Optimize Custom Antenna using TR-SADEA Optimizer
This example shows how to optimize a custom antenna using the TR-SADEA optimizer. The example maximizes gain of a custom antipodal Vivaldi antenna at 5 GHz, while limiting the return loss to –10 dB or less. A TR-SADEA optimizer belongs to the class of surrogate-assisted optimizers that use mathematical models to replace time-consuming electromagnetic (EM) simulations. TR-SADEA optimizer enables faster optimization through efficient exploration of search space.
Define Geometry Parameters of Antipodal Vivaldi Antenna
Define dimensions of the aperture, feed line, inner and outer edge taper, ground plane, and circuit board.
baseDimensions = struct; baseDimensions.ROpening = 30; % Opening rate of taper baseDimensions.WAperture = 0.024; % Width of the aperture in meter baseDimensions.WStrip = 0.0021; % Width of the feed line in meter baseDimensions.LInnerTaper = 0.187; % Length of inner edge taper in meter baseDimensions.LOuterTaper = 0.08; % Length of outer edge taper in meter baseDimensions.WGroundPlane = 0.05; % Width of the ground plane in meter baseDimensions.LBoard = 0.2020; % Length of the printed circuit board in meter baseDimensions.WBoard = 0.12; % Width of the printed circuit board in meter baseDimensions.N = 30; % Number of points along taper
Set the taper opening rate to 'ROpening', aperture width to 'WAperture', and feed width to 'Wstrip'. Use these design variables for the optimization. Create the antipodal Vivaldi antenna using the createVivaldi function defined in the Supporting Functions section. View the antenna.
designVariables = [baseDimensions.ROpening,baseDimensions.WAperture,baseDimensions.WStrip];
ca = createVivaldi(designVariables,baseDimensions);
figure
show(ca)
title("Antipodal Vivaldi Antenna")
Plot Radiation Pattern
Plot the radiation pattern of this antenna at 5 GHz and observe the gain. The current design yields a maximum gain of around 6 dBi.
pattern(ca,5e9);
Plot Reflection Coefficient
Plot the reflection coefficient of the antenna in the 4 to 6 GHz frequency band with a reference impedance of 50 ohms.
freq = 1e9; freqRange = linspace(freq*4,freq*6,30); sparam = sparameters(ca,freqRange); rfplot(sparam);
Optimize Antenna for Maximum Gain
Use the OptimizerTRSADEA object to optimize this antenna. The OptimizerTRSADEA object gives you access to the TR-SADEA optimizer provided in the Antenna Toolbox™. To initialize the OptimizerTRSADEA object, provide the lower and upper bounds of the chosen design variables as input arguments to the OptimizerTRSADEA object creation function. Use the customEvaluation function defined in the Supporting Functions section to set the evaluation criteria for the optimization. Use the optimizeWithPlots function with 10 iterations to optimize the antenna.
s = OptimizerTRSADEA([20 0.03 0.002;30 0.11 0.003]); s.CustomEvaluationFunction = @customEvaluation; s.optimizeWithPlots(10);
Use the getBestMemberData function to fetch the optimized values for the design variables.
bestData = s.getBestMemberData; optimized_values = bestData.member;
Use the optimized values of the design variables to create the optimized antenna.
ca = createVivaldi(optimized_values,baseDimensions);
figure
show(ca)
title("Optimized Antipodal Vivaldi Antenna")
Plot Radiation Pattern of Optimized Antenna
Plot the radiation pattern of the optimized antenna at 5 GHz, and observe the gain. The optimized design yields an improvement in the gain over the original design.
pattern(ca,5e9);
Plot Reflection Coefficient of Optimized Antenna
Plot the reflection coefficient of the optimized antenna in the 4 to 6 GHz frequency band with a reference impedance of 50 ohms. Return loss is mostly within 10 dB and has improved compared to the initial design.
freq = 1e9; freqRange = linspace(freq*4, freq*6, 30); sparam = sparameters(ca,freqRange); rfplot(sparam);
Get Optimization Data from Object
Get the iteration data. The columns in the IterationMembers variable represent the 'ROpening', 'WAperture', and 'Wstrip' design variables, respectively.
iterData = s.getIterationData; IterationMembers = iterData.members
IterationMembers = 10×3
20.4302 0.0405 0.0021
21.0351 0.0318 0.0021
24.7859 0.0390 0.0022
26.0689 0.0318 0.0021
20.2303 0.0823 0.0020
20.2042 0.0381 0.0030
20.4302 0.0622 0.0027
26.6422 0.0492 0.0029
23.5453 0.1077 0.0024
20.3114 0.0318 0.0030
Get the surrogate model data (initial population). The columns in the InitializationMembers variable represent the 'ROpening', 'WAperture', and 'Wstrip' design variables, respectively.
initialData = s.getInitializationData; InitializationMembers = initialData.members
InitializationMembers = 12×3
28.1789 0.0545 0.0026
23.2548 0.0884 0.0027
23.4392 0.0416 0.0029
21.5945 0.0659 0.0021
27.1936 0.0610 0.0028
25.0813 0.0978 0.0022
21.8987 0.0947 0.0025
28.7891 0.1035 0.0023
24.9646 0.0318 0.0021
29.9707 0.0703 0.0029
20.1313 0.0773 0.0024
26.6422 0.0488 0.0024
⋮
Check if the algorithm has converged. The algorithm has not converged yet. Increasing the iterations might provide a better antenna in some use cases.
convergence = s.isConverged
convergence = logical
0
Get the number of times the customEvaluation function has been evaluated.
NumberOfEvaluations = s.getNumberOfEvaluations
NumberOfEvaluations = 27
Supporting Functions
This section defines the supporting createVivaldi and customEvaluation functions.
Create Custom Antipodal Vivaldi Antenna
Define the geometry of the Vivaldi antipodal antenna.
function ca = createVivaldi(designVariables,baseDimensions) % Define geometry parameters ROpening = designVariables(1); % Opening rate of taper WAperture = designVariables(2); % Width of the aperture in meter WStrip = designVariables(3); % Width of the feed line in meter LInnerTaper = baseDimensions.LInnerTaper; % Length of inner edge taper in meter LOuterTaper = baseDimensions.LOuterTaper; % Length of outer edge taper in meter WGroundPlane = baseDimensions.WGroundPlane; % Width of the ground plane in meter LBoard = baseDimensions.LBoard; % Length of the printed circuit board in meter WBoard = baseDimensions.WBoard; % Width of the printed circuit board in meter N = baseDimensions.N; % Number of points along taper % P1(x1,y1) - point at which inner taper starts % P2(x2,y2) - point at which inner taper ends x2 = LBoard/2; y2 = WAperture/2; x1 = x2 -LInnerTaper; y1 = -WStrip/2; % P3(x3,y3) - point at which outer taper starts % P4(x4,y4) - point at which outer taper ends x4 = x1 + LOuterTaper; y4 = WBoard/2; x3 = x1; y3 = -y1; % Compute coefficients for taper equation a = y2 - y1; b = exp(ROpening*x2) - exp(ROpening*x1) ; c = y1*exp(ROpening*x2) - y2*exp(ROpening*x1) ; c1 = a/b; c2 = c/b; a1 = y4 - y3; b1 = exp(ROpening*x4) - exp(ROpening*x3) ; ca = y3*exp(ROpening*x4) - y4*exp(ROpening*x3) ; c3 = a1/b1; c4 = ca/b1; % Discretize taper length xInner = linspace(x1,x2,N); xOuter = linspace(x3,x4,N); % Equation for exponential taper yInner = c1*exp(ROpening*xInner) + c2; yOuter = c3*exp(ROpening*xOuter) + c4; % Assemble curve co-ordinates pointsInnerTaper = [xInner;yInner;... zeros(size(xInner))]; pointsOuterTaper = [xOuter;yOuter;... zeros(size(xOuter))]; vivaldiBoundary_pos_InnerTaper = pointsInnerTaper; vivaldiBoundary_pos_OuterTaper = pointsOuterTaper; vivaldiboundary_pos = [( vivaldiBoundary_pos_InnerTaper) ... [LBoard/2 WBoard/2 0]' ... fliplr(vivaldiBoundary_pos_OuterTaper) ] ; vivaldiboundary_neg = vivaldiboundary_pos; vivaldiboundary_neg(2,:) = -1.*vivaldiboundary_pos(2,:); vivaldiboundary_pos = vivaldiboundary_pos'; vivaldiboundary_neg = vivaldiboundary_neg'; % Creating top and bottom polygons vivaldiboundary_top = shape.Polygon(Vertices=vivaldiboundary_pos); vivaldiboundary_bottom = shape.Polygon(Vertices=vivaldiboundary_neg); % Create strip line striplineboundary = shape.Rectangle(Length=(LBoard-LInnerTaper),... Width=WStrip,Center=[-LBoard/2+(LBoard-LInnerTaper)/2 0],NumPoints=2); % Create ground plane groundplaneboundary = shape.Rectangle(Length=LBoard-LInnerTaper,Width=WGroundPlane,Center=[-LBoard/2+(LBoard-LInnerTaper)/2 0],NumPoints=2); patch1 = vivaldiboundary_top + striplineboundary; patch2 = vivaldiboundary_bottom + groundplaneboundary; diel_height = 1e-3; patch_Top = shape.Polygon(Vertices=patch1.Vertices); [~] = translate(patch_Top,[0 0 diel_height]); patch_Bot = shape.Polygon(Vertices=patch2.Vertices); tmetal = patch_Top + patch_Bot; box = shape.Box(Length=LBoard,Width=WBoard,Height=diel_height,Center=[0 0 0.5*diel_height],Dielectric="FR4",Color="g"); % Create Feed Rectangle feedrect = shape.Rectangle(Length=diel_height,Width=WStrip); [~] = rotateY(feedrect,90); [~] = translate(feedrect,[-0.101 0 diel_height/2]); tmetal = tmetal + feedrect; % Create Antenna from Geometry sb = addSubstrate(tmetal,box); % Create custom antenna ca = customAntenna(Shape=sb); % Assign Feed [~] = createFeed(ca,[-101,0,0]*1e-3,1); % Manually Mesh Antenna [~] = mesh(ca,MaxEdgeLength=0.007); end
Custom Objective Function
This function defines the objective for optimization.
function fitness = customEvaluation(designVariables) fitness = []; try % call custom function to create geometry for the design % variables passed baseDimensions = struct; baseDimensions.ROpening = 30; % Opening rate of taper baseDimensions.WAperture = 0.024; % Width of the aperture in meter baseDimensions.WStrip = 0.0021; % Width of the feed line in meter baseDimensions.LInnerTaper = 0.187; % Length of inner edge taper in meter baseDimensions.LOuterTaper = 0.08; % Length of outer edge taper in meter baseDimensions.WGroundPlane = 0.05; % Width of the ground plane in meter baseDimensions.LBoard = 0.2020; % Length of the printed circuit board in meter baseDimensions.WBoard = 0.12; % Width of the printed circuit board in meter baseDimensions.N = 30; % Number of points along taper ca = createVivaldi(designVariables,baseDimensions); catch % Handle errors during geometry creation % High penalty value is used to handle errors fitness = 1e6; end if isempty(fitness) try % calculate realized gain objective = pattern(ca,5e9,0,0,Type="realizedgain"); objective = -objective; % As optimizer always minimizes objective, % sign is reversed to maximize gain catch % Handle errors during gain computation % High penalty value is used to handle errors objective = 1e6; end try objectiveFactor = 1; % Factor used for the objective to provide priority constraintsFactor = 100; % Factor used for the constraint to provide priority % constraints s11 < -10 % Calculate S-parameters freq = 1e9; freqRange = linspace(freq*4, freq*6, 10); s = sparameters(ca,freqRange); actVal = 20*log10(max(abs(rfparam(s,1,1)))); expVal = -10; % As constraint is satisfied when it is less than -10 dB, better % values are made to be equal to -10 dB to not affect optimizer % direction constraint = actVal - expVal; % Constraint value of -10 dB produces 0 in above statement. Constraint values % better than -10 dB produce negative value. These negative values are made zero, % as constraint is satisfied. constraint = max(constraint,0); catch % Handle errors during S-parameters computation % High penalty value is used to handle errors constraint = 1e6; end performances = [objective, constraint]; % Compute fitness by combining objective and constraints fitness = objectiveFactor*performances(1) + constraintsFactor*performances(2); end end
Conclusion
Basic structure of the antipodal Vivaldi antenna is built and analyzed. By using a TR-SADEA optimizer object, the antenna is optimized for maximizing gain at 5 GHz while satisfying the constraint on acceptable return loss. The gain for the optimized antenna shows an improvement over the initial design. The return loss of the optimized antenna also shows levels below 10 dB in the 4 to 6 GHz band.
References
[1] Balanis, C.A. Antenna Theory. Analysis and Design, 3rd Ed. New York: Wiley, 2005.
