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An SMA Connector on a Grounded Coplanar Waveguide
Introduction
SMA connectors are popularly used on printed circuit boards (PCB) for testing. This example shows how to excite an SMA connector on a microwave substrate and how to terminate a grounded coplanar waveguide (GCPW) with 50 Ω using a lumped port and an air-bridge.
Figure 1: An SMA connector is soldered onto a GCPW line. The other end of the GCPW line is terminated with 50 ohms using a lumped port.
Model Definition
The purpose of this example is to show how to excite a grounded coplanar waveguide with the signal from a coaxial cable through an SMA connector. The model also illustrates a particular 50 Ω passive termination constructed with and without an air-bridge.
The signal in the coaxial cable is carried by the TEM mode at 1 GHz. Inside the cable, the electric field of the TEM mode points radially between the inner and outer conductors. (In the cross-section of the cable, the electric field is the same as the electrostatic field with a DC voltage between the conductors.) This field passes through the SMA connector and excites a symmetric mode of the coplanar waveguide. The symmetric electric field in the coplanar waveguide points from the center conductor outward to the conductors on either side, or depending on the phase, inward from the outer conductors toward the center conductor.
The ground plane on the bottom of the PCB with εr = 3.38 is connected to the outer conductors of the CPW with metalized vias to prevent unwanted surface waves.
The domain between the inner and outer conductor of the SMA connector is filled with PTFE and all metal parts including the SMA connector, CPW, metalized vias and air-bridge are modeled as perfect electric conductors. The entire modeling domain is bounded by scattering boundaries that represent an open space except the ground plane.
Figure 2: Three ways to add a port on a CPW.
This example evaluates the passive 50 Ω termination on the GCPW in three ways (Figure 2). The first approach is extending the lumped port horizontally from the center conductor to the outer conductor of the GCPW. The second approach is using an air-bridge which extends above the substrate and connects the outer conductors while maintaining an air gap between itself and the center conductor. In this case, the lumped port extends vertically from the center conductor to the air-bridge. The third approach is using a multi-element uniform lumped port that terminate/excites two slots equally.
All domains are meshed by a tetrahedral mesh with maximum element size of five elements per wavelength so that the wave is well-resolved. The parts in SMA connector and vias are meshed more finely to provide good resolution of the curved surfaces.
Results and Discussion
The norm of electric fields is plotted in Figure 3. The plot setting is modified to show the fields on xy-plane confined between the center conductor and outer conductor (ground plane) of the GCPW. The evaluated S-parameters for all passive termination methods are better than −20 dB.
Figure 3: The plotted electric field distribution is symmetric due to the geometry setup.
Application Library path: RF_Module/Transmission_Lines_and_Waveguides/sma_connectorized_gcpw
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
Click  Study.
5
In the Select Study tree, select General Studies > Frequency Domain.
6
Click  Done.
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.
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
In the table, enter the following settings:
Name
Expression
Value
Description
w_c
2.8[mm]
0.0028 m
CPW, center conductor width
w_s
5.8[mm]
0.0058 m
CPW, center conductor and slot width
Geometry 1
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 60.
4
In the Depth text field, type 40.
5
In the Height text field, type 20.
6
Locate the Position section. In the y text field, type -5.
7
Click the  Wireframe Rendering button in the Graphics toolbar.
Block 2 (blk2)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 60.
4
In the Depth text field, type 30.
5
In the Height text field, type 1.524.
6
Click  Build Selected.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane type list, choose Face parallel.
4
On the object blk2, select Boundary 4 only.
It might be easier to select the correct boundary by using the Selection List window. To open this window, in the Home toolbar click Windows and choose Selection List. (If you are running the cross-platform desktop, you find Windows in the main menu.)
5
Click  Go to Plane Geometry.
Work Plane 1 (wp1) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 60.
4
In the Height text field, type w_c.
5
Locate the Position section. In the xw text field, type -30.
6
In the yw text field, type -w_c/2.
Work Plane 1 (wp1) > Rectangle 2 (r2)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 60.
4
In the Height text field, type w_s.
5
Locate the Position section. In the xw text field, type -30.
6
In the yw text field, type -w_s/2.
Work Plane 1 (wp1) > Rectangle 3 (r3)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Height text field, type w_s.
4
Locate the Position section. In the xw text field, type -25.
5
In the yw text field, type -w_s/2.
Part Libraries
1
From the Windows menu, choose Part Libraries.
2
In the Model Builder window, click Geometry 1.
3
In the Part Libraries window, select RF Module > Connectors > SMA Connectors > connector_sma_flange4 in the tree.
4
Click  Add to Geometry.
Geometry 1
SMA Connector, Square Flange with Four Holes 1 (pi1)
1
In the Model Builder window, under Component 1 (comp1) > Geometry 1 click SMA Connector, Square Flange with Four Holes 1 (pi1).
2
In the Settings window for Part Instance, locate the Position and Orientation of Output section.
3
Find the Displacement subsection. In the ywi text field, type 15.
4
In the zwi text field, type 1.524+0.635.
This is the sum of the substrate thickness and the inner radius of the imported SMA connector part.
5
Locate the Input Parameters section. In the table, enter the following settings:
Name
Expression
Value
Description
l_dielectric
8[mm]
8 mm
Length of dielectric
l_pin
2[mm]
2 mm
Length of pin from flange
6
Click to expand the Domain Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Dielectric
√
√
None
7
Click to expand the Boundary Selections section. In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Conductive surface
√
√
None
8
Click  Build Selected.
Cylinder 1 (cyl1)
1
In the Geometry toolbar, click  Cylinder.
2
In the Settings window for Cylinder, locate the Size and Shape section.
3
In the Height text field, type 1.524.
4
Locate the Position section. In the x text field, type 5.
5
In the y text field, type 7.
Array 1 (arr1)
1
In the Geometry toolbar, click  Transforms and choose Array.
2
Select the object cyl1 only.
3
In the Settings window for Array, locate the Size section.
4
In the x size text field, type 11.
5
In the y size text field, type 2.
6
Locate the Displacement section. In the x text field, type 5.
7
In the y text field, type 16.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the objects blk1 and blk2 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the objects arr1(1,1,1), arr1(1,2,1), arr1(10,1,1), arr1(10,2,1), arr1(11,1,1), arr1(11,2,1), arr1(2,1,1), arr1(2,2,1), arr1(3,1,1), arr1(3,2,1), arr1(4,1,1), arr1(4,2,1), arr1(5,1,1), arr1(5,2,1), arr1(6,1,1), arr1(6,2,1), arr1(7,1,1), arr1(7,2,1), arr1(8,1,1), arr1(8,2,1), arr1(9,1,1), and arr1(9,2,1) only.
6
Click  Build All Objects.
The vias are not part of the model domain. By removing from the model domain, the exterior boundaries of those vias are set to PEC by default.
Work Plane 2 (wp2)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane list, choose zy-plane.
4
In the x-coordinate text field, type 54.
5
Click  Go to Plane Geometry.
Work Plane 2 (wp2) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Height text field, type w_s.
4
Locate the Position section. In the xw text field, type 1.524.
5
In the yw text field, type 12.1.
Work Plane 2 (wp2) > Rectangle 2 (r2)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 1.6.
4
In the Height text field, type 6.8.
5
Locate the Position section. In the xw text field, type 1.524.
6
In the yw text field, type 11.6.
Work Plane 2 (wp2) > Difference 1 (dif1)
1
In the Work Plane toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object r2 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object r1 only.
Work Plane 2 (wp2) > Rectangle 3 (r3)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Height text field, type 2.8.
4
Locate the Position section. In the xw text field, type 1.524.
5
In the yw text field, type 13.6.
6
In the Model Builder window, right-click Geometry 1 and choose Build All.
The finished geometry should look like this.
Disable the analysis of the geometry as the remaining small geometric details can be kept.
7
In the Model Builder window, click Geometry 1.
8
In the Settings window for Geometry, locate the Cleanup section.
9
Clear the Automatic detection of small details checkbox.
Electromagnetic Waves, Frequency Domain (emw)
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
Click  Paste Selection.
4
In the Paste Selection dialog, type 68 69 77 89 210 211 212 in the Selection text field.
5
Click OK.
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 Conductive surface (SMA Connector, Square Flange with Four Holes 1).
Lumped Port 1
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
Select Boundary 4 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.
Lumped Port 2
1
In the Physics toolbar, click  Boundaries and choose Lumped Port.
2
Select Boundary 203 only.
Scattering Boundary Condition 1
1
In the Physics toolbar, click  Boundaries and choose Scattering Boundary Condition.
2
Select Boundaries 62–66, 73, 90, 91, 93, 94, 215, and 216 only.
Materials
Material 1 (mat1)
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
In the Settings window for Material, locate the Material Contents section.
3
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Material 2 (mat2)
1
Right-click Materials and choose Blank Material.
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Dielectric (SMA Connector, Square Flange with Four Holes 1).
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
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Material 3 (mat3)
1
Right-click Materials and choose Blank Material.
2
Select Domain 6 only.
3
In the Settings window for Material, locate the Material Contents section.
4
In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
3.38
1
Basic
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Coarser.
4
Click  Build All.
Definitions
Hide for Physics 1
1
In the Model Builder window, expand the Component 1 (comp1) > Definitions node.
2
Right-click View 1 and choose Hide for Physics.
3
In the Settings window for Hide for Physics, locate the Geometric Entity Selection section.
4
From the Geometric entity level list, choose Boundary.
5
Select Boundaries 62, 63, 65, 94, and 215 only.
Mesh 1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
Study 1
In the Study toolbar, click  Compute.
Results
Multislice 1
1
In the Model Builder window, expand the Results > Electric Field (emw) node, then click Multislice 1.
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 Y-planes subsection. In the Planes text field, type 0.
5
Find the Z-planes subsection. From the Entry method list, choose Coordinates.
6
In the Coordinates text field, type 1.5.
7
Click to expand the Range section. Select the Manual color range checkbox.
8
In the Maximum text field, type 1500.
9
Locate the Coloring and Style section. From the Color table list, choose HeatCameraLight.
10
In the Electric Field (emw) toolbar, click  Plot.
Electric Field, Logarithmic (emw)
In the Model Builder window, under Results click Electric Field, Logarithmic (emw).
S-Parameter (emw)
Add the PEC air-bridge and place the listener port between the CPW center conductor and air-bridge. Then, compute again.
Electromagnetic Waves, Frequency Domain (emw)
Perfect Electric Conductor 4
1
In the Model Builder window, expand the Results > S-Parameter (emw) node.
2
Right-click Component 1 (comp1) > Electromagnetic Waves, Frequency Domain (emw) and choose the boundary condition Perfect Electric Conductor.
3
Select Boundary 200 only.
Lumped Port 2
1
In the Model Builder window, click Lumped Port 2.
2
In the Settings window for Lumped Port, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundary 202 only.
Study 1
In the Study toolbar, click  Compute.
Results
Multislice 1
In the Model Builder window, under Results > Electric Field (emw) click Multislice 1.
Electromagnetic Waves, Frequency Domain (emw)
Perfect Electric Conductor 2
1
In the Model Builder window, expand the Results > S-Parameter (emw) node, then click Component 1 (comp1) > Electromagnetic Waves, Frequency Domain (emw) > Perfect Electric Conductor 2.
2
Select Boundaries 68, 69, 77, 89, and 203 only.
Lumped Port 2
1
In the Model Builder window, click Lumped Port 2.
2
In the Settings window for Lumped Port, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundaries 201 and 204 only.
5
Locate the Lumped Port Properties section. From the Type of lumped port list, choose Multielement uniform.
Uniform Element 1
1
In the Model Builder window, click Uniform Element 1.
2
In the Settings window for Uniform Element, locate the Boundary Selection section.
3
Click  Clear Selection.
4
Select Boundary 204 only.
5
Locate the Uniform Element Properties section. Specify the ah vector as
0
x
1
y
0
z
Uniform Element 2
1
In the Model Builder window, click Uniform Element 2.
2
Select Boundary 201 only.
3
In the Settings window for Uniform Element, locate the Uniform Element Properties section.
4
Specify the ah vector as
0
x
-1
y
0
z
Perfect Electric Conductor 4
1
In the Model Builder window, under Component 1 (comp1) > Electromagnetic Waves, Frequency Domain (emw) right-click Perfect Electric Conductor 4 and choose Disable.
2
In the Home toolbar, click  Compute.
Results
S-Parameter (emw)
1
In the Model Builder window, under Results > S-Parameter (emw) click S-Parameter (emw).
2
In the S-Parameter (emw) toolbar, click  Evaluate.
Multislice 1
1
In the Model Builder window, under Results > Electric Field (emw) click Multislice 1.
2
Right-click Results > Electric Field (emw) > Multislice 1 and choose Disable.
Surface 1
In the Model Builder window, right-click Electric Field (emw) and choose Surface.
Selection 1
1
In the Model Builder window, right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Conductive surface (SMA Connector, Square Flange with Four Holes 1).
Surface 1
1
In the Model Builder window, click Surface 1.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose AuroraAustralis.
4
Clear the Color legend checkbox.
Electric Field (emw)
1
In the Model Builder window, click Electric Field (emw).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges checkbox.
Volume 1
1
Right-click Electric Field (emw) and choose Volume.
2
In the Settings window for Volume, locate the Coloring and Style section.
3
From the Color table list, choose AuroraBorealis.
Selection 1
1
Right-click Volume 1 and choose Selection.
2
Select Domain 6 only.
3
In the Electric Field (emw) toolbar, click  Plot.