Changes

EM.Picasso

22 bytes added, 20:54, 25 August 2014
/* Computing The Far Fields */
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|[[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]]
Unlike differential-based methods, MoM simulators do not need a radiation box to calculate the far field data. The far-zone fields are calculated directly by integrating the currents on the traces and across the embedded objects using the asymptotic form of the background structure’s dyadic Green's functions:
:<math> \mathbf{E^{ff}(r)} = \iiint_V \mathbf{ \overline{\overline{G}}_{EJ,ff}(r|r') \cdot J(r') } \, d\nu ' + \iiint_V \mathbf{ \overline{\overline{G}}_{EM,ff}(r|r') \cdot M(r') } \, d\nu '</math>
:<math> \mathbf{H^{ff}(r)} = \dfrac{1}{\eta_0} \mathbf{ \hat{r} \times E^{ff}(r) }</math>
where &eta;<sub>0</sub> = 120&pi; is the characteristic impedance of the free space. As can be seen from the above equations, the far fields have the form of a TEM wave propagating in the radial direction away from the origin of coordinates. This means that the far-field magnetic field is always perpendicular to the electric field and the propagation vector, which in this case happens to be the radial unit vector in the spherical coordinate system. In other words, one only needs to know the far-zone electric field and can easily calculate the far-zone magnetic field from it. In [[EM.Cube]]'s mixed potential integral equation formulation, the far-zone electric field can be expressed in terms of the asymptotic form of the vector electric and magnetic potentials '''A''' and '''F''':
:<math>\mathbf{E^{ff}}(x,y,z) = j k_0 \eta_0 \hat{r} \times [\hat{r} \times \mathbf{A}(r \to \infty)] +j k_0 \hat{r} \times \mathbf{F}(r \to \infty)</math>
<!--[[File:PMOM113.png]]-->
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