RF Safety

Conductivity (Tissue)

Q: How much does the conductivity of muscle change between 900 MHz and 28 GHz?

Tissue conductivity rises steeply with frequency because dielectric relaxation losses grow as omega increases. For high-water-content muscle, the effective conductivity is roughly 0.94 S/m at 900 MHz, about 1.74 S/m at 2.45 GHz, near 11 S/m at 10 GHz, and approximately 28 to 35 S/m at 28 GHz. The Gabriel parametric (4-region Cole-Cole) model is the standard source for these values. The practical consequence is that at millimeter-wave frequencies almost all absorbed power is deposited within the first 1 to 2 mm of skin, so exposure metrics shift from whole-body SAR to surface power density above about 6 GHz in IEEE C95.1 and ICNIRP guidelines.

Q: Why is effective conductivity used instead of static (DC) conductivity for RF tissue models?

At RF frequencies the loss in tissue comes from two mechanisms: ionic (Ohmic) conduction from mobile ions in the electrolyte, and dielectric relaxation as bound water and cell membranes fail to follow the oscillating field. Effective conductivity sigma_eff bundles both into a single number, sigma_eff = sigma_ionic + omega times epsilon_0 times epsilon_double_prime, where epsilon_double_prime is the imaginary part of the relative permittivity. The DC conductivity captures only the ionic term, which dominates below a few MHz but is a small fraction of the total above 1 GHz. Full-wave SAR solvers always use the effective (frequency-dependent) value extracted from the complex permittivity.

Q: How does tissue conductivity convert to SAR in a dosimetry simulation?

Local specific absorption rate is SAR = sigma times |E|^2 divided by rho, where sigma is the effective tissue conductivity in S/m, |E| is the internal RMS electric field in V/m, and rho is the mass density in kg/m^3 (about 1040 to 1090 for soft tissue). Because conductivity appears as a direct multiplier, a 30 percent error in the tabulated sigma produces a 30 percent error in computed SAR. That is why standardized phantom liquids and the IEEE/IEC 62704 voxel models tightly specify the dielectric properties at each compliance frequency such as 835 MHz, 1900 MHz, 2450 MHz, and 5800 MHz.

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Measured in siemens per meter (S/m), the effective electrical conductivity of biological tissue describes how readily an oscillating RF field drives ionic currents and dielectric relaxation losses inside the body. It is the loss term that, together with the internal electric field, sets local specific absorption rate and is inseparable from the permittivity of tissue as the imaginary part of the complex permittivity. Tissue conductivity climbs sharply with frequency, from roughly 0.94 S/m for muscle at 900 MHz to tens of S/m near 28 GHz, which is why deep-body heating dominates compliance below 6 GHz while shallow surface heating governs millimeter-wave exposure. Standardized values come from the Gabriel four-region Cole-Cole model used in every IEEE and ICNIRP dosimetry assessment.

Category: RF Safety

Unit: S/m

Muscle @ 2.45 GHz: ≈ 1.74 S/m

How Tissue Conductivity Sets RF Energy Deposition

Biological tissue behaves as a lossy dielectric rather than a simple conductor. The electrolyte filling and surrounding cells contains mobile ions that carry an Ohmic current, while bound water molecules and the polarized lipid bilayers of cell membranes lag the applied field and dissipate energy as dielectric relaxation. RF engineers fold both mechanisms into a single effective conductivity, σ_eff, so that a full-wave solver only needs one loss number per material per frequency. This is the quantity that appears directly in the local heating term, which is why an inaccurate conductivity table propagates straight into the computed dose.

The frequency dependence is dramatic and is the single most important fact for safety work. Below a few MHz the ionic term dominates and σ_eff is close to the static value (about 0.2 to 0.5 S/m for soft tissue). As frequency rises, the relaxation term ωε₀ε″ grows linearly with ω, so by 10 GHz muscle conductivity reaches roughly 11 S/m and by 28 GHz it approaches 28 to 35 S/m. Higher conductivity at high frequency means shorter penetration: the skin depth in muscle collapses from about 23 mm at 900 MHz to under 1 mm above 20 GHz, concentrating almost all absorbed power in the epidermis and dermis.

Because the conductivity is so water-dependent, tissues split into two broad families. High-water-content tissue (muscle, skin, brain, internal organs, blood) is lossy and has high permittivity; low-water-content tissue (fat, bone, bone marrow) is far less lossy, with conductivity often an order of magnitude lower at the same frequency. Phantom liquids and gels used for compliance testing of handsets and wearables are formulated to match the high-water tissue values at each regulatory band.

The Effective Conductivity and SAR Relationships

Effective Conductivity (two loss mechanisms):
σ_eff = σ_ionic + ω × ε₀ × ε″_r (S/m)

Local Specific Absorption Rate:
SAR = σ_eff × |E|² / ρ (W/kg)

Plane-wave Penetration (skin) Depth:
δ ≈ 1 / [ ω√(με′/2) × √(√(1 + (σ_eff/ωε′)²) − 1) ]

Where ω = 2πf, ε₀ = 8.854 × 10⁻¹² F/m, ε″_r = imaginary relative permittivity, |E| = internal RMS field (V/m), ρ = tissue density (≈ 1040 to 1090 kg/m³). Example: muscle at 2.45 GHz with σ_eff = 1.74 S/m and |E| = 30 V/m gives SAR ≈ 1.74 × 900 / 1060 ≈ 1.48 W/kg.

Typical Tissue Conductivity vs. Frequency

Tissue	Water content	900 MHz	2.45 GHz	10 GHz	28 GHz
Muscle	High	0.94 S/m	1.74 S/m	10.6 S/m	~30 S/m
Skin (dry)	High	0.87 S/m	1.46 S/m	8.0 S/m	~27 S/m
Brain (grey matter)	High	0.94 S/m	1.81 S/m	11.0 S/m	~28 S/m
Fat	Low	0.10 S/m	0.27 S/m	1.5 S/m	~5 S/m
Cortical bone	Low	0.14 S/m	0.39 S/m	2.1 S/m	~6 S/m

Common Questions

Frequently Asked Questions

How much does the conductivity of muscle change between 900 MHz and 28 GHz?

It climbs sharply because relaxation loss scales with ω. High-water muscle is roughly 0.94 S/m at 900 MHz, about 1.74 S/m at 2.45 GHz, near 11 S/m at 10 GHz, and 28 to 35 S/m at 28 GHz, per the Gabriel four-region Cole-Cole model. Above about 6 GHz nearly all power lands in the first 1 to 2 mm of skin, so compliance shifts from whole-body SAR to surface power density.

Why is effective conductivity used instead of static (DC) conductivity for RF tissue models?

RF loss comes from two sources: ionic (Ohmic) conduction and dielectric relaxation of bound water and cell membranes. Effective conductivity bundles both: σ_eff = σ_ionic + ωε₀ε″_r. The DC value captures only the ionic term, which is a small fraction of the total above 1 GHz, so full-wave SAR solvers always use the frequency-dependent effective value from the complex permittivity.

How does tissue conductivity convert to SAR in a dosimetry simulation?

Local SAR = σ_eff × |E|² / ρ, where σ_eff is in S/m, |E| is the internal RMS field in V/m, and ρ is density (1040 to 1090 kg/m³). Conductivity is a direct multiplier, so a 30% error in σ gives a 30% SAR error. That is why phantom liquids and IEC 62704 voxel models tightly specify dielectric properties at 835, 1900, 2450, and 5800 MHz.

Related Terms

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