# EM.Picasso Tutorial Lesson 1: Analyzing A Microstrip-Fed Patch Antenna

 Tutorial Project: Analyzing A Microstrip-Fed Patch Antenna Objective: In this project, the basic concepts of EM.Picasso are demonstrated, and a microstrip-fed patch antenna is modeled and examined. Concepts/Features: CubeCAD Background Structure Substrate Stack-up PEC Trace De-embedded Source Visualization Current Distribution S-Parameters Radiation Pattern Minimum Version Required: All versions ' Download Link: EMPicasso_Lesson1

## What You Will Learn

This tutorial will guide you through all necessary steps required to set up and perform a basic planar method of moments (PMOM) simulation and visualize and graph the simulation results. Specifically, you will use a wizard to build and analyze a simple microstrip-fed patch antenna on a conductor-backed dielectric substrate.

 We strongly recommend that you read through the first few tutorials and study them carefully before setting up your own projects.

## Getting Started

Open the EM.Cube application by double-clicking on its icon on your desktop. By default, EM.Cube opens a blank project with the name “UntitledProj0” in its CubeCAD Module. You can start drawing objects and build up your physical structure right away. Or you can initiate a new project by selecting the New button of the System Toolbar or using the keyboard shortcut Ctrl+N. This opens up the New Project Dialog, where you can enter a title for your new project and set its path on your hard drive. From the same dialog, you can also set the project’s Length Units, Frequency Units, Center Frequency and Bandwidth.

 The project workspace.
 The New Project dialog.

For this tutorial lesson, set the following parameters in the new project dialog:

 Name EMPicasso_Lesson1 Millimeters GHz 2.4GHz 0.5GHz

Click the Create button of the dialog to accept the settings. A new project folder with your given name is immediately created at your specified path.

To navigate to EM.Picasso, simply select its icon from the Module Toolbar on the left side of the screen. Selecting the module icon changes the contents of the navigation tree to reflect the types of objects supported by the current module.

## A Note on the Background Substrate Structure

Every time you switch to EM.Picasso from another module of EM.Cube, the Stackup Manager pops up to remind you of the current settings of the background structure. In EM.Picasso, your physical structure is always immersed in a background structure of infinite extents in all ±X, ±Y and ±Z directions. In other words, EM.Picasso is an open-boundary structure simulator and assumes a layered planar background structure with an arbitrary number of finite layers stacked up along the vertical (Z) direction.

The Stackup Settings Dialog allows you to define the layers of your substrate structure. You can open this dialog by simply switching back and forth to other EM.Cube modules or by right clicking on the Layer Stackup item in the “Computational Domain” section of the navigation tree and selecting Layer Stackup Settings… from the contextual menu. The layer stack-up always ends in two unbounded half-spaces from the top and bottom. When you start a new blank project, the default background structure consists of a vacuum top half-space at the top of the stackup, a vacuum layer of unit thickness sandwiched in the middle, and a perfect electric conductor (PEC) bottom half-space at the bottom of the stackup. The vacuum medium (εr = μr = 1, σ = σr = 0) represents the free space, while the bottom PEC medium ((εr = μr = 1, σ = 1020 S/m, σm = 0) models the ground plane.

 EM.Picasso's Stackup Settings dialog when you start a new project.

## Creating the Patch Antenna Geometry

Click on the Microstrip-Fed Patch Wizard button of the Wizard Toolbar or select the menu item Tools → Antenna Wizards → Microstrip-Fed Patch Antenna. A dialog pops up asking you if you would like a patch design with a recessed feed. Answer "No" and let the wizard draw the geometry of the patch antenna in the project workspace.

 EM.Picasso's wizard toolbar.
 The patch antenna geometry in the project workspace and the highlighted additions to the navigation tree.

Note that an orange domain box is placed around your patch antenna structure. Since EM.Picasso is an open-boundary solver, it doesn't have a finite computational domain. The orange box is simply use to visualize the substrate stackup configuration in the background of your physical structure.

In EM.Picasso, objects are grouped together as traces under the “Physical Structure” node of the navigation tree. There are four trace types:

1. PEC Traces
2. Slot Traces
3. Conductive Sheet Traces
4. Embedded Object Sets
5. Virtual Objects

All the objects belonging to the same trace group have the same material properties, and additionally, they are located on the same Z-plane in the layer stackup hierarchy. The wizard automatically created a PEC trace called "PATCH_PEC" in the navigation tree. Under this node there are two objects:

1. "ANCHOR": A rectangle strip object representing the square patch antenna
2. "Feed": A rectangle strip object representing the microstrip feed line, which is attached to the right edge of the patch

The last define trace group remain active, and its name in the navigation tree is displayed in bold letters. This means that all the new object you draw will belong to the active trace object.

 When a trace group is active in EM.Picasso, its horizontal Z-plane is set as the active work plane. In other words, the mouse cursor moves on this plane with a fixed Z-coordinate, and all new objects are drawn in this plane.

## Modifying the Substrate Properties

The patch antenna geometry the wizard created earlier is fully parameterized. The objective of this tutorial lesson is to teach the basics of running a simulation rather than parameterizing a geometrical construction. Therefore, we will not get into the details of defining variables at this point. At this time, open the Variable Dialog by clicking the button on the Simulate Toolbar or selecting the menu item Simulate → Functions....

 The variables dialog.

You can see that the relative permittivity of the dielectric substrate layer is represents by the variable "er" and has a default value of 2.2. Also, the substrate thickness is represented by the variable "h" and has a default value of 0.0015m or 1.5mm. You can change the definitions and values all variables. To change any variable, first select and highlight it in the list and click the Edit button of the variables dialog to open the "Edit Variable" dialog. Then, change the definition of the variable, which is typically either a numeric value or an expression. Change the variable "er" and "h" according to the table below and click the OK button:

Variable Name Original Definition New Definition
er 2.2 2.54
h 0.0015*to_meters 0.0016*to_meters
 Changing the value of variable "er".
 Changing the value of variable "h".

After these changes, your substrate now has a thickness of 1.6mm and a relative permittivity of εr = 2.54. The variables list now looks like this:

 The variables dialog showing the new values of some variables.

If you open the stackup manager again, you will see the changes you made to the properties of the "Layer_1". Note that you can also change the substrate properties from the stackup manager by selecting an item's name in the table and clicking the Edit button of this dialog.

 EM.Picasso's stackup manager showing the new substrate parameters.

## Examining the Geometric Objects in the Project Workspace

You can view or modify the properties of the two rectangle strip objects "ANCHOR" and "Feed" the wizard created for this project. If you click on the surface of an object in the project workspace, it is selected, and its color becomes yellow (the default selection color). If you right-click on the surface of the object, or right-click on its name in the navigation tree, and select Properties... from the contextual menu, the object's property dialog opens up at the lower right corner of the screen. You can also open the property dialog by double-clicking on the surface of a geometric object. The figure below shows the property dialog of "ANCHOR".

 The property dialog of the rectangle strip object representing the patch.

The coordinates of the center of the object's local coordinate system (LCS) is set to (0, 0, 0). Note that the dimensions of the rectangle strip have both been set equal to the variable "patch_len". The value of this variable is controlled from the variables dialog. You may also simply replace these by fixed numeric values at any time.

Note that at the center frequency fc = 2.4GHz, the operating wavelength is:

$\lambda_0 = \frac{c}{f} \approx \frac{3\times 10^8}{2.4 \times 10^9} = 0.125m = 125mm$

In the variables dialog, "patch_len" has been defined as a dependent variable using the expression "floor(0.5*lambda0_unit*100/sqrt(er))/100", which means:

$L_{patch} = \frac{\lambda_0}{2\sqrt{\epsilon_r}} = 39.18mm$

In other words, the wizard set the length of the patch equal to half the material wavelength at the center frequency of the project. Note that the function "floor(x*100)/100" has been used here to truncate the results to two decimal digits.

## Examining the Excitation Source & Simulation Observables

The wizard already took care of everything you need to run a planar MoM simulation of your patch antenna. It defined a source to excite your antenna as well as a current distribution observable, far-field radiation pattern and a port definition for the computation of S/Z/Y parameters.

EM.Picasso provides several different types of excitation sources. The most useful one is the scattering wave port source, which is used to calculate the S/Z/Y parameters of your planar structure. This type of source has to be defined on an open-ended rectangle strip object. To calculate the S-parameters accurately, EM.Picasso extends the source's rectangle strip host object from its open end to about two effective wavelengths (2λeff). At this extended length, EM.Picasso samples and measures a clean standing wave pattern in the current distribution. The standing wave current data are then used to calculate the scattering parameters of your planar structure. Right-click on the "WP_1" item under Scattering Wave Ports in the “Sources” section of the navigation tree, and select Properties… from the contextual menu to open the source dialog. Note that the host rectangle strip has been set to "Feed", and the Direction is "-X" as the port looks. A conical arrow is placed at the left end of the narrow strip object. The Offset box shows a zero value. The dark red arrow points to the reference phase plane where the port characteristics are calculated. You can change the offset value and move the reference phase plane inside the strip. Note that the location of the arrow does not show the actual gap source location, which is hidden somewhere close to the open end of the strip object. Keep all the other default values and click the OK button to accept the changes.

 EM.Picasso's scattering wave port/source dialog.

Project observables are output quantities that you would like to compute at the end of a planar MoM simulation. By default, EM.Picasso's engine does not generate any output data unless you define one or more project observables before you start a simulation. The simplest observable in EM.Picasso is a current distribution, which is the direct solution of the MoM integral equations. Each trace group has its own current distribution observable. Right-click on the "Patch_PEC" item under Current Distributions in the “Observables” section of the navigation tree and select Properties… from the contextual menu to open the Current Distribution Dialog.

 EM.Picasso's current distribution dialog.

To plot the radiation patterns of a radiating structure, you need to define a far-field observable. Right-click on the "FF_1" item under Far-Field Radiation Patterns in the Observables section of the navigation tree, and select Properties… from the contextual menu to open the radiation pattern dialog. Note that the Theta and Phi angle increments have both been set equal to 5°. To produce radiation pattern plots of a higher resolution, you may want to set smaller values of Angle Increment.

 EM.Picasso's far-field radiation pattern dialog.

For calculating the port characteristics of the patch antenna such as the S-parameters and input impedance, your EM.Picasso project needs one or more ports associated with the sources. This is done through Port Definition dialog. To open it, right-click on the "PD_1" item under Port Definitions in the Observables section of the navigation tree, and select Properties… from the contextual menu. Since you have only one source, it is assigned as "Port_1". Note that the port reference impedance has a default value of 50Ω.

 EM.Picasso's port definition dialog.

## Viewing the Planar Mesh of the Patch Antenna

EM.Picasso's simulation engine uses the "Planar Method of Moments (PMOM)" to solve the integral equations governing the physics of your planar structure. To produce a numerical solution of these integral equations, EM.Picasso first needs to discretize your planar structure into a collection of elementary cells. By default, EM.Picasso generates a hybrid mesh of your planar structure that contains both rectangular and triangular cells. Rectangular objects are typically discretized using a rectangular mesh as far as possible. Triangular cells appear on non-rectangular objects or in the junction areas between connected rectangular regions. The resolution of EM.Picasso's planar mesh is controlled by a parameter called Mesh Density, which has a default value of 20 Cells/λeff. For resonant structures, a higher mesh density is recommended. A low mesh density may fail to provide an adequate level of numerical accuracy. Extremely high mesh densities in PMOM may lead to numerical instability.

 The accuracy and integrity of the PMOM simulation results greatly depend on the quality and consistency of the mesh of your planar structure. It is highly recommended that you inspect the planar mesh before running a simulation.

The planar mesh properties can be accessed by clicking the Mesh Settings button of the Simulate Toolbar or using the keyboard shortcut Ctrl+G or via the menu item Simulate → Discretization → Mesh Settings. Since a patch antenna is a resonant structure, the wizard automatically set the value of mesh density to 30 Cells/λeff.

 EM.Picasso's mesh settings dialog.

To view the mesh, click the Show/Generate Mesh button of the Simulate Toolbar or alternatively use the keyboard shortcut Ctrl+M. You should see a mesh like this:

 The planar mesh of the patch antenna structure.

Pay attention to how the feed line has been extended to 2λeff. In general, the mesh view shows how the simulation engine sees your physical structure. The feed line containing the scattering wave port grows to 2λeff only in the mesh view mode and returns to its original length in the normal view mode. To exit the mesh view mode and return to the normal view mode, use the keyboard’s Esc key or click the Show/Generate Mesh button of the Simulate Toolbar one more time. Keep in mind that in the mesh view mode, you can perform view operations such as rotate view, zoom in/out or pan view, but you cannot select objects or edit them.

## Running the Planar MoM Simulation

At this time, your project is ready for PMOM simulation. Click the Run button of the Simulate Toolbar to open up the Simulation Run Dialog. Or alternatively, use the keyboard shortcut Ctrl+R, or the menu item Simulate → Run… The simplest simulation mode in EM.Picasso is “Single-Frequency Analysis”. In this mode, your physical structure is taken “As Is”, and its mesh is passed to the PMOM simulation engine along with the necessary information regarding the sources and observables. Keep in mind that an “Analysis” is a single-frequency simulation carried out at the specified center frequency of your project.

 EM.Picasso's simulation run dialog.

To run the simulation, click the Run button of the run Dialog. A separate window pops up displaying messages from the simulation engine. In three separate fields, the engine reports the current step of PMOM simulation, progress percentage of the current task, and the elapsed time in seconds. Since your project contains a port definition, the scattering, impedance and admittance parameters of your structure are calculated. In this case, your project involves a one-port structure. Therefore, the PMOM engine computes the S11, Z11 and Y11 parameters. These parameters are reported in the Message Window at the end of the simulation:

S11: 0.348364 -0.657921j

S11(dB): -2.563198

Z11: 25.993465 -76.726375j

Y11: 0.003961 +0.011691j

 EM.Picasso's output window dialog.

Once the simulation has been completed, you can close the message window and return to the project workspace. The navigation tree is now populated with simulation results, most notably under "Current Distributions" and "Far Fields" nodes.

## Viewing the Simulation Results

EM.Picasso usually generate two types of data: 2D and 3D. Examples of 2D data are S/Z/Y parameters and polar radiation patterns. 2D data are graphed. Examples of 3D data are electric and magnetic current distributions, near field distributions and 3D radiation patterns. 3D data are visualized in EM.Picasso’s project workspace, and the plots are usually overlaid on the physical structure.

To plot the current distributions, go to the Current Distributions section of the navigation tree. Under “PATCH_PEC”, you will see a total of 14 nodes. These include magnitude and phase plots for each of the three components of the electric surface current density (J) and magnetic surface current density (M), plus two additional plots for total electric and total magnetic currents. In this project, your physical structure does not contain magnetic currents (no slot traces). Therefore, all the magnetic current nodes contain zero-value plots. The plot of total electric current (JTOT) distribution should look like the figure below. Notice the visible standing wave pattern that has been formed on the feed line of your patch antenna. Also, remember that your microstrip feed line was extended to 2λeff during the simulation. These standing wave data were used by the PMOM engine to calculate the S11 parameter using Prony’s method of exponential approximation.

 The plot of total electric current (JTOT) distribution of the patch antenna.

The Far-Field Radiation Patterns section of the navigation tree contains three different 3D radiation pattern plots: the Theta component of the far-zone electric field, the Phi component of the far-zone electric field, and the Total far field. Click on “FF_1.3D.Total” to view a 3D visualization of the total far field. You will notice that the far-field plots are all centered at the origin of coordinates. This is due to the fact that the radiation patterns are calculated in a standard spherical coordinate system center at (0, 0 , 0). Once you are in a near field or far field visualization view, you can always go back to the normal view mode of the project workspace using the keyboard’s Esc key or by clicking on an empty space in the project workspace.

 Theta component of the 3D radiation pattern plot of the patch antenna. Phi component of the 3D radiation pattern plot of the patch antenna. The total 3D radiation pattern plot of the patch antenna.

A list of all the 2D output data files generated at the end of a simulation can be viewed in EM.Picasso’s Data Manager. To open this dialog, click the Data Manager button of Simulate Toolbar, or use the keyboard shortcut Ctrl+D, or access the menu item Simulate → Data Manager, or right-click on the Data Manager item in the “Observables” section of the navigation tree and select Open Data Manager… The S/Z/Y parameters are written into complex data files with a “.CPX” file extension. These ASCII data files are called “S11.CPX”, “Z11.CPX” and “Y11.CPX”, respectively. You can view the contents of these files using the View button of data manager.

 EM.Picasso's Data Manager Dialog.

Besides the 3D visualization of the radiation patterns, you can plot 2D graphs of the patterns at certain plane cuts. The 2D radiation patterns can be plotted as both Cartesian and polar graphs. Open up the data manager dialog and spot Cartesian pattern data files with a “.DAT” file extension as well as the polar (angular) data files with a “.ANG” file extension. The figure below shows the polar radiation pattern plots in the YZ and ZX plane cuts. These are the data files called "FF_1_PATTERN_Polar_YZ.ANG" and "FF_1_PATTERN_Polar_YZ.ANG", respectively. To plot them, select their name or row in the Data Manager's list and highlight them and then click the Plot button. Besides the three principal XY, YZ and ZX plane cuts, there are also data files for one additional user defined Phi-plane cut, which by default is calculated at φ = 45°.

 The 2D polar graph of the YZ-plane radiation pattern. The 2D polar graph of the ZX-plane radiation pattern.