Changes
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<td> [[Image:FDTD5E.png|thumb|left|300px320px|The Add New Material dialog.]]
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<td> [[Image:FDTD5F.png|thumb|left|600px720px|A new custom material entry in the Materials List.]] </td>
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== Calculating Scattering Parameters Using Prony's Method ==
[[EM.Picasso]] provides a special source type called '''[[Glossary of EMGlossary_of_EM.Cube's Excitation Sourcess_Materials,_Sources,_Devices_&_Other_Physical_Object_Types#Scattering Wave Port Scattering_Wave_Port | Scattering Wave Port]]''' that is specifically intended for computing the S-parameters of planar structures. This is done by analyzing the current distribution patterns on the port transmission lines. The discontinuity at the end of a port line (junction region) gives rise to a standing wave pattern in the line's current distribution. From the location of the current minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, <i>i.e.</i> the S<sub>11</sub> parameter. A more rigorous technique is Prony’s method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following form:
:<math> f(x) \approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math>
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<td> [[Image:PMOM49.png|thumb|left|480px|Defining gap sources on an array of rectangle strip objects.]] </td><td> [[Image:PMOM49_2nd.png|thumb|left|480px|Defining gap sources on an array of rectangle strip objects with a Chebyshev amplitude distribution.]] </td>
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<b> The Nonlinear Diode Device </b>
A diode is a rectifying device. The time-domain relationship between the voltage and current of a diode is given by the nonlinear equation:
# Click the '''Mesh Settings''' [[File:mesh_settings.png]] button of the Simulate Toolbar.
# The Mesh Settings dialog of the currently c=active [[EM.Cube]] module opens up.
# From the '''Host''' drop-down list, select a line object. Note that only line parallel to one of the three principal axes are listed.
# By default, the lumped source is placed at the midpoint of the host line object. You can modify the '''Offset''' parameter, which is measured from the start point of the line and is always positive.
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<td> [[Image:PO2.png|thumb|360px420px|Two ellipsoids of different compositions.]] </td></tr><tr><td> [[Image:PO3.png|thumb|360px420px|Trinagular surface mesh of the two ellipsoids.]] </td>
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[[Image:MESH MAN12.png|thumb|left|480px600px|Locking the mesh density in the property dialog of a material group.]]
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[[Image:MESH MAN9.png|thumb|left|640px540px|The geometry of two dielectric spheres with the same material properties but belonging to two different object groups.]]
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[[Image:MESH MAN11.png|thumb|left|640px540px|The FDTD mesh of the two dielectric spheres. The left sphere is meshed using a global density of 20 cells/λ<sub>eff</sub>, while the right sphere is meshed using a locked density of 100 cells/λ<sub>eff</sub>.]]
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[[Image:MESH MAN10.png|thumb|left|640px540px|The top view of the mesh of the two dielectric spheres also showing the XY grid plane.]]
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