accurate results, it is highly recommended to use a square mesh as much as possible.}} ) </math>
[[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]]'''.
where <b>M(r)</b> is the magnetization vector[[Image:Info_icon. In SI units system, png|30px]] Click here to learn more about the magnetic field <b>H</b> and magnetization <b>M</b> both have the same units properties of A/m'''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's Fixed-Cell Brick Mesh Generator]]'''.
It can be shown that for magnetostatic analysis, the effect of the permanent magnetization can be modeled as an equivalent volume current source<table><tr> <td> [[Image:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]] </td></tr></table>
<table><mathtr> \mathbf{J_{eq}(r)} = \nabla \times \mathbf{M(r)} <td> [[Image:Qsource2.png|thumb|360px|Geometry of a spherical charge source and the enclosing domain box.]] </td><td> [[Image:Qsource3.png|thumb|360px|Fixed-cel mesh of the spherical charge object.]] </td></tr></mathtable>
== Running Static Simulations in EM.Ferma ==
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=== EM. In this case, the permanent magnetic can be effectively modeled by an equivalent surface current density on the surface of the permanent magnetic object: Ferma's Simulation Modes ===
[[EM.Ferma]] currently offers three different simulation modes as follows:
<math> \mathbf{J_{s,eq}(r)} | class= \mathbf{M(r)} \times \hat{\mathbf{n}} </math>"wikitable"|-! scope="col"| Simulation Modewhere <math> \hat{\mathbf{n}} </math> is the unit outward normal vector at the surface ! scope="col"| Usage! scope="col"| Number of the permanent magnet object. Note that the volume of the permanent magnet still acts as a permeable material in the magnetostatic analysis. Engine Runs! scope="col"| Frequency To add a new permanent magnet source group to a project, right! scope="col"| Restrictions|-click on | style="Permanent Magnetswidth:120px;" on the Navigation Tree, and select | [[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]| style="Insert New Permanent Magnet Source...width:270px;" From | Simulates 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. physical structure "As Is"| style="width:100px;" | Single run| style="width:200px;" | N/A{| borderstyle="0width:150px;"| None
|-
| valignstyle="topwidth:120px;"|[[File:vsourceParametric_Modeling_%26_Simulation_Modes_in_EM.pngCube#Running_Parametric_Sweep_Simulations_in_EM.Cube |thumb|left|250px|EM.Ferma's Voltage Source DialogParametric Sweep]]| valignstyle="bottomwidth:270px;"|Varies the value(s) of one or more project variables[[File| style="width:qsource.png100px;" |thumb|left|250px|EM.Ferma's Charge Source Dialog]]Multiple runs| valignstyle="topwidth:200px;"|N/A[[File| style="width:isource.png150px;" |thumb|left|250px|EM.Ferma's Current Source Dialog]]None
|-
| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Performing_Optimization_in_EM.Cube | Optimization]]
| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal
| style="width:100px;" | Multiple runs
| style="width:200px;" | N/A
| style="width:150px;" | None
|}
=== Running an Electrostatic, Magnetostatic or Thermal Analysis ===
== Computational Domain [[EM.Ferma]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Boundary Conditions ==Thermal. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in the presence of electric sources (volume charges and fixed-potential PEC blocks) and dielectric material media. The magnetostatic engine solves the magnetic form of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, in the presence 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 equation 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.
[[Image:fermbc.png|thumb|200px|Boundary Condition To run a static simulation, first you have to open the Run Dialog]]In EM.FermaThis is done by clicking the "Run" button of the Simulate Toolbar, or by selecting the Poisson "Run" item of the Simulate Menu, or Laplace equations are solved subject to boundary conditions simply using the Finite Difference techniquekeyboard shortcut "Ctrl+R". As a result, you need to specify a finite computational domain There are two available options for the simulation engine: '''Electrostatic-Magnetostatic Solver''' and then specify '''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 domain boundary conditionscurrent simulation.
<table><tr> <td> [[Image:qsource2Ferma L1 Fig11.png|thumb|200pxleft|The blue wireframe around the CAD objects defines the extents of the computational domain600px|EM. The specified boundary conditions are applied on the domain wallsFerma's Simulation Run dialog. ]]</td></tr></table>
In EM.Fermayou don's computational domain defines where t have to choose between the domain boundary condition will be specifiedelectrostatic or magnetostatic simulation engines. The domain can be seen as a blue cubic wireframe that surrounds all program looks at the types of the CAD sources and material objects present in the your project workspaceand then it determines whether an electrostatic analysis or a magnetostatic analysis or possibly both should be performed. To modify the domain settings, find the "3D Static Domain" entry in the navigation tree, right-click on itWhen there are only electric sources present, you will get nonzero electric fields and select "Domain Settingszero magnetic fields...". The domain dialog When there are only magnetic sources present, you will appearget nonzero magnetic fields and zero electric fields. In On the domain dialogother hand, since the domain boundary electrostatic and thermal solvers share the same navigation resources, you can be specified in terms run only one of either the two engines at a customtime. By default, fixed location, or as custom offsets from CAD objects in the sceneelectrostatic solver is enabled.
An "Analysis" is the simplest simulation mode of EM.Ferma allows . It is a 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 user to either specify Poisson equation is solved numerically everywhere in the computational domain. The field and potential on the boundary (Dirichlet boundary condition)values at each mesh node are computed, or specify and the normal derivative on the boundary (Neumann boundary condition) via a specified field strengthobservables are written into data files. To modify the boundary condition, find "Boundary Conditions" on the navigation treeThe other available simulation modes, parametric sweep and select "Boundary Conditions...". The user will be prompted with optimization, involve multiple runs of the dialog seen at rightstatic solvers.
===Static Simulation Engine Settings===
== Observables in 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 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 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 value of convergence error is reduced by a factor 1000 automatically. Therefore, the default convergence error in this case is 10<sup>-6</sup>.
=== Field Sensor ==={{Note|The value of convergence error affect the accuracy of your simulation results. For most practical scenarios, the default values are adequate. You can reduce the convergence error for better accuracy at the expense of longer computation time.}}
Just like other <table><tr> <td> [[EMImage:Qsource7.Cubepng|thumb|left|480px|EM.CUBE]] Modules, EM.Ferma has a standard Field Sensor observable. To specify a Field Sensor, right-click on "Field Sensors" in the navigation tree and click "Add New...". The Field Sensor 's Static Engine Settings dialog allows the user to select the direction of the sensor, visualization type, and whether E-field output or H-field output will be shown during a sweep analysis. ]]</td></tr></table>
In EM.Ferma, Field Sensors are also used to specify == The 2D solution planes for EM.Ferma's 2D solution mode. This will be detailed shortly. Quasi-Static Simulation Mode==
The E-fields and H-fields are computed at each mesh node within 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". A 2D solution plane is defined based on a "Field Sensor plane" definition that already exists in your project. To explore EM.Ferma's 2D 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 other wordsthe 2D Static Domain dialog, check the resolution of checkbox labeled "Reduce the Field Sensor 3D Domain to a 2D Solution Plane". The first field sensor observable in the navigation tree is controlled by used for the mesh resolutiondefinition of the 2D solution plane.
=== Transmission Line Characteristics ===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</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.
In EM.Ferma's quasistatic mode, transmission-line <table><tr> <td> [[parametersImage:Qsource14.png|thumb|left|450px|The 2D static domain dialog.]] Z0 and EpsEff are computed, in addition to output due to the Field Sensor, which is required to define the 2D solution plane. Text files corresponding to these observables will be placed in the project's working directory after each analysis.</td></tr> </table>
[[Image:Info_icon.png|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> [[Image:Qsource16.png|thumb|left|480px|A field sensor and 2D Solution Planes in EMsolution plane defined for a microstrip line.Ferma ==]]</td></tr></table>
<table><tr> <td> [[Image:qstaticQsource17.png|thumb|300pxleft|Setting up a Transmission Line simulation480px|Electric field distribution of the microstrip line on the 2D solution plane.]]</td>EM</tr> <tr> <td> [[Image:Qsource18.Ferma features a 2D solution mode where the model is treated as a longitudinally infinite structure at a list png|thumb|left|480px|Electric scalar potential distribution of specified the microstrip line on the 2D Solution Planes. The 2D planes are defined by a Field Sensor definition that already exists in the projectsolution plane.]] </td></tr></table>
To explore EM.Ferma's 2D mode, right-click on "2D Solution Planes" in the navigation tree and select "2D Domain Settings...". 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. === Setting up a Transmission Line Simulation === 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]]. Quasistatic analysis can only be performed with a Dirichlet boundary condition with 0V specified on the boundaries. For a step-by-step demonstration (including transmission line [[optimization]]), take a look at this video on our YouTube channel: [http:<br //www.youtube.com/watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization] == Simulation Modes == EM.Ferma currently offers Analysis, Parametric Sweep, and [[Optimization]] simulation modes. More information about these simulation modes can be found on the [[Optimization]] page. {{Note|All of these simulation modes are subject to 2D Solution mode being disabled or enabled. Before starting a simulation, you may wish to review the current state of this settings in the 2D Domain dialog.}} == Simulation Examples / Gallery == {| border="0"|-| valign="top"|[[File:ScreenCapture1.png|thumb|left|350px|Classic Example: Two oppositely charged spheres.]]| valign="top"|[[File:iarray.png|thumb|left|350px|H-Field from array of current loops.]]|-|}{| border="0"|-| valign="top"|[[File:ustrip.png|thumb|left|350px|Potential near microstrip conductor from a quasistatic simulation.]]| valign="top"|[[File:ustrip2.png|thumb|left|350px|Electric field near microstrip conductor from a quasistatic simulation. This Field Sensor's view mode has been set to Vector mode.]]|-|}>
== 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.]'''
