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Modeling of a Differential Microstrip Line
Introduction
A differential line is composed of two transmission lines excited by two out-of-phase signals. This configuration is known to be useful to enhance the signal-to-noise ratio. The model example shows how to set up differential and single-ended microstrip lines using TEM-type ports. The impact on computed S-parameters due to a fictitious noise source is demonstrated for each microstrip line configuration, respectively.
Figure 1: A differential line composed of two microstrip lines: the TEM type of ports is used to set up differential line properties.
Model Definition
The differential line model consists of two single microstrip lines printed on a substrate with a permittivity value of 3.38. The differential line is excited and terminated by port features. The port types are set to transverse electromagnetic (TEM) that is configured with electric potential and ground subfeatures. To generate the differential mode, the positive electric potential is assigned on one of the single-ended microstrip line edges while the negative electric potential is added on the end of the adjacent microstrip line. If the coupling between two lines is marginal, the characteristic port impedance of a differential line can be approximated as a series connection of two 50 Ω lumped devices, that is 100 Ω when the characteristic impedance of a single-ended microstrip line is 50 Ω. Note that two positive potential subfeatures are required to model a common mode and the characteristic impedance of the port with negligible coupling effects can be approximated as a parallel connection of two 50 Ω lumped devices, that is 25 Ω. Perfect electric conductor (PEC) is used to address all metallic parts. By default, all exterior boundaries are set to PEC. So, the model can be seen as enclosed by a metallic box.
The physics settings include all possible modeling cases such as single-ended line, differential line, and a fictitious noise. In each study step, these settings can selectively be enabled or disabled before running computation.
Results and Discussion
Figure 2 describes the electric field norm on the circuit board for a single-ended microstrip line. The field distribution on the top surface shows that the excited signal propagates to the other side and is terminated by the same type of port. Strong fields are confined around the edges of the PEC boundaries.
Figure 2: The electric field norm on the top surface of the circuit board when a single-ended microstrip line is computed.
The performance of the single-ended line is checked in terms of the S-parameters through the default global evaluation. The input impedance matching (S33dB) is below −30 dB and insertion loss (S43dB) is better than 0.05 dB. For the single-ended microstrip line, the port mode impedance (Zmode_3), calculated characteristic impedance, is about 49.5 Ω.
When the single-ended microstrip line is under the influence of undesirable noise, the signal integrity can be degraded. The impact on the circuit board due to a fictitious noise made by a point source is visualized in Figure 3. By reviewing the computed S-parameters, it is more obvious quantitatively. With the noise source, the input impedance matching (S33dB) is higher than −15 dB and insertion loss (S43dB) is worse than 2 dB.
Figure 3: The electric field norm on the top surface of the circuit board when a fictitious noise is added next to a single-ended microstrip line.
The electric field norm of a differential line composed of two microstrip lines is plotted in Figure 4. When visualizing the z-component of the electric field, the polarity of differential signals can be displayed with a couple of colors (Figure 5). Since there is coupling between two single-ended lines, the computed port mode impedance (Zmode_1) is around 97 Ω deviated from the value of 100 Ω for the case of no coupling. The input impedance matching (S11dB) is below −30 dB and insertion loss (S21dB) is better than 0.05 dB.
Figure 4: The electric field norm on the top surface of the circuit board when a differential microstrip line is computed.
Figure 5: The z-component of the electric field on the bottom surface of the circuit board when a differential microstrip line is computed.
After reactivating the noise source in the differential line, its effect on the circuit board is presented in Figure 6. The input impedance matching (S11dB) is below −30 dB and insertion loss (S21dB) is better than 0.05 dB. So, those characteristics are not degraded as shown in the single-ended line case when the noise equally affects each line component of the differential pair.
Figure 6: The electric field norm on the top surface of the circuit board when a fictitious noise is added.
Application Library path: RF_Module/Transmission_Lines_and_Waveguides/microstrip_line_tem_differential
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 Preset Studies for Selected Physics Interfaces>TEM Boundary Mode Analysis.
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.
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 20.
4
In the Depth text field, type 10.
5
In the Height text field, type 6.
6
Locate the Position section. In the y text field, type -5.
7
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
20[mil]
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
In the z-coordinate text field, type 20[mil].
Work Plane 1 (wp1)>Plane Geometry
In the Model Builder window, click 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 20.
4
In the Height text field, type 1.13.
5
Locate the Position section. In the yw text field, type -0.565+1.5.
Work Plane 1 (wp1)>Mirror 1 (mir1)
1
In the Work Plane toolbar, click  Transforms and choose Mirror.
2
Select the object r1 only.
3
In the Settings window for Mirror, locate the Input section.
4
Select the Keep input objects check box.
5
Locate the Normal Vector to Line of Reflection section. In the xw text field, type 0.
6
In the yw text field, type 1.
Point 1 (pt1)
1
In the Model Builder window, right-click Geometry 1 and choose More Primitives>Point.
2
In the Settings window for Point, locate the Point section.
3
In the x text field, type 10.
4
In the z text field, type 20[mil].
5
Click  Build All Objects.
6
Click the  Wireframe Rendering button in the Graphics toolbar.
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
Material 2 (mat2)
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
Select Domain 1 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
Electrical conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
0
S/m
Basic
Electromagnetic Waves, Frequency Domain (emw)
1
Click the  Show More Options button in the Model Builder toolbar.
2
In the Show More Options dialog box, select Physics>Advanced Physics Options in the tree.
3
In the tree, select the check box for the node Physics>Advanced Physics Options.
4
Click OK.
5
In the Model Builder window, under Component 1 (comp1) click Electromagnetic Waves, Frequency Domain (emw).
6
In the Settings window for Electromagnetic Waves, Frequency Domain, click to expand the Port Options section.
7
From the Port formulation list, choose Constraint-based.
Port 1
1
In the Physics toolbar, click  Boundaries and choose Port.
2
Select Boundaries 1 and 4 only.
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Transverse electromagnetic (TEM).
5
In the Zref text field, type 100[ohm].
Electric Potential 1
1
In the Physics toolbar, click  Attributes and choose Electric Potential.
2
Select Edge 13 only.
Port 1
In the Model Builder window, click Port 1.
Electric Potential 2
1
In the Physics toolbar, click  Attributes and choose Electric Potential.
2
Select Edge 9 only.
3
In the Settings window for Electric Potential, locate the Electric Potential section.
4
From the V0 list, choose Negative electric potential.
Port 1
In the Model Builder window, click Port 1.
Ground 1
In the Physics toolbar, click  Attributes and choose Ground.
Port 2
1
In the Physics toolbar, click  Boundaries and choose Port.
2
Select Boundaries 14 and 15 only.
3
In the Settings window for Port, locate the Port Properties section.
4
From the Type of port list, choose Transverse electromagnetic (TEM).
5
In the Zref text field, type 100[ohm].
Electric Potential 1
1
In the Physics toolbar, click  Attributes and choose Electric Potential.
2
Select Edge 29 only.
Port 2
In the Model Builder window, click Port 2.
Electric Potential 2
1
In the Physics toolbar, click  Attributes and choose Electric Potential.
2
Select Edge 27 only.
3
In the Settings window for Electric Potential, locate the Electric Potential section.
4
From the V0 list, choose Negative electric potential.
Port 2
In the Model Builder window, click Port 2.
Ground 1
In the Physics toolbar, click  Attributes and choose Ground.
Perfect Electric Conductor 2
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
Select Boundary 10 only.
Perfect Electric Conductor 3
1
In the Physics toolbar, click  Boundaries and choose Perfect Electric Conductor.
2
Select Boundary 8 only.
Electric Point Dipole 1
1
In the Physics toolbar, click  Points and choose Electric Point Dipole.
2
Select Point 11 only.
3
In the Settings window for Electric Point Dipole, locate the Dipole Parameters section.
4
Specify the np vector as
0
x
0
y
-1
z
5
In the p text field, type 5e-4.
Port 3
1
In the Model Builder window, under Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw) right-click Port 1 and choose Duplicate.
2
In the Settings window for Port, locate the Port Properties section.
3
In the Zref text field, type 50[ohm].
Electric Potential 2
1
In the Model Builder window, expand the Port 3 node.
2
Right-click Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Port 3>Electric Potential 2 and choose Delete.
Port 4
1
In the Model Builder window, under Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw) right-click Port 2 and choose Duplicate.
2
In the Settings window for Port, locate the Port Properties section.
3
In the Zref text field, type 50[ohm].
Electric Potential 2
1
In the Model Builder window, expand the Port 4 node.
2
Right-click Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Port 4>Electric Potential 2 and choose Delete.
Port 1, Port 2
1
In the Model Builder window, under Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw), Ctrl-click to select Port 1 and Port 2.
2
Right-click and choose Group.
Differential Line Port Group
In the Settings window for Group, type Differential Line Port Group in the Label text field.
Port 3, Port 4
1
In the Model Builder window, under Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw), Ctrl-click to select Port 3 and Port 4.
2
Right-click and choose Group.
Single-Ended Line Port Group
In the Settings window for Group, type Single-Ended Line Port Group in the Label text field.
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 5 and 7 only.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Electromagnetic Waves, Frequency Domain (emw) section.
3
Select the Refine conductive edges check box.
4
From the Size type list, choose User defined.
5
Click  Build All.
Study 1
Step 1: TEM Boundary Mode Analysis
1
In the Model Builder window, under Study 1 click Step 1: TEM Boundary Mode Analysis.
2
In the Settings window for TEM Boundary Mode Analysis, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Differential Line Port Group.
5
Click  Disable.
6
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Perfect Electric Conductor 3.
7
Click  Disable.
8
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Electric Point Dipole 1.
9
Click  Disable.
Step 2: Frequency Domain
1
In the Model Builder window, click Step 2: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Differential Line Port Group.
5
Click  Disable.
6
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Perfect Electric Conductor 3.
7
Click  Disable.
8
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Electric Point Dipole 1.
9
Click  Disable.
10
In the Model Builder window, click Study 1.
11
In the Settings window for Study, type Study 1, Single-Ended Line in the Label text field.
12
In the Home toolbar, click  Compute.
Results
S-parameter, Single-Ended Line
1
In the Model Builder window, expand the Results>Derived Values node, then click S-parameter (emw).
2
In the Settings window for Global Evaluation, type S-parameter, Single-Ended Line in the Label text field.
Port Mode Impedance, Single-Ended Line
1
In the Results toolbar, click  Global Evaluation.
2
In the Settings window for Global Evaluation, type Port Mode Impedance, Single-Ended Line in the Label text field.
3
Click Replace Expression in the upper-right corner of the Expressions section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>TEM boundary mode analysis>emw.Zmode_3 - TEM mode port characteristic impedance - Ω.
4
Click  Evaluate.
Electric Field Norm, Single-Ended Line
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, type Electric Field Norm, Single-Ended Line in the Label text field.
Multislice
1
In the Model Builder window, expand the Electric Field Norm, Single-Ended Line node.
2
Right-click Results>Electric Field Norm, Single-Ended Line>Multislice and choose Delete.
Surface 1
1
In the Model Builder window, right-click Electric Field Norm, Single-Ended Line and choose Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
Click  Change Color Table.
4
In the Color Table dialog box, select Thermal>ThermalWave in the tree.
5
Click OK.
6
In the Settings window for Surface, locate the Coloring and Style section.
7
From the Scale list, choose Logarithmic.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
Select Boundaries 6 and 8–11 only.
3
In the Electric Field Norm, Single-Ended Line toolbar, click  Plot.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces>TEM Boundary Mode Analysis.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2
Step 1: TEM Boundary Mode Analysis
1
In the Settings window for TEM Boundary Mode Analysis, locate the Physics and Variables Selection section.
2
Select the Modify model configuration for study step check box.
3
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Differential Line Port Group.
4
Right-click and choose Disable.
5
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Perfect Electric Conductor 3.
6
Click  Disable.
Step 2: Frequency Domain
1
In the Model Builder window, click Step 2: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Differential Line Port Group.
5
Right-click and choose Disable.
6
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Perfect Electric Conductor 3.
7
Click  Disable.
8
In the Model Builder window, click Study 2.
9
In the Settings window for Study, type Study 2, Single-Ended Line with Noise in the Label text field.
10
In the Home toolbar, click  Compute.
Results
S-parameter, Single-Ended Line with Noise
1
In the Model Builder window, under Results>Derived Values click S-parameter (emw).
2
In the Settings window for Global Evaluation, type S-parameter, Single-Ended Line with Noise in the Label text field.
Electric Field Norm, Single-Ended Line with Noise
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, type Electric Field Norm, Single-Ended Line with Noise in the Label text field.
Multislice
1
In the Model Builder window, expand the Electric Field Norm, Single-Ended Line with Noise node.
2
Right-click Results>Electric Field Norm, Single-Ended Line with Noise>Multislice and choose Delete.
Surface 1
In the Model Builder window, under Results>Electric Field Norm, Single-Ended Line right-click Surface 1 and choose Copy.
Surface 1
In the Model Builder window, right-click Electric Field Norm, Single-Ended Line with Noise and choose Paste Surface.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces>TEM Boundary Mode Analysis.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 3
Step 1: TEM Boundary Mode Analysis
1
In the Settings window for TEM Boundary Mode Analysis, locate the Physics and Variables Selection section.
2
Select the Modify model configuration for study step check box.
3
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Electric Point Dipole 1.
4
Right-click and choose Disable.
5
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Single-Ended Line Port Group.
6
Right-click and choose Disable.
Step 2: Frequency Domain
1
In the Model Builder window, click Step 2: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Electric Point Dipole 1.
5
Right-click and choose Disable.
6
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Single-Ended Line Port Group.
7
Right-click and choose Disable.
8
In the Model Builder window, click Study 3.
9
In the Settings window for Study, type Study 3, Differential Line in the Label text field.
10
In the Home toolbar, click  Compute.
Results
S-parameter, Differential Line
1
In the Model Builder window, under Results>Derived Values click S-parameter (emw).
2
In the Settings window for Global Evaluation, type S-parameter, Differential Line in the Label text field.
Port Mode Impedance, Differential Line
1
In the Results toolbar, click  Global Evaluation.
2
In the Settings window for Global Evaluation, type Port Mode Impedance, Differential Line in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3, Differential Line/Solution 5 (sol5).
4
Click Replace Expression in the upper-right corner of the Expressions section. From the menu, choose Component 1 (comp1)>Electromagnetic Waves, Frequency Domain>TEM boundary mode analysis>emw.Zmode_1 - TEM mode port characteristic impedance - Ω.
5
Click  Evaluate.
Electric Field Norm, Differential Line
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, type Electric Field Norm, Differential Line in the Label text field.
Multislice
1
In the Model Builder window, expand the Electric Field Norm, Differential Line node.
2
Right-click Results>Electric Field Norm, Differential Line>Multislice and choose Delete.
Surface 1
In the Model Builder window, under Results>Electric Field Norm, Single-Ended Line right-click Surface 1 and choose Copy.
Surface 1
In the Model Builder window, right-click Electric Field Norm, Differential Line and choose Paste Surface.
Electric Field Ez, Differential Line
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Electric Field Ez, Differential Line in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3, Differential Line/Solution 5 (sol5).
Surface 1
1
Right-click Electric Field Ez, Differential Line and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type emw.Ez.
4
Locate the Coloring and Style section. Click  Change Color Table.
5
In the Color Table dialog box, select Rainbow>Dipole in the tree.
6
Click OK.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
Select Boundary 3 only.
3
In the Electric Field Ez, Differential Line toolbar, click  Plot.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces>TEM Boundary Mode Analysis.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 4
Step 1: TEM Boundary Mode Analysis
1
In the Settings window for TEM Boundary Mode Analysis, locate the Physics and Variables Selection section.
2
Select the Modify model configuration for study step check box.
3
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Single-Ended Line Port Group.
4
Right-click and choose Disable.
Step 2: Frequency Domain
1
In the Model Builder window, click Step 2: Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Physics and Variables Selection section.
3
Select the Modify model configuration for study step check box.
4
In the tree, select Component 1 (comp1)>Electromagnetic Waves, Frequency Domain (emw)>Single-Ended Line Port Group.
5
Right-click and choose Disable.
6
In the Model Builder window, click Study 4.
7
In the Settings window for Study, type Study 4, Differential Line with Noise in the Label text field.
8
In the Home toolbar, click  Compute.
Results
S-parameter, Differential Line with Noise
1
In the Model Builder window, under Results>Derived Values click S-parameter (emw).
2
In the Settings window for Global Evaluation, type S-parameter, Differential Line with Noise in the Label text field.
Electric Field Norm, Differential Line with Noise
1
In the Model Builder window, under Results click Electric Field (emw).
2
In the Settings window for 3D Plot Group, type Electric Field Norm, Differential Line with Noise in the Label text field.
Multislice
1
In the Model Builder window, expand the Electric Field Norm, Differential Line with Noise node.
2
Right-click Results>Electric Field Norm, Differential Line with Noise>Multislice and choose Delete.
Surface 1
In the Model Builder window, under Results>Electric Field Norm, Single-Ended Line right-click Surface 1 and choose Copy.
Surface 1
In the Model Builder window, right-click Electric Field Norm, Differential Line with Noise and choose Paste Surface.