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name: matlab-optimize-pcb-design description: "Optimize RF PCB dimensions for bandwidth, return loss, or area via patternsearch and surrogateopt with constraints. TRIGGER: user asks to optimize an RF PCB component for performance (bandwidth, return loss, insertion loss, area) or apply constraints to a design. Invoke BEFORE writing optimization code — RF PCB Toolbox has a built-in optimize() function that differs from generic fmincon/ga approaches. SKIP: designing a component from scratch without an optimization objective (use the specific matlab-design-pcb-* skill), EM analysis without optimization (use matlab-analyze-em), material/stackup setup only (use matlab-manage-pcb-material)." license: https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md metadata: author: MathWorks version: "1.0"

Optimizing RF PCB Designs

Critical: Always Use optimize() First

The RF PCB Toolbox provides a built-in optimize() function that handles all standard optimization scenarios. Always use it as the first approach — do NOT write manual optimization loops with patternsearch, surrogateopt, fmincon, or ga called directly unless optimize() is demonstrably insufficient for the specific problem.

When to Use

• Tuning filter, coupler, or splitter dimensions for return loss, bandwidth, or area
• Running optimize() on catalog objects with bounds and constraints
• Using SADEA/TR-SADEA, patternsearch, or surrogateopt via the optimize() interface
• Defining custom objective functions over S-parameter responses

When NOT to Use

• Designing components from scratch — use matlab-design-pcb-filter, matlab-design-pcb-coupler, etc. first, then optimize
• Running EM analysis without optimization — use matlab-analyze-em
• Parameter sweeps without an objective — just loop over sparameters calls directly
• Antenna-only optimization without PCB context — use Antenna Toolbox docs

Typical Workflow

1. Before: A design skill (matlab-design-pcb-filter, matlab-design-pcb-transmission-line, etc.) — create the initial component; matlab-analyze-em — baseline S-parameters
2. This skill: Define objective, bounds, constraints; run optimize()
3. After: matlab-analyze-em — validate optimized design → matlab-integrate-pcb-circuit — cascade into system → matlab-write-pcb-layout — export Gerber

Quick Reference

| Task | Code | |------|------| | Design at frequency | obj = design(ObjectType, fc) | | Optimize | optObj = optimize(obj, freq, objective, props, bounds, solver) | | With constraints | optimize(..., 'Constraints', constraints) | | With options | optimize(..., 'OptimizerOptions', opts) |

Algorithm Overview

| Algorithm | Source | Best For | Typical Time | |---|---|---|---| | sadea | Antenna Toolbox (SADEA) | Default global search, few EM evaluations | 5--30 min | | trsadea | Antenna Toolbox (TR-SADEA) | Trust-region variant, better local refinement | 5--30 min | | patternsearch | Global Optimization Toolbox | Derivative-free, smooth/noisy EM objectives, fine-tuning | 2--15 min | | surrogateopt | Global Optimization Toolbox | Expensive black-box functions, many variables, global optimum | 10--60 min |

• Start with SADEA -- it requires no additional toolbox beyond Antenna Toolbox and handles most RF/PCB optimization problems well.
• Use patternsearch for fine-tuning -- after SADEA finds a good region, refine with patternsearch starting from the SADEA result.
• surrogateopt for expensive models -- builds a surrogate model and is more sample-efficient when each EM solve is costly.

Timing and Practical Considerations

• MoM simulation per evaluation: 2--30 seconds for simple components, minutes for high-order filters
• Behavioral mode: Use pcbElement(comp, Behavioral=true) for fast analytical evaluations during optimization sweeps
• Iteration budget: Set MaxIterations to 20--50 when running interactively to stay responsive; use 100--200 for batch runs
• Parallel computing: Set UseParallel=true if Parallel Computing Toolbox is available for significant speedup with patternsearch and surrogateopt

design() — Initial Sizing

The design function sizes any catalog component for a target frequency:

ws = design(wilkinsonSplitter, 3e9);
bl = design(couplerBranchline, 5e9);
fh = design(filterHairpin, 2.4e9);
ms = design(microstripLine, 3e9);

This produces a starting point for subsequent optimization. All geometric parameters are auto-computed for the target frequency.

optimize() Syntax

optObj = optimize(obj, freq, objective, properties, bounds, solver, ...
    'Constraints', constraints, 'OptimizerOptions', opts)

| Argument | Type | Description | |----------|------|-------------| | obj | Object | Catalog object (initial design) | | freq | Scalar or vector | Single frequency or frequency vector for optimization | | objective | String | Built-in or custom objective function name | | properties | Cell array | Property names to vary | | bounds | 2-element cell | {[lower1 lower2 ...]; [upper1 upper2 ...]} | | solver | String | 'patternsearch', 'surrogateopt', 'sadea', or 'trsadea' | | constraints | Struct | S-parameter constraints (optional NV pair) | | opts | optimoptions | Optimizer options object created with optimoptions() |

Built-in Objectives

| Objective String | Minimizes/Maximizes | |-----------------|---------------------| | "minimizeArea" | Minimizes board area | | "maximizeBandwidth" | Maximizes -10 dB return loss bandwidth | | "maximizeReturnLoss" | Maximizes worst-case return loss | | "minimizeBandwidth" | Narrows the passband |

Example: Minimize Area with Constraints

obj = design(wilkinsonSplitter, 3e9);

props = {'SplitLineLength', 'SplitLineWidth', 'Resistance', ...
         'PortLineLength', 'GroundPlaneWidth'};
bounds = {[10e-3 1e-3  50 2e-3  10e-3];    % Lower bounds
          [50e-3 8e-3 100 20e-3 50e-3]};    % Upper bounds (cell array!)

constraints.S11 = '<-10';
constraints.S21 = '>-4';
constraints.S22 = '<-10';
constraints.S12 = '>-4';

optObj = optimize(obj, 3e9, "minimizeArea", props, bounds, ...
    "patternsearch", 'Constraints', constraints);

show(optObj);
sp = sparameters(optObj, linspace(1e9, 5e9, 51), 'SweepOption', 'interp');
rfplot(sp);

% Verify area from shapes
s = shapes(optObj);           % Returns struct of shapes by layer
boardArea = area(s.GroundPlane);
fprintf('Optimized board area: %.2f mm²\n', boardArea * 1e6);

Querying Area After Optimization

For catalog objects, use shapes() to extract the individual layer shapes, then area():

s = shapes(optObj);              % Catalog object → struct with named shapes
boardArea = area(s.GroundPlane); % Area of the board outline shape

For pcbComponent, shapes are in the Layers property:

pcb = pcbComponent(optObj);
boardArea = area(pcb.BoardShape);

Example: Maximize Return Loss for Hairpin Filter

f = design(filterHairpin, 3e9);

props = {'CoupledLineLength', 'CoupledLineWidth', 'CoupledLineSpacing'};
bounds = {[5e-3 0.5e-3 0.1e-3];
          [40e-3 5e-3 2e-3]};

optF = optimize(f, 3e9, "maximizeReturnLoss", props, bounds, "patternsearch");
show(optF);

S-Parameter Constraints

Constraints use string format '<threshold' or '>threshold' (in dB):

constraints.S11 = '<-15';    % S11 below -15 dB
constraints.S21 = '>-1';     % S21 above -1 dB (low insertion loss)
constraints.S31 = '<-20';    % Isolation below -20 dB

Any S-parameter index can be constrained. The optimizer evaluates constraints across the entire frequency vector.

Custom Objective Functions

For objectives beyond the built-in set, provide a function handle:

% Objective function signature: cost = objFcn(obj, freq)
function cost = myObjective(obj, freq)
    sp = sparameters(obj, freq, 'SweepOption', 'interp');
    S21 = squeeze(sp.Parameters(2,1,:));
    S11 = squeeze(sp.Parameters(1,1,:));
    % Minimize worst-case insertion loss while maintaining match
    cost = -min(20*log10(abs(S21)));  % Negative because we maximize |S21|
end

optObj = optimize(obj, fc, @myObjective, props, bounds, "patternsearch");

Surrogate-Based Optimization

For expensive EM solves, surrogate optimization builds a model and is more sample-efficient:

opts = optimoptions('surrogateopt', 'MaxFunctionEvaluations', 50);
optObj = optimize(obj, 3e9, "maximizeReturnLoss", props, bounds, ...
    "surrogateopt", 'OptimizerOptions', opts);

Solver Options

The OptimizerOptions NV pair takes an optimoptions object for the chosen solver:

opts = optimoptions('patternsearch', 'MaxFunctionEvaluations', 100, 'Display', 'off');
optObj = optimize(obj, fc, objective, props, bounds, 'patternsearch', ...
    'OptimizerOptions', opts);

Available solvers: 'patternsearch', 'surrogateopt', 'sadea', 'trsadea'.

For sadea/trsadea, pass a struct instead of an optimoptions object:

opts = struct('MaxIterations', 50, 'UseParallel', false);
optObj = optimize(obj, fc, objective, props, bounds, 'sadea', ...
    'OptimizerOptions', opts);

Nested Property Optimization

Optimize nested properties using dot notation:

% Optimize substrate thickness along with width
optObj = optimize(ml, 2.4e9, 'maximizeReturnLoss', ...
    {'Width', 'Substrate.Thickness'}, ...
    {0.001 0.5e-3; 0.01 3e-3}, 'sadea');

Decision: optimize() vs Manual Loop

Always use optimize(). It wraps all four solvers (sadea, trsadea, patternsearch, surrogateopt) internally. There is no performance or capability advantage to calling these solvers directly. The only scenario where direct solver usage is justified is a non-S-parameter, non-EM objective function that optimize() cannot express (extremely rare).

Optimization Workflow

1. Design initial geometry: obj = design(Type, fc)
2. Select properties to vary: Choose 3-6 most impactful dimensions
3. Set reasonable bounds: ±50% of initial values is a good starting range
4. Define constraints: Ensure feasibility (S11 < -10 dB at minimum)
5. Choose solver: Start with 'sadea'; use 'patternsearch' for refinement
6. Run optimize(): optObj = optimize(obj, freq, objective, props, bounds, solver)
7. Validate: Check optimized design meets specs across full band

Antenna Objects with optimize()

The same optimize() function works on antenna objects with antenna-specific objectives:

| Objective | Description | |---|---| | 'maximizeGain' | Maximize antenna gain at target frequency | | 'frontToBackRatio' | Maximize front-to-back lobe ratio | | 'maximizeSLL' | Maximize sidelobe level suppression |

ant = design(patchMicrostrip, 2.4e9);
optAnt = optimize(ant, 2.4e9, 'maximizeGain', ...
    {'Length', 'Width'}, {[0.02 0.02]; [0.06 0.06]}, 'sadea', ...
    'OptimizerOptions', struct('MaxIterations', 100));
pattern(optAnt, 2.4e9);

These objectives are for antenna objects only. RF PCB catalog objects use the objectives in the Built-in Objectives table above.

Fallback: Direct Solver Usage (Last Resort)

Direct solver calls are almost never needed — optimize() already wraps patternsearch, surrogateopt, sadea, and trsadea. Only bypass optimize() for non-EM objectives it cannot express (e.g., multi-objective Pareto front via paretosearch).

% Extremely rare: multi-objective Pareto (not supported by optimize())
objFcn = @(x) [emObjective(obj, x, freq); thermalObjective(obj, x)];
[xopt, fval] = paretosearch(objFcn, nVars, [], [], [], [], lb, ub);

Design Iteration Patterns

Variable Naming Conventions

Use these names consistently across optimization scripts and iterative design loops:

sub    % dielectric substrate
cond   % metal conductor
ml     % microstripLine
sl     % stripLine
cpw    % coplanarWave