COMSOL 6.4 - Microstrip Patch Antenna Surrogate Model

Microstrip Patch Antenna Surrogate Model

This example builds surrogate models with deep neural network (DNN) training to quickly estimate the performance of a microstrip patch antenna based on four design parameters: patch length, tuning stub length, dielectric constant of a substrate, and frequency. The model also simulates a full finite element (FEM) model using asymptotic waveform evaluation of the computed S-parameters to efficiently evaluate the frequency response with fine frequency resolution. This approach can be much faster than a conventional discrete frequency sweep, which may take a long time due to the large number of samples. The full model is used to verify the accuracy of the surrogate models.

Figure 1: Base microstrip patch antenna model with four parameters, used for generating surrogate models.

Model Definition

The embedded model is based on the Microstrip Patch Antenna model from the RF Module Application Library. It includes:

•

Surrogate model training data generation

•

Deep neural network (DNN) training for fast antenna performance evaluation via the surrogate model

•

Full finite element simulation using adaptive frequency sweep for reference comparison of antenna performance metrics, such as 2D and 3D far-field realized gain (dBi), the norm of the electric field on the top surface of the antenna (in the logarithmic scale), and S-parameters (S11) with given design parameters

Study for Training Data Generation

To efficiently generate the input parameter space and the output quantities of interest, two geometry sampling features are added separately under the Definitions. One is for the antenna’s realized gain configured based on the far-field calculation boundary feature selections. The other is for near field, sampling the norm of the electric field on the top surface of the antenna substrate.

Table 1: Quantities of Interest.
Expression	Note
comp1.emw.S11dB	Set without geometry sampling, as the S-parameter is global variable and does not depend on the geometry configuration
comp1.emw.normE	Geometry Sampling, Fa-Field Calculation
comp1.emw.rGaindBEfar	Geometry Sampling, Substrate

Table 2: Input Parameters.
Parameter	Description	Distribution	Range
l_patch	Patch length	Uniform	from 50 to 54 mm
e_r	Dielectric constant	Uniform	from 3.13 to 3.63
l_stub	Tuning stub length	Uniform	from 12.5 to 18.5 mm
f0	Frequency	Uniform	from 1.525 to 1.625 GHz

The number of input point is set to 1000. The Surrogate Modeling study step is executed in combination with a Frequency Domain study step.

Deep Neural Network (DNN) Training

DNN training for each quantity of interest is performed with separate layer configurations and training settings.

Table 3: DNN Settings.
	S-parameter	Norm of E-field	Realized gain
Hidden layer number	6	5	4
Node configuration	{128, 128, 128, 64, 32, 16}	{64, 128, 128, 64, 32}	{32, 64, 64, 32}
Activation function, hidden layers	tanh	tanh, last layer Sigmoid	tanh, last layer Sigmoid
Activation function, output	Linear	Linear	Linear
Learning rate	4e-4	5e-4	2e-4
Weight decay	2e-4	1e-6	2e-7
Batch size	512	512	1024
Loss function	Mean absolute error	Mean absolute error	Mean absolute error

Learning rate, weight decay, and batch size were tuned to minimize the validation loss with the given training data and preventing overfitting.

Study for Full FEM model

The output from the DNN-trained surrogate model can be visualized by comparing it to results from the full FEM model. Adaptive Frequency Sweep, based on asymptotic waveform evaluation with computed S-parameters, is used to achieve S-parameter and other quantities of interest with a finer frequency resolution, 0.5 MHz. To reduce the file size, only the solutions on the far-field calculation boundaries and the top surface of the substrate were saved.

Results and Discussion

The following analyses are addressed between the full model and DNN-trained surrogated models:

•

S-parameter (S11) in dB comparison.

•

Norm of electric field comparison.

•

3D realized gain (dBi) comparison.

The DNN-trained surrogate models can predict quantities of interest such as S-parameters, near- and far-field intensities, almost instantly, while producing results that closely resembles those of full models. Minor discrepancies are anticipated to diminish with improved DNN configuration.

Figure 2: Comparison of S-parameters between the full model and the DNN-trained surrogate model.

Figure 3: Norm of the electric field on the top surface of the antenna for the full model (right) and the DNN-trained surrogated model (left).

Figure 4: Realized far-field gain for the full model (right) and the DNN-trained surrogate model (left).

Notes About the Implementation

The size of the data generated for surrogate model training and the DNN configurations may be subjected to change in order to improve the regression models and enhance accuracy. The specific numbers used in this app are merely examples and maybe adjusted, which could affect the output of the surrogate models.

RF_Module/Antenna_Arrays/microstrip_patch_antenna_surrogate

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select > > in the tree.

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
freq_min	1.525[GHz]	1.525E9 Hz	Minimum frequency
freq_max	1.625[GHz]	1.625E9 Hz	Maximum frequency
e_r	3.38	3.38	Dielectric constant
f0	1.575[GHz]	1.575E9 Hz	Frequency

Several parameters have been introduced for deep neural network training. The parameters l_patch, l_stub, e_r, and f0 will be used as input parameters for generating surrogate model training data.

Component 1 (comp1)

In the window, expand the node.

Materials

Substrate (mat2)

In the window, expand the > node, then click .

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	e_r	1	Basic

Electromagnetic Waves, Frequency Domain (emw)

In the window, expand the > node.

Far-Field Calculation 1

In the window, expand the > > node, then click .

In the window for , locate the section.

Click

In the dialog, type Far-Field Calculation in the text field.

Click .

The explicit selection created directly from the feature assists in configuring the geometry sampling area for generating training data.

Definitions

Geometry Sampling, Far-Field Calculation

In the toolbar, click

In the window for , type Geometry Sampling, Far-Field Calculation in the text field.

Locate the section. From the list, choose .

From the list, choose .

Surrogate Model Sampling

Geometry Sampling, Substrate

In the toolbar, click

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

Locate the section. From the list, choose .

Select Boundaries 16 and 21 only.

The surrogate model training data for deep neural network training is not generated across the entire simulation domain, but only within specific areas of interest. For example, the near-field data, specifically the electric field norm, is sampled and trained on the substrate surface, including the radiating patch area. Far-field values are collected at the boundaries where the near-field to far-field transformation is performed.

In the first study, surrogate model training data is generated for S-parameters, electric field norm, and realized far-field gain. For each variable of interest, data is generated by systematically varying the patch length, impedance-matching stub length, dielectric constant, and operating frequency.

Study 1

Solver Configurations

In the window, expand the node.

Right-click > and choose .

Step 1: Frequency Domain

In the window for , locate the section.

In the text field, type f0.

In the window, click .

In the window for , type Study, Data Generation for Surrogate Model Training in the text field.

Surrogate Model Training

In the toolbar, click

and choose .

In the window for , locate the section.

Click

In the table, enter the following settings:


Expression	Include study-dependent input	Study-dependent input description
comp1.emw.S11dB	Configure study-dependent input	1 Study-dependent input parameters

S-parameter S11dB is a global variable and geometry sampling is not required.

Click

In the table, enter the following settings:


Expression	Include study-dependent input	Study-dependent input description
comp1.emw.normE	Configure study-dependent input	1 Study-dependent input parameters

From the list, choose .

Click

In the table, enter the following settings:


Expression	Include study-dependent input	Study-dependent input description
comp1.emw.rGaindBEfar	Configure study-dependent input	1 Study-dependent input parameters

From the list, choose .

Locate the section. Click

In the table, enter the following settings:


Parameter	Source type	Source description
l_patch (Patch length)	Analytic	Uniform

In the text field, type 50[mm].

In the text field, type 54[mm].

Click

In the table, enter the following settings:


Parameter	Source type	Source description
l_stub (Tuning stub length)	Analytic	Uniform

In the table, click to select the cell at row number 2 and column number 3.

In the text field, type 12.5[mm].

In the text field, type 18.5[mm].

Click

In the table, enter the following settings:


Parameter	Source type	Source description
e_r (Dielectric constant)	Analytic	Uniform

In the text field, type 3.13.

In the text field, type 3.63.

Click

In the table, enter the following settings:


Parameter	Source type	Source description
f0 (Frequency)	Analytic	Uniform

In the text field, type freq_min.

In the text field, type freq_max.

In the text field, type Hz.

Find the subsection. In the text field, type 1000.

In the toolbar, click

Click

The necessary data for training is generated in the form of tables, and there is no need to retain the solution. By removing the solution, the model file size can be reduced.

Results

2D Far Field (emw), 3D Far Field, Gain (emw), Electric Field (emw), Electric Field, Logarithmic (emw)

In the window, under , Ctrl-click to select , , , and .

Right-click and choose .

Train each quantity of interest using a deep neural network. Each hidden layer uses the tanh> activation function, except for the last hidden layer for the field quantities, which uses the Sigmoid function to prevent over-truncation of maximum values. The output layer uses a linear activation function to leave the output unmodified.

Global Definitions

Deep Neural Network 1

In the toolbar, click

and choose > .

In the window for , locate the section.

From the list, choose .

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


Columns	Type	Settings
f0 (Hz)	Ignored column

In the table, click to select the cell at row number 6 and column number 3.

In the text field, type dnn_S11dB.

Locate the section. Click

In the text field, type 256.

Click

In the text field, type 256.

Click

In the text field, type 256.

Click

In the text field, type 128.

Click

In the text field, type 64.

Click

In the text field, type 32.

In the table, click to select the cell at row number 8 and column number 2.

From the list, choose .

Locate the section. In the text field, type 3e-4.

In the text field, type 2e-4.

In the text field, type 1024.

From the list, choose .

Find the subsection. In the text field, type 20000.

Find the subsection. In the text field, type 1e-6.

Tuning parameter values for , , , , , and is application-specific and can vary depending on the quantity of interest and the layer configuration. Minor modifications may reduce the risk of overfitting or lead to undesired results. Therefore, tuning should be done gradually and in small increments.

Deep Neural Network 2

In the toolbar, click

and choose > .

In the window for , locate the section.

From the list, choose .

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


Columns	Type	Settings
Z (mm)	Ignored column
e_r	Argument	Name=x6, Scaling=Normalization
f0 (Hz)	Ignored column
freq (GHz)	Argument	Name=x8, Scaling=Normalization

Since only the flat surface of the substrate is evaluated and there is no height variation, the spatial coordinate z is not included.

In the table, click to select the cell at row number 9 and column number 3.

In the text field, type dnn_normE.

Locate the section. Click

In the text field, type 64.

Click

In the text field, type 128.

Click

In the text field, type 128.

Click

In the text field, type 64.

Click

In the text field, type 32.

From the list, choose .

In the table, click to select the cell at row number 7 and column number 2.

From the list, choose .

Locate the section. In the text field, type 5e-4.

In the text field, type 1e-6.

From the list, choose .

Find the subsection. In the text field, type 500.

Deep Neural Network 3

In the toolbar, click

and choose > .

In the window for , locate the section.

From the list, choose .

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


Columns	Type	Settings
e_r	Argument	Name=x6, Scaling=Normalization
f0 (Hz)	Ignored column
freq (GHz)	Argument	Name=x8, Scaling=Normalization

In the table, click to select the cell at row number 9 and column number 3.

In the text field, type dnn_rGaindBEfar.

Locate the section. Click

In the text field, type 32.

Click

In the text field, type 64.

Click

In the text field, type 64.

Click

In the text field, type 32.

From the list, choose .

In the table, click to select the cell at row number 6 and column number 2.

From the list, choose .

Locate the section. In the text field, type 2e-4.

In the text field, type 2e-7.

In the text field, type 1024.

From the list, choose .

Find the subsection. In the text field, type 3000.

Deep Neural Network 1 (dnn_S11dB)

In the window, click .

In the window for , click

While performing deep neural network training, the validation and training losses can be monitored to determine whether the loss values have converged to a desirable level. Once training is complete, the plotted values are volatile and will be overwritten by subsequent training sessions. To preserve the data, activate the window and click the first toolbar button, . This will generate a table containing up to the last 20,000 epochs. When the Table window is active, click the toolbar button to generate the loss plot.

Deep Neural Network 2 (dnn_normE)

In the window, click .

In the window for , click

In the window, click the button in the window toolbar.

Deep Neural Network 3 (dnn_rGaindBEfar)

In the window, click .

In the window for , click

In the window, click the button in the window toolbar.

The results from the surrogate models will be verified using a full finite element method (FEM) simulation with an adaptive frequency sweep study. This study uses a very fine frequency resolution, which leads to a large model file. Therefore, only the solution on the boundary selection of interest is stored by using the option.

Definitions

FEM Data Storage

In the toolbar, click

In the window for , type FEM Data Storage in the text field.

Locate the section. From the list, choose .

Click

In the dialog, type 9-12, 16, 21, 26, 32, 33, 37, 40 in the text field.

Click .

Study, Full Model

In the window, click .

In the window for , type Study, Full Model in the text field.

Step 1: Adaptive Frequency Sweep

In the window, under click .

In the window for , locate the section.

In the text field, type range(freq_min,500[kHz],freq_max).

Click to expand the section. In the table, click to select the cell at row number 1 and column number 3.

In the list box, select .

Under , click

In the dialog, select in the list.

Click .

Solver Configurations

In the window, under right-click and choose .

In the toolbar, click

Functions, including the output of a deep neural network, can be mapped to a dataset for visualization. Use a dataset to plot the regression model of the S-parameters. For field quantities, use a based on a dataset.

Results

Grid 1D for DNN S-parameter Plot

In the toolbar, click

and choose > .

In the window for , type Grid 1D for DNN S-parameter Plot in the text field.

Locate the section. In the text field, type 1.525.

In the text field, type 1.625.

Locate the section. From the list, choose .

From the list, choose .

Click to expand the section. Click to expand the section. Locate the section. In the text field, type 401.

Grid 3D for DNN Near Field on Substrate

In the toolbar, click

and choose > .

In the window for , type Grid 3D for DNN Near Field on Substrate in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Find the subsection. In the text field, type -0.8*l_sub/1e-3.

In the text field, type 0.8*l_sub/1e-3.

Find the subsection. In the text field, type -0.8*l_sub/1e-3.

In the text field, type 0.8*l_sub/1e-3.

Find the subsection. In the text field, type -0.8*l_sub/1e-3.

In the text field, type 0.8*l_sub/1e-3.

Click to expand the section. In the text field, type 201.

In the text field, type 201.

In the text field, type 2.

The factor 1e-3 is for scaling based on the geometry unit of millimeters (mm) used in the model.

Parametric Surface for DNN Near Field on Substrate

In the toolbar, click

and choose .

In the window for , type Parametric Surface for DNN Near Field on Substrate in the text field.

Locate the section. From the list, choose .

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

Find the subsection. In the text field, type -1.

Locate the section. In the text field, type s1*w_sub/2/1e-3.

In the text field, type s2*l_sub/2/1e-3.

In the text field, type d/2/1e-3.

Grid 3D for DNN Far Field

In the window, right-click and choose .

In the window for , type Grid 3D for DNN Far Field in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type 71.

In the text field, type 71.

Parametric Surface for Far Field

In the toolbar, click

and choose .

In the window for , type Parametric Surface for Far Field in the text field.

Locate the section. From the list, choose .

Locate the section. Find the subsection. In the text field, type pi*2.

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

Locate the section. In the text field, type 0.8*l_sub*cos(s1)*sin(s2)/1e-3.

In the text field, type 0.8*l_sub*sin(s1)*sin(s2)/1e-3.

In the text field, type 0.8*l_sub*cos(s2)/1e-3.

S-parameters, Surrogate (DNN) vs. FEM

In the toolbar, click

In the window for , type S-parameters, Surrogate (DNN) vs. FEM in the text field.

Locate the section.

Select the checkbox. In the associated text field, type Frequency [GHz].

Locate the section. From the list, choose .

Line Graph 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type dnn_S11dB(l_patch,l_stub,e_r,x[GHz]).

Locate the section. From the list, choose .

In the text field, type (x/1[m])[GHz].

From the list, choose .

The expression for the is modified to plot the surrogate model output alongside the results of the FEM simulation.

Click to expand the section. Select the checkbox.

From the list, choose .

In the table, enter the following settings:


Legends
S11, Surrogate (DNN)

Global 1

In the window, 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:


Expression	Unit	Description
emw.S11dB	dB	S11

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

In the table, enter the following settings:


Legends
S11, FEM

In the toolbar, click

normE, Surrogate (DNN) vs. FEM

In the toolbar, click

In the window for , type normE, Surrogate (DNN) vs. FEM in the text field.

Locate the section. Clear the checkbox.

Surface 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 20*log10(dnn_normE(x,y,l_patch,l_stub,e_r,f0)+1e1).

Adding 1e1 helps produce a more vivid color distribution when plotting on a logarithmic scale.

Locate the section. From the list, choose .

Surface 2

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 20*log10(emw.normE+1e1).

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

Selection 1

Right-click and choose .

Select Boundaries 16 and 21 only.

Transformation 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 120.

Click the

button in the toolbar.

Click the

button in the toolbar.

The output of the function mapped to the is not compatible with the conventional Radiation Pattern plot. Therefore, a surface plot is used and deformed to create a volumetric 3D radiation pattern shape.

rGaindBEfar, Surrogate (DNN) vs. FEM

In the toolbar, click