# Artificial Intelligence (AI) for Rapid Analysis and Design of Patch Antenna

This example shows how to use artificial intelligence (AI) to rapidly analyze and design antennas from the Antenna Toolbox™ catalog.

Learn how the `AIAntenna`

object can be used to take advantage of the speed of AI-based analysis without the need for prior machine learning experience. Follow this example to:

Create an antenna for AI-based analysis using

`AIAntenna.`

Use AI to analyze a specific antenna design.

Rapidly explore antennas across the design space.

### Create Antenna for AI-Based Analysis

Using `design`

with `ForAI=true`

, create an `AIAntenna`

for AI-based analysis of a planar inverted-F antenna (PIFA) designed to resonate around 2.4 GHz.

antType = pifa; fd = 2.4e9; pifaAI = design(antType,fd,ForAI=true);

Calculate the resonant frequency of the prototype antenna using AI-based analysis by calling `resonantFrequency`

on the `AIAntenna`

object, noting that the calculated resonant frequency is higher but approximately equal to the design frequency of 2.4 GHz.

resonantFrequencyAI0 = resonantFrequency(pifaAI)

resonantFrequencyAI0 = 2.4091e+09

Now calculate the bandwidth using AI-based analysis. The `bandwidth`

function outputs the absolute bandwith, the lower and upper frequencies of the bandwidth, and whether the antenna is matched at 50 ohms. An antenna is matched when its S11 plot dips below -10 dB. Here, the antenna has a bandwidth, indicating it is matched because a frequency range exists where the S11 is less than -10 dB.

[bandwidthAI0,lowerFrequencyAI0,upperFrequencyAI0,matchingAI0] = bandwidth(pifaAI)

bandwidthAI0 = 1.4809e+08

lowerFrequencyAI0 = 2.3186e+09

upperFrequencyAI0 = 2.4667e+09

`matchingAI0 = `*categorical*
Matched

### Calculate Resonant Frequency and Bandwidth of Specific Antenna Design

To achieve a wider bandwidth [1], increase the width to be 0.7 times the length while keeping the short pin width equal to the width.

First, query the `AIAntenna`

object. The tunable parameters of a PIFA for AI-based analysis are length, width, height, and short pin width.

pifaAI

pifaAI = AIAntenna with properties: Antenna Info AntennaType: 'pifa' InitialDesignFrequency: 2.4000e+09 Tunable Parameters Length: 0.0292 Width: 0.0194 Height: 0.0097 ShortPinWidth: 0.0194 Use 'showReadOnlyProperties(pifaAI)' to show read-only properties

View the non-tunable properties by calling `showReadOnlyProperties`

.

showReadOnlyProperties(pifaAI)

SubstrateName: 'Air' SubstrateEpsilonR: 1 SubstrateLossTangent: 0 SubstrateThickness: 0.0097 GroundPlaneLength: 0.0350 GroundPlaneWidth: 0.0350 PatchCenterOffset: [0 0] FeedOffset: [-0.0019 0] ConductorName: 'PEC' ConductorConductivity: Inf ConductorThickness: 0 Tilt: 0 TiltAxis: [1 0 0] LoadImpedance: [] LoadFrequency: [] LoadLocation: 'feed'

Define the desired design specifications.

W = pifaAI.Length*0.7; shortPinW = W

shortPinW = 0.0204

Before modifying your prototype to meet the desired design, use `tunableRanges`

to verify that your desired value is within the tunable ranges supported for AI-based analysis of your antenna. In this case, the desired width of 0.0204 m is within the tunable range of 0.0165 m and 0.0224 m. The same can be said of the short pin width.

tRanges = tunableRanges(pifaAI)

`tRanges=`*2×4 table*
Length Width Height ShortPinWidth
____________________ ____________________ _____________________ ____________________
min max min max min max min max
________ ________ ________ ________ _________ ________ ________ ________
resonantFrequency 0.024792 0.033542 0.016532 0.022366 0.0082605 0.011176 0.016532 0.022366
bandwidth 0.024792 0.033542 0.016532 0.022366 0.0082605 0.011176 0.016532 0.022366

assert(all(W>=tRanges.Width.min) && all(W<=tRanges.Width.max)) assert(all(shortPinW>=tRanges.ShortPinWidth.min) && all(shortPinW<=tRanges.ShortPinWidth.max))

Set the antenna width and short pin width to their desired values.

pifaAI.Width = W; pifaAI.ShortPinWidth = shortPinW;

Use the `show`

function to visualize the design.

show(pifaAI)

#### Calculate Resonant Frequency and Bandwidth Using AI-Based Analysis

Use AI-based analysis to calculate the resonant frequency and bandwidth for your antenna. The AI-based calculation shows the resonant frequency of the antenna to be 2.3991 GHz and the bandwidth to be 155.64 MHz.

tic resonantFrequencyAI = resonantFrequency(pifaAI)

resonantFrequencyAI = 2.3991e+09

[bandwidthAI,lowerFrequencyAI,upperFrequencyAI,matchingAI] = bandwidth(pifaAI)

bandwidthAI = 1.5564e+08

lowerFrequencyAI = 2.3063e+09

upperFrequencyAI = 2.4619e+09

`matchingAI = `*categorical*
Matched

timeAI = toc;

The AI-based calculation indicates that increasing the width and short pin width of the antenna decreases the resonant frequency. Furthermore, as expected from increasing the width, the bandwidth has also increased from the original design value, which was 148.09 MHz.

#### Calculate Resonant Frequency and Bandwidth Using Full-Wave EM Solver

To perform the full-wave electromagnetic (EM) solver simulation on your antenna, export the design from the `AIAntenna`

object by calling the `exportAntenna`

function.

pifaAnt = exportAntenna(pifaAI);

Run the full-wave EM solver on the exported antenna design. The resonant frequency is calculated by identifying the frequency at which the reactance of the antenna is zero. Here, there is more than one zero-crossing, so use the helper function `getResonanceCloseToDesign`

to pick the resonance closest to the design frequency (2.4 GHz) that is the same type of resonance (series) as the zero-crossing from the response of the original antenna. The absolute bandwidth is calculated as the difference between the frequencies that the S11 plot intersects with -10 dB; since there is only one negative S11 peak, simply select the calculated bandwidth.

fSweep = linspace(0.75,1.25,151)*fd; tic [resonantFrequencyFullAll,~,~,typeAll] = resonantFrequency(pifaAnt,fSweep); [bandwidthFull,~,lowerFrequencyFull,upperFrequencyFull] = bandwidth(pifaAnt,fSweep)

bandwidthFull = 1.5424e+08

lowerFrequencyFull = 2.3069e+09

upperFrequencyFull = 2.4612e+09

```
timeFull = toc;
idxFull = getResonanceCloseToDesign(resonantFrequencyFullAll,typeAll,fd,"Series");
resonantFrequencyFull = resonantFrequencyFullAll(idxFull)
```

resonantFrequencyFull = 2.3990e+09

#### Compare AI-Based Results with Full-Wave EM Solver Results

Plot the results of the full-wave EM solver by calling `resonantFrequency`

and `bandwidth`

on the antenna object without outputs. Use the helper function `compareResonantFrequencies`

to visually compare the full-wave EM result against the result of the AI-based analysis, and use the helper function `compareBandwidth`

to do the same.

fig = figure; resonantFrequency(pifaAnt,fSweep); compareResonantFrequencies(fig,idxFull,resonantFrequencyAI)

fig = figure; bandwidth(pifaAnt,fSweep); compareBandwidth(fig,bandwidthAI,lowerFrequencyAI,upperFrequencyAI)

The AI-based analysis is nearly indistinguishable from the full-wave EM solver results, but the AI-based calculations are significantly faster than the full-wave EM solver calculation time.

Now compare the results in a table.

allAIResults = [ ... resonantFrequencyAI; ... bandwidthAI; lowerFrequencyAI; upperFrequencyAI; ]; allFullResults = [ ... resonantFrequencyFull; ... bandwidthFull; lowerFrequencyFull; upperFrequencyFull; ]; absErr = abs(allAIResults - allFullResults); relativeErrorPercent = 100*absErr./allFullResults; tErr = table(allAIResults,allFullResults,relativeErrorPercent, ... RowNames=["resonantFrequency";"bandwidth";"lowerFrequency";"upperFrequency"])

`tErr=`*4×3 table*
allAIResults allFullResults relativeErrorPercent
____________ ______________ ____________________
resonantFrequency 2.3991e+09 2.399e+09 0.0045166
bandwidth 1.5564e+08 1.5424e+08 0.90996
lowerFrequency 2.3063e+09 2.3069e+09 0.029536
upperFrequency 2.4619e+09 2.4612e+09 0.02934

tTime = table(timeAI,timeFull)

`tTime=`*1×2 table*
timeAI timeFull
_______ ________
0.13648 13.736

### Rapidly Explore and Characterize Antenna Across Design Space

Optimize your antenna design by reducing the height by 5%, but maintain the same the resonant frequency, width-to-length and width-to-short pin width ratio, and the existence of the bandwidth. To find the desired length, use AI-based analysis to rapidly explore this design space.

First, define the parameters for tuning the height and length incrementally to characterize the space by using `defaultTunableParameters`

to track the default values. To maintain the resonant frequency, specify the tuning range of the length to be a narrow range, because the length is the resonant dimension [1] and the resonant frequency of your antenna is already relatively close to the desired frequency.

n = 50; hScaler = linspace(0.86,1.14,n); lScaler = linspace(0.968,1.032,n); H0 = pifaAI.defaultTunableParameters.Height; L0 = pifaAI.defaultTunableParameters.Length;

Keeping the width-to-length ratio locked at 0.7, explore the design space by calculating the resonant frequency with respect to the antenna's height and length. For the sake of maintaining the bandwidth, use the AI-based `bandwidth`

function to verify that the tuned antenna is still matched at 50 ohms.

fResAI = zeros(n); numNotMatched = 0; tic for hIdx = 1:n for lIdx = 1:n pifaAI.Height = H0*hScaler(hIdx); pifaAI.Length = L0*lScaler(lIdx); pifaAI.Width = pifaAI.Length*0.7; pifaAI.ShortPinWidth = pifaAI.Width; [~,~,~,matching] = bandwidth(pifaAI); switch string(matching) case "Matched" fResAI(lIdx,hIdx) = resonantFrequency(pifaAI); case {"Almost","Not Matched"} fResAI(lIdx,hIdx) = NaN; numNotMatched = numNotMatched + 1; end end end timeAI1 = toc; if numNotMatched >= 1 disp("Antenna is not matched for " + num2str(numNotMatched) + " geometries. These geometries have been discarded from design space.") end

Antenna is not matched for 49 geometries. These geometries have been discarded from design space.

Visualize the AI-based calculations of the resonant frequency across the design space.

fig1 = figure; surf(hScaler*H0*100,lScaler*L0*100,fResAI*1e-9) view(105,15) xlabel("Height (cm)") ylabel("Length (cm)") zlabel("Resonant Frequency (GHz)") title(sprintf("Design Space (%1.3f sec)",timeAI1))

Plot where the resonant frequency intersects with the desired value of 2.4 GHz.

hold on surf(hScaler*H0*100,lScaler*L0*100,ones(n)*fd*1e-9, ... FaceAlpha=0) text(H0*hScaler(end)*100,L0*lScaler(1)*100,fd*1e-9, ... strcat("\uparrow",sprintf("\nDesired (%1.1f GHz)\n",fd*1e-9)), ... VerticalAlignment="top", ... FontWeight="bold")

Notice that you were able to calculate 50 * 50 = 2500 points in the design space within a couple of seconds. This would not have been practical using full-wave EM analysis due to the substantially longer computation time.

#### Examine Response Surface to Identify Desired Design Point

Calculate the desired size-reduced height.

H1 = H0*0.95

H1 = 0.0092

Find the desired length based on this desired height. Inspect the design space to find the point where the resonant frequency is 2.4 GHz and the height is 0.0297978 m.

L1 = 0.0297978;

Calculate the resonant frequency at the desired length and height using AI-based analysis, and visualize the point which the desired length and height was inspected.

pifaAI.Height = H1; pifaAI.Length = L1; pifaAI.Width = pifaAI.Length*0.7; pifaAI.ShortPinWidth = pifaAI.Width; F1 = resonantFrequency(pifaAI); s = fig1.CurrentAxes.Children(2); s.DataTipTemplate.DataTipRows(1).Label = "Height"; s.DataTipTemplate.DataTipRows(2).Label = "Length"; s.DataTipTemplate.DataTipRows(3).Label = "Resonant Frequency"; dt = datatip(s,H1*100,L1*100,F1*1e-9);

#### Calculate and Analyze Final Design From AI-Based Results

Get your final antenna design along with its analysis results. Throughout this AI-aided optimization process, you have reduced the height of the PIFA while maintaining the existence of the bandwidth and keeping resonant frequency around 2.4 GHz.

lengthFinal = pifaAI.Length; heightFinal = pifaAI.Height; widthFinal = pifaAI.Width; resonantFrequencyFinalAI = F1; [bandwidthFinalAI,lowerFrequencyFinalAI,upperFrequencyFinalAI] = ... bandwidth(pifaAI); W0 = pifaAI.defaultTunableParameters.Width; lengthPifa = [lengthFinal;L0]; heightPifa = [heightFinal;H0]; widthPifa = [widthFinal;W0]; resonantFrequencyPifa = [resonantFrequencyFinalAI;resonantFrequencyAI0]; bandwidthPifa = [bandwidthFinalAI;bandwidthAI0]; lowerFrequencyPifa = [lowerFrequencyFinalAI;lowerFrequencyAI0]; upperFrequencyPifa = [upperFrequencyFinalAI;upperFrequencyAI0]; tFinal = table(lengthPifa,heightPifa,widthPifa, ... resonantFrequencyPifa,bandwidthPifa,lowerFrequencyPifa,upperFrequencyPifa, ... RowNames=["Final Design","Initial Prototype"])

`tFinal=`*2×7 table*
lengthPifa heightPifa widthPifa resonantFrequencyPifa bandwidthPifa lowerFrequencyPifa upperFrequencyPifa
__________ __________ _________ _____________________ _____________ __________________ __________________
Final Design 0.029798 0.0092324 0.020858 2.3982e+09 1.1813e+08 2.3187e+09 2.4368e+09
Initial Prototype 0.029167 0.0097183 0.019449 2.4091e+09 1.4809e+08 2.3186e+09 2.4667e+09

#### Verify AI-Based Results Against Full-Wave EM Simulation

Finally, run the full-wave EM solver on your final antenna.

```
pifaAntFinal = exportAntenna(pifaAI);
[resonantFrequencyFinalFullAll,~,~,typeAllFull] = resonantFrequency(pifaAntFinal,fSweep);
idxFullFinal = getResonanceCloseToDesign(resonantFrequencyFinalFullAll,typeAllFull,fd,"Series");
resonantFrequencyFinalFull = resonantFrequencyFinalFullAll(idxFullFinal)
```

resonantFrequencyFinalFull = 2.3990e+09

```
[bandwidthFinalFull,~,lowerFrequencyFinalFull,upperFrequencyFinalFull] = ...
bandwidth(pifaAntFinal,fSweep)
```

bandwidthFinalFull = 1.1840e+08

lowerFrequencyFinalFull = 2.3169e+09

upperFrequencyFinalFull = 2.4353e+09

Verify that the AI-based design of your antenna was accurate by comparing it against the full-wave EM solver results.

allAIResultsFinal = [ ... resonantFrequencyFinalAI; ... bandwidthFinalAI; lowerFrequencyFinalAI; upperFrequencyFinalAI; ]; allFullResults = [ ... resonantFrequencyFinalFull; ... bandwidthFinalFull; lowerFrequencyFinalFull; upperFrequencyFinalFull; ]; absErrFinal = abs(allAIResultsFinal - allFullResults); relativeErrorPercentFinal = 100*absErrFinal./allFullResults; tErrFinal = table(allAIResultsFinal,allFullResults,relativeErrorPercentFinal, ... RowNames=["resonantFrequency";"bandwidth";"lowerFrequency";"upperFrequency"])

`tErrFinal=`*4×3 table*
allAIResultsFinal allFullResults relativeErrorPercentFinal
_________________ ______________ _________________________
resonantFrequency 2.3982e+09 2.399e+09 0.033832
bandwidth 1.1813e+08 1.184e+08 0.23182
lowerFrequency 2.3187e+09 2.3169e+09 0.074195
upperFrequency 2.4368e+09 2.4353e+09 0.059317

### Summary of AI-Based Analysis

AI-based analysis allows for the characterization of antennas with:

Faster calculation time

High accuracy

This enables workflows that were not previously practical. As demonstrated in this example, you can explore a design space with high resolution within a couple of seconds.

With `AIAntenna`

, you can take advantage of AI-based analysis without prior machine learning experience.

### Reference

[1] Jackson, David. "Chapter 7: Microstrip Antennas," in *Antenna Engineering Handbook*, edited by John Volakis, 4th ed., New York: McGraw-Hill Co., 2007.