[[Image:Splash-static.jpg|right|750px720px]]<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.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:planar-ico.png | link=EM.Picasso]] [[image:metal-ico.png | link=EM.Libera]] [[image:po-ico.png | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Ferma_Documentation | EM.Ferma Primer Tutorial Gateway]]'''Â [[Image:Back_icon.png|30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''==Product Overview==
=== EM.Ferma in a Nutshell ===
[[EM.Ferma]] 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. Both 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 electric and magnetic potentialsand temperature.
With 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 (permeable) 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-static mode to compute the characteristic impedance (Z0) and effective permittivity of transmission line structures with complex cross section profiles.
{{Note|EM.Ferma is the low-frequency '''Static Module''' of '''[[EMImage:Info_icon.Cubepng|30px]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Ferma shares Click here to learn more about the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCADElectrostatic & Magnetostatic Field Analysis | Theory of Electrostatic and Magnetostatic Methods]]''' with all of [[EM.Cube]]'s other computational modules.}}
[[Image:Info_icon.png|40px30px]] Click here to learn more about the '''[[Getting_Started_with_EM.CUBE Steady-State_Thermal_Analysis | EM.Cube Modeling EnvironmentTheory of Steady-State Heat Transfer Methods]]'''.
<table><tr><td>[[Image:Info_iconMagnet lines1.png|40px]] Click here to learn more about the basic functionality thumb|left|400px| Vector plot of '''[[CubeCADmagnetic field distribution in a cylindrical permanent magnet.]]'''.</td></tr></table>
=== EM.Ferma as the Static Modeling Methods Module of EM.Cube ===
[[Image:Info_iconEM.png|40px]] Click here to learn more about Ferma is the theory low-frequency '''Static Module''' of '''[[Electrostatic and Magnetostatic MethodsEM.Cube]]''', 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.
== Defining the Physical Structure in [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Ferma ==Cube Modeling Environment]]'''.
[[Image:Static7.png|thumb|270px| === Advantages & Limitations of EM.Ferma's Navigation Tree.]]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. As soon as you introduce a dielectric object next to a charge source 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 Poisson'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. Static Simulator ===
=== A Note EM.Ferma computes the electric and magnetic fields independent of each other based on Material electrostatic and Source Types 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.
In <table><tr><td>[[EMImage:Ferma L8 Fig title.Cube]]'s other modules, material types are specified under the "Physical Structure" section png|thumb|left|400px| Vector plot of the navigation tree, and sources are organized under electric field distribution in a separate "Sources" sectioncoplanar waveguide (CPW) transmission line. In those modules, the physical structure and its various material types typically represent all the CAD objects you draw in your project. Sources are virtual entities that might be associated with certain physical objects and provide the excitation of your boundary value problem. ]]</td></tr></table>
In == EM.Ferma, materials and sources are all listed under the "Physical Structure" section of the navigation tree. In other words, there is no separate "Sources" section. For example, you can define default zero-potential perfect electric conductors (PEC) in your project to model metal objects. You can also define fixed-potential PEC objects with Features at a nonzero voltage, which can effectively act 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 objects are defined from the same PEC node of the navigation tree by assigning different voltage values. Charge and current sources are defined as CAD objects, and you have to draw them in the project workspace just like other material objects.Glance ==
=== Variety of Material and Source Objects Physical Structure Definition ===
EM.Ferma offers the following types of material <ul> <li> Perfect electric conductor(PEC) solids and source surfaces (Electrostatics)</li> <li> Dielectric objects to construct your physical structure for electrostatic or magnetostatic simulation:(Electrostatics)</li> <li> Magnetic (permeable) objects (Magnetostatics)</li> <li> Perfect thermal conductor (PTC) solids and surfaces (Thermal)</li> <li> Insulator objects (Thermal)</li></ul>
* Fixed-Potential Perfect Electric Conductor (PEC) Objects * Fixed-Potential Perfect Electric Conductor (PEC) Objects * Dielectric/Magnetic Materials* Volume Charge Charges* Wire Currents* Volume Currents* Permanent Magnets=== Sources ===
All the <ul> <li> Fixed-potential PEC for maintaining equi-potential metal objects belonging to the same group share the same properties including color and electric or magnetic [[parameters]]. (Electrostatics)</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)</li></ul>
=== Fixed-Potential PEC ObjectsMesh generation ===
A perfect electric conductor (PEC) is a material with <ul> <li> Fixed-size brick&epsilonnbsp;cells<sub/li>r</subul> = 1 and σ = ∞. Under the static condition, every point on a PEC object has the same electric potential. By default, this is a zero potential, meaning the PEC object is "grounded". You can define a nonzero voltage value for a PEC group. In that case, all the PEC objects belonging to that group are effectively turned into voltage sources. For example, two parallel PEC plates, one with a zero potential and the other with a nonzero potential represent a simple air-filled capacitor.
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. === 3D Electrostatic & Magnetostatic Simulation ===
{{Note| You can define any solid or surface object as a fixed-<ul> <li> Finite difference solution of Laplace and Poisson equations for the electric scalar potential PEC 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>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces |Perfect Electric Conductor (PEC) Objects]]'''.=== 2D Quasi-Static Simulation ===
=== Dielectric<ul> <li> 2D Finite difference solution of cross section of transmission line structures</Magnetic Materials === 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></ul>
In 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". For a dielectric material, you specify the relative permittivity ε<sub>r</sub> and electric conductivity σ. For a magnetic material, you specify the relative permeability μ<sub>r</sub>. === Steady-State Thermal Simulation ===
{{Note| Excluding surface <ul> <li> Finite difference solution of Laplace and curve CAD objects, you can define any solid CAD object as a dielectric or magnetic material object.}} Poisson equations for the temperature with Dirichlet and Neumann domain boundary conditions </li> <li> Calculation of temperature and heat flux density</li> <li> Calculation of thermal energy density on field sensor planes</li> <li> Calculation of thermal flux over user defined flux boxes</li> <li> Calculation of thermal energy</li></ul>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_Dielectric_Materials | Dielectric === Data Generation & Magnetic Objects]]'''.amp; Visualization ===
[[Image:Info_icon.png|40px]] Click here for a general discussion <ul> <li> Electric and magnetic field 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 '''[[Defining Materials in EM.Cube]]'''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>
<table><tr><td> [[Image:Static1.png|thumb|270px| == Building the Physical Structure in EM.Ferma's PEC dialog.]] </td><td> [[Image:Static2.png|thumb|270px| EM.Ferma's Dielectric/Magnetic Material dialog.]] </td></tr></table>==
=== Volume Charge Sources Variety of Physical Objects in EM.Ferma ===
You can define volume charge sources with The simplest static problems involve a specified charge density source in C/m<sup>3</sup> confined to certain region of your projectthe free space that produces an electric field, or a current source in the free space that produces a magnetic field. You use [[EM.Cube]]'s [[Solid Objects|solid objects]] to define volume charge sources. All In such cases, the charge sources belonging to only applicable boundary conditions are defined at the same group have boundary of the same color and same charge density valuecomputational domain. The As soon as you introduce a dielectric object next to a charge density can be positive source or negative. To add a new charge magnetic (permeable) material next to a current source group , you have to deal with a projectcomplex boundary value problem. In other words, right-click on "Volume Charges" on you need to solve the Navigation Tree, and select "Insert New Charge Sourceelectric 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.." From the Charge Source DialogOnce you introduce material blocks, you can change have to enforce conductive and convective boundary conditions at the default purple color of interface between different materials and air. EM.Ferma uses the source group or set the values Finite Difference (FD) technique to find a numerical solution of the Charge Densityyour static boundary value problem.
=== Volume Current Sources ===[[EM.Ferma]] offers the following types of physical objects:
You can define {| class="wikitable"|-! 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 (PEC)]]| 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/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 & Other Physical Object Types#Volume Charge |Volume Charge]]| style="width:300px;" | Modeling volume current charge sources with a specified current fixed charge density or an expression in A/m<sup>2</sup> confined to certain region the global coordinates (x,y,z) | 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 your projectEM. Note that 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 is vector or expressions in the global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a vectorial quantity and has magnetic source|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Permanent Magnet |Permanent Magnet]]| style="width:300px;" | Modeling permanent magnet sources with a magnitude and unit direction fixed magnetization vectoror expressions in the global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a magnetic source|-| style="width:30px;" | [[File:thin_group_icon. You use 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 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 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 ambient temperature (shares the same navigation tree node as PEC object)|-| style="width:30px;" | [[Solid ObjectsFile:diel_group_icon.png]]|solid 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]] to define volume current sources| style="width:200px;" | [[Glossary of EM. All the Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Heat Source |Volume Heat Source]]| style="width:300px;" | Modeling volume current heat sources belonging to with a fixed heat density or an expression in the same group have global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a thermal source (shares the same color and same current density magnitude and unit vectornavigation 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|}
To add a new volume current source group Click on each category to a project, right-click on "Volume Currents" on learn more details about it in the Navigation Tree, and select "Insert New Current Source[[Glossary of EM..." From the Volume Current Source DialogCube's Materials, you can change the default brown color of the source group or set the values of the Current Density magnitude and unit direction vector components. The default direction vector is z-directedSources, Devices & Other Physical Object Types]].
=== Wire Current Sources Grouping Objects by Material or Source Type ===
Your physical structure in EM.Ferma allows you to define idealized wire current sources. You can use this is typically made up of some kind of source type to model filament currents or coils. Wire currents are defined using only line and polyline objects. You also need to define a current value I in Amperes and a wire radius r object either in the project units. The line free space or polyline object is then approximated as a volume current with a current density of J = I/(πr<sup>2</sup>) flowing along in the line presence of one or polyline sidemore material objects. EM.Ferma's direction. All electrostatic and magnetostatic or thermal simulation engines then discretize the wire current sources belonging to the same group have the same color, same current value entire computational domain including these source and same wire radius. The direction of material objects and solve the current can be reversed Laplace or Poisson equations to find the electric or magnetic fields or temperature everywhere in wire current sourcesthe computational domain.
All the geometric objects in the project workspace are organized together into object groups which share the same properties including color and electric or magnetic parameters. It is recommended that you first create object groups, and then draw new objects under the active group. To add create a new wire current source object group to a project, right-click on its category name in the "Wire CurrentsPhysical Structure" on section of the Navigation Tree, navigation tree and select one of the "Insert New Current SourceGroup..." From items from the Wire Current Source Dialogcontextual menu. However, if you can change the default brown color of the source group or set the values of the Current and Wire Radius. There is also start a check box for "Reverse Current Direction"new EM. Note that this will reverse the direction of all the wire currents belonging to the same group. When you draw Ferma project from scratch, and start drawing a line or polyline new 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 without having previously defined any curve object in the project workspace groups, a new default "Fixed-Potential PEC" object group with a zero voltage is created and convert it added to a polyline using [[EM.Cube]]'s Polygonize Toolthe navigation tree to hold your new geometric object.
It is important to note that there is a one-to-one correspondence between electrostatic and thermal simulation entities:Â {| 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|}Â {{Note| If you draw curve CAD Electrostatic and thermal solvers share the same material categories on the navigation tree. This means that PEC objects are treated as PTC objects under a wire current group, they will be permanently converted to polyline dielectric objects are treated as insulator objects before running and volume charges are treated as volume heat sources when the simulation enginethermal solver is enabled.}} Â Once a new object group node has been created in the navigation tree, it becomes and remains the "Active" object group, which is always listed in bold 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. Â [[Image:Info_icon.png|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.
<table>
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<td> [[Image:Static3STAT MAN1.png|thumb|270pxleft| EM.Ferma's Charge Source dialog.]] </td><td> [[Image:Static4.png|thumb|270px| EM.Ferma's Wire Current Source dialog.]] </td><td> [[Image:Static5.png|thumb|270px480px| EM.Ferma's Volume Current Source dialognavigation tree.]] </td>
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=== Permanent MagnetsA Note on Material and Source Types in EM.Ferma ===
In [[Image:Static6.png|thumb|270px| EM.Ferma's Permanent Magnet Source dialog.Cube]]A permanent magnet is typically a ferromagnetic 's other modules, material with types are categorized under the "Physical Structure" section of the navigation tree, and sources are organized under a fixed inherent magnetization vectorseparate "Sources" section. As a resultIn those modules, it can be used as a source all the geometric objects you draw in an magnetostatic problem. When a permeable your project workspace typically represent material has a permanent magnetization, bodies. All of [[EM.Cube]] modules except for EM.Ferma require at least one excitation source to be selected from the following relationship holds: "Sources" section of the navigation tree before you can run a simulation.
<math> \mathbf{BIn EM.Ferma, materials and sources are all lumped together and listed under the "Physical Structure" section of the navigation tree. In other words, there is no separate "Sources" section. For example, you can define default zero-potential perfect electric conductors (rPEC)} = {\mu} (\mathbf{H(r)} + \mathbf{M(r)} ) </math>in your project to model metal objects. You can also define fixed-potential PEC objects with a nonzero voltage, which can effectively act 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 objects are defined from the same PEC node of the navigation tree by assigning different voltage values. Charge and current sources are also defined as geometric objects, and you have to draw them in the project workspace just like other material objects.
where <b>M(r)</b> is the magnetization vector. In SI units system, the magnetic field <b>H</b> and magnetization <b>M</b> both have the same units of A/m.  It can be shown that for magnetostatic analysis, the effect of the permanent magnetization can be modeled as an equivalent volume current source: <math> \mathbf{J_{eq}(r)} = \nabla \times \mathbf{M(r)} </math> 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:  <math> \mathbf{J_{Ferma's,eq}(r)} = \mathbf{M(r)} \times \hat{\mathbf{n}} </math> 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.  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. == Computational Domain and Discretization==
===The Domain Box===
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.
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===Domain Boundary Conditions===
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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.
<table>
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<td> [[Image:Qsource5.png|thumb|350pxleft|480px|EM.Ferma's Domain Settings dialog.]] </td><td> [[Image:fermbc.png|thumb|350px|EM.Ferma's Boundary Conditions dialog.]] </td>
</tr>
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[[Image:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]]===The Static MeshDomain Boundary Conditions===
The Finite Difference technique discretizes *EM.Ferma allows you to specify the electric potential boundary conditions on the computational domain using a 3D rectangular gridbox. EMTwo options are available.Ferma generates The Dirichlet boundary condition is the default option and is specified as a fixed-cell meshpotential 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 means that is equivalent to a constant normal electric field component on the extents 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 mesh cells along magnetic vector potential to zero on all the principal axes are domain walls.  *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: Δx, Δy, Δztemperature value on the surface of the domain walls. By default, this value is 0°C. The Neumann boundary condition specifies the mesh cell size normal derivative of the temperature on the surface of the domain walls. This is set equivalent to one unit project along all a constant heat flux passing through the three directions (with Δx = Δy = Δz)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. To modify the cell sizeboundary conditions, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static MeshBoundary Conditions" in the Navigation Treenavigation tree, and select "Mesh SettingsBoundary Conditions..." from the contextual menu to open the Mesh Settings Boundary Conditions Dialog. {{Note|To obtain accurate resultsWhen 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 check this box in the Boundary Conditions dialog, the solver type is highly recommended set to use a square mesh as much as possiblethe thermal solver in the Simulation Run dialog.}}In the "Global Thermal Properties" section of the Boundary Conditions dialog, you can set the values of the ambient 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>
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<td> [[Image:Qsource2fermbc.png|thumb|350pxleft|Geometry of a spherical charge source and the enclosing domain box480px|EM.]] </td><td> [[Image:Qsource3.png|thumb|350px|Fixed-cel mesh of the spherical charge objectFerma's Boundary Conditions dialog.]] </td>
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== Running Static Simulations in EM.Ferma 's Simulation Data & Observables ==
[[Image:Qsource6At the end of an electrostatic simulation, the electric field vector and electric scalar potential values are computed at all the mesh grid points of the entire computational domain.png|thumb|400px|EMAt the end of an magnetostatic simulation, the magnetic field vector and magnetic vector potential values are computed at all the grid nodes.Ferma's Simulation Run dialogAt the end of a thermal simulation, the temperature and heat flux vector are computed at all the mesh grid points of the entire computational domain.]] ===Two Simulation Engines===
Besides the electric and magnetic fields and temperature, EM.Ferma has two independent but functionally similar static simulation engines: Electrostatic and Magnetostaticcan compute a number of field integral quantities such as voltage, current, flux, energy, etc. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditionscomponents, in the presence of electric sources (volume charges and fixed-potential PEC blocks) values and dielectric material mediafield integrals are written into output data files and can be visualized on the screen or graphed in Data Manager only if you define a field sensor or a field integral observable. The magnetostatic engine solves In the magnetic form absence of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, any observable defined in the presence of magnetic sources (wire navigation tree, the static simulation will be carried out and volume currents and permanent magnetic blocks) and magnetic material mediacompleted, but no output simulation data will be generated.
In EM.Ferma you don't have to select any specific simulation engine. The program looks at offers the following types sources and material 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.of output simulation data:
To run a static simulation, first you have to open the Run Dialog. This is done by clicking the {| class="Runwikitable" button of the Simulate Toolbar, or by selecting the |-! scope="Runcol" item of the Simulate Menu, or simply using the keyboard shortcut | Icon! scope="Ctrl+Rcol". The only available simulation engine is | Simulation Data Type! scope="Staticcol". Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation. | Observable Type! scope=== Simulation Modes ==="col"| Applications|-EM.Ferma currently offers three different simulation modes| style="width: Analysis, Parametric Sweep and 30px;" | [[OptimizationFile:fieldsensor_icon.png]]. An | style="Analysiswidth:150px;" is a single| Near-shot finite difference solution Field Distribution Maps| style="width:150px;" | [[Glossary of your static structureEM. The structure is first discretized using a fixedCube's Simulation Observables & Graph Types#Near-cell mesh Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and the Poisson equation is solved numerically everywhere in your computational domain. The magnetic field and components, electric scalar potential values at each mesh node are computed and magnitude of magnetic vector potential on a planar cross section of the specified observables are written into data files.computational domain |-In a | style="Parametric Sweepwidth:30px;", one ore more | [[variables]] are varied at the specified steps(s)File:fieldsensor_icon. This means that you must first define one or more [[variablespng]] in your projects. | style="width:150px;" | Electric and Magnetic Energy and Dissipated Power Density Maps | style="width:150px;" | [[Variables]] can be associated with CAD object properties like dimensions, coordinates, rotation angles, etc. or with material properties or source properties. For each single variable sample or each combination Glossary of variable samples, first all the associated CAD object properties, material properties or source properties are updated in the project workspaceEM. Then is 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 finite difference solution planar cross section of your updated static structure is computed and parametric sweep proceeds to the next variable sample or combination.computational domain |-The | style="width:30px;" | [[optimizationFile:fieldsensor_icon.png]] mode requires definition of one or more objectives based on the standard output quantities. At the present time, the | style="width:150px;" | Temperature and Heat Flux Distribution Maps| style="width:150px;" | [[optimizationGlossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] mode is only available for the 2D Quasi-Static Mode | style="width:450px;" | Computing temperature and heat flux components on a planar cross section of the EM.Ferma, which will be discussed separately later. computational domain |-| style="width:30px;" | [[ImageFile:Qsource7fieldsensor_icon.png]]|thumbstyle="width:150px;" |400pxThermal Energy Density Maps |style="width:150px;" | [[Glossary of EM.FermaCube's Static Engine Settings dialog.Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style===Static Simulation Engine Settings=== EM.Ferma currently uses a single iterative linear system solver based "width:450px;" | Computing thermal energy density on a planar cross section of the stabilized Bicomputational domain |-Conjugate Gradient (BiCG) method to solve the matrix equations which result from the discretization of Poisson's equation. You can specify some numerical | style="width:30px;" | [[parametersFile:field_integ_icon.png]] related to the Bi-CG solver. To do that, you need to open the Simulation Engine Settings Dialog by clicking the | style="Settingswidth:150px;" button located next to the | Field Integral Quantities| style="Select Enginewidth:150px;" drop-down list. From this dialog you can set the maximum number | [[Glossary of BiCG iterations, which has a default value of 10,000EM. You can also set a value for Cube's Simulation Observables & Graph Types#Static_Field_Integral_Observable | Static Field Integral]] | style="Convergence Errorwidth:450px;". The default value for electrostatic analysis is 0.001. For magnetostatic analysis| Computing line, the specified value surface and volume integrals of convergence error is reduced by a factor 1000 automatically. Therefore, the default convergence error in this case is 1e-6. electric and magnetic fields and heat flux  {{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.}} == Working with Static Simulation Data ==
At the end of an electrostatic simulation, the electric field and electric scalar potential values are computed at all the mesh grid points of the entire computational domain. At the end of an magnetostatic simulation, the magnetic field and magnetic vector potential values are computed at all the grid nodes. The field and potential values are written into output data files and can be visualized Click on each category to learn more details about it in the screen only if you define a field sensor observable. In the absence of a defined observable, the static simulation will be carried out and completed, but to action will take place.  === Defining Field Sensors === [[Image:Qsource8.png|thumb|350px|Glossary of EM.FermaCube's Field Sensor dialog.Simulation Observables & Graph Types]] Just like other [[EM.Cube|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 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.  The E-fields and H-fields are computed at each mesh node within the specified 2D Field Sensor plane. In other words, the resolution of the Field Sensor is controlled by the mesh resolution. [[Image:Info_icon.png|40px]] Click here to learn more about defining field sensor observables for '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near-Field Maps]]'''.
<table>
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<td> [[Image:Qsource9Ferma L1 Fig15.png|thumb|450pxleft|640px|Electric field distribution of a spherical charge on a horizontal field sensor plane.]] </td></tr> <tr><td> [[Image:Qsource10Ferma L1 Fig16.png|thumb|450pxleft|640px|Electric scalar potential distribution of a spherical charge on a horizontal field sensor plane.]] </td>
</tr>
</table>
=== Defining Field Integrals ===Â It is often needed to compute integrals of the electric or magnetic fields to define other related quantities. The following table shows some below list the different types of widely used field integrals in electrostatics and magnetostatics. In EM.Ferma, you can define a path integral along a line segment that is parallel to one of the three principal axes, or a loop integral on a rectangle that is parallel to one of the principal planes. You can also define flux planes or flux boxes. All this is done from the same Field Integral Dialog. To define a Field Integral, right-click on "Field Integrals" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Integral Type drop-down list gives nine options as listed in the table belowtheir definitions:Â
{| class="wikitable"
|-
! scope="row"| Electric Energy
| <math> W_E = \frac{1}{2} \int \int \int_V \mathbf{D(r)} . \mathbf{E(r)} dv = \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 \mathbf{B(r)} . \mathbf{H(r)} dv = \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 \mathbf{J(r)} . \mathbf{E(r)} dv = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| ohmic.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"| Capacitance
| <math> C = Q/V = \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>
| inductancemutual_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>
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<td>
[[Image:Qsource13.png|thumb|left|480px|Defining the capacitance observable in the field integral dialog.]]
</td>
</tr>
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<tr>
<td>
[[Image:Qsource11.png|thumb|left|480px|The electric flux box for calculation of charge around a capacitor.]]
</td>
</tr>
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<td>
[[Image:Qsource12.png|thumb|left|480px|A line defining the voltage path for calculation of voltage between capacitor plates.]]
</td>
</tr>
</table>
In == Discretizing the above table, C represents an open curve (path), C<sub>o</sub> represents a closed curve (loop), S represents an open surface like a plane, S<sub>o</sub> represents a closed surface like a box, and V represents a volumePhysical Structure in EM. In the case of mutual inductance, S' represents an open surface or plane passing through the second (coupled) inductor, and Φ'<sub>H</sub> represents the magnetic flux linkage due to the magnetic field of the first inductor passing through the second inductor. Ferma ==
===The domain of the field integral is set using the "Integration Box Coordinates" section of the Field Integral dialog. Box domains are specified by the coordinates of two opposite corners. Voltage Path requires a line; therefore, two of the coordinates of the two corners must be identical. Otherwise, an error message will pop up. For example, (0, 0, 0) for Corner 1 and (10, 0, 0) for Corner 2 define a Z-directed line segment. Current Loop requires a rectangle; therefore, one of the coordinates of the two corners must be identical. For example, (0, 0, 0) for Corner 1 and (10, 10, 0) for Corner 2 define a rectangle in the XY plane. Static Mesh===
After The Finite Difference technique discretizes the completion of computational domain using a static simulation, 3D rectangular grid. EM.Ferma generates a fixed-cell mesh. This means that the result extents of the field integrals mesh cells along the principal axes are written into "fixed: Δx, Δy, Δz.DATBy 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 " data filesMesh Settings. These files can be accessed using [[EM.Cube]]'s Data Manager." 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.}}
== Modeling Transmission Lines Using 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==
[[Image:qstaticInfo_icon.png|thumb30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh |300px|Setting up a Transmission Line simulationEM.Ferma's Fixed-Cell Brick Mesh Generator]]'''.
===2D Electrostatic Simulation Mode===<table><tr> <td> [[Image:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]] </td></tr></table>
EM<table><tr> <td> [[Image:Qsource2.Ferma's electrostatic simulation engine features png|thumb|360px|Geometry of a 2D solution mode where spherical charge source and the model is treated as a longitudinally infinite structure in the direction normal to specified "2D Solution Plane"enclosing domain box. More than one 2D solution plane may be defined]] </td><td> [[Image:Qsource3. In that case, multiple 2D solutions are obtained. A 2D solution plane is defined based on a "Field Sensor" definition that already exists in png|thumb|360px|Fixed-cel mesh of the projectspherical charge object.]] </td></tr></table>
To explore == Running Static Simulations in EM.Ferma's 2D mode, right-click on "2D Solution Planes" in the Navigation Tree and select "2D Domain Settings..." from the contextual menu. 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. In the Add/Edit 2D Solution Plane dialog, you can choose a name other than the default name and select one of the available field sensor definitions in your project. ==
At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the respective field sensor planes=== EM. 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. Ferma's Simulation Modes ===
=== 2D Quasi-Static Solution of Transmission Lines ===[[EM.Ferma]] currently offers three different simulation modes as follows:
At lower microwave frequencies (f < 10GHz), it is usually possible to perform a 2D electrostatic analysis {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of a transmission line Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]| style="width:270px;" | Simulates the physical structure and compute its characteristics impedance Z<sub>0</sub> and effective permittivity &epsilon"As Is"| style="width:100px;<sub>eff<" | Single run| style="width:200px;" | N/sub>A| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM. This Cube | Parametric Sweep]]| style="quasiwidth: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|-static approach| style=" involves two stepswidth: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|}
<ol><li>First=== Running an Electrostatic, you have remove all the dielectric materials from your structure and replace them with free space (Magnetostatic or air). Obtain a 2D electrostatic solution of your "air-filled" transmission line structure and compute its capacitance per unit length C<sub>a</sub>.</li><li>Next, obtain a 2D electrostatic solution of your actual transmission line structure with all of its dielectric parts and compute its true capacitance per unit length C.</li></ol>Thermal Analysis ===
Then effective permittivity [[EM.Ferma]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Thermal. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in the transmission line structure is then calculated from 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: <math> \epsilon_{eff} = \frac{C}{C_a} </math>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.
and its characteristic impedance To run a static simulation, first you have to open the Run Dialog. This is given done byclicking 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: <math> Z_0 = \eta_0 \sqrt{ \frac{C_a}{C} } </math>'''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.
where η<subtable>0</subtr> = 120π Ω is the intrinsic impedance of the free space<td> [[Image:Ferma L1 Fig11. png|thumb|left|600px|EM.Ferma's Simulation Run dialog.]] </td></tr></table>
In EM.Ferma you don't have to choose between the electrostatic or magnetostatic simulation engines. The guide wavelength program looks at the types of sources and material objects present in your transmission line 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. On the other hand, since the electrostatic and thermal solvers share the same navigation resources, you can run only one of the two engines at a given frequency f time. By default, the electrostatic solver is then calculated from:enabled.
<math> \lambda_g = \frac{\lambda_0}{\sqrt{\epsilon_{eff}}} = \frac{c}{f\sqrt{\epsilon_{eff}}} </math>An "Analysis" is the simplest simulation mode of EM.Ferma. 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 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.
and its propagation constant is given by:===Static Simulation Engine Settings===
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<mathsup> \beta = k_0\sqrt{\epsilon_{eff}} = \frac{2\pi f}{c}\sqrt{\epsilon_{eff}} -6</mathsup>.
where c is {{Note|The value of convergence error affect the speed accuracy of light in your simulation results. For most practical scenarios, the free spacedefault values are adequate. You can reduce the convergence error for better accuracy at the expense of longer computation time. }}
<table><tr> <td> [[Image:Qsource7.png|thumb|left|480px|EM.Ferma's 2D Quasi-Static mode automatically performs the two-step process described above and calculates εEngine Settings dialog.]]<sub/td>eff</subtr> and Z<sub>0</subtable>. So you don't need to modify your structure in the first step.
=== Setting up a Transmission Line The 2D Quasi-Static Simulation =Mode==
To perform a transmission line EM.Ferma's electrostatic simulation, first draw engine features a 2D solution mode where your physical model is treated as a longitudinally infinite structure in the project workspace just like a typical 3D structuredirection normal to specified "2D Solution Plane". Define A 2D solution plane is defined based on a "Field Sensor" observable definition that already exists in your project. To explore EM.Ferma's 2D mode, right-click on '''2D Solution Planes''' in the Navigation Tree so as "Computational Domain" section of the navigation tree and select '''2D Domain Settings...''' from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Reduce the 3D Domain to capture a 2D Solution Plane". The first field sensor observable in the cross section navigation tree is used for the definition of your structure as your desired transmission line profilethe 2D solution plane.
Next, define At the end of a "2D Solution Plane" in electrostatic analysis, you can view the Navigation Tree based electric field and potential results on your existing the field sensorplane. When defining It is assumed that your structure is invariant along the direction normal to the 2D solution plane. Therefore, check your computed field and potential profiles must be valid at all the box labeled "Perform planes perpendicular to the specified longitudinal direction. A 2D Quasi-Static Simulation"structure of this type can be considered to represent a transmission line of infinite length. If an EM.Ferma also performs a quasi-static analysis is run with this option checkedof the transmission line structure, and usually provides good results at lower microwave frequencies (f < 10GHz). It computes the characteristic characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> will be computed for of the corresponding 2D Solution Planemulti-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, where "solution_plane" is the default name of your 2D plane.
Many 2D quasi-static solutions can be obtained in the same analysis,for example, when your design contains many types of <table><tr> <td> [[Transmission Lines|transmission lines]]Image:Qsource14. At the end of a quasi-static analysis, the electric field components and scalar potential at the selected png|thumb|left|450px|The 2D planes will still be computed and can be visualized. In the case of a parametric sweep, the data files will contain multiple data entries listed against the corresponding variable samples. Such data files can be plotted in EM.Gridstatic domain dialog.]] </td> </tr> === Optimizing a Transmission Line ===</table>
In an [[optimizationImage:Info_icon.png|30px]] simulation, Click here to learn more about the values theory of one or more '''[[variablesElectrostatic_%26_Magnetostatic_Field_Analysis#2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures | 2D Quasi-Static Analysis of Transmission Lines]] are varied over their specified ranges, and a design objective is tested at each simulation run. A design objective is typically a logical expression that sets an expression equal to a target value. EM.Ferma currently offers two standard outputs: ε<sub>eff</sub> and Z<sub>0</sub>. Two possible objectives are "Z<sub>0</sub> == 50" or "sqrt(ε<sub>eff</sub>) == 1.5". To define an objective, click the "Objectives" button of the Simulate Toolbar, or select the "Objectives" item of the Simulate Menu, or simply use the keyboard shortcut "Ctrl+J". In the Objectives Dialog, you can add new objective or edit the existing objectives'''.
<table>
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<td>
[[Image:Qsource16.png|thumb|left|480px|A field sensor and 2D solution plane defined for a microstrip line.]]
</td>
</tr>
</table>
For a step-by-step demonstration (including transmission line [[optimization]]), take a look at this video on our YouTube channel: [http://www.youtube.com/watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization]<table><tr> == Simulation Examples / Gallery ==Â {| border="0"|-| valign="top"|<td> [[FileImage:ScreenCapture1Qsource17.png|thumb|left|350px480px|Classic Example: Two oppositely charged spheres.]]| valign="top"|[[File:iarray.png|thumb|left|350px|H-Field from array Electric field distribution of current loopsthe microstrip line on the 2D solution plane.]]</td>|-</tr> |}{| border="0"|-| valign="top"|<tr> <td> [[FileImage:ustripQsource18.png|thumb|left|350px|Potential near microstrip conductor from a quasistatic simulation.]]| valign="top"|[[File:ustrip2.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>|}Â == Version History ==</table>
* First available in [[EM.Cube|EM.CUBE]] 14.2<br />
== More Resources ==<hr>
* [http[Image://en.wikipedia.org/wiki/Electrostatics Wikipedia: ElectrostaticsTop_icon.png|30px]]* '''[[http://www.youtube.com/watch?v=Iiu9rQf1QI4 YouTube: EM.Ferma Optimization Example.#Product_Overview | Back to the Top of the Page]* [http://www.emagtech.com/content/emferma More about EM.Ferma.]'''
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