COMSOL 6.4 - SMA Connectorized Wilkinson Power Divider

SMA Connectorized Wilkinson Power Divider

Resistive power dividers and T-junction power dividers are two conventional types of three-port power dividers. Such dividers are either lossy or not matched to the system reference impedance at all ports. In addition, isolation between two coupled ports is not guaranteed. The Wilkinson power divider outperforms both the lossless T-junction divider and the resistive divider and does not have the issues mentioned above. This example shows how to model such a device.

Figure 1: A Wilkinson power divider is fabricated on a 60 mil substrate. An SMA receptacle is added on each port and the circuit board is suspended in the metal package using screws.

Model Definition

The Wilkinson power divider is a three-port device composed of 50 Ω and 70.7 Ω microstrip lines on a dielectric substrate with a ground plane and a 100 Ω resistor mounted between two ports. The model also includes a metal enclosure, screws, and SMA receptacles connected to each port representing a complete package of a power divider shown in Figure 1. Except for the microstrip lines and ground plane, model all the SMA receptacles, screws, and the metal package using perfect electric conductor (PEC) boundaries. The SMA receptacle and screw domains enclosed by these PEC boundaries are not part of the example analysis, so they are set to PEC by default. The microstrip lines and ground plane made of 1 oz copper layers are modeled using a transition boundary condition with 35 μm thickness to address lossy conductive surfaces due to finite copper conductivity. The relative dielectric constant, εr, of the 60 mil substrate is 3.38. The boundaries facing the dielectric-filled coaxial connector of the SMA receptacles are specified as coaxial lumped ports. The 100 Ω resistor is realized via a uniform lumped port with100 Ω characteristic impedance.

Results and Discussion

Figure 2 shows the symmetric E-field norm distribution on the top of the substrate. The input energy is equally coupled to each output port.

Figure 2: The E-field norm plot shows that the input is evenly split between the two output ports.

The S-parameters plotted in Figure 3 show the frequency response of the Wilkinson power divider. Good input impedance matching characteristics are observed and the coupled power at each output port is about −3 dB around 3 GHz.

Figure 3: The S-parameters show very good input matching at 3 GHz and evenly divided power at the two output ports.

References

1. D.M. Pozar, Microwave Engineering, John Wiley & Sons, 1998.

2. R.E. Collin, Foundation of Microwave Engineering, McGraw Hill, 1992.

RF_Module/Couplers_and_Power_Dividers/wilkinson_power_divider

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Study 1

Step 1: Frequency Domain

Define the study frequency ahead of performing any frequency-dependent operation such as building mesh. The physics-controlled mesh uses the highest frequency value in the specified range.

In the window, under click .

In the window for , locate the section.

In the text field, type range(2[GHz],0.1[GHz],4[GHz]).

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file wilkinson_power_divider_parameters.txt.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

First, create the substrate.

Substrate

In the toolbar, click

In the window for , type Substrate in the text field.

Locate the section. In the text field, type w_subs.

In the text field, type l_subs.

In the text field, type 1.524.

Locate the section. From the list, choose .

In the text field, type -0.762.

Add a block for the metal package.

Package

In the toolbar, click

In the window for , type Package in the text field.

Locate the section. In the text field, type w_subs.

In the text field, type l_subs.

In the text field, type 20.

Locate the section. From the list, choose .

In the text field, type 2.

Click

Click the

button in the toolbar.

Add a work plane for drawing the layout of the power divider.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1) > Plane Geometry

In the window, click .

Add two circles to create the ring strip part.

Ring outer

In the toolbar, click

In the window for , type Ring outer in the text field.

Click the

button in the toolbar.

Locate the section. In the text field, type r_ring.

Ring inner

In the toolbar, click

In the window for , type Ring inner in the text field.

Locate the section. In the text field, type r_ring-1.9.

Ring cut

In the toolbar, click

In the window for , type Ring cut in the text field.

Locate the section. In the text field, type 2.

In the text field, type 3.

Locate the section. In the text field, type -1.

In the text field, type -9.

Work Plane 1 (wp1) > Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Click to select the

toggle button for .

Select the objects and only.

Click

Add a rectangle for the 100 ohm resistor.

Lumped element

In the toolbar, click

In the window for , type Lumped element in the text field.

Locate the section. In the text field, type 2.

Locate the section. In the text field, type -1.

In the text field, type -8.

Add rectangles for the 50 ohm microstrip feed lines.

Work Plane 1 (wp1) > Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type 3.2.

In the text field, type 5.

Locate the section. From the list, choose .

In the text field, type 10.5.

Work Plane 1 (wp1) > Rectangle 4 (r4)

In the toolbar, click

In the window for , locate the section.

In the text field, type 3.2.

In the text field, type 2.

Locate the section. In the text field, type -7.

From the list, choose .

In the text field, type -12.

Work Plane 1 (wp1) > Rectangle 5 (r5)

In the toolbar, click

In the window for , locate the section.

In the text field, type 3.2.

In the text field, type 6.

Locate the section. In the text field, type -8.6.

In the text field, type -11.

Locate the section. In the text field, type -28.

Work Plane 1 (wp1) > Mirror 1 (mir1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Select the checkbox.

Create a union of all objects except the small rectangle for the resistor (r2) to remove unnecessary boundaries.

Work Plane 1 (wp1) > Union 1 (uni1)

In the toolbar, click

and choose .

Select the objects , , , , , and only.

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

The power divider layout drawn on the substrate.

Add a coaxial SMA connector from the part library.

Part Libraries

From the menu, choose .

In the window, click .

In the window, select > > > in the tree.

Click

Geometry 1

SMA Connector, Square Flange with Four Holes 1 (pi1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
l_dielectric	8[mm]	8 mm	Length of dielectric
l_pin	1[mm]	1 mm	Length of pin from flange

Locate the section. Find the subsection. In the text field, type l_subs/2.

In the text field, type 0.635.

Find the subsection. In the text field, type -90.

Click to expand the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
All		√	None
Dielectric	√	√	None
Conductor		√	None

Click to expand the section. In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Exterior		√	None
Conductive surface	√	√	None

Click

Add two more SMA connectors.

Copy 1 (copy1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type -7,7.

Rotate 1 (rot1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

In the text field, type 180.

Screw

In the toolbar, click

Add a cylinder for the metal screw.

In the window, click .

In the window for , type Screw in the text field.

Locate the section. In the text field, type 8.

Locate the section. In the text field, type -12.

In the text field, type -10.

In the text field, type -8.

Add a cylinder for the metal screw head.

Screw head

In the toolbar, click

In the window for , type Screw head in the text field.

Locate the section. In the text field, type 1.5.

Locate the section. In the text field, type -12.

In the text field, type -10.

Union 1 (uni1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Clear the checkbox.

Array 1 (arr1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type 2.

Locate the section. In the text field, type 24.

In the text field, type 20.

The domain inside the screw body is not part of the model analysis.

Difference 1 (dif1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Click to select the

toggle button for .

Select the objects , , , and only.

Click

Disable the analysis of the geometry as the remaining small geometric details can be kept.

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Definitions

Suppress some boundaries to get a view of the interior while setting the physics and mesh.

Hide for Physics 1

In the window, expand the > node.

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 7, 8, and 10 only.

Now, set up the physics.

Electromagnetic Waves, Frequency Domain (emw)

Perfect Electric Conductor 1

The Perfect Electric Conductor applies by default to all exterior boundaries. After restricting the Electromagnetics Waves, Frequency Domain interface to the model domain, these outer boundaries include the metal screws. Add a Transition Boundary Condition to the microstrip line and the substrate ground plane.

Transition Boundary Condition 1

In the toolbar, click

and choose .

Select Boundaries 6 and 80 only.

In the window for , locate the section.

In the d text field, type 35[um].

Perfect Electric Conductor 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Proceed with the Lumped Port conditions.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 160 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 75 only.

In the window for , locate the section.

From the list, choose .

Lumped Port 3

In the toolbar, click

and choose .

Select Boundary 242 only.

In the window for , locate the section.

From the list, choose .

Add a lumped element for the 100Ω resistor.

Lumped Element 1

In the toolbar, click

and choose .

Select Boundary 164 only.

In the window for , locate the section.

In the Zelement text field, type 100[ohm].

Materials

Next, assign material properties. First, specify air for all domains.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Copper (mat2)

In the window for , locate the section.

From the list, choose .

Select Boundaries 6 and 80 only.

Override the material for the substrate domains with a dielectric material of εr = 3.38.

Substrate

In the window, right-click and choose .

In the window for , type Substrate in the text field.

Select Domain 2 only.

Locate the section. 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

PTFE

Right-click and choose .

In the window for , type PTFE in the text field.

Locate the section. From the list, choose .

Locate the 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

Mesh 1

In the window, under right-click and choose .

Study 1

In the toolbar, click

Results

Electric Field (emw)

The default plot shows the E-field norm distribution.

In the window for , locate the section.

From the list, choose .

Multislice 1

In the window, expand the node.

Right-click and choose .

Electric Field (emw)

In the window, click .

In the window for , locate the section.

Clear the checkbox.

Volume 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Selection 1

Right-click and choose .

Select Domain 2 only.

Surface 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Clear the checkbox.

Selection 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Material Appearance 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Select the checkbox.

In the toolbar, click

The resulting plot shows the E-field equally split between Port 2 and Port 3. Compare with Figure 2.

S-Parameter (emw)

The reproduced plot shows the calculated S-parameters. Compare with Figure 3.

Smith Plot (emw)

In the window, click .

Electric Field, Logarithmic (emw)

In the window, click .

Analyze the same model with a much finer frequency resolution using based on asymptotic waveform evaluation (AWE). When a device presents a slowly varying frequency response, the AWE method provides a faster solution time when running the simulation on many frequency points. The following example with the Adaptive Frequency Sweep can be computed 10 times faster than regular Frequency Domain sweeps with a same finer frequency resolution.

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, under > click .

In the window for , locate the section.

Click

In the dialog, type Lumped port 1 in the text field.

Click .

Lumped Port 2

In the window, click .

In the window for , locate the section.

Click

In the dialog, type Lumped port 2 in the text field.

Click .

Lumped Port 3

In the window, click .

In the window for , locate the section.

Click

In the dialog, type Lumped port 3 in the text field.

Click .

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 2

Step 1: Adaptive Frequency Sweep

In the window for , locate the section.

In the text field, type range(2[GHz],10[MHz],4[GHz]).

Use a five times finer frequency resolution.

From the list, choose .

In the table, enter the following settings:


Asymptotic waveform evaluation (AWE) expressions
abs(comp1.emw.S11)

A slowly varying scalar value curve works well for AWE expressions. Use abs(comp1.emw.S11) for this model.

In the text field, type 0.1.

A moderate value may expedite the computation by sacrificing accuracy. For rapid prototyping, it is worthwhile to try.

Because such a fine frequency step generates a memory-intensive solution, the model file size will increase tremendously when it is saved. When only the frequency response of port related variables are of interest, it is not necessary to store all of the field solutions. By selecting the checkbox in the section, we can control the part of the model on which the computed solution is saved. We only add the selection containing these boundaries where the port variables are calculated. The lumped port size is typically very small compared to the entire modeling domain, and the saved file size with the fine frequency step is more or less that of the regular discrete frequency sweep model when only the solutions on the port boundaries are stored.

Click to expand the section. In the table, enter the following settings: