Analyzing EM Performance of RF PCB Components

When to Use

• Extracting S-parameters from any RF PCB component (catalog or custom pcbComponent)
• Comparing MoM vs FEM solvers or selecting the right solver for a structure
• Using interpolating sweeps or frequencySweep objects for faster multi-frequency analysis
• Controlling mesh density for accuracy vs speed tradeoffs
• Visualizing E/H fields, surface currents, or charge distributions
• Using behavioral (analytic) S-parameter models for fast estimates or optimization

When NOT to Use

• Building or assembling custom PCB structures — use matlab-assemble-pcb-layout
• Designing standard transmission lines or catalog objects — use matlab-design-pcb-txline
• Defining dielectric or metal materials — use matlab-manage-pcb-material
• Cascading or connecting multiple components into circuits — use matlab-integrate-pcb-circuit
• Importing PCB layouts from Gerber, ODB++, or Allegro — use matlab-read-pcb-layout

Typical Workflow

1. Before: matlab-manage-pcb-material — substrate/conductor setup; then a design skill or matlab-assemble-pcb-layout — create the component
2. This skill: Extract S-parameters, visualize fields and currents, verify performance
3. After: matlab-optimize-pcb-design — tune dimensions if specs not met → matlab-integrate-pcb-circuit — cascade into larger network → matlab-write-pcb-layout — export Gerber

Quick Reference

S-Parameter Extraction

The sparameters function is the primary analysis method for all RF PCB components.

Basic Usage

obj = design(couplerBranchline, 5e9);
freq = linspace(1e9, 10e9, 101);
sp = sparameters(obj, freq, 'SweepOption', 'interp');
figure;
rfplot(sp);

Specifying Port Impedance

sp = sparameters(obj, freq, 50, 'SweepOption', 'interp');   % 50-ohm reference
sp = sparameters(obj, freq, 75, 'SweepOption', 'interp');   % 75-ohm reference

Plotting Specific S-Parameters

rfplot(sp, [2 1], 1);              % Plot S21 only
rfplot(sp, [1 1], 1);              % Plot S11 only
rfplot(sp, 2:4, 1);               % Plot S21, S31, S41 vs port 1

Extracting Numeric Data

sp = sparameters(obj, freq, 'SweepOption', 'interp');
S21_dB = 20*log10(abs(squeeze(sp.Parameters(2,1,:))));
S11_dB = 20*log10(abs(squeeze(sp.Parameters(1,1,:))));

Solver Selection

RF PCB Toolbox supports two electromagnetic solvers:

Switching to FEM

FEM is available via pcbComponent:

pcb = pcbComponent(couplerBranchline);
pcb.SolverType = 'FEM';
sp_fem = sparameters(pcb, freq);

FEM Boundary Condition Configuration

After setting SolverType to 'FEM', retrieve the solver object via solver() to configure boundary conditions:

pcb = pcbComponent(catalogObj);
pcb.SolverType = 'FEM';

s = solver(pcb);                          % Returns em.solvers.fem.FEM object
s.BoundaryCondition = 'absorbing';        % or 'perfectly-matched-layer' (default)

Gotcha: solver(comp, 'SolverType', 'FEM') errors with "Too many input arguments." SolverType is a property of pcbComponent, not an argument to solver(). BoundaryCondition is a property of the returned FEM solver object, not of the component.

FEM Prerequisites

The FEM solver (introduced R2025a) requires two dependencies:

1. Integro-Differential Modeling Framework for MATLAB (IDMF) — Install via Home > Add-Ons > search "Integro-Differential Modeling Framework for MATLAB". Verify with matlab.addons.installedAddons.
2. Windows Subsystem for Linux (WSL) — Required on Windows. Install via wsl --install from an elevated PowerShell prompt. Verify with wsl --status.

If WSL is available, the FEM solver can be used when designing custom structures via pcbComponent. For shielded catalog elements, FEM is used automatically.

Firewall note: Windows Defender may block the PostgreSQL server used by IDMF (<matlabroot>\sys\postgresql\win64\PostgreSQL\bin\postgres.exe). If FEM solves hang on first use, inform the user of this potential cause and defer to them on what action to take per their IT/security policies. Do not modify firewall settings autonomously.

WSL Memory Tuning

WSL is allocated only 50% of system RAM by default. Large FEM problems may fail with out-of-memory errors. If the user hits OOM during an FEM solve, inform them that WSL memory can be increased by editing C:/Users/%UserProfile%/.wslconfig:

[wsl2]
memory=48GB
swap=8GB

Followed by wsl --shutdown and restart-service LxssManager (elevated PowerShell). Values should be adjusted based on system specs. This may require IT involvement — ask the user to make this change manually and resume when ready. Do not create or modify .wslconfig autonomously.

FEM-Only Properties

When SolverType='FEM', additional properties become available on pcbComponent:

FEM Constraints

• No mode impedance extraction: getZEven/getZOdd are not available with the FEM solver. Use S-parameters only for shielded comparisons.
• PEC required: FEM requires Conductivity=Inf (PEC). Finite conductivity metals (e.g., Copper) will error. For shielded vs unshielded comparisons, use PEC for both.
• Connector spacing: The RFConnector outer radius (default 1.5 mm) must fit between adjacent ports. If port spacing is tight, increase Spacing/GroundPlaneWidth or reduce OuterRadius on the connector.

Comparing Solvers

obj = design(couplerBranchline, 5e9);
freq = linspace(1e9, 5e9, 21);

sp_mom = sparameters(obj, freq, 'SweepOption', 'interp');

pcb = pcbComponent(obj);
pcb.SolverType = 'FEM';
sp_fem = sparameters(pcb, freq);  % FEM: interp not applicable

figure;
rfplot(sp_mom); hold on;
rfplot(sp_fem, '--');
legend('MoM', 'FEM');

Interpolating Sweep

For faster multi-frequency analysis, use interpolating sweep instead of discrete point-by-point solves. This is significantly faster, especially for large structures.

Basic Interpolation

freq = linspace(4.5e9, 5.5e9, 101);
sp = sparameters(obj, freq, 50, 'SweepOption', 'interp');

Interpolation with Gradient

More accurate interpolation using gradient information:

freq = [4.5e9, 5.5e9];  % Only need start/end — solver picks internal points
sp = sparameters(obj, freq, 50, 'SweepOption', 'interpWithGrad');

When to Use Interpolation

frequencySweep Object (R2025a)

For finer control over interpolation-based sweeps, use the frequencySweep object. It exposes error tolerance, iteration limits, and rational fitting — useful when the default 'SweepOption' settings are not sufficient.

fsweep = frequencySweep;
fsweep.SweepType = "interp";        % "interp" (default) | "interpWithGrad"
fsweep.ErrTol = -80;                % dB, default -80
fsweep.NumFreqs = 100;              % points to discretize frequency range, default 100
fsweep.NumIters = 25;               % max fitting iterations, default 25

freq = linspace(1e9, 10e9, 200);
sp = sparameters(comp, freq, 'SweepOption', fsweep);

% Extract rational fitting model after the sweep
rmodel = getRationalModel(fsweep);

Mesh Control

Mesh density directly affects accuracy and computation time.

Setting Maximum Edge Length

Rule of thumb: MaxEdgeLength ≤ λ/8 at the highest frequency.

fc = 10e9;
lambda = 3e8 / fc;
mesh(obj, 'MaxEdgeLength', lambda/8);

Viewing the Mesh

figure;
mesh(obj);                              % Visualize default mesh
figure;
mesh(obj, 'MaxEdgeLength', 1e-3);       % Visualize refined mesh

Mesh Configuration

Switch between automatic and manual meshing:

meshconfig(obj, 'manual');
mesh(obj, 'MaxEdgeLength', 0.5e-3, 'MinEdgeLength', 0.1e-3);

meshconfig(obj, 'auto');   % Revert to automatic meshing

Pre-Solve Checkpoint: Inspect Mesh and Memory

Catalog components generate dense auto-meshes that can dominate runtime even with interpolating sweep. Always inspect before committing to a full solve:

fc = 10e9;
memoryEstimate(obj, fc, 'RetainMesh', true);  % Estimate RAM; retain mesh for inspection
mesh(obj);                                     % Visualize — check if overly dense

% If too dense or memory too high, coarsen
lambda = physconst('LightSpeed') / fc;
mesh(obj, 'MaxEdgeLength', lambda/6);          % Relax from default
memoryEstimate(obj, fc, 'RetainMesh', true);   % Re-check after coarsening

The 'RetainMesh', true option keeps the generated mesh attached to the object so you can visualize it immediately. Without it, the mesh is discarded after estimation.

Field Visualization

EHfields — Electric and Magnetic Fields

#### At a Single Point

ind = spiralInductor;
[e, h] = EHfields(ind, 4e9, [0; 0; 1]);  % Point at (0,0,1) meters

#### Near-Field on a Planar Grid

fc = 5e9;
Nx = 80; Ny = 60;
xVec = linspace(-0.02, 0.02, Nx);
yVec = linspace(-0.015, 0.015, Ny);
[Xg, Yg] = meshgrid(xVec, yVec);
Zg = 2e-3 * ones(size(Xg));  % Observation plane at z = 2 mm
points = [Xg(:)'; Yg(:)'; Zg(:)'];

[eNear, hNear] = EHfields(obj, fc, points);
eMag2D = reshape(vecnorm(eNear), Ny, Nx);

figure;
imagesc(xVec*1e3, yVec*1e3, 20*log10(eMag2D));
xlabel('x (mm)'); ylabel('y (mm)');
title(sprintf('|E| at z=2mm, f=%.1f GHz', fc/1e9));
colorbar; axis equal tight;

#### Observation Plane Selection

Far-Field (Default Sphere)

EHfields(obj, fc, ViewField="E");   % Plot only, no output

Current and Charge Distribution

Surface Current

figure;
current(obj, 5e9);                  % Linear scale
figure;
current(obj, 5e9, scale="log");     % Log scale for dynamic range

Charge Distribution

figure;
charge(obj, 5e9);                   % On metal surface
figure;
charge(obj, 5e9, 'dielectric');     % On dielectric surface

Feed Current vs. Frequency

freq = linspace(1e9, 10e9, 101);
feedCurrent(obj, freq);             % Plots feed current magnitude

Transmission Line RLGC and Impedance

For pcb2D cross-section analysis, RLGC extraction, characteristic impedance (getZ0), and propagation delay, see matlab-design-pcb-txline.

Behavioral S-Parameters (Fast Analytic Models)

Behavioral models compute S-parameters using closed-form analytic approximations instead of full-wave EM. They are orders of magnitude faster — useful for initial exploration, circuit-level simulation, and optimization inner loops.

Syntax

S = sparameters(obj, freq, Behavioral=true);       % Named argument
S = sparameters(obj, freq, 'Behavioral', true);     % Name-value pair

Supported Objects

Behavioral mode works on:

Common Patterns

Transmission line discontinuities — wrap a shape in pcbComponent, then compare behavioral vs full-wave:

m = microstripLine(Length=0.04, Width=2.7e-3, Height=1.6e-3);
shape = bendMitered(Length=[m.Length/2, m.Length/2], ...
    Width=[m.Width, m.Width], MiterDiagonal=sqrt(2)*m.Width);
pcb = pcbComponent(shape);
pcb.BoardThickness = m.Substrate.Thickness;
pcb.Layers{2} = m.Substrate;

freq = (1:40)*100e6;
S_fast = sparameters(pcb, freq, Behavioral=true);     % ~instant
S_em   = sparameters(pcb, freq, 'SweepOption', 'interp');  % Full MoM solve

Direct on catalog objects:

cpw = design(coplanarWaveguide, 3e9, LineLength=0.5, Z0=75);
cpw.Conductor = metal("Gold");
S = sparameters(cpw, 3e9, Behavioral=true);

When to Use Behavioral vs Full-Wave

Accuracy Limitations

Behavioral models assume ideal microstrip/stripline geometry and may diverge from full-wave at:

• High frequencies (above first higher-order mode)
• Very wide or narrow traces (outside quasi-TEM regime)
• Complex multi-layer substrates
• Structures with significant radiation or surface wave coupling

Pitfalls

1. Ask for frequency range first: Do not assume the analysis frequency range. Always ask the user what frequency band they want before running sparameters. Wrong assumptions waste solve time and may miss the structure's operating band.

1. Memory exhaustion from dense auto-meshes: Catalog components often generate overly dense meshes. Always run memoryEstimate(obj, fc, 'RetainMesh', true) before committing to a full-band sweep, then mesh(obj) to visualize. If the mesh is too fine or memory too high, coarsen with mesh(obj, 'MaxEdgeLength', lambda/6) before solving. This applies even when using interpolating sweep — the mesh drives per-frequency cost.

1. FEM only works via pcbComponent and requires WSL on Windows: The SolverType property exists on both catalog objects and pcbComponent, but setting it to 'FEM' on a catalog object errors (e.g., "FEM solver for couplerBranchline is not supported"). Convert catalog objects first: pcb = pcbComponent(catalogObj); pcb.SolverType = 'FEM';. Additionally, FEM requires Windows Subsystem for Linux (WSL) — if WSL is not installed, the solve will fail. Use MoM (default) when WSL is unavailable.

1. Feed errors: If sparameters fails with a feed-related error, verify that FeedLocations coordinates fall within the metal trace and that FeedDiameter fits inside the trace width. Inset feed at least FeedDiameter/2 from any trace edge.

1. Interpolating sweep frequency range: For 'interpWithGrad', you can specify just [fmin, fmax] — the solver picks internal sample points. For 'interp', provide a full frequency vector; the solver interpolates between computed points.

1. Close figures between large solves: EHfields with many figures or large grids can consume session memory. Use close all between analysis sections when running interactively.

1. Behavioral models don't support field/current/charge. current(), charge(), and EHfields() always use the full-wave solver regardless of the Behavioral flag. Only sparameters() honors it.

1. `solver()` takes no name-value arguments: Do not pass solver(comp, 'SolverType', 'FEM') — it errors with "Too many input arguments." Set comp.SolverType = 'FEM' first, then call s = solver(comp) to get the FEM solver object. Boundary conditions are configured on that solver object (s.BoundaryCondition), not on the component.

1. EHfields points must be 3×N, not N×3: The points argument to EHfields(obj, fc, points) must be a 3-row matrix where each column is [x; y; z]. Do NOT pass N×3. Build with: points = [Xg(:)'; Yg(:)'; Zg(:)'].

Related Skills

• matlab-manage-pcb-material — Material properties affect solver accuracy and loss modeling
• matlab-assemble-pcb-layout — Building custom structures to analyze
• matlab-design-pcb-txline — Transmission line parameter extraction, pcb2D, RLGC, crosstalk
• matlab-design-pcb-passive — Behavioral S-parameters for inductors/capacitors

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