Electromagnetic waves and antennas
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Transmission lines
Exercise no. 2
The aim of this exercise is to study the coaxial cables with numerical modeling using the
ANSYS HFSS software. The following tasks are to be performed:
1.
The characteristic impedance of the coaxial line (characterized by the ratio of the
outside diameter of the inner conductor d and the inside diameter of the shield D, the
dielectric constant of the insulator  and the permeability ) can be calculated according
to the equation:
Z0 
1
2
  D  138
D
ln   
log10  
  d  r
d
(2.1)
Note that the above equation uses the notations of the relative dielectric constant r and
the relative permeability r = 1.
Fig. 2.1 The coaxial cable cutaway.
Taken from http://en.wikipedia.org/wiki/coaxial_cable.
In the exercise, a coaxial cable LMR-100A, http://www.timesmicrowave.com, should
be used. A copper inner conductor is of diameter d = 0.92 mm. The polyethylene (PE),
used as a dielectric insulator, has the relative permittivity r = 2.30 and the loss factor
tan  = 0.001. The inner diameter of the shield is D = 3.04 mm. The outer conductor
consists of aluminum foil which is covered with the copper braid and a layer of plastic.
The characteristic impedance of the LMR-100A transmission line has to be calculated.
In the HFSS program, create the described above coaxial line which has a length of 10 mm.
2.
Consider the distribution of the electric and magnetic fields inside the coaxial cable
when the line is terminated with a perfectly radiating surface. To perform the initial
analysis, use the frequency f = 3 GHz.
3.
Select the frequency range 1.0 – 5.0 GHz, step 0.2 GHz. Estimate the frequency
dependence of the reflection coefficient S11 and the frequency response of the input
impedance (the cable is terminated by a perfectly radiating surface).
4.
Repeat the calculations from the previous step for the shortened line. Verify the results
of HFSS simulations by the MATLAB script.
How to do it …
Transmission (coaxial) line is formed by two cylinders. The inner cylinder has to be filled by
vacuum, while its outer surface is completely electrically conductive. In this exercise, the
outer cylinder is formed from polyethylene and its outer surface is covered with a perfect
electric conductor.
After starting the program, proceed as follows:
 Menu: Project  Insert HFSS Design
Create a numerical model that is based on the finite element method in the frequency
domain (a harmonic steady state is assumed).
 Menu: Draw  Cylinder
In a graphics editor, determine the coordinates of the center of the computational
domain, the radius and height of the inner cylinder. For the inner and outer cylinders set
the coordinates of the center of the frame by Center Position (0mm, 0mm, 0mm) and
height by Height (4.0mm) in the similar way. Specify the radius for each of the
cylinders by varying Radius (0.46mm and 1.81mm).
 Menu: Edit  Copy, Edit  Paste
The second cylinder is advantageous to copy via the clipboard and change only the
radius.
 Menu: Modeler  Boolean  Subtract
Subtract the inner cylinder from the outer conductor. Both cylinders have to be chosen.
In the dialog that opens, before deducting the cylinder, we have to move the outer
cylinder into the Tool Parts and the inner cylinder to the Blank Parts.
Continue by setting the properties of the coaxial cable:

Click on the object and change the material from vacuum to polyethylene. The electrical
characteristics of polyethylene are adjusted to fit the data r = 2.30, tan  = 0.001.

Click on the inner and outer walls of the cylinder while pressing the key, and mark them
as perfect electrical conductors:
HFSS  Boundaries  Assign  Perfect E
 Click on the top of the cylinder and mark it as a perfectly radiating surface that absorbs
all of the electromagnetic energy:
HFSS  Boundaries  Assign  Radiation Boundary
 Click on the bottom of the cylinder wall and set it as the wave port:
HFSS  Excitation  Assign  Wave Port
The properties of the wave port can be specified in the following dialog boxes:
1.
General. Name of the port (you can leave the default value 1).
2.
Modes. At the line Mode = 1, click on the column Integration line and in the
middle of the input surface draw the arrow between the inner and outer PEC walls.
The center of the wall is indicated by the cursor in the shape of a triangle.
3.
Post processing. Leave the default setting (we do not want to renormalize the port
impedance).
 Menu: HFSS  Analysis Setup  Add solution setup
On the first tab of this dialog (General), set the frequency solutions (Solution frequency)
to 3GHz. Leave the other settings unchanged.
 Menu: HFSS  Validation check
Display the dialog to verify the correctness of the created model. If everything is set up
right, you can start the calculation.
 Menu: HFSS  Analyze all
Before starting the calculations, HFSS requests to save the model. The progress of the
calculation is indicated in the lower right window. Once the calculation is completed,
we can go ahead to view the results.
 Select: Cylinder2 (in the object window), Field overlays (right mouse button)
Menu: Plot fields  H  Vector H
 Select: Cylinder2 (in the object window), Field overlays (right mouse button)
Menu: Plot fields  E  Vector E
The described procedure is to demonstrate the vector distribution of the electric and
magnetic fields of the wave under investigation.
As a next task of the exercise, you are asked to calculate the input impedance of the
cable in the frequency band of 1GHz to 5GHz. In order to do this, add the frequency sweep by
selecting menu items HFSS  Analysis Setup  Add solution setup. The impedance
frequency response can be displayed after right-clicking on Results in the project window and
then selecting Create Modal Solution Data Report  Add Solution
The preparation of this exercise was supported by the project CZ.1.07/2.3.00/30.0039
of Brno University of Technology