Finite Element Method Based Open Problem

This example shows how to create, visualize and analyze a Finite Element Method (FEM) based open problem.

Prerequisites

The example requires the Integro-Differential Modeling Framework for MATLAB add-on. To enable the add-on:

In the Home tab Environment section, click on Add-Ons. This opens the add-on explorer. You need an active internet connection to download the add-on.
Search for Integro-Differential Modeling Framework for MATLAB and click Install
To verify if the download is successful, run matlab.addons.installedAddons in your MATLAB® session command line.
On Windows, to run the FEM based open problem, you must install the Windows Subsystem for Linux (WSL).

Create Variables

Create variable for the frequency range.

freq = linspace(1e9,5e9,21);

Create Branch-line Coupler

Create a branch-line coupler with default properties.

branchline = couplerBranchline;

Visualize the coupler.

figure
show(branchline)

Figure contains an axes object. The axes object with title couplerBranchline element, xlabel x (mm), ylabel y (mm) contains 8 objects of type patch, surface. These objects represent PEC, feed, Teflon.

Use the sparameters function to calculate the S-parameters in the frequency range of 1 - 5 GHz. The default solver is a Method of Moments (MoM).

sparam_mom = sparameters(branchline,freq);

Plot the S-parameters of the coupler.

figure
rfplot(sparam_mom)

$Figure contains an axes object. The axes object with xlabel Frequency (GHz), ylabel Magnitude (dB) contains 16 objects of type line. These objects represent dB(S_{11}), dB(S_{21}), dB(S_{31}), dB(S_{41}), dB(S_{12}), dB(S_{22}), dB(S_{32}), dB(S_{42}), dB(S_{13}), dB(S_{23}), dB(S_{33}), dB(S_{43}), dB(S_{14}), dB(S_{24}), dB(S_{34}), dB(S_{44}).$

Create FEM based Branch-line Coupler

Convert the branch-line coupler to the pcbComponent object.

pcb = pcbComponent(branchline)

pcb = 
  pcbComponent with properties:

              Name: 'couplerBranchline'
          Revision: 'v1.0'
        BoardShape: [1×1 antenna.Rectangle]
    BoardThickness: 0.0016
            Layers: {[1×1 antenna.Polygon]  [1×1 dielectric]  [1×1 antenna.Rectangle]}
     FeedLocations: [4×4 double]
      FeedDiameter: 0.0026
      ViaLocations: []
       ViaDiameter: []
      FeedViaModel: 'strip'
         Conductor: [1×1 metal]
              Tilt: 0
          TiltAxis: [0 0 1]
              Load: [1×1 lumpedElement]
        SolverType: 'MoM'
        IsShielded: 0

Set the SolverType property to 'FEM'.

pcb.SolverType = 'FEM';

Visualize the FEM based coupler.

figure
show(pcb)

Figure contains an axes object. The axes object with title pcbComponent element, xlabel x (mm), ylabel y (mm) contains 21 objects of type patch. These objects represent PEC, Teflon, Coax feed Inner conductor, Coax feed Dielectric.

Design RF Connector

Unlike a delta gap source feed model in MoM, the FEM uses a coaxial wave port model. Use the design function to design a coaxial connector model.

c = design(RFConnector(PinLength=0),pcb);

Set the designed coaxial connector to the coupler.

pcb.Connector = c;

Visualize the coupler.

figure
show(pcb)

Calculate S-parameters

Use the sparameters function to calculate the S-parameters in the frequency range of 1 - 5 GHz.

sparam_fem = sparameters(pcb,freq);

Plot the S-parameters of the coupler.

figure
rfplot(sparam_fem)