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|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]]
Figure 1: Minimum and maximum current locations of the standing wave pattern on a microstrip line feeding a patch antenna.
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=== De-Embedded Sources ===
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[[File:PMOM74.png|thumb|300px|The [[Planar Module]]'s De-embedded Source dialog]]
[[EM.Cube]]'s [[Planar Module]] provides de-embedded sources for the exclusive purpose of accurate S parameter calculation based on Prony's method. A de-embedded source is indeed a gap source that is placed close to an open end of a feed line. The other end of the line is typically connected to a planar structure of interest. Like gap sources, de-embedded sources can be placed only on rectangle strip objects. '''During mesh generation, [[EM.Cube]] automatically extends the length of a port line that hosts a de-embedded source to about two effective wavelengths.''' This is done to provide enough length for formation of a clean standing wave current pattern. The effective wavelength of a transmission line for length extension purposes is calculated in a similar manner as for the planar mesh resolution. It is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where ε<sub>eff</sub> is the effective permittivity. For metal and conductive sheet traces, the effective permittivity is defined as the larger of the permittivities of the two substrate layers just above and below the metallic trace. For slot traces, the effective permittivity is defined as the mean (average) of the permittivities of the two substrate layers just above and below the metallic trace. The host port line must always be open from one end to allow for its length extension. You have to make sure that there are no objects standing on the way of the extended port line to avoid any unwanted overlaps.
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[[File:PMOM72.png|800px]]
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Figure 1: The mesh of a patch antenna excited with a de-embedded source. Note the feed line extension in the mesh view.
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You can define de-embedded source on metal (PEC), slot (PMC) and conductive sheet traces. To define a de-embedded source, follow these steps:
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* Open the De-Embedded Source Dialog by right clicking on the '''De-Embedded 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''' or arrays of such objects that are available in the project workspace. The box labeled '''Direction''' shows the direction the phase reference plane for S parameter calculation and determines which end of the host line to place the source at. You have the option to select either the positive or negative direction to bounce the source between the two ends of the line.
* In the box labeled '''Offset''', enter the distance of the phase reference plane from the end of the feed line object. The value of '''Offset''' by default is initially set to zero, meaning that the S [[parameters]] are calculated at the plane passing through the end of the feed line. Type in a new offset value or use the spin buttons to move the source arrow along the line away from its end. As you change the offset value, you can see the source arrow move along its host object.
* In the '''Source Properties''' section, you can specify the '''Source Amplitude''' in Volts (or in Amperes in the case of slot traces) and '''Phase''' in degrees.
* In the '''Prony Mode Extraction''' section, you can specify the '''Number of Prony Modes''', which refers to the number of positive-negative exponential pairs that are extracted from the standing wave current data. The default value is 1 and represents the dominant quasi-TEM incident/reflected signal pair.
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In a planar project with de-embedded sources, if you do not define any ports, the feed lines will simply be extended, and the exciting gap sources will be placed at the open ends of these extended lines. Note that if you define a de-embedded source along with a port definition in your project, then all the other port-assigned sources of your project must be of the same de-embedded type. You can define de-embedded sources for coplanar waveguides (CPW) on slot traces. To do so, you need to place two collocated, de-embedded sources with identical offsets (same phase reference plane), same source amplitudes but 180° phase difference. Note that for CPW structures, setting the number of Prony modes to 2 can get you more accurate results. In this case, the two extracted Prony modes will include the incident and reflected, odd and even, propagating modes of the CPW.
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=== Short Dipole Sources ===
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[[File:PMOM110.png|thumb|250px|Short Dipole Source dialog]]
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A short dipole is the simplest type of radiator, which consists of a short current element of length &DELTA;l, aligned along a unit vector û and carrying a current of I Amperes. The product I&DELTA;l is often called the dipole moment and gives a measure of the radiator's strength. A short dipole in the free space generates an azimuth-symmetric, almost omni-directional, far field. However, the radiated fields of a short dipole above a layered planar background structure are greatly altered by the presence of the substrate layers. Note that the electric and magnetic field radiated by a short dipole in the presence of a layered background structure are indeed nothing but the dyadic Green's functions of that structure:
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:<math> E^{inc}(r) = \int_{\Delta_L} \overline{\overline{G_{EJ}}}(r|r') \cdot (I\Delta l \hat{u}) \, dl' </math>
:<math> H^{inc}(r) = \int_{\Delta_L} \overline{\overline{G_{HJ}}}(r|r') \cdot (I\Delta l \hat{u}) \, dl' </math>
<!--[[File:PMOM109(1).png]]-->
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To define a short dipole source, follow these steps:
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* Right click on the '''Short Dipoles''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' The Short Dipole Dialog opens up.
* In the section titled '''Source Location''', enter values for the X, Y and Z coordinates of the dipole's center. By default, a new dipole is placed at the origin of coordinates. As you change the coordinates using the spin buttons, you will see the dipole move in the project workspace.
* In the section titled '''Source Properties''', you can change the values of the dipole's '''Amplitude''' (in A), '''Phase''' (in degrees) and '''Length''' in the project's length units. A new dipole, by default, is Z-directed. You can change its orientation by entering the components of its unit vector in the three boxes labeled '''Direction Unit Vector'''.
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=== Plane Wave Sources ===
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[[File:PMOM77.png|thumb|300px|[[Planar Module]]'s Plane Wave dialog]]
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You can excite a planar structure with an incident plane wave to explore its scattering characteristics such as radar cross section (RCS). Exciting an antenna structure with an incident plane wave is equivalent to operating it in the "receive" mode. Plane wave excitation in the [[Planar Module]] is particularly useful for calculation of reflection and transmission coefficients of periodic surfaces. Note that the incident plane wave in your project bounces off the layered background structure and part of it also penetrates the substrate layers. The total incident field that is used to calculate the excitation vector of the MoM linear system is a superposition of the incident, reflected and transmitted plane waves at various regions of your planar structure:
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:<math> \mathbf{E^{inc}(r)} = E_0 (\mathbf{\hat{e}_1} e^{ -jk_0 \mathbf{\hat{k}_1\cdot r} } + R \mathbf{\hat{e}_2} e^{ -jk_0 \mathbf{\hat{k}_2\cdot r} } ) </math>
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:<math> \mathbf{H^{inc}(r)} = \frac{E_0}{\eta_0} ( \mathbf{\hat{k}_1 \times \hat{e}_1} e^{-jk_0 \mathbf{\hat{k}_1 \cdot r} } + R \mathbf{\hat{k}_2 \times \hat{e}_2} e^{-jk_0 \mathbf{\hat{k}_2\cdot r} } ) </math>
<!--[[File:PMOM111.png]]-->
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where <math>\eta_0 = 120\pi</math> is the characteristic impedance of the free space, '''k<sub>1</sub>''' and '''k<sub>2</sub>''' are the unit propagation vectors of the incident plane wave and the wave reflected off the topmost substrate layer, respectively, and '''ê<sub>1</sub>''' and '''ê<sub>2</sub>''' are the polarization vectors corresponding to the electric field of those waves. R is the reflection coefficient at the interface between the top half-space and the topmost substrate layer and has different values for the TM and TE polarizations.
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[[EM.Cube]]'s [[Planar Module]] provides the following polarization options:
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* TMz
* TEz
* LCPz
* RCPz
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The direction of incidence is defined through the theta and phi angles of the propagation vector in the spherical coordinate system. The default values are θ = 180° and φ = 0°, representing a normally incident plane wave propagating along the -Z direction with a +X-polarized electric field vector. In the TM<sub>z</sub> and TE<sub>z</sub> polarization cases, the magnetic and electric fields are parallel to the XY plane, respectively. The left-hand (LCP) and right-hand (RCP) circular polarization cases are restricted to normal incidences only (θ = 180°).
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To define a plane wave source, follow these steps:
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* Right click on the '''Plane Waves''' item in the '''Sources''' section of the Navigation Tree and select '''Insert New Source...''' The Plane wave Dialog opens up.
* In the Field Definition section of the dialog, you can enter the '''Amplitude''' of the incident electric field in V/m and '''Phase''' in degrees. The default field Amplitude is 1 V/m, with a zero Phase.
* The direction of the Plane Wave is determined by the incident '''Theta''' and '''Phi''' angles expressed in the spherical coordinate system in degrees. You have to choose the '''Polarization''' of the plane wave from the four options: '''TM<sub>z</sub>''', '''TE<sub>z</sub>''', '''LCP<sub>z</sub>'''and '''RCP<sub>z</sub>'''. The components of the unit propagation vector are shown based on your choice of the angles of incidence. The components of the normalized E- and H-field vectors are also displayed based on your choice of polarization.
== Running Planar MoM Simulations ==