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EM.Ferma Tutorial Lesson 8: Simulating Coaxial Cables

3,528 bytes removed, 21:45, 13 September 2015
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Define a voltage source called VS_1 with a default voltage of 1V and associate it with the PEC_1 group. Your inner conductor is held at a voltage of 1V, while your outer conductor is held at zero potential. Also, define a horizontal (Z-directed) field sensor and place it at (0, 0, 5mm).
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==Running a Quasi-Static Simulation and Visualizing the Results==
The effective permittivity of 1 is expected as you have an air-filled two-conductor TEM transmission line. You can also view the electric field and electric potential results.
 
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Keep the same voltage source, field sensor and mesh density as in the previous part. Note that you used a solid dielectric cylinder instead of a hollow dielectric cylinder to model the dielectric core of your coaxial cable. This is because in [[EM.Cube]]'s Static and FDTD Modules, a material hierarchy system is in effect, in which a PEC has precedence over a dielectric material. This means that if a PEC object and a dielectric object overlap each other over some region in the space, the common overlapped regions is assumed to be PEC rather than dielectric.
{{Note| In [[EM.Cube]]'s Static Module, overlapped regions between PEC and dielectric objects are always assumed to be PEC rather than dielectric. This hierarchical rule make construction of concentric structures much easier.}}
 
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Run a quasi-static analysis of your dielectric-filled coaxial line. At the end of the simulation, the output message window reports the computed values of the characteristic impedance and effective permittivity of the transmission line:
 
Z0: 49.1214 Ohms
Epsilon_Effective: 5.3994
 
An effective permittivity of &epsilon;<sub>eff</sub> = &epsilon;<sub>r</sub> = 5.4 is expected as you have an homogenous two-conductor TEM transmission line. Visualize the electric field and electric potential distributions and plot the 2D graphs of the total electric field along the X-axis.
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You can validate your simulation results using the analytical formulas for a dielectric-filled coaxial cable:
 
<math> Z_0 = \frac{60}{\sqrt{\epsilon_{r}}} ln(b/a) = \frac{60}{\sqrt{5.4}} ln(6.93) \approx 50\Omega </math>
 
 
==Considering a Partial Dielectric Filling==
 
In the last part of this tutorial lesson, you will analyze a coaxial cable with a partial dielectric filling. Open the property dialog of Cylinder_3 from the previous part and reduce its radius to 4mm. The following table summarizes the geometrical [[parameters]]:
 
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! Object !! Group !! LCS Coordinates !! Radius !! Height !! Cap Ends?
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| Cylinder_1 || PEC_1 || (0, 0, 0) || 1mm || 10mm || Yes
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| Cylinder_2 || PEC_2 || (0, 0, 0) || 6.93mm || 10mm || No
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| Cylinder_3 || Dielectric_1 || (0, 0, 0) || 4mm || 10mm || Yes
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Keep the same voltage source, field sensor and mesh density as in the previous part. The material hierarchy rules apply here, too. So you can simply use a solid dielectric cylinder to model your partial dielectric filling.
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[[Image:STAT145.png|thumb|400px|The geometry of the partially dielectric-filled coaxial cable.]]
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[[Image:STAT146.png|thumb|400px|The static mesh of the partially dielectric-filled coaxial cable.]]
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Run a quasi-static analysis of your dielectric-filled coaxial line. At the end of the simulation, the output message window still reports the computed values of the characteristic impedance and effective permittivity of the transmission line as Z0 = 142.278&Omega; and &epsilon;<sub>eff</sub> = 0.643592. However, these results are wrong, particularly the effective permittivity which cannot be less than one. This is because your partially filled coaxial cable is now an inhomogeneous waveguide and no longer supports a dominant TEM mode. As we mentioned in Tutorial Lesson 4, the quasi-static analysis of [[EM.Cube]]'s Static Module calculated the characteristic impedance and effective permittivity of [[Transmission Lines|transmission lines]] based on the dominant TEM or TEM-like mode.
 
 
Visualize the electric field and electric potential distributions and plot the 2D graphs of the total electric field along the X-axis. From the figures below, you can see that the electric field is zero inside the inner conductor and outside the outer conductor, as you would expect. Between the two conductors, the electric field is still radial as in the homogeneous case of the previous part. However, the field inside the dielectric cylinder is much smaller than the field in the air region. This can be explained based on the boundary condition for the normal field component at the interface between the dielectric and air media at r = 4mm, which requires that E<sub>n</sub><sup>air</sup> = &epsilon;<sub>r</sub> E<sub>n</sub><sup>dielectric</sup>.
 
 
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[[Image:STAT147.png|thumb|390px|The electric field distribution plot of the partially dielectric-filled coaxial line.]]
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[[Image:STAT149.png|thumb|320px|The vector plot of the total electric field distribution in the partially dielectric-filled coaxial line.]]
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[[Image:STAT148.png|thumb|390px|The electric potential distribution plot of the partially dielectric-filled coaxial line.]]
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[[Image:STAT150.png|thumb|420px|The graph of the total electric field of the partially dielectric-filled coaxial line along the X-axis.]]
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{{Note|The computed characteristic impedance and effective permittivity of [[Transmission Lines]] at the end of a 2D quasi-static analysis are valid only for homogenous multi-conductor structures that support a dominant TEM or TEM-like propagating mode.}}
 
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Kazem Sabet
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