Click here to learn more about [[Planar Traces & Object Types]].
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=== Modeling Metallic Traces ===
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A trace is a group of finite-sized planar objects that have the same conductive properties and same Z-coordinate. In other words, they are located on the same horizontal plane, or at the same vertical level on the layer stack-up. You can define two types of metallic traces in the [[Planar Module]]:
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# '''PEC Traces:''' These represent perfect conductor objects that have zero thickness and no editable material properties.
# '''Conductive Sheet Traces:''' These represent imperfect metal objects. They have a very small finite thickness t and a finite conductivity s.
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The conductive sheet traces are modeled using the surface impedance boundary condition:
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:<math> \hat{n} \times \hat{n} \times \mathbf{E} = -Z_s\mathbf{J_s} </math>
<!--[[File:PMOM17(1).png]]-->
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where <math>Z_s</math> is the surface impedance of the conductive sheet. If the thickness of the sheet is greater than the skin depth of the metal at the project frequency, then the surface impedance is given by
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:<math> Z_s = \dfrac{1+j}{\sigma \delta}, \quad \delta = \sqrt{\dfrac{2}{k_0 Z_0 \sigma}} </math>
<!--[[File:PMOM18.png]]-->
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If the thickness t of the sheet is less than the skin depth, then the conductive sheet transition boundary condition is used instead, and the surface impedance is given by
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:<math> Z_s = \dfrac{1}{[j k_0 Y_0 (\varepsilon_r - 1) + \sigma] \tau} = \dfrac{1}{\sigma_{tot} \tau} </math>
<!--[[File:PMOM19(2).png]]-->
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When you start a new project in [[Planar Module]] with no traces defined, if you simply draw a new object, a default PEC trace is created and added to the Navigation Tree to hold that object. Alternatively, you can define your own new traces from the Layer Stack-up Settings dialog or directly from the Navigation Tree.
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NOTE: Two or more PEC and conductive sheet traces can coexist at the same Z-coordinate. In this case, the Layer Stack-up Settings dialog shows these trace rows stacked up on top of each other between their common top and bottom substrate layers.
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[[File:PMOM15.png]] [[File:PMOM16.png]]
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Figure 1: The [[Planar Module]]'s PEC and Conductive Sheet Trace dialogs.
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=== Modeling Slot Traces ===
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Slots and apertures are cut-out and removed metal in an infinite perfectly conducting (PEC) ground plane. When a slot is excited, tangential electric fields are formed on the aperture, which can be modeled as finite magnetic surface currents confined to the area of the slot. Therefore, instead of modeling the electric surface currents on the PEC ground around the slot, one can alternatively model the finite-extent magnetic surface currents on PMC traces. In [[EM.Cube]]'s [[Planar Module]], you define slot objects under PMC traces. A PMC trace at a certain Z-plane implies the presence of an infinite PEC plane at that Z-coordinate. Therefore, you do not need to define an additional PEC plane at that location on the layer stack-up. The slot (PMC) objects provide the electromagnetic coupling between the two sides of this infinite ground plane. By the same token, you cannot place a PEC trace and a PMC trace at the same Z-level, as the latter's ground will short the former. However, you can define two or more PMC traces at the same Z-plane. In this case, all the slot objects lie on the same infinite PEC ground plane. <br />
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[[File:PMOM20.png]]
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Figure 1: The [[Planar Module]]'s PMC Trace dialog.
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=== Defining Embedded Object Sets ===
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Embedded object sets represent short material insertions inside substrate layers. They can be metal or dielectric. Metallic embedded objects can be used to model vias, plated-through holes, shorting pins and interconnects. These are called PEC via sets. Embedded dielectric objects can be used to model air voids, thin films and material inserts in metamaterial structures. Embedded magnetic object are not currently supported by [[EM.Cube]]âs [[Planar Module]].
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Embedded objects can be defined either from the Layer Stack-up Settings dialog or directly from the Navigation Tree. In the former case, open the "Embedded Sets" tab of the stack-up dialog. This tab has a table that lists all the embedded object sets along with their material type, the host substrate layer, the host material and their height.
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{{Note|The height of an embedded object is always identical to the thickness of its host substrate layer.}}
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[[File:PMOM23.png]]
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Figure 1: [[Planar Module]]'s Layer Stack-up dialog showing the Embedded Sets tab.
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To add a new object set, click the arrow symbol on the '''Insert''' button of the dialog and select one of the two options, '''PEC Via Set''' or '''Embedded Dielectric Set''', from the dropdown list. This opens up a new dialog where first you have to set the host layer of the new object set. A dropdown list labeled "'''Host Layer'''" gives a list of all the available finite substrate layers. You can also set the properties of the embedded object set, including its label, color and material properties. Keep in mind that you cannot control the height of embedded objects. Moreover, you cannot assign material properties to PEC via sets, while you can set values for the '''Permittivity'''(ε<sub>r</sub>) and '''Electric Conductivity'''(σ) of embedded dielectric sets. Vacuum is the default material choice. You may use [[EM.Cube]]'s Material List for this purpose, which can be opened up by clicking the '''Material''' button. Once embedded object sets are added to the Embedded Sets table, you can edit their properties at any time by selecting their row and clicking the '''Edit''' button.
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[[File:PMOM21.png]] [[File:PMOM22.png]]
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Figure 2: The [[Planar Module]]'s PEC Via Set and Embedded Dielectric Set dialogs.
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To define an embedded set from the Navigation Tree, right click on the '''Embedded Object Sets''' item in the '''Physical Structure''' section of the Navigation Tree and select either '''Insert New PEC Via Set...''' or '''Insert New Embedded Dielectric Set...''' The respective New Embedded Object Set dialog opens up, where you set the properties of the new object set. As soon as you close this dialog, it takes you to the Layer Stack-up Settings dialog, where you can examine the location of the new object set on the layer hierarchy.
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After a new embedded object set has been defined and added to the Navigation Tree, it becomes the active trace. You are now ready to create geometrical objects in the new active trace. Remember that [[Planar Module]] does not allow you to draw 3D objects. The solid object buttons in the '''Object Toolbar''' are disabled to prevent you from doing so. Instead, you draw planar [[Surface Objects|surface objects]] as the cross section of embedded sets. [[EM.Cube]] extends these planar objects across their host layer automatically and displays them as wire-frame, 3D extruded objects. Extrusion of embedded object sets happen after meshing and before every simulation. You can enforce this extrusion manually by right clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section of the Navigation Tree and selecting '''Update Planar Structure...''' from the contextual menu.
=== Planar Module's Rules & Limitations ===
You can excite a planar structure in a number of different ways. The excitation source you choose depends on the observables you seek in your project. [[Planar Module]] provides the following source for exciting planar structures:
* Lumped Sources with three varieties: [[#Gap Sources|Gap Sources]], * [[#De-embedded Probe Sources|De-embedded Probe Sources]] and * [[#Probe De-embedded Sources|Probe De-embedded Sources]]
* [[#Plane Wave Sources|Plane Wave Sources]]
* [[#Short Dipole Sources|Short Dipole Sources]]
For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal. Gap sources are placed across metal or slot traces. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parameters]] can be calculated accurately. To calculate the scattering characteristics of a planar structure, e.g. its radar cross section (RCS), you excite it with a plane wave source. Short dipole sources are used to explore propagation of points sources along a layered structure. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure possibly in another [[EM.Cube]] computational module and bring them as a new source to excite your planar structure.
=== Gap Sources === [[File:PMOM47.png|thumb|250px|The [[Planar Module]]'s Gap Source dialog]] A gap is an infinitesimally narrow discontinuity that is placed on the path of current flow on a feed line. In planar structures, feed lines are typically in the form of a microstrip, stripline, slotline or coplanar waveguide (CPW). You use rectangle strip objects Click here to construct such feed lines. A gap source can be placed on any rectangle strip object on a PEC, PMC or conductive sheet trace. Depending on the type of the trace on which a gap source is placed, it will have a different physical interpretation. A rectangle strip object on a PEC or conductive sheet trace can be regarded as a strip transmission line that carries electric currents along its length (local X direction). The characteristic impedance of the line is a function of its width (local Y direction). A gap source is placed somewhere along the length and across the width of such a rectangle strip object, thus creating an infinitesimally narrow gap at its location. In this case, the gap source represents an ideal voltage source in series with a lumped impedance that is connected across the gap to excite the strip transmission line. When the impedance is zero, the gap acts like an ideal lumped source and creates a uniform electric field across the gap. The source pumps electric current into the line. If the voltage source is shorted (having a zero amplitude), then the gap acts like a series lumped element on the transmission line. A rectangle strip object on a PMC trace can be regarded as a slot transmission line on an infinite PEC ground plane that carries a magnetic current along its length (local X direction). The characteristic impedance of the slot line is a function of its width (local Y direction). A slot gap source is placed somewhere along the length and across the width of the rectangle strip object on a PMC trace and creates an infinitesimally narrow gap at its location. In this case, the slot gap source represents an ideal current source with a shunt lumped admittance that is connected across the slot to excite the slot transmission line. When the admittance is zero, the gap acts like an ideal current filament, which creates electric fields across the slot, equivalent to a magnetic current flowing into the slot line. If the current source is open (having a zero amplitude), then the gap acts like a shunt (parallel) lumped element on the slot line. As you will see later, a coplanar waveguide (CPW) can be realized using two parallel slot lines with two aligned, collocated gap sources. To define a gap source, follow these steps: * Open the Gap Source Dialog by right clicking on the '''Gap Sources''' item in the '''Sources''' section of the Navigation Tree and selecting '''Insert New Source...'''* In the '''Source Location''' section of the dialog, you will find a list of all the '''Rectangle Strip Objects''' available in the project workspace. Select the desired host rectangle strip object. The box labeled '''Direction''' shows the direction or polarity of the new gap source on its host rectangle strip object. You have the option to select either the positive or negative direction for the source polarity.* In the box labeled '''Offset''', enter the distance of the gap source from the start point of the rectangle strip feed line. The value of '''Offset''' by default is initially set to the center of the line. As you change the offset value, you can see the gap move on its host object.* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of a gap on a slot trace) and '''Phase''' in degrees.* You can also change the default label as well as the default color of the gap source using the '''Color''' button of the dialog and selecting the desired color from the color palette. === Probe Sources === [[File:PMOM48.png|thumb|250px|The learn more about [[Planar Module]]'s Probe MoM Source dialogTypes]] Another way of exciting a planar structure is by placing a gap on the path of a vertical current on a PEC via. This represents a filament source, which is used to model coaxial probe excitation. A probe source can be placed only on a PEC via object. Most planar [[Transmission Lines|transmission lines]] are fed using SMA connectors. The outer conductor of the coaxial line is connected to the ground and its inner conductor is extended across the substrate layer and connected to a metallic line. [[EM.Cube]]'s [[Planar Module]] models a coaxial probe as an infinitesimal gap discontinuity placed across a thin via, representing an ideal voltage source in series with a lumped impedance. When the impedance is zero, the gap acts like an ideal lumped source and creates a uniform electric field across the via. The source pumps vertical electric current into the probe. If the voltage source is shorted (having a zero amplitude), then the gap acts like a shunt lumped element across the via. To define a probe source, follow these steps: * Open the Probe Source Dialog by right clicking on the '''Probe Sources''' item in the '''Sources''' section of the Navigation Tree and selecting '''Insert New Source...'''* In the '''Source Location''' section of the dialog, in the dropdown list labeled '''Embedded Objects''', you will find a list of all the PEC via objects available in the project workspace. Select the desired host PEC via object. The box labeled '''Direction''' shows the direction or polarity of the new probe source on its host PEC via object. You have the option to select either the positive or negative direction for the source.* In the box labeled '''Offset''', enter the distance of the probe source from the bottom of the via object. The value of '''Offset''' by default is initially set to the center of the via.* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts and '''Phase''' in degrees. Unlike gap sources, whose offset parameter determines their exact location on their host line, the offset parameter of a probe source is not relevant except for long host vias. In the case of a short via that is discretized using a single prismatic element across its host substrate layer, the probe gap is always placed at the middle of its height. Longer vias may have a mesh that consists of two or more stacked prismatic elements. In this case, the probe source's offset determines which prismatic element will host the probe gap discontinuity at its middle.
=== Defining Source Arrays ===
You couple two or more sources using the '''Port Definition Dialog'''. To do so, you need to change the default port assignments. First, delete all the ports that are to be coupled from the Port List of the dialog. Then, define a new port by clicking the '''Add''' button of the dialog. This opens up the Add Port dialog, which consists of two tables: '''Available''' sources on the left and '''Associated''' sources on the right. A right arrow ('''-->''') button and a left arrow ('''<--''') button let you move the sources freely between these two tables. You will see in the "Available" table a list of all the sources that you deleted earlier. You may even see more available sources. Select all the sources that you want to couple and move them to the "Associated" table on the right. You can make multiple selections using the keyboard's '''Shift''' and '''Ctrl''' keys. Closing the Add Port dialog returns you to the Port Definition dialog, where you will now see the names of all the coupled sources next to the name of the newly added port.
{{Note|It is your responsibility to set up coupled ports and coupled [[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|transmission lines]]]]]]]]]]]]]]]] properly. For example, to excite the desirable odd mode of a coplanar waveguide (CPW), you need to create two rectangular slots parallel to and aligned with each other and place two gap sources on them with the same offsets and opposite polarities. To excite the even mode of the CPW, you use the same polarity for the two collocated gap sources. Whether you define a coupled port for the CPW or not, the right definition of sources will excite the proper mode. The couple ports are needed only for correct calculation of the port characteristics.}}
[[File:PMOM51(2).png|800px]]