# Maximizing Gain and Improving Impedance Bandwidth of E-Patch Antenna

This example shows how to optimize an E-patch antenna in the Antenna Designer app using the SADEA optimizer.

### Antenna Selection

Enter `antennaDesigner`

at the `MATLAB`

® command prompt to open the app.

In the blank canvas, click **NEW**.

From the **ANTENNA GALLERY dropdown**, under **PATCH FAMILY**, select an E-patch antenna.

Set the design frequency to 6.6 GHz. To analyze the antenna, click **Accept**.

### Analyze 3D Radiation Pattern

Click on **3D Pattern. **Observe the radiation pattern and the maximum gain.

The maximum gain of the antenna is **6.16 dBi** as shown on the top left side of the pattern figure.

### Analyze ${\mathit{S}}_{11}$

Click **S Parameter**.

Observe that the ${\mathit{S}}_{11}$ of the antenna does not show any impedance bandwidth within the frequency range and the current E-patch antenna design might not be an optimized one. To improve the gain and the impedance bandwidth, optimize the antenna using the optimizer tab.

### Setup Optimization Problem

Any optimization problem typically requires following inputs.

Objective function: Main goal of the optimization. It evaluates the analysis function and minimizes or maximizes the output of the function.

**In this example, maximizing the gain of the antenna is the objective function.**Design variables: The input variables to the objective function. These variables are changed by the optimizer within a pre-set range of values called as the bounds of the variables.

**In this example, the dimensions of the E-patch are the design variables.**Constraint functions (if necessary): Functions which restrict a desired analysis function value on the antenna.

**In this example, the constraint function is S11 less than -10 db to obtain an impedance bandwidth.**Other inputs: Other inputs may include the number of iterations, the input center frequency, and the input frequency, the number of iterations, the frequency at which the analysis is performed, etc.

### Optimization Function

To optimize the E-patch, click on the **Optimize** button.

To select an objective function, use the **OBJECTIVE FUNCTION** Gallery drop down. Since the goal is to maximize the gain of the antenna, click on **Maximize Gain**.

### Design Variables and Constraints

To set up the design variables, click on the **Design Variables tab**. Click on the checkboxes present on the left-hand side of the properties to choose the required design variables. The optimizer would change these chosen properties to obtain a maximum gain for the antenna.

Enter bounds for the design variables as follows:

Click **Apply **to set the variables.

To set up the constraints, click on the **Constraints** tab.

Select **S11 (dB) **from the **Constraint Function**. Select **<** operator from s**ign** and enter value as **-10**.

Click **Apply**.

In the **SETTINGS **section, enter **Iterations** as **300** to give the number of iterations to run for the optimizer. Click **Parallel Computing **in** Settings **section if you have Parallel Computing Toolbox™ license and want to use it for the optimization. To start the start optimization, click the **Run **button.

### Optimization

The **SADEA** is a surrogate model-based optimization which contains two stages

Building model

Optimizing

#### Building Model:

In the model building stage, the optimizer makes a surrogate model from the design space, and the specified objective and the constraints function. It diversely goes through the design space and performs analysis on these sample points.

So, the *x*-axis shows the number of samples and the *y*-axis shows the value of the analysis function value at that sample. The bottom left side show the current sample value and the bottom right side shows the design variables. The optimizer within decides and takes appropriate number of samples to build the model. After the model is built, the optimizer starts running iterations.

#### Optimizing

In the optimizing stage, the *x*-axis shows the number of iterations and the *y*-axis shows the objective function values. From the plots shown on the optimizing stage, you can understand the trend of convergence.

Notice that, the objective as well as the constraint plots show fewer deviations from after the 150th iteration. This indicates that the objective is **converging**.

**Optimized 3D Pattern and Bandwidth**

Once the optimization is complete, click on **Accept. **This takes you back to the previous page.

Click on **Pattern **to observe the 3D radiation pattern of the optimized antenna. Now, the maximum directivity is 8.7 dBi.

Click on **S Parameter **to observe the impedance bandwidth of the antenna. The optimized antenna shows a bandwidth of around **6.25 GHz to 6.669 GHz**.

## See Also

Surrogate Based Optimization Design of Six-Element Yagi-Uda Antenna