[[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 ==
=== Grouping Objects by Material or Source Type Physical Structure Definition ===
Your physical structure in EM.Ferma is typically made up of some kind of source either in the free space or in the presence of one or more material objects. EM.Ferma's electrostatic <ul> <li> Perfect electric conductor(PEC) solids and magnetostatic simulation engines then discretize these source and material surfaces (Electrostatics)</li> <li> Dielectric objects (Electrostatics)</li> <li> Magnetic (permeable) objects (Magnetostatics)</li> <li> Perfect thermal conductor (PTC) solids and solve the Laplace or Poisson equations to find the electric or magnetic fields everywhere in the computational domain. surfaces (Thermal)</li> <li> Insulator objects (Thermal)</li></ul>
All the CAD objects in the project workspace are organized together into object groups which share the same properties including color and electric or magnetic [[parameters]]. Once a new object group node has been created on the navigation tree, it becomes the "Active" object group of the project workspace, which is always listed in bold letters. When you draw a new CAD object such as a Box or a Sphere, it is inserted under the currently active surface type. 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. It is recommended that you first create object groups, and then draw new objects under the active surface group. 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 PEC object group is created and added to the navigation tree to hold your new CAD object.=== Sources ===
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining a New Object Group]]'''.<ul> <li> Fixed-potential PEC for maintaining equi-potential metal objects (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>
[[Image:Info_icon.png|40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups | Moving Objects among Different Groups]]'''.=== Mesh generation ===
=== Variety of Material Objects ===<ul> <li> Fixed-size brick cells</li></ul>
[[Image:Static1.png|thumb|330px| EM.Ferma's PEC dialog.]] EM.Ferma offers the following types of material objects for construction of your physical structure:=== 3D Electrostatic & Magnetostatic Simulation ===
* '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces | Perfect Electric Conductors (PEC)]]''': A perfect <ul> <li> Finite difference solution of Laplace and Poisson equations for the electric conductor (PEC) is a material scalar potential with Dirichlet and Neumann domain boundary conditions&epsilonnbsp;<sub/li>r </subli> = 1 Finite difference solution of Laplace and Poisson equations for the magnetic vector potential with Dirichlet domain boundary conditions&sigmanbsp; = ∞. </li>* '''[[Defining_Materials_in_EM.Cube#Defining_Dielectric_Materials | Dielectric <li> Calculation of electric scalar potential and electric field</Magnetic Materials]]''': You can define dielectric materials with the relative permittivity εli> <subli>r Calculation of magnetic vector potential and magnetic field</subli> <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 conductivity σ for electrostatic analysis or and magnetic (permeable) materials energies, Ohmic power loss and resistance</li> <li> Parametric sweep with the relative permeability μvariable object properties or source parameters<sub/li>r</subul> for magnetostatic analysis.
[[Image:Info_icon.png|40px]] Click here for a general discussion of '''[[Defining Materials in EM.Cube]]'''.=== 2D Quasi-Static Simulation ===
{{Note| You can define any solid or surface object <ul> <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 fixed- 2D plane </li> <li> Calculation of electric potential PEC object.}}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>
{{Note| Excluding surface and curve CAD objects, you can define any solid CAD object as a dielectric or magnetic material object.}} === Steady-State Thermal Simulation ===
=== Variety <ul> <li> Finite difference solution of Source Objects ===Laplace and 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>
EM.Ferma also offers the following types of source objects for excitation of your physical structure:=== Data Generation & Visualization ===
* '''[[#Using_Fixed-Potential_PEC_Objects_as_Voltage_Sources | Fixed-Potential PEC Objects]]'''<ul>* '''Volume Charges''': For volume charge sources you need to specify a positive or negative charge density in C <li> Electric and magnetic field intensity and vector plots on planes</mli> <supli>3 Electric and magnetic potential intensity plots on planes</supli>. You can draw all kinds of solid CAD objects under this group.* '''Volume Currents''': For volume current sources you need to specify a current <li> Temperature and heat flux intensity and vector plots on planes</li> <li> Electric and magnetic energy density in A, dissipated power density and thermal energy density plots on planes</mli> <supli>2 Animation of field and potential plots after parametric sweeps</supli>. You can draw all kinds <li> Graphs of solid CAD objects under this group. Note that current density is a vectorial quantity characteristic impedance and has a magnitude and a unit direction vectoreffective permittivity of transmission line structures vs.sweep variables</li>* '''[[#Wire_Current_Sources | Wire Currents]]''' <li>* '''[[#Permanent_Magnets | Permanent Magnets]]''' Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
<table><tr><td> [[Image:Static3.png|thumb|330px| == Building the Physical Structure in EM.Ferma's Charge Source dialog.]] </td><td> [[Image:Static5.png|thumb|330px| EM.Ferma's Volume Current Source dialog.]] </td></tr></table>==
=== Using Fixed-Potential PEC Variety of Physical Objects as Voltage Sources in EM.Ferma ===
[[Image:Static4.png|thumb|330px| EM.Ferma's Wire Current Source dialog.]] Under the The simplest static condition, every point on problems involve a PEC object has charge source in the same free space that produces an electric potential. By defaultfield, this is or a zero potential, meaning current source in the PEC object is "grounded"free space that produces a magnetic field. In EMsuch cases, the only applicable boundary conditions are defined at the boundary of the computational domain.Ferma, As soon as you introduce a PEC group has dielectric object next to a ''Fixed Potential''' property, which is expressed in Volts and has charge source or a zero default value. If you define magnetic (permeable) material next to a new PEC group and keep its default zero voltagecurrent source, the objects belonging you have to that group will simply act as metal objects of your physical structure. However, you can define deal with a nonzero voltage complex boundary value for a PEC groupproblem. You can do in the property dialog of the PEC groupIn other words, which you can access by right-clicking on need to solve the group's name in electric or magnetic Poisson equation subject to the navigation tree and selecting '''Propertiesdomain 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 contextual menu. In the case of a nonzero voltageOnce you introduce material blocks, all the PEC objects belonging you have to that group effectively turn into voltage sources. For example, two parallel PEC plates, one with a zero potential enforce conductive and convective boundary conditions at the other with a nonzero potential represent a simple interface between different materials and air-filled capacitor. Note that EM.Ferma uses the voltage Finite Difference (FD) technique to find a numerical solution of your static boundary value can be positive or negativeproblem.
=== Wire Current Sources ===[[EM.Ferma]] offers the following types of physical objects:
{| 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.Ferma allows you to define idealized wire current sources. You can use this 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 type to model filament currents or coilsif the fixed voltage is nonzero |-| style="width:30px;" | [[File:diel_group_icon. Wire currents are defined using only line and polyline 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. You also need to define 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 charge sources with a current value I in Amperes and a wire radius r fixed charge density or an expression in the project units. The line or polyline object is then approximated global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a 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 of J = I/vector or 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:pmc_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices &piOther Physical Object Types#Permanent Magnet |Permanent Magnet]]| style="width:300px;r<sup>2</sup>) flowing along the line " | Modeling permanent magnet sources with a fixed magnetization vector or polyline sideexpressions 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.png]]| style="width:200px;" | [[Glossary of EM.Cube's direction. All the Materials, Sources, Devices & Other Physical Object Types#Wire Current |Wire Current]]| style="width:300px;" | Modeling wire current sources belonging to | 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 same group have fixed temperature is different than the ambient temperature (shares the same colornavigation 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 current value and same wire radiusnavigation tree node as dielectric material)|-| style="width:30px;" | [[File:aniso_group_icon. The direction png]]| style="width:200px;" | [[Glossary of the current can be reversed in wire current EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Heat Source |Volume Heat Source]]| style="width:300px;" | Modeling volume heat sourceswith a fixed heat density or an expression in the global 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|}
To add a new wire current source group to a project, right-click Click on "Wire Currents" on the Navigation Tree, and select "Insert New Current Source..." From the Wire Current Source Dialog, you can change the default brown color 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 each category to the same group. When you draw a line or polyline object under a wire current group learn more details about it in the Navigation Tree, you will notice that direction arrows are placed on the drawn CAD object. You can draw any curve object in the project workspace and convert it to a polyline using [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'s Polygonize Tool.
{{Note| If you draw curve CAD objects under a wire current group, they will be permanently converted to polyline objects before running the simulation engine.}} === Grouping Objects by Material or Source Type ===
=== Permanent Magnets===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.
[[Image:Static6.png|thumb|330px| EMAll 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.Ferma's Permanent Magnet Source dialog.]]A permanent magnet It is typically a ferromagnetic material with a fixed inherent magnetization vectorrecommended that you first create object groups, and then draw new objects under the active group. As To create a resultnew object group, it can be used as a source right-click on its category name in an magnetostatic problemthe "Physical Structure" section of the navigation tree and select one of the "Insert New Group. When .." items from the contextual menu. However, if you start a permeable material has new EM.Ferma project from scratch, and start drawing a permanent magnetizationnew 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 following relationship holds: navigation tree to hold your new geometric object.
<math> \mathbf{B(r)} = {\mu} (\mathbf{H(r)} + \mathbf{M(r)} ) </math>It is important to note that there is a one-to-one correspondence between electrostatic and thermal simulation entities:
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. {| 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|}
It can be shown that for magnetostatic analysis, {{Note|Electrostatic and thermal solvers share the effect of same material categories on the permanent magnetization can be modeled navigation tree. This means that PEC objects are treated as an equivalent PTC objects, dielectric objects are treated as insulator objects and volume current source: <math> \mathbf{J_{eqcharges are treated as volume heat sources when the thermal solver is enabled.}(r)} = \nabla \times \mathbf{M(r)} </math>
If Once a new object group node has been created in the magnetization vector is uniform navigation tree, it becomes and constant inside remains the volume"Active" object group, then its curl which is zero everywhere inside the volume except on its boundary surfacealways listed in bold letters. In this caseWhen you draw a new geometric object such as a box or a sphere, its name is added under the permanent magnetic currently active object group. There is only one object group that is active at any time. Any group can be effectively modeled made active by an equivalent surface current density right-clicking on its name in the navigation tree and selecting the surface '''Activate''' item of the permanent magnetic object: contextual menu.
<math> \mathbf{J_{s,eq}(r)} = \mathbf{M(r)} \times \hat{\mathbf{n}} </math>[[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]]'''.
where <mathtable> \hat{\mathbf{n}} </mathtr> is the unit outward normal vector at the surface of the permanent magnet object<td> [[Image:STAT MAN1. Note that the volume of the permanent magnet still acts as a permeable material in the magnetostatic analysispng|thumb|left|480px|EM. Ferma's navigation tree.]] </td></tr></table>
To add a new permanent magnet source group to a project, right-click === A Note on "Permanent Magnets" on the Navigation Tree, Material and select "Insert New Permanent Magnet SourceTypes in EM..." 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.Ferma ===
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.  In 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 (PEC) 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. == EM.Ferma's 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>
<tr>
<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>
</table>
[[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|360pxleft|Geometry of a spherical charge source and the enclosing domain box480px|EM.]] </td><td> [[Image:Qsource3.png|thumb|360px|Fixed-cel mesh of the spherical charge objectFerma's Boundary Conditions dialog.]] </td>
</tr>
</table>
== 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{| class="wikitable"|-! scope="col"| Icon! scope="col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications|-| style="width:30px;" | [[File:fieldsensor_icon. This is done by clicking the png]]| style="width:150px;" | Near-Field Distribution Maps| style="Runwidth:150px;" button | [[Glossary of the Simulate ToolbarEM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and magnetic field components, or by selecting electric scalar potential and magnitude of magnetic vector potential on a planar cross section of the computational domain |-| style="Runwidth:30px;" item | [[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 Simulate Menu, or simply using the keyboard shortcut computational domain |-| style="Ctrl+Rwidth:30px;"| [[File:fieldsensor_icon. The only available simulation engine is png]]| style="Staticwidth:150px;"| Temperature and Heat Flux Distribution Maps| style="width:150px;" | [[Glossary of EM. Clicking 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 Run button computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Thermal Energy Density Maps | style="width:150px;" | [[Glossary of this dialog starts a static analysisEM. A separate window pops up which reports the progress 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 current simulationcomputational 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 |}
=== Simulation Modes === EM.Ferma currently offers three different simulation modes: Analysis, Parametric Sweep and [[Optimization]]. An "Analysis" is a single-shot finite difference solution of your static structure. The structure is first discretized using a fixed-cell mesh and the Poisson equation is solved numerically everywhere in your computational domain. The field and potential values at Click on each mesh node are computed and the specified observables are written into data files. In a "Parametric Sweep", one ore category to learn more [[variables]] are varied at the specified steps(s). This means that you must first define one or more [[variables]] details about it in your projects. [[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 of variable samples, first all the associated CAD object properties, material properties or source properties are updated in the project workspace. Then is a finite difference solution of your updated static structure is computed and parametric sweep proceeds to the next variable sample or combination. The [[optimization]] mode requires definition Glossary of one or more objectives based on the standard output quantities. At the present time, the [[optimization]] mode is only available for the 2D Quasi-Static Mode of the EM.Ferma, which will be discussed separately later.  [[Image:Qsource7.png|thumb|400px|EM.FermaCube's Static Engine Settings dialog.]] ===Static Simulation Engine Settings=== EM.Ferma currently uses a single iterative linear system solver based on the stabilized Bi-Conjugate Gradient (BiCG) method to solve the matrix equations which result from the discretization of Poisson's equation. You can specify some numerical [[parameters]] related to the Bi-CG 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 1e-6.  {{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 on 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|EM.Ferma's Field Sensor dialog.]] 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 '''[[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Field Sensor Observables& Graph Types]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near-Field Maps]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Plotting_Field_Distribution_Graphs_Along_Lines | Plotting Field Distribution Graphs Along Lines]]'''.
<table>
<tr>
<td> [[Image:Qsource9Ferma L1 Fig15.png|thumb|360pxleft|640px|Electric field distribution of a spherical charge on a horizontal field sensor plane.]] </td></tr> <tr><td> [[Image:Qsource10Ferma L1 Fig16.png|thumb|360pxleft|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
|}
Â
Â
[[Image:Qsource13.png|thumb|400px|Defining the capacitance observable in the Field Integral dialog.]]
In 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 volume. 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.
Â
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.
Â
After the completion of a static simulation, the result of the field integrals are written into ".DAT" data files. These files can be accessed using [[EM.Cube]]'s Data Manager.
<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|360pxleft|480px|The electric flux box for calculation of charge around a capacitor.]] </td></tr> <tr><td> [[Image:Qsource12.png|thumb|360pxleft|480px|A line defining the voltage path for calculation of voltage between capacitor plates.]] </td>
</tr>
</table>
== Modeling Transmission Lines Using Discretizing the Physical Structure in EM.Ferma==
[[Image:qstatic.png|thumb|300px|Setting up a Transmission Line simulation.]]===The Static Mesh===
The Finite Difference technique discretizes the computational domain using a 3D rectangular grid. EM.Ferma generates a fixed-cell mesh. This means that the extents of the mesh cells along the principal axes are fixed: Δx, Δy, Δz. By default, the mesh cell size is set to one unit project along all the three directions (with Δx =Δy ==2D Electrostatic Simulation Mode===Δz). To modify the cell size, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static Mesh" in the Navigation Tree, and select "Mesh Settings..." from the contextual menu to open the Mesh Settings Dialog. {{Note|To obtain accurate results, it is highly recommended to use a square mesh as much as possible.}}
EM[[Image:Info_icon.Ferma's electrostatic simulation engine features a 2D solution mode where the model is treated as a longitudinally infinite structure in the direction normal png|30px]] Click here to specified "2D Solution Plane"learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. More than one 2D solution plane may be definedCube. In that case, multiple 2D solutions are obtained. A 2D solution plane is defined based on a "Field Sensor" definition that already exists in the project27s_Mesh_Generators | Working with Mesh Generator]]'''.
To explore [[Image:Info_icon.png|30px]] Click here to learn more about the properties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's 2D mode, rightFixed-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 projectCell Brick Mesh Generator]]'''.
At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the respective field sensor planes<table><tr> <td> [[Image:Qsource4. It is assumed that your structure is invariant along the direction normal to the 2D solution planepng|thumb|350px|EM. Therefore, your computed field and potential profiles must be valid at all the planes perpendicular to the specified longitudinal directionFerma's Mesh Settings dialog. ]] </td></tr></table>
<table>
<tr>
<td> [[Image:Qsource14Qsource2.png|thumb|360px|The 2D Static Domain dialogGeometry of a spherical charge source and the enclosing domain box.]] </td><td> [[Image:Qsource15Qsource3.png|thumb|360px|A Add/Edit 2D Solution Plane dialogFixed-cel mesh of the spherical charge object.]] </td>
</tr>
</table>
=== 2D Quasi-Running Static Solution of Transmission Lines =Simulations in EM.Ferma ==
At lower microwave frequencies (f < 10GHz), it is usually possible to perform a 2D electrostatic analysis of a transmission line structure and compute its characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub>=== EM. This "quasi-static approach" involves two steps:Ferma's Simulation Modes ===
<ol><li>First, you have remove all the dielectric materials from your structure and replace them with free space (or air)[[EM. 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>Ferma]] currently offers three different simulation modes as follows:
Then effective permittivity {| class="wikitable"|-! scope="col"| Simulation Mode! scope="col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]| style="width:270px;" | Simulates the transmission line physical structure is then calculated from "As Is"| style="width:100px;" | Single run| style="width:200px;" | N/A| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.Cube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style="width:270px;" | Varies the equationvalue(s) of one or more project variables| style="width:100px;" | Multiple runs | style="width:200px;" | N/A<math> \epsilon_{eff} | style= \frac{C}{C_a} <"width:150px;" | 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/math>A| style="width:150px;" | None|}
and its characteristic impedance is given by: <math> Z_0 = \eta_0 \sqrt{ \frac{C_a}{C} } </math>== Running an Electrostatic, Magnetostatic or Thermal Analysis ===
where η<sub>0</sub> = 120π Ω is [[EM.Ferma]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Thermal. The electrostatic engine solves the intrinsic impedance electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in the free spacepresence 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.
The guide wavelength of your transmission line at To run a given frequency f static simulation, first you have to open the Run Dialog. This is then calculated fromdone by clicking the "Run" button of the Simulate Toolbar, or by selecting the "Run" item of the Simulate Menu, or simply using the keyboard shortcut "Ctrl+R". There are two available options for the simulation engine:'''Electrostatic-Magnetostatic Solver''' and '''Steady-State Thermal Solver'''. Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation.
<mathtable> \lambda_g = \frac{\lambda_0}{\sqrt{\epsilon_{eff}}} = \frac{c}{f\sqrt{\epsilon_{eff}}} <tr> <td> [[Image:Ferma L1 Fig11.png|thumb|left|600px|EM.Ferma's Simulation Run dialog.]] </td></tr></mathtable>
In EM.Ferma you don't have to choose between the electrostatic or magnetostatic simulation engines. The program looks at the types of sources and its propagation constant 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. 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 time. By default, the electrostatic solver is given by:enabled.
<math> \beta = k_0\sqrt{\epsilon_{eff}} = \frac{2\pi f}{c}\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.
where c is the speed of light in the free space. ===Static Simulation Engine Settings===
EM.Fermaoffers two different types of linear system solver for solving the matrix equations that result from discretization of Poisson's 2D Quasi-Static mode automatically performs equation: an iterative solver based on the twostabilized Bi-step process described above Conjugate Gradient (BiCG) method and calculates ε<sub>eff</sub> and Z<sub>0</sub>a Gauss-Seidel solver. So The default solver type is BiCG. You can specify some numerical parameters related to the BiCG solver. To do that, you don't need to modify your structure in open the first stepSimulation 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>.
=== Setting up a Transmission Line Simulation ==={{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.}}
To perform a transmission line simulation, first draw your structure in the project workspace just like a typical 3D structure<table><tr> <td> [[Image:Qsource7. Define a "Field Sensor" observable in the Navigation Tree so as to capture the cross section of your structure as your desired transmission line profilepng|thumb|left|480px|EM. Ferma's Static Engine Settings dialog.]]</td></tr></table>
Next, define a "2D Solution Plane" in the Navigation Tree based on your existing field sensor. When defining the 2D plane, check the box labeled "Perform == The 2D Quasi-Static Simulation". If an analysis is run with this option checked, the characteristic impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> will be computed for the corresponding 2D Solution Plane. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively, where "solution_plane" is the default name of your 2D plane. Mode==
Many EM.Ferma's electrostatic simulation engine features a 2D quasi-static solutions can be obtained solution mode where your physical model is treated as a longitudinally infinite structure in the same analysis,for example, when direction normal to specified "2D Solution Plane". A 2D solution plane is defined based on a "Field Sensor" definition that already exists in your design contains many types of [[Transmission Lines|transmission lines]]project. At To explore EM.Ferma's 2D mode, right-click on '''2D Solution Planes''' in the end "Computational Domain" section of a quasi-static analysis, the electric field components navigation tree and scalar potential at the selected select '''2D planes will still be computed and can be visualizedDomain Settings. ..''' from the contextual menu. In the case of a parametric sweep2D Static Domain dialog, check the data files will contain multiple data entries listed against checkbox labeled "Reduce the corresponding variable samples3D Domain to a 2D Solution Plane". Such data files can be plotted The first field sensor observable in EMthe navigation tree is used for the definition of the 2D solution plane.Grid. === Optimizing a Transmission Line ===
In an [[optimization]] simulation, At the values end of one or more [[variables]] are varied over their specified rangesa 2D electrostatic analysis, you can view the electric field and a design objective potential results on the field sensor plane. It is tested 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 each simulation runall the planes perpendicular to the specified longitudinal direction. A design objective is typically a logical expression that sets an expression equal 2D structure of this type can be considered to represent a target valuetransmission line of infinite length. EM.Ferma currently offers two standard outputs: ε<sub>eff</sub> also performs a quasi-static analysis of the transmission line structure, and Zusually provides good results at lower microwave frequencies (f <sub>0</sub>10GHz). Two possible objectives are "It computes the characteristics impedance Z<sub>0</sub> == 50" or "sqrt(and effective permittivity ε<sub>eff</sub>) == 1.5". To define an objective, click the "Objectives" button of the Simulate Toolbar, multi-conductor TEM or select the quasi-TEM transmission line. The results are written to two output data files named "Objectivessolution_plane_Z0.DAT" item of the Simulate Menu, or simply use the keyboard shortcut and "Ctrl+Jsolution_plane_EpsEff.DAT". In the Objectives Dialog, you can add new objective or edit the existing objectivesrespectively.
<table>
<tr>
<td> [[Image:Qsource14.png|thumb|left|450px|The 2D static domain dialog.]] </td>
</tr>
</table>
For a step-by-step demonstration (including transmission line [[optimizationImage:Info_icon.png|30px]]), take a look at this video on our YouTube channel: Click here to learn more about the theory of '''[http://www.youtube.com/watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization[Electrostatic_%26_Magnetostatic_Field_Analysis#2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures | 2D Quasi-Static Analysis of Transmission Lines]]'''.
<!--== Simulation Examples table><tr> <td> [[Image:Qsource16.png|thumb|left|480px|A field sensor and 2D solution plane defined for a microstrip line.]]</ Gallery ==td></tr></table>
{| border="0"<table>|-| valign="top"|<tr> <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>|}--</table>Â == Version History ==
* 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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