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A coaxial transmission line consists of two concentric metallic cylinders. The interior cylinder is typically solid and is called the inner conductor. The exterior cylinder is hollow and is called the outer conductor. The space between the two concentric cylinder is filled with a dielectric material. The dielectric filling can be air or any other material.

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

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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]]:

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