Transient Analysis of a Printed Dual-Band Strip Antenna

A wideband antenna study, such as an S-parameter or far-field pattern analysis, can be obtained by performing a transient response analysis and a time-to-frequency fast Fourier transform (FFT). This model runs a time dependent study first and then transforms the dependent variable, the magnetic vector potential A, and a voltage signal at a lumped port from time domain to frequency domain. S-parameters and far-field radiation data are generated from the frequency domain data. The computed S-parameters shows two resonance in the given frequency range, as expected for this dual-band antenna design.

Figure 1: Printed dual-band antenna strip. The surrounding air domain is not included for visualization purposes.

Model Definition

A metallic strip modeled as perfect electric conductor (PEC) is patterned on a dielectric block. A low permittivity value of εr = 1.05 is used for the dielectric block to describe a polystyrene foam board. A lumped port with 50 Ω characteristic impedance is added on a small rectangular surface in the middle of the strip to excite the antenna structure. The antenna is enclosed by a spherical air domain. The exterior surfaces of the air are finished by a scattering boundary condition that is an absorbing boundary to describe an open radiating space. On these surfaces, the near field to far field transformation is executed in the frequency domain.

In the lumped port settings window, by clicking the check box “Calculate S-parameter” on the excitation port, the voltage excitation type is set to the modulated Gaussian and the center frequency (f0) of the modulating sinusoidal function can be specified. The modulated Gaussian excitation voltage is defined as:

where σ is the standard deviation 1/2f0, f0 is the center frequency and ηf is the modulating frequency shift ratio. A small ratio value, for example 3 %, of ηf may enhance the frequency response around the highest frequency.

The frequency here has to be matched to the center frequency of the S-parameter calculation used in the Time to Frequency FFT study step. The end time of the Time Dependent study step is set to 100 times of the period of the modulating sinusoidal function, which is long enough in this model to ensure that the input energy is fully decayed. This would work for a typical passive circuit except for closed cavity type devices, where the energy decay time can be much longer. The stop condition is automatically added under the Time-Dependent solver (the check box activates this stop condition in the solver settings). When the sum of total electric and magnetic energy in the modeling domain is less than 70 dB compared to the input energy, the Time Dependent study is terminated by the stop condition and all time-domain data will be passed to the FFT step. To generate the frequency-domain data without significant distortion in the frequency range between 0 and 2f0, the time step, satisfying the Nyquist criterion, is set to 1/4f0 = 1/2B, where B is the bandwidth 2f0.

To provide a fine frequency resolution, the end time of the FFT study step is much longer than that of the Time Dependent study. Zero-padding is applied to the Time Dependent study data before the FFT study step.

Results and Discussion

The electric field norm on top of the dielectric block is plotted at the first antenna resonance frequency in Figure 2. It is observed that the electric field reacts with the entire metallic strip structure when the frequency is around the first resonance. The S-parameters up to 3 GHz in Figure 3 shows two resonance regions where the computed S11 is below -10 dB. While the far-field radiation pattern around the low frequency resonance is isotropic on the H-plane, which resembles that of a half-wave dipole antenna, the radiation characteristic at the high frequency resonance shows a higher directivity toward the up and downside of the dielectric block as shown in Figure 4.

Figure 2: The electric field norm distribution on top of the dielectric board. The resonance behavior is observed at each tip of the printed strip.

Figure 3: The S-parameter plot describes two resonances where S11 is less than -10 dB.

Figure 4: The 3D far-field radiation pattern around the first (top) and second resonance (bottom). The directivity at the second resonance is stronger than that at the first resonance.

Notes About the COMSOL Implementation

The time to frequency fast Fourier transform (FFT) study step transforms the solution of dependent variables in time domain to frequency domain. After running the FFT, only the postprocessing variables that can be expressed with the dependent variables and far-field variables in the frequency domain are valid for the result analysis. Since the solutions are typically transformed with a very small frequency step, it is recommended to use the option to reduce the size of the model.

RF_Module/Antennas/dual_band_antenna_transient

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

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
f0	1.5[GHz]	1.5E9 Hz	Center frequency
T0	1/f0	6.6667E-10 s	Period
Tend	100*T0	6.6667E-8 s	End time

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window, click .

In the window for , locate the section.

From the list, choose .

First, create a block for a dielectric layer.

In the window, click .

In the window for , locate the section.

In the text field, type 160.

In the text field, type 110.

In the text field, type 10.

Locate the section. From the list, choose .

Add a work plane where the printed antenna will be placed.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

On the object , select Boundary 4 only.

It might be easier to select the correct boundary 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.)

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Draw the antenna strip.

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 5.

In the text field, type 10.

Locate the section. From the list, choose .

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 50.

In the text field, type 10.

Locate the section. From the list, choose .

Click

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 5.

In the text field, type 60.

Locate the section. In the text field, type -30.

In the text field, type -30.

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 45.

In the text field, type 5.

Locate the section. In the text field, type -70.

In the text field, type 30.

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 45.

In the text field, type 5.

Locate the section. In the text field, type -70.

In the text field, type -35.

Click

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 check box.

Click

Add a sphere for the surrounding air domain.

Sphere 1 (sph1)

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 120.

Click

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

Click the

button in the toolbar.

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

Material 2 (mat2)

In the window, under right-click and choose .

Select Domain 2 only.

In the window for , 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	1.05	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, Transient (temw)

Perfect Electric Conductor 2

In the window, under right-click and choose .

Select Boundaries 10–13 and 19–22 only.

All metallic parts are set to PEC.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 14 only.

In the window for , locate the section.

Select the check box.

In the f0 text field, type f0.

The center frequency of the modulated Gaussian pulse is f0 that is defined in Parameters node. For the first port, wave excitation is by default.

Far-Field Domain 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the list, select .

Click

Select Domain 1 only.

The far-field domain includes only the air region.

Scattering Boundary Condition 1

In the toolbar, click

and choose .

Select Boundaries 1–4 and 15–18 only.

The exterior boundaries is used to absorb the outgoing wave.

Mesh 1

In the window, under right-click and choose .

Hide some boundaries from the view. This helps to see the interior parts when reviewing the mesh.

Click the

button in the toolbar.

Select Boundary 2 only.

Select Boundary 16 only.

Click the

button in the toolbar.

In the window for , locate the section.

From the list, choose .

Size 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundary 14 only.

Use on the lumped port boundary.

Locate the section. From the list, choose .

Size

In the window, click .

In the window for , locate the section.

Click the button.

Locate the section. In the text field, type c_const/f0/5.

The maximum mesh size is 0.2 wavelengths at the center frequency.

Click

Electromagnetic Waves, Transient (temw)

Lumped Port 1

In the window, under click .

In the window for , locate the section.

Click

The added selection will be used to define where to store the results.

In the dialog box, click .

Far-Field Calculation 1

In the window, expand the node, then click .

In the window for , locate the section.

Click

The added selection will be used to define where to store and visualize the results for the far-field radiation pattern.

In the dialog box, click .

Definitions

Explicit 3

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Boundaries 8, 10–13, and 19–22 only.

The model evaluates the solution on these boundaries in time and frequency domain.

Study 1

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,1/(4*f0),Tend). The Sampling rate 4*f0 satisfies the Nyquist condition for the time to frequency fast Fourier transform (FFT) where its bandwidth is 2*f0 excluding negative frequencies.

Click to expand the section. Find the subsection. From the list, choose .

Under , click

In the dialog box, in the list, choose , , and .

Click .

By choosing only the boundaries of interest for settings, it is possible to reduce the size of a model file a lot. It is necessary to include the port boundaries to calculate S-parameters and far-field calculation boundaries for visualizing the radiation pattern.

Step 2: Time to Frequency FFT

In the window, click .

In the window for , locate the section.

In the text field, type Tend*3. This makes sure that the FFT end time is longer than the simulation time so zero-padding can be applied during the time to frequency FFT. This will generate a finer frequency resolution in the resulting frequency response.