Branch-Line Coupler

A branch line coupler, also known as a quadrature (90°) hybrid, is a four-port network device with one input port, two output ports, with a 90° phase difference between them, and one isolated port. Due to its symmetry, any port can be used as the input port.

Figure 1: The geometry of a branch line coupler is symmetric.

Model Definition

The form of the branch line coupler is shown schematically in Figure 1. The layout design is based upon Ref. 1, and is tuned to operate at 3 GHz. The design is realized as microstrip lines patterned onto a 0.060 inch dielectric substrate. The microstrip lines are modeled as perfect electric conductor (PEC) surfaces, and another PEC surface on the bottom of the dielectric substrate acts as a ground plane. The entire modeling domain is bounded by PEC boundaries that represent the device packaging. The four ports are modeled as small rectangular faces that bridge the gap between the PEC face that represents the ground plane, and the PEC faces that represent the microstrip line at each port.

Figure 2: The model of the branch line coupler. Some exterior faces are removed for visualization.

The model is shown in Figure 2. A small air domain bounded by a PEC surface around the device is also modeled. The model is meshed using a tetrahedral mesh. A good rule of thumb is to use approximately five elements per wavelength in each material. The physics-controlled mesh is used to generate the mesh automatically.

After the first study, the model is modified to utilized the SMA connector in the part library. The SMA connector with two holes at the flange is added at each end of the microstrip line and the type of lumped port is changed from uniform to coaxial.

Results and Discussion

The computed S-parameters are plotted in Figure 3. At a frequency of 3 GHz, the signal is evenly split between the two output ports with a very small amount of losses. The input signal is barely coupled to the isolation port where S41 is less than −30 dB at 3 GHz. The evaluated phase shift between the two output ports is 89.9°.

Figure 3: The frequency response of the branch line coupler shows good input matching (S11) and isolation (S41) around 3 GHz. The coupled signal at the two output ports (S21 and S31) is about -3 dB at 3 GHz.

Figure 4: The amplitude and phase imbalance on the two output ports. The phase difference at 3 GHz is approximately 90 degrees.

Because the metallic housing works as a rectangular cavity, there is a resonance observed around 4.6 GHz. The resonant frequency of an air-filled hollow rectangular cavity is

where a and b are the dimensions of the sidewall of the cavity and d is the length of the cavity. The dominant resonant frequency at TE101 mode is close to 5 GHz. Because the cavity is partially filled by the dielectric substrate, the resonance is expected lower than the that of the air-filled cavity. This resonance can easily be removed by adding a metallic post in the middle of the cavity connecting the bottom ground plane to the top ceiling if necessary.

The results after adding the SMA connectors are similar to those without the connectors and they are presented in the step by step instructions.

Reference

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

RF_Module/Couplers_and_Power_Dividers/branch_line_coupler

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

In the window, under click .

In the window for , locate the section.

In the text field, type range(1[GHz],100[MHz],5[GHz]).

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
thickness	60[mil]	0.001524 m	Substrate thickness
l_s	40[mm]	0.04 m	Length, substrate
w_line2	5[mm]	0.005 m	Width, line 2
l_line2	13[mm]	0.013 m	Length, line 2
l_line1	(l_s-l_line2)/2	0.0135 m	Length, line 1
w_line1	3.2[mm]	0.0032 m	Width, line 1
w_line3	3[mm]	0.003 m	Width, line 3
l_line3	13.6[mm]	0.0136 m	Length, line 3

Here, mil refers to the unit milliinch.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Work Plane 1 (wp1)

In the toolbar, click

, to add an xy-plane for the coupler layout’.

In the window for , click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2*w_line1+l_line3.

In the text field, type l_s.

Locate the section. From the list, choose .

Click

Work Plane 1 (wp1)>Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_line2*2+l_line3.

In the text field, type l_line2.

Locate the section. From the list, choose .

In the toolbar, click

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

In the toolbar, click

In the window for , locate the section.

In the text field, type l_line3.

In the text field, type l_line2.

Locate the section. In the text field, type -l_line3/2.

In the text field, type l_line2/2+w_line3.

Click

Click the

button in the toolbar.

Work Plane 1 (wp1)>Array 1 (arr1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

From the list, choose .

In the text field, type 3.

Locate the section. In the text field, type -l_line2-w_line3.

In the toolbar, click

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

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select the objects , , and only, the three rectangles belonging to the array object (arr1).

Clear the check box.

In the toolbar, click

Work Plane 1 (wp1)

Extrude the xy-plane with the thickness of the substrate. Additional rectangular boundaries at each end of the feed lines are created by this extrusion, too. Use these boundaries to assign lumped ports later.

Extrude 1 (ext1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (mm)
thickness

Click

Click the

button in the toolbar.

Choose wireframe rendering to get a better view of the interior parts.

Click the

button in the toolbar.

Create a block for the substrate.

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_s.

In the text field, type thickness.

Locate the section. From the list, choose .

In the text field, type thickness/2.

Click

Substrate

In the toolbar, click

and choose .

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

Locate the section. Clear the check box.

Click in the window and then press Ctrl+A to select both objects.

Locate the section. Select the check box.

Click

Package

In the toolbar, click

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

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

In the text field, type l_s+l_s/8.

In the text field, type thickness*5.

Locate the section. From the list, choose .

In the text field, type thickness*5/2.

Click

The completed geometry describes the microstrip line device on a substrate enclosed by a metal housing.

Definitions

Hide three boundaries to get a better view of the interior parts when reviewing the 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 1, 2, and 4 only.

It might be easier to select the boundaries by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

Electromagnetic Waves, Frequency Domain (emw)

Now set up the physics. The default boundary condition is perfect electric conductor, which is applied to all exterior boundaries. Apply this condition also to the interior boundaries of the microstrip lines.

Perfect Electric Conductor 2

In the window, under right-click and choose .

Select Boundary 13 only.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 24 only.

For the first port, wave excitation is by default.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 25 only.

Lumped Port 3

In the toolbar, click

and choose .

Select Boundary 15 only.

Lumped Port 4

In the toolbar, click

and choose .

Select Boundary 14 only.

Lumped ports are assigned at each end of the microstrip lines. Wave excitation is on only at the first port.

Materials

Assign material properties to the model. First, apply air to all domains.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Create a dielectric material of er = 3.38 overriding air in the substrate.

Substrate

In the window, under right-click and choose .

In the window for , type Substrate 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	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

Mesh 1

In the window, under right-click and choose .

Three exterior boundaries are hidden in this view.

Study 1

In the toolbar, click

Results

Electric Field (emw)

Begin the results analysis and visualization by modifying the first default plot to show the E-field norm in the middle of the substrate at 3 GHz.

In the window for , locate the section.

From the list, choose .

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Find the subsection. From the list, choose .

In the text field, type thickness/2.

In the toolbar, click

The input power is evenly split between the two output ports.

S-parameter (emw)

In the window, click .

In the window for , click to expand the section.

Locate the section. From the list, choose .

Compare the resulting plot with that shown in Figure 3.

Smith Plot (emw)

Plot the amplitude and phase imbalance on two output ports (Figure 4).

Imbalance

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

In the text area, type Amplitude and Phase Imbalance at the Coupled Ports.

Locate the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Expression	Unit	Description
emw.S21dB-emw.S31dB	dB	Amplitude difference

Global 2

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Expression	Unit	Description
if(arg(emw.S21)-arg(emw.S31)<0, arg(emw.S21)-arg(emw.S31)+360[deg],arg(emw.S21)-arg(emw.S31))	deg	Phase difference

The unit is degree.

Imbalance

In the window, click .

In the window for , locate the section.

Select the check box.

In the table, select the check box for .

In the toolbar, click

The phase difference between two output ports is approximately 90 degrees at 3 GHz.

Evaluate the phase difference between two output ports at 3 GHz.

Global Evaluation 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the list, select .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
arg(emw.S21)-arg(emw.S31)	°

Click

When the designed circuit is measured with a network analyzer, the circuit is connected to cables through connectors. Those connectors are not part of the network analyzer calibration process, and they may change the frequency response due to an additional reactive loading. By adding connectors, the simulation becomes closer to the real world device. The RF part library helps to quickly add SMA connectors to the coupler without handling multiple geometry operations.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
w_line2	5.2[mm]	0.0052 m	Width, line 2

Geometry 1

Package (blk2)

In the window, under click .

In the window for , locate the section.

In the text field, type thickness+0.635.

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

In the text field, type 20.

Click

Part Libraries

In the toolbar, click

and choose .

In the window, click .

In the window, select in the tree.

Click

Geometry 1

SMA Connector, Flange with Two 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 -8.4.

In the text field, type -l_s/2.

In the text field, type thickness+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

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 16.8.

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 0 180.

Click

The duplicated trace on the bottom ground plane can be removed as necessary. In this model, it is optional.

Form Composite Faces 1 (cmf1)

In the toolbar, click

and choose .

On the object , select Boundaries 6, 44, 153, 156, 158, and 319 only.

In the toolbar, click

Electromagnetic Waves, Frequency Domain (emw)

Perfect Electric Conductor 2

In the window, under click .

Select Boundaries 6 and 44 only.

Lumped Port 1

In the window, click .

In the window for , locate the section.

Click

Select Boundary 234 only.

Locate the section. From the list, choose .

Lumped Port 2

In the window, click .

In the window for , locate the section.

Click

Select Boundary 243 only.

Locate the section. From the list, choose .

Lumped Port 3

In the window, click .

In the window for , locate the section.

Click

Select Boundary 80 only.

Locate the section. From the list, choose .

Lumped Port 4

In the window, click .

In the window for , locate the section.

Click

Select Boundary 71 only.

Locate the section. From the list, choose .

Perfect Electric Conductor 3

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Materials

Material 3 (mat3)

In the window, under right-click and choose .

In the window for , 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
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic