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Dipole Antenna with a Quarter-Wave Coaxial Balun
Introduction
An antenna balun blocks undesirable currents on the outside of a cable. A quarter-wave coaxial balun (1:1) is one of the easiest designs: it works as a transformer and makes the input impedance from the inner conductor to the outer conductor infinite. This example simulates an antenna prototype including an SMA Receptacle, an ABS enclosure, and a quarter-wave coaxial balun. The frequency is tuned to GPS range, 1.57542 GHz. Such an antenna can be useful for indoor measurements with a single polarization.
Figure 1: A quarter-wave balun is added on a half-wave dipole antenna with an ABS enclosure. The entire domain is bounded by a perfectly matched layer.
Model Definition
The antenna model shown in Figure 1 is composed of a half-wave dipole antenna connected to a coaxial cable, a SMA receptacle (connector), an antenna enclosure, and a perfectly matched layer (PML). Model all metal parts as perfect electric conductors (PEC). The space between the inner and outer conductors of the coaxial cable is filled with polytetrafluoroethylene (PTFE), εr = 2.1. Furthermore, model the antenna enclosure using acrylonitrile butadiene styrene (ABS), a plastic material with εr = 2.4. The rest of the simulation domain is air and the entire simulation domain is enclosed by the PML.
Figure 2: Zoomed view of the antenna interior shows the configuration of the balun.
The antenna balun part shown in Figure 2 can be analyzed using the transmission line theory. The input impedance of the short-circuited transmission line is
This can also be calculated via the quarter-wave transformer analysis:
The input impedance of the short-circuited quarter-wavelength transmission line is calculated as infinite from both equations. This infinite input impedance prevents a current flow or coupling from the antenna radiator to the outer conductor of the coaxial cable. Thus, the antenna radiators connected to the inherently unbalanced coaxial cable can be balanced without generating the current on an undesired location.
Results and Discussion
The default plots after the simulation show the norm of the electric fields, 2D far-field polar plot, and 3D far-field radiation pattern. The symmetric and balanced E-fields excited on each antenna radiator are observed in Figure 3.
Figure 3: The E-field norm on each antenna radiator looks symmetric.
Figure 4 shows the far-field radiation pattern on the H-plane. The pattern looks almost isotropic and omnidirectional. The magnitude of the far field is slightly decreased around 180? where the body of the antenna enclosure and connector are located. The 3D far-field radiation pattern is plotted in Figure 5 and it is very like that of a conventional half-wave dipole antenna.
Figure 4: The far-field pattern on the H-plane is isotropic as expected.
Figure 5: The visualized 3D far-field pattern is a little bit distorted due to the balun and the antenna enclosure.
Figure 6: The S-parameter plot shows the antenna is resonant around the GPS frequency, 1.57542 GHz.
The calculated S-parameters plotted in Figure 6 are less than −10 dB around the GPS frequency range.
References
1. D.M. Pozar, Microwave Engineering, John Wiley & Sons, 1998.
2. C.A. Balanis, Antenna Theory, John Wiley & Sons, 1997.
Application Library path: RF_Module/Antennas/dipole_antenna_balun
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Radio Frequency>Electromagnetic Waves, Frequency Domain (emw).
3
Click Add.
4
In the Added physics interfaces tree, select Electromagnetic Waves, Frequency Domain (emw).
5
Click  Study.
6
In the Select Study tree, select General Studies>Frequency Domain.
7
Click  Done.
Study 1
Step 1: Frequency Domain
1
In the Model Builder window, under Study 1 click Step 1: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type range(1.5[GHz],25[MHz],1.65[GHz]).
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file dipole_antenna_balun_parameters.txt.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
First, import the antenna enclosure structure.
Import 1 (imp1)
1
In the Home toolbar, click  Import.
2
In the Settings window for Import, locate the Import section.
3
Click Browse.
4
Browse to the model’s Application Libraries folder and double-click the file dipole_antenna_balun.mphbin.
5
Click Import.
Choose wireframe rendering to see the interior of the enclosure.
6
Click the  Wireframe Rendering button in the Graphics toolbar.
Add a cylinder for the inner conductor of the coaxial cable.
Coax inner
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Coax inner in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_inner.
4
In the Height text field, type 54.95.
5
Locate the Position section. In the x text field, type -57.
6
In the z text field, type 1.2.
7
Locate the Axis section. From the Axis type list, choose x-axis.
Add a cylinder for the outer conductor for the coaxial cable.
Coax outer
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Coax outer in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_outer.
4
In the Height text field, type 54.
5
Locate the Position section. In the x text field, type -57.
6
In the z text field, type 1.2.
7
Locate the Axis section. From the Axis type list, choose x-axis.
8
Click  Build Selected.
Add a one-quarter of a torus for the 90-degree bend part connecting the antenna radiator and the inner conductor of the coaxial cable.
90 degree bend
1
In the Geometry toolbar, click  Torus.
2
In the Settings window for Torus, type 90 degree bend in the Label text field.
3
Locate the Size and Shape section. In the Major radius text field, type r_outer.
4
In the Minor radius text field, type r_inner.
5
In the Revolution angle text field, type 90.
6
Locate the Position section. In the x text field, type -r_outer.
7
In the z text field, type 3.25.
8
Locate the Axis section. From the Axis type list, choose y-axis.
9
Locate the Rotation Angle section. In the Rotation text field, type 270.
Add a cylinder for an antenna radiator.
Radiator
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Radiator in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_inner.
4
In the Height text field, type l_wire.
5
Locate the Position section. In the z text field, type 3.25.
6
Click  Build Selected.
Create a second antenna radiator by mirroring one side.
Mirror 1 (mir1)
1
In the Geometry toolbar, click  Transforms and choose Mirror.
2
Select the objects cyl3 and tor1 only.
3
In the Settings window for Mirror, locate the Input section.
4
Select the Keep input objects check box.
Add a cylinder to connect another 90 degree bend with the outer conductor of the coaxial cable.
Solder to ground: radiator
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Solder to ground: radiator in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_inner.
4
In the Height text field, type 2.95.
5
Locate the Position section. In the x text field, type -5.
6
In the z text field, type -1.2.
7
Locate the Axis section. From the Axis type list, choose x-axis.
8
Click  Build Selected.
Create the quarter-wave coaxial balun by performing a couple of geometry transform operations.
Rotate 1 (rot1)
1
In the Geometry toolbar, click  Transforms and choose Rotate.
2
Select the objects mir1(1) and mir1(2) only.
3
In the Settings window for Rotate, locate the Input section.
4
Select the Keep input objects check box.
5
Locate the Rotation section. In the Angle text field, type -90.
6
From the Axis type list, choose y-axis.
Move 1 (mov1)
1
In the Geometry toolbar, click  Transforms and choose Move.
2
Select the objects rot1(1) and rot1(2) only.
3
In the Settings window for Move, locate the Displacement section.
4
In the x text field, type -l_wire-3.25.
5
In the z text field, type 5.8.
Add a cylinder to connect the balun and the outer conductor of the coaxial cable.
Solder to ground: balun
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Solder to ground: balun in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type 1.5.
4
In the Height text field, type 1.25.
5
Locate the Position section. In the x text field, type -l_wire-r_outer.
6
In the z text field, type 2.5.
Create unions of some of the objects to remove unnecessary edges that would increase the mesh complexity.
Union 1 (uni1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Select the objects cyl2 and cyl5 only.
3
In the Settings window for Union, locate the Union section.
4
Clear the Keep interior boundaries check box.
Union 2 (uni2)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Union.
2
Select the objects cyl3 and mov1(1) only.
3
In the Settings window for Union, locate the Union section.
4
Clear the Keep interior boundaries check box.
5
Click  Build Selected.
Add a couple of cylinders for the SMA connector.
SMA
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type SMA in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type 2.45.
4
In the Height text field, type 5.
5
Locate the Position section. In the x text field, type -57.
6
In the z text field, type 1.2.
7
Locate the Axis section. From the Axis type list, choose x-axis.
SMA flange
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type SMA flange in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type 5.
4
Locate the Position section. In the x text field, type -52.
5
In the z text field, type 1.2.
6
Locate the Axis section. From the Axis type list, choose x-axis.
Add a cylinder on the back side of the coaxial port. This domain is not a part of the model space.
Connector cap
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Connector cap in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_outer.
4
In the Height text field, type 2.
5
Locate the Position section. In the x text field, type -59.
6
In the z text field, type 1.2.
7
Locate the Axis section. From the Axis type list, choose x-axis.
Add a cylinder to tune the antenna for generating balanced current distributions on each wire radiator.
Tuning wire
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, type Tuning wire in the Label text field.
3
Locate the Size and Shape section. In the Radius text field, type r_inner.
4
In the Height text field, type 0.1*l_wire.
5
Locate the Position section. In the z text field, type -l_wire-3.25.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object mir1(1) only.
3
In the Settings window for Difference, locate the Difference section.
4
Find the Objects to subtract subsection. Select the  Activate Selection toggle button.
5
Select the object cyl9 only.
6
Click  Build Selected.
Add a sphere for the PML.
PML
1
In the Geometry toolbar, click  Sphere.
2
In the Settings window for Sphere, type PML in the Label text field.
3
Locate the Size section. In the Radius text field, type 100.
4
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
30
5
Click  Build All Objects.
6
Click the  Zoom Extents button in the Graphics toolbar.
7
Click the  Zoom In button in the Graphics toolbar.
8
Click the  Zoom In button in the Graphics toolbar.
Definitions
Create a set of selections for use before setting up the physics. First, create selections for the conductor boundaries.
Coax inner and radiator boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coax inner and radiator boundaries in the Label text field.
3
Locate the Input Entities section. Click  Paste Selection.
4
In the Paste Selection dialog box, type 9,12,17,25-27,29,40-42 in the Selection text field.
5
Click OK.
6
In the Settings window for Explicit, locate the Output Entities section.
7
From the Output entities list, choose Adjacent boundaries.
Coax outer boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coax outer boundaries in the Label text field.
3
Locate the Input Entities section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 59-60, 68, 71, 85-86, 91-92, 98-100, 104, 107 in the Selection text field.
6
Click OK.
Add a selection for the dielectric material inside the coaxial cable.
Coax dielectric
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coax dielectric in the Label text field.
3
Select Domains 8, 11, 16, and 28 only.
Add a selection for the SMA connector.
SMA boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type SMA boundaries in the Label text field.
3
Select Domains 7 and 10 only.
4
Locate the Output Entities section. From the Output entities list, choose Adjacent boundaries.
Add a selection for the antenna enclosure.
Enclosure
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Enclosure in the Label text field.
3
Locate the Input Entities section. Click  Paste Selection.
4
In the Paste Selection dialog box, type 13-15, 18-21, 23-24, 30-39, 45-48, 51-58 in the Selection text field.
5
Click OK.
6
Click the  Zoom Extents button in the Graphics toolbar.
7
Click the  Zoom In button in the Graphics toolbar.
Add a selection for the connector cap.
Coax cap
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coax cap in the Label text field.
3
Select Domain 6 only.
Add a selection for the model domain. Use the complement of the connector cap selection.
Model domain
1
In the Definitions toolbar, click  Complement.
2
In the Settings window for Complement, type Model domain in the Label text field.
3
Locate the Input Entities section. Under Selections to invert, click  Add.
4
In the Add dialog box, select Coax cap in the Selections to invert list.
5
Click OK.
Add the PML using the PML selection you defined earlier.
Perfectly Matched Layer 1 (pml1)
1
In the Definitions toolbar, click  Perfectly Matched Layer.
2
Select Domains 1–4, 43, 44, 49, and 50 only.
3
In the Settings window for Perfectly Matched Layer, locate the Geometry section.
4
From the Type list, choose Spherical.
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
Select Domains 1, 2, 43, and 44 only.
Hide for Physics 2
1
Right-click View 1 and choose Hide for Physics.
2
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 9, 10, 195, and 196 only.
Electromagnetic Waves, Frequency Domain (emw)
Now, set up the physics. Choose an appropriate selection when you assign each boundary condition.
1
In the Model Builder window, under Component 1 (comp1) click Electromagnetic Waves, Frequency Domain (emw).
2
In the Settings window for Electromagnetic Waves, Frequency Domain, locate the Domain Selection section.
3
From the Selection list, choose Model domain.
4
Click the  Zoom In button in the Graphics toolbar.
Perfect Electric Conductor 2
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
In the Settings window for Perfect Electric Conductor, locate the Boundary Selection section.
3
From the Selection list, choose Coax inner and radiator boundaries.
Perfect Electric Conductor 3
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
In the Settings window for Perfect Electric Conductor, locate the Boundary Selection section.
3
From the Selection list, choose Coax outer boundaries.
Perfect Electric Conductor 4
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
In the Settings window for Perfect Electric Conductor, locate the Boundary Selection section.
3
From the Selection list, choose SMA boundaries.
Lumped Port 1
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
Select Boundary 21 only.
3
In the Settings window for Lumped Port, locate the Lumped Port Properties section.
4
From the Type of lumped port list, choose Coaxial.
For the first port, wave excitation is on by default.
Far-Field Domain 1
In the Physics toolbar, click  Domains and choose Far-Field Domain.
Materials
Assign material properties. Use air for all domains, first.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Override the coax dielectric domains with a dielectric material of εr = 2.1.
PTFE
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, type PTFE in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Coax dielectric.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
2.1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Override the antenna enclosure with a dielectric material of εr = 2.4.
ABS
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, type ABS in the Label text field.
3
Locate the Geometric Entity Selection section. From the Selection list, choose Enclosure.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
2.4
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Mesh 1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Build All.
Study 1
In the Home toolbar, click  Compute.
Results
The default plot shows the E-field norm, 2D far-field polar plot, and 3D far-field radiation pattern. Switch the parameter value to the center frequency in the sweep to plot the results on the resonant frequency.
Electric Field (emw)
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (freq (GHz)) list, choose 1.575.
Multislice
1
In the Model Builder window, expand the Electric Field (emw) node, then click Multislice.
2
In the Settings window for Multislice, locate the Multiplane Data section.
3
Find the X-planes subsection. In the Planes text field, type 0.
4
Find the Z-planes subsection. In the Planes text field, type 0.
5
Find the Y-planes subsection. From the Entry method list, choose Coordinates.
6
In the Coordinates text field, type 0.
7
Click the  Go to ZX View button in the Graphics toolbar.
8
Click the  Zoom In button in the Graphics toolbar.
9
Click to expand the Range section. Select the Manual color range check box.
10
In the Maximum text field, type 1000.
11
In the Electric Field (emw) toolbar, click  Plot.
The plot shows the symmetric E-field norm distribution on the wires; compare with Figure 3.
S-parameter (emw)
Compare the result with the S-parameter plot in Figure 6.
Smith Plot (emw)
2D Far Field (emw)
Adjust the axis range.
1
In the Model Builder window, click 2D Far Field (emw).
2
In the Settings window for Polar Plot Group, locate the Axis section.
3
Select the Manual axis limits check box.
4
In the r minimum text field, type 0.
5
In the 2D Far Field (emw) toolbar, click  Plot.
The plotted H-plane patterns are almost isotropic as shown in Figure 4.
3D Far Field (emw)
1
In the Model Builder window, click 3D Far Field (emw).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (freq (GHz)) list, choose 1.575.
Radiation Pattern 1
The visualized 3D radiation pattern looks like the radiation pattern of a typical dipole antenna. Compare the reproduced plot with Figure 5.