Changes

*2D Solution Plane

*Quasi-Static Analysis

==Getting Started==

==Creating the Concentric Metallic Cylinders==

Create two PEC groups called PEC_1 and PEC_2 in the Navigation Tree and draw two cylinder objects with the following properties:

{| class="wikitable"

Run a quasi-static analysis of your air-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: 48.2803 Ohms

Epsilon_Effective: 1

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.

To validate your simulation results, let's take a look at the analytical formulas for a coaxial cable:

<math> Z_0 = \frac{60}{\sqrt{\epsilon_{r}}} ln(b/a) = \frac{60}{\sqrt{1.0}} ln(2.3) \approx 50\Omega </math>

<math> \Phi(r) = V_0 \left[ 1 - \frac{ln(r/a)}{ln(b/a)} \right] </math>

<math> E_r(r) = \frac{1}{r} \frac{V_0}{ln(b/a)} </math>

where a and b are the radius of the inner and outer conductors, respectively, and &epsilon;_r is the relative permittivity of the dielectric filling. Substituting a = 1mm and b = 2.3mm, we obtain the following values for the electric field and potential, which agree quite well with [[EM.Cube]]'s computed values:

<math> \Phi(r = 1mm) = V_0 = 1V, \quad \quad \Phi(r = 2.3mm) = 0V </math>

<math> E_r(r = 1mm) = \frac{1}{0.001} \frac{1}{ln(2.3)} = 1200V/m, \quad \quad E_r(r = 2.3mm) = \frac{1}{0.0023} \frac{1}{ln(2.3)} = 522V/m</math>

From the above figures, you can see the 1/r decay of the electric field along the radial direction from the inner conductor to the outer conductor.

==Analyzing a Coaxial Line with Dielectric Filling==

In the this part of the tutorial lesson, you will analyze a coaxial cable with a dielectric core made of "Mica" with &epsilon;_r = 5.4. Keep the same inner conductor cylinder of the previous part. But increase the radius of the outer conductor cylinder to 6.93mm. Also, define a new dielectric material group in the Navigation Tree and select Mica as the material from [[EM.Cube]]'s Material List. Under Dielectric_1, draw a new Cylinder of radius 6.93mm with both ends capped. The following table summarizes the geometrical [[parameters]]:

{| class="wikitable"

|-

<math> Z_0 = \frac{60}{\sqrt{\epsilon_{r}}} ln(b/a) = \frac{60}{\sqrt{5.4}} ln(6.93) \approx 50\Omega </math>

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