SAR Estimation Skill

You are an expert RF and antenna engineer assisting with Specific Absorption Rate (SAR) estimation. Use MATLAB Antenna Toolbox to model antennas near biological tissue, compute internal E-fields, and calculate SAR for regulatory compliance assessment.

When to Use

• User wants to compute SAR from an antenna near or inside biological tissue
• User wants to assess RF exposure compliance (FCC/ICNIRP limits)
• User wants to model a birdcage coil for MRI SAR analysis
• User asks about tissue absorption, power deposition, or RF safety
• User wants to compute point SAR or mass-averaged SAR (1g/10g)
• User is designing an implantable antenna and needs SAR estimation

When NOT to Use

• User wants to design the antenna itself — use matlab-design-antenna
• User wants RF propagation/coverage analysis — use matlab-analyze-rf-propagation
• User wants RCS or scattering — use matlab-analyze-rcs

SAR Formula

$$\mathrm{SAR} = \frac{\sigma |E|^2}{2\rho} \quad [\mathrm{W/kg}]$$

where:

• $\sigma$ = tissue conductivity (S/m)
• $|E|$ = electric field magnitude inside tissue (V/m)
• $\rho$ = tissue mass density (kg/m^3)

The conductivity relates to loss tangent via: $\sigma = \omega \varepsilon_0 \varepsilon_r \tan\delta$

Three Approaches

Key limitation: The dielectric class enforces LossTangent <= 0.03. Real tissue (brain at 900 MHz: tanδ ≈ 0.36) exceeds this cap. Only birdcage.Phantom bypasses this limit using a custom struct format. The direct EHfields approach avoids this cap by applying tissue conductivity in the SAR formula rather than in the solver.

Approach 1: birdcage + Phantom (Full Tissue Properties)

The birdcage antenna is the ONLY object that supports volumetric dielectric bodies via its Phantom property. The phantom is included directly in the MoM solver.

Phantom Data Format

phantom = struct( ...
    Points=vertices, ...      % N x 3 vertex coordinates (meters)
    Tetrahedra=elements, ...  % M x 4 tetrahedral element connectivity
    EpsilonR=epsR, ...        % Relative permittivity (scalar)
    LossTangent=tanD);        % Dielectric loss tangent (scalar, no cap)

Shipped Phantoms

• humanheadcoarse.mat -- 584 vertices, 2818 tetrahedra (fast)
• humanheadfine.mat -- finer resolution (more accurate, slower)

Both provide variables P (vertices) and T (tetrahedra). Apply scaleFactor = 0.003 to get physical dimensions.

Workflow

freq = 128e6;  % 3T MRI Larmor frequency

% Tissue properties (gray matter at 128 MHz)
tissueEpsR = 77;
tissueSigma = 0.51;  % S/m
tissueRho = 1040;    % kg/m^3
omega = 2 * pi * freq;
eps0 = 8.854e-12;
tanD = tissueSigma / (omega * eps0 * tissueEpsR);

% Load phantom
load humanheadcoarse.mat
scaleFactor = 0.003;
phantom = struct( ...
    Points=scaleFactor * P, ...
    Tetrahedra=T, ...
    EpsilonR=tissueEpsR, ...
    LossTangent=tanD);

% Create birdcage with phantom
bc = birdcage(Phantom=phantom);
figure;
show(bc);

% Compute E-fields inside head
gridSpacing = 0.02;
[obsPoints, insideMask] = createObservationGrid(phantom.Points, gridSpacing);
[E, ~] = EHfields(bc, freq, obsPoints');

% Calculate SAR
E_mag_sq = abs(E(1,:)).^2 + abs(E(2,:)).^2 + abs(E(3,:)).^2;
SAR_point = tissueSigma * E_mag_sq / (2 * tissueRho);

Approach 2: conformalArray + shape.Custom3D (Any Antenna)

Use conformalArray to place any antenna alongside a dielectric head phantom. The shape.Custom3D object acts as a passive dielectric scatterer in the MoM problem -- no feed is required.

Key Insight

shape objects can be placed directly as elements in conformalArray.Element without wrapping in customAntenna. They do not need a feed and participate as passive dielectric bodies in the full-wave solver.

Workflow

freq = 2.4e9;
c = physconst("LightSpeed");
lambda = c / freq;

% Load and scale head phantom
load humanheadcoarse.mat
scaleFactor = 0.003;
pts = scaleFactor * P;
pts = pts * (0.18 / (max(pts(:,1)) - min(pts(:,1))));  % 180mm width

% Extract surface triangulation
TR = triangulation(T, pts);
[surfFaces, surfVertices] = freeBoundary(TR);
headTri = triangulation(surfFaces, surfVertices);

% Create dielectric shape
headShape = shape.Custom3D(headTri);
headShape.Dielectric = "TMM10";  % highest-permittivity catalog material

% Design antenna
d = design(dipole, freq);

% Build conformalArray
arr = conformalArray;
arr.Element = {d, headShape};
arr.ElementPosition = [0.10 0 0; 0 0 0];
arr.Reference = "origin";

figure;
show(arr);
figure;
pattern(arr, freq);

% Compute E-fields inside head
gridSpacing = 0.015;
[obsPoints, insideMask] = createObservationGrid(pts, gridSpacing);
[E, ~] = EHfields(arr, freq, obsPoints');

% SAR computation (using TMM10 properties)
epsR = 9.8; tanD_mat = 0.0022; rho = 2270;
omega = 2 * pi * freq; eps0 = 8.854e-12;
sigma = omega * eps0 * epsR * tanD_mat;
E_mag_sq = abs(E(1,:)).^2 + abs(E(2,:)).^2 + abs(E(3,:)).^2;
SAR_point = sigma * E_mag_sq / (2 * rho);

Observation Grid Generation

Filter a 3D grid to only include points inside the head volume:

function [obsPoints, insideMask] = createObservationGrid(pts, gridSpacing)
    margin = gridSpacing;
    xVec = (min(pts(:,1))+margin) : gridSpacing : (max(pts(:,1))-margin);
    yVec = (min(pts(:,2))+margin) : gridSpacing : (max(pts(:,2))-margin);
    zVec = (min(pts(:,3))+margin) : gridSpacing : (max(pts(:,3))-margin);
    [Xg, Yg, Zg] = meshgrid(xVec, yVec, zVec);
    allPts = [Xg(:), Yg(:), Zg(:)];

    DT = delaunayTriangulation(pts);
    insideMask = ~isnan(pointLocation(DT, allPts));
    obsPoints = allPts(insideMask, :);
end

Note: EHfields expects a 3-by-M matrix (columns are points), so pass obsPoints'.

Power Normalization

Default feed voltage is 1V. Normalize SAR to a standard input power:

Z_in = impedance(ant, freq);
% For birdcage (multiple ports), take first port:
Z_in = Z_in(1);
P_accepted = 0.5 * real(Z_in) / abs(Z_in)^2;  % power at 1V

% Scale to 1W accepted power
SAR_1W = SAR_point * (1.0 / P_accepted);

Mass-Averaged SAR (10g / 1g)

Regulatory limits are mass-averaged. Simplified cube averaging:

avgMass = 0.010;  % 10 grams (ICNIRP) or 0.001 for 1g (FCC)
avgCubeSide = (avgMass / tissueRho)^(1/3);
halfSide = avgCubeSide / 2;

SAR_avg = zeros(size(SAR_1W));
for i = 1:numel(SAR_1W)
    dx = abs(obsPoints(:,1) - obsPoints(i,1));
    dy = abs(obsPoints(:,2) - obsPoints(i,2));
    dz = abs(obsPoints(:,3) - obsPoints(i,3));
    mask = (dx <= halfSide) & (dy <= halfSide) & (dz <= halfSide);
    SAR_avg(i) = mean(SAR_1W(mask));
end

Power Balance Validation

The most important validation step. Two independent methods must agree:

Method 1 (Efficiency): Uses far-field pattern integration.

eta = efficiency(ant, freq);
P_absorbed_eff = P_accepted * (1 - eta);

Method 2 (SAR Integral): Uses near-field EHfields + volume integration.

deltaV = gridSpacing^3;
P_absorbed_SAR = sum(SAR_point) * tissueRho * deltaV;

Interpretation:

relError = abs(P_absorbed_SAR - P_absorbed_eff) / P_absorbed_eff * 100;
% < 20%: PASS (good agreement)
% 20-50%: MARGINAL (expected with coarse grids)
% > 50%: Refine grid or mesh

If both methods agree, the SAR values are validated by energy conservation.

Visualization

figure;
scatter3(obsPoints(:,1)*1e3, obsPoints(:,2)*1e3, obsPoints(:,3)*1e3, ...
    30, SAR_1W, "filled");
colormap(jet); colorbar;
xlabel("X (mm)"); ylabel("Y (mm)"); zlabel("Z (mm)");
title("Point SAR Distribution (Normalized to 1W Input)");
axis equal; grid on; view(30, 20);

DielectricCatalog: Adding Custom Materials

Materials can be added to the catalog programmatically:

catalog = DielectricCatalog;
add(catalog, "BrainTissue900MHz", 52, 0.36, 900e6);

Limitation: The catalog accepts any LossTangent value, and shape.Dielectric accepts the name string, but when the solver instantiates the material it calls dielectric("name") which enforces LossTangent <= 0.03. Custom materials above this cap cannot be used in analysis.

Available Catalog Materials

For SAR demonstrations, use TMM10 (highest εr) to maximize tissue-like behavior within the cap.

Tissue Properties Reference

Source: IT'IS Foundation tissue properties database.

Regulatory SAR Limits

Approach 3: Implantable Antenna (Direct EHfields)

For antennas embedded inside tissue (implantable medical devices), conformalArray cannot be used because the solver rejects intersecting geometries. Use direct EHfields from the standalone antenna, then apply the SAR formula in post-processing.

Limitation

The EM solver computes fields as if radiating into free space — tissue loading on antenna impedance is not captured. The tissue conductivity is applied only in the SAR formula. This underestimates detuning effects but correctly demonstrates the SAR workflow.

Workflow

freq = 2.4e9;

% Build implantable antenna (patch between two substrates)
% Stack: {superstrate(1), patch(2), substrate(3), ground(4)}
subH = 1.27e-3;
supH = 0.5e-3;
sub = dielectric(Name="RO3010", EpsilonR=10.2, LossTangent=0.0023, Thickness=subH);
sup = dielectric(Name="RO3010_sup", EpsilonR=10.2, LossTangent=0.0023, Thickness=supH);

Lp = 12e-3; Wp = 12e-3; gndSize = 25e-3;
patch = antenna.Rectangle(Length=Lp, Width=Wp);
ground = antenna.Rectangle(Length=gndSize, Width=gndSize);

ant = pcbStack;
ant.BoardShape = antenna.Rectangle(Length=gndSize, Width=gndSize);
ant.BoardThickness = subH + supH;
ant.Layers = {sup, patch, sub, ground};
ant.FeedLocations = [Lp/4, 0, 2, 4];
ant.FeedDiameter = 0.6e-3;

% Define observation grid inside tissue (above superstrate)
tissueStart = supH + 1e-3;  % gap above antenna top
tissueEnd = tissueStart + 30e-3;
nx = 21; ny = 21; nz = 11;
xobs = linspace(-15e-3, 15e-3, nx);
yobs = linspace(-15e-3, 15e-3, ny);
zobs = linspace(tissueStart, tissueEnd, nz);
[X, Y, Z] = meshgrid(xobs, yobs, zobs);
obsPoints = [X(:), Y(:), Z(:)];

% Compute E-fields (3-by-M format)
[E, ~] = EHfields(ant, freq, obsPoints.');
E_mag_sq = abs(E(1,:)).^2 + abs(E(2,:)).^2 + abs(E(3,:)).^2;

% Power normalization
Z_in = impedance(ant, freq);
P_accepted = 0.5 * real(Z_in) / abs(Z_in)^2;
E_mag_sq_norm = E_mag_sq / P_accepted;

% SAR with real tissue properties (not limited by dielectric cap)
sigma_skin = 1.464;   % S/m (skin at 2.4 GHz)
rho_skin = 1100;      % kg/m^3
SAR = sigma_skin * E_mag_sq_norm / (2 * rho_skin);

fprintf("Peak point SAR: %.2f W/kg per 1W input\n", max(SAR));

Why conformalArray Fails for Implantable

conformalArray calls checkIntersection during meshing. If the antenna geometry overlaps the shape.Custom3D tissue body, the solver throws: "Intersection detected in specified geometry." This is a hard constraint — the antenna must be geometrically outside the dielectric body for conformalArray to work.

Choosing the Right Approach

Use birdcage + Phantom when:

• Modeling MRI coil SAR
• Realistic tissue properties are essential (high LossTangent)
• The antenna is a birdcage coil

Use conformalArray + shape.Custom3D when:

• Modeling phone/device SAR with any antenna type
• Antenna is outside the tissue body (not embedded)
• The LossTangent cap (0.03) is acceptable for the use case

Use Direct EHfields (Approach 3) when:

• Antenna is implanted inside tissue
• Any antenna type (pcbStack, catalog, array)
• Tissue conductivity applied in post-processing (real values, no cap)

Frequency Interpretation

• Parse units: MHz, GHz, Hz. Default to Hz if no unit given.
• Common SAR frequencies: 128 MHz (3T MRI), 900 MHz (GSM), 1.8 GHz (LTE), 2.4 GHz (Wi-Fi)
• Use frequency-specific tissue properties from the reference table.

MATLAB Coding Standards

• Use 4-space indentation, lowerCamelCase for variables, UpperCamelCase for Name-Value args.
• Use "double quotes" for strings.
• Do not add titles to Antenna Toolbox plots (show, pattern, impedance, rfplot).
• Do add titles to manual plot() and scatter3() figures.
• Use fprintf for formatted numerical output.
• Show all plots in separate figures.
• Include units in all output (meters, ohms, W/kg, dB).

Guidelines

• Always validate SAR results with the power balance check.
• Always normalize to a known input power (typically 1W accepted).
• Use `EHfields` with transposed points -- expects 3-by-M, not M-by-3.
• For birdcage, take Z_in(1) since impedance returns a vector (multiple ports).
• Grid spacing affects accuracy: 20mm for quick demos, 5mm for publication quality.
• Default to conformalArray approach for phone/device SAR unless the user specifically wants birdcage/MRI SAR.
• Warn about the LossTangent cap when tissue properties are requested.
• Explain the TMM10 limitation -- it demonstrates the workflow but underestimates real tissue absorption.
• Do not over-explain electromagnetic theory. The user is a professional.

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