Cylindrical Model
How the Equivalent Cylinder Predicts Body Resonance
RF exposure standards are written in terms of basic restrictions on whole-body average SAR, but SAR cannot be measured directly in a living person, so it must be related to the external fields a meter can read. The cylindrical model bridges that gap analytically. By representing a standing person as a vertical cylinder of equivalent height and cross-sectional area filled with lossy tissue-equivalent dielectric, the absorbed power can be evaluated from the boundary-value solution for a finite lossy cylinder in a uniform field, far faster than meshing an anatomical voxel phantom.
The dominant feature the cylinder captures is whole-body resonance. When the incident electric field is polarized along the long axis of the body and the body height H approaches about 0.4 of a free-space wavelength, the induced longitudinal current and the absorbed power maximize. The factor is below the ideal half-wave value because the lossy, high-permittivity tissue electrically shortens the cylinder. A grounded body behaves like a quarter-wave monopole over its image plane, so its resonant frequency drops to roughly half the isolated value, with H near 0.2 wavelengths, which is why a 1.75 m grounded adult peaks near 34 MHz while an isolated adult peaks near 69 MHz. This is the physical reason that RF exposure limits dip to their most restrictive values across the 30 to 100 MHz band.
Away from resonance the cylinder still gives useful bounds. Below resonance, absorption rises roughly as frequency squared; above resonance, SAR per unit power density falls and the body becomes electrically large, so surface heating dominates and peak spatial-average SAR rather than whole-body SAR becomes the limiting quantity. RF Essentials applies these scaling relationships when assessing exposure around high-power millimeter-wave and microwave assemblies.
Governing Relationships
SARwb = Pabs / m (W/kg), m = ρ × π × a2 × H
Local SAR from internal field:
SAR = σ × |Eint|2 / ρ (W/kg)
Free-space (isolated) resonance:
fres ≈ 0.4 c / H, H ≈ 0.4λ at resonance
Grounded whole-body resonance:
fres ≈ 0.2 c / H, H ≈ 0.2λ over the image plane
Where Pabs = absorbed power, m = body mass, ρ ≈ 1000 to 1050 kg/m3, a = cylinder radius, H = body height, σ = tissue conductivity, Eint = internal E-field, c = speed of light. The 0.4λ free-space factor reflects electrical shortening by the lossy high-permittivity body; grounding halves the resonant frequency. Example: H = 1.75 m isolated → fres ≈ 69 MHz; grounded → ≈ 34 MHz.
Body Models Compared
| Body model | Geometry | Resonance accuracy | Whole-body SAR error | Compute cost | Best use |
|---|---|---|---|---|---|
| Cylindrical | Uniform lossy cylinder | ±10 to 15% | 20 to 30% | Closed form | Reference-level derivation, screening |
| Prolate spheroid | Tapered ellipsoid | ±5 to 10% | 15 to 20% | Series solution | Smooth resonance, planar-wave SAR |
| Block (parallelepiped) | Stacked rectangular cells | ±15% | 25 to 35% | Low | Early induced-current estimates |
| Voxel phantom | MRI-derived anatomy | ±2 to 5% | 5 to 10% | Very high (FDTD) | Peak 10 g SAR, compliance |
Frequently Asked Questions
At what frequency does the cylindrical body model predict whole-body resonance?
For a grounded standing adult with the E-field polarized along the body axis, resonance occurs where height approaches about 0.2λ over the image plane, near 35 to 45 MHz for a 1.75 m adult on a ground plane. An isolated adult resonates higher, near 70 to 80 MHz, where height is roughly 0.4λ (electrically short of the half-wave value because the lossy tissue loads the cylinder). Whole-body SAR per unit incident power density peaks there, so reference levels in the 30 to 100 MHz band are set lower to protect the 0.08 W/kg general-public basic restriction.
Why use a cylinder instead of a prolate spheroid or voxel phantom?
The cylinder yields a fast closed-form estimate of whole-body SAR and resonant frequency without meshing anatomy, ideal for early reference-level work and screening. A prolate spheroid captures tapered ends and a smoother resonance; a voxel phantom resolves organ-level peak spatial SAR. The cylinder is typically within 10 to 15% on resonance and 20 to 30% on whole-body SAR, fine for conservative bounding but not for 10 g spatial-average compliance.
What dielectric properties are assigned to the cylinder?
The cylinder is filled with homogeneous lossy dielectric mimicking volume-averaged tissue, roughly two-thirds muscle. At 100 MHz that is about εr 65 to 70 and σ 0.7 S/m; at 900 MHz about εr 55 and σ 1.0 S/m; at 2.45 GHz about εr 52 and σ 1.8 S/m, with density 1000 to 1050 kg/m3. These dispersive values follow the Gabriel tissue database and directly scale absorbed power and SAR.