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Design Matching Network Using Lumped Components from Modelithics Library

This example shows you how to:

  • Design a matching network for a reference antenna using ideal components from RF Toolbox™ and real-world components from Modelithics SELECT+ Library™ . Ideal components do not take parasitic effects into account. To include these effects in your simulation, you need to build the matching network with real-world components.

  • Analyze the ideal and the real-world matching network.

  • Compare the performance of the ideal and the real-world matching network with respect to a reference antenna.

The presence of parasitics changes the response of the matching network with real-world lumped components. The non-ideal behavior results from variations in the material properties of the substrate and packing material, solder and pad properties, and orientation.

Video Walkthrough

For a walkthrough of the example, play the video.

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Create Inset-Fed Patch Antenna

The first step before designing the matching network for the reference antenna is to design the reference antenna itself. This example uses an inset-fed patch antenna as a reference antenna. Create simple inset-fed patch antenna using the design function from Antenna Toolbox™ implemented on a PCB. Set the antenna dimensions and use an FR4 substrate in this design. And the set the substrate thickness to 0.0014 m.

antennaObject = design(patchMicrostripInsetfed, 2400*1e6);
antennaObject.Length = 0.0265;
antennaObject.Width = 0.0265;
antennaObject.Height = 0.0014;
antennaObject.Substrate.Name = 'FR4';
antennaObject.Substrate.EpsilonR = 4.8;
antennaObject.Substrate.LossTangent = 0.026;
antennaObject.Substrate.Thickness = 0.0014;
antennaObject.FeedOffset = [-0.02835, 0];
antennaObject.StripLineWidth = 0.0016223;
antennaObject.NotchLength = 0.0037853;
antennaObject.NotchWidth = 0.002839;
antennaObject.GroundPlaneLength = 0.0567;
antennaObject.GroundPlaneWidth = 0.0567;

Visualize Inset-Fed Patch Antenna

Use the show function to visualize the structure of this patch antenna.

figure;
show(antennaObject)

Figure contains an axes object. The axes object with title patchMicrostripInsetfed antenna element, xlabel x (mm), ylabel y (mm) contains 5 objects of type patch, surface. These objects represent PEC, feed, FR4.

Analyze Inset-Fed Patch Antenna

Perform full-wave analysis on the inset-fed patch antenna over 2.3–2.5 GHz and save the S-parameter results to a MAT file. Load the MAT file to view the impedance and reflection coefficient response.

load InsetPatchAntenna.mat
plotFrequency = 2400*1e6;
freqRange = linspace(2.3e9, 2.5e9, 11);

Plot the impedance of the inset-fed patch antenna.

figure;
impedance(antennaObject, freqRange);

Figure contains an axes object. The axes object with title Impedance, xlabel Frequency (GHz), ylabel Impedance (ohms) contains 2 objects of type line. These objects represent Resistance, Reactance.

Plot the reflection coefficient response of the inset-fed patch antenna.

figure; 
s = sparameters(antennaObject, freqRange);
rfplot(s)

Figure contains an axes object. The axes object with xlabel Frequency (GHz), ylabel Magnitude (dB) contains an object of type line. This object represents dB(S_{11}).

Build Rational Model

Build a rational model for the antenna S-parameter data. This allows you to refine the frequency points in the analysis range and not simulate the antenna again during full-wave analysis.

s_rat = rational(s);
[resp,~] = freqresp(s_rat,freqRange);
hold on
plot(freqRange/1e9,20*log10(abs(resp)))
title('Antenna Reflection Coefficient')
legend('Full-Wave','Rational Model')

Figure contains an axes object. The axes object with title Antenna Reflection Coefficient, xlabel Frequency (GHz), ylabel Magnitude (dB) contains 2 objects of type line. These objects represent Full-Wave, Rational Model.

Design Matching Network

Load the S-parameter data from the workspace to the Matching Network Designer app. Set the matching frequency to 2.35 GHz and the network topology to L-Topology. Once the app generates the networks, select series C, shunt L from the network list and export the network. The app saves the network to MAT file.

mod_update.png

To build the matching network, convert the S-parameter data to an nport object and add it to a circuit. Assign ports to the circuit for RF analysis.

ant = nport(s);
load mnapp_LTopo_CserLsh.mat
ckt_lumped = circuit;
add(ckt_lumped,[1 2 0 0],mnckt)
add(ckt_lumped,[2 0],ant)
setports(ckt_lumped,[1 0])

Perform S-Parameters Frequency Sweep

Select 100 points in the analysis frequency range and analyze the matching network response with the antenna S-parameters as the load. Overlay the antenna-only port reflection coefficient over this response. This shifts the antenna response in the lower band to 2.35 GHz.

freqRange = linspace(2.3e9, 2.5e9, 100);
lumped_s = sparameters(ckt_lumped,freqRange);
[resp,freq] = freqresp(s_rat,freqRange);
figure
rfplot(lumped_s,1,1)
hold on
plot(freqRange/1e9,20*log10(abs(resp)))
legend('ANT+Matching N/W','ANT','Location','Best')
title('Reflection Coefficient of Antenna and Matching Network')

Figure contains an axes object. The axes object with title Reflection Coefficient of Antenna and Matching Network, xlabel Frequency (GHz), ylabel Magnitude (dB) contains 2 objects of type line. These objects represent ANT+Matching N/W, ANT.

Build Matching Network with Non-Ideal Lumped Component Models

Select the non-ideal lumped components from Modelithics Select+ Library. You must have the Modelithics Select+ Library license to run the following code. For more information, see Modelithics SELECT+ Library for MATLAB.

Create RF Component using Modelithics SELECT+ Library

Set up the Modelithics Select+ Library by specifying the full path to the library.

mdlxSetup('C:\mdlx_library\SELECT')

Create the Modelithics library object.

mdlx = mdlxLibrary;

Search the library for a 1.6117 pF capacitor mounted on a 59 mil FR4 substrate. Note that Modelithics components are substrate scalable, and that 59 mil is chosen to match the antenna substrate thickness of 1.4mm.

search(mdlx,'FR4Standard59mil',Type='Capacitors',Value=1.6117e-12)

SearchResults_Capacitors.png

Search the library for a 2.6611 nH inductor mounted on a 59 mil FR4 substrate.

search(mdlx,'FR4Standard59mil',Type='Inductors',Value=2.6611e-9)

SearchResults_Inductors.png

Create an array of Modelithics capacitors.

cList = search(mdlx,'FR4Standard59mil',Type='Capacitors',Value=1.6117e-12);

Create an array of Modelithics inductors.

lList = search(mdlx,'FR4Standard59mil',Type='Inductors',Value=2.6611e-9);

Create Matching Network with Modelithics Components

Create a matching network with L-Topology, series C, and shunt L using the first element in the array of Modelithics capacitors and inductors. Most Modelithics lumped components have two ports.

mdlxckt = circuit;
add(mdlxckt,[1 2 0 0],cList(1));
add(mdlxckt,[2 0 0 0],lList(1));
setports(mdlxckt,[1 0],[2 0]);

As with the matching network with ideal lumped components, add the matching network with the Modelithics lumped components and the S-parameters of the inset-fed patch antenna to a circuit. Assign ports to the circuit for RF analysis.

mdlxckt_lumped = circuit;
add(mdlxckt_lumped,[1 2 0 0],mdlxckt)
add(mdlxckt_lumped,[2 0],nport(s))
setports(mdlxckt_lumped,[1 0])

Analyze Matching Network and Antenna

Analyze the matching network response with the antenna S-parameters as the load.

mdlxlumped_s = sparameters(mdlxckt_lumped,freqRange);

Compare Ideal and Non-Ideal Reflection Coefficients

Overlay the reflection coefficient from the antenna S-parameters with the ones using ideal matching network and the one with real-world components from the Modelithics Select+ Library.

figure
rfplot(mdlxlumped_s,1,1)
hold on
plot(freqRange/1e9,20*log10(abs(resp)))
rfplot(lumped_s,1,1)
legend('ANT+Modelithics Components','ANT','ANT+Ideal Components','Location','Best')
title('Reflection Coefficient of Antenna and Ideal/Non-ideal Matching Network')

reflection_coefficient_comparison.png

Inspect Component Data Sheets

The two L and C components are available only in a limited set of discrete values. Use the datasheet function to inspect their respective data sheets to identify the values that are closer to the nominal values identified before.

datasheet(cList(1));
datasheet(lList(1));

Discrete component values from the data sheets are shown in this figure.

landcdatshet.png

Build Matching Network Using Discrete Component Values

Build a new matching network, and try a few of the discrete values close to the nominal values. The best working values for a matching network operating at 2.35 GHz are 1.3 pF and 1.8 nH. The discrete values are slightly different from the nominal values due to parasitic effects.

c = clone(cList(1));
c.Value = 1.3e-12;
l = clone(lList(1));
l.Value = 1.8e-9;
mdlxcktD = circuit;
add(mdlxcktD,[1 2 0 0],c);
add(mdlxcktD,[2 0 0 0],l);
add(mdlxcktD,[2 0],nport(s))
setports(mdlxcktD,[1 0]);
mdlxlumpeddiscrete_s = sparameters(mdlxcktD,freqRange);

Overlay the reflection coefficient from the ideal matching network, the one with real-world components from the Modelithics Select+ Library using nominal values, and the one with real-world components from the Modelithics Select+ Library using discrete values.

figure
rfplot(mdlxlumpeddiscrete_s,1,1)
hold on
rfplot(mdlxlumped_s,1,1);
rfplot(lumped_s,1,1)
legend('ANT+Modelithics Components Discrete Values', ...
    'ANT+Modelithics Components Nominal Values', ...
    'ANT+Ideal Components','Location','Best')
title('Reflection Coefficient of Antenna and Ideal/Non-ideal Matching Network')

The resulting matching network now works at the target frequency.

mod_update2.png

See Also

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