RF power density and field-strength metrics

A field meter can display V/m and then show W/m² after a change of setting. That second number may be calculated from the first; it need not be a separate measurement of power flow. Before converting a reading, identify the quantity, the field model and the averaging interval. This lesson develops that chain and the checks needed to interpret the result.

Build on electric and magnetic fields in an RF wave and near-field and far-field regions. We use free-space travelling-wave relations where justified. A completed calculation does not establish an exposure-limit comparison.

Distinguish field strength from power flow

Electric field strength E is measured in V/m; magnetic field strength H in A/m. They describe the local fields. Power density is measured in W/m²: power crossing a unit area. Total transmitted power in watts, local field strength and power density are different quantities. Antenna direction, distance and the surroundings affect their relationship.

The instantaneous Poynting vector gives both the magnitude and direction of electromagnetic energy flow:

The cross product matters: field directions as well as magnitudes determine the flow. For a single travelling plane wave in free space, the fields are perpendicular and in phase. Its scalar mean flux S therefore obeys

An RMS value is the square root of the time mean of the field’s squared magnitude. Squaring the RMS field in this relation already includes the sinusoid’s time averaging. Doubling the field multiplies S by four; a unit check gives (V/m)²/Ω = W/m².

Test the conversion before trusting it

A justified far-field approximation can make the plane-wave conversion useful. Being a stated distance from an antenna does not establish that approximation at every point: reflections can superpose waves and change the local relationship between E and H. See wave propagation near boundaries.

Outside the travelling-wave model, E²/377 is an electric-field-based plane-wave-equivalent value. It is not automatically the local net energy flux. Measuring both field magnitudes can expose an inconsistent E/H ratio, but magnitudes alone still omit relative direction and phase. For example, perpendicular sinusoidal fields in quadrature have zero mean real power flow even though both field magnitudes are nonzero. That does not imply absence of fields or safe exposure.

The phasor form makes the phase dependence explicit. For sinusoidal fields described by peak-amplitude phasors,

⟨S⟩ = (1/2)Re{E tilde × H tilde *}.

The star means complex conjugation; the real part accounts for relative phase. RMS-amplitude phasors use the same expression without the factor 1/2. Mixing the two conventions creates a factor-of-two error.

A standard’s named metric also needs its own definition. Here S describes mean travelling-wave flux. ICNIRP 2020 defines its incident power-density metric using the modulus of the complex Poynting vector; outside a plane wave that need not equal the magnitude of the mean real flux. The allowed quantities and substitutions depend on field region, frequency and exposure scenario. Use the adopted assessment method rather than replacing its metric with whichever value the meter can display. See ICNIRP 2020, reference levels and Appendix A, equations 18–19.

Combine components without adding their magnitudes

For RMS components along perpendicular spatial axes, measured over the same interval,

Take the square root for total field strength. This is the length of the field vector, not the sum of its component lengths. A probe’s axes need suitable calibration and isotropy; sequential axis readings also need a stable source to represent the same state.

Adding separate sources is a different question. Uncorrelated contributions can add in mean square over the specified interval. Coherent fields must be added with their directions and phases before squaring; interference can increase or decrease the local result. A broadband total also loses the frequency information needed for a frequency-weighted assessment.

Convert the area unit as well as the power unit

One milliwatt is 10⁻³ W, while one square centimetre is 10⁻⁴ m². Thus

In the reverse direction,

Converting the numerator alone loses the much larger change in the denominator. Check the direction: the same flux through the smaller area corresponds to a smaller numerical power per square centimetre.

Average the squared field

Specify the interval behind a meter reading. A peak hold, an on-state RMS field, a full-interval RMS field and an arithmetic mean of displayed field magnitudes are different results. The meter’s detector mode, bandwidth and time constant determine what it can capture.

For constant on-state RMS field, zero field between bursts and duty fraction D over complete periods, the travelling-wave model gives

Power averages in proportion to duty; the corresponding RMS field follows the square root of duty. Multiplying the field by D would calculate an average of the envelope magnitude, not the RMS field. The adopted method determines the comparison window and any additional short-duration checks.

Spatial averaging also starts with the quantity being averaged. Under a specified equal-weight mean-square rule, square each point’s RMS field, average those squares, then take the square root. Do not substitute the arithmetic mean of field magnitudes. Keep the individual readings and the highest point: an allowed spatial average does not answer a separate maximum-value question. Real methods prescribe their own geometry, weighting and averaging area. Perform the averaging in linear units; averaging logarithmic dB readings does not give the same result.

Carry a reading through the measurement chain

Review a survey with a changed averaging rule

Keep the assessment quantity and reporting chain explicit

External field readings do not directly measure SAR or absorbed power density in tissue. A reference-level assessment is usable only under the method’s frequency, field-region and exposure conditions. Do not replace an absorbed or surface-dose metric with an incident-field reading unless the method permits that substitution. Continue with SAR and above-6-GHz metrics for those distinctions. Where the adopted method requires induced fields or currents, an external magnetic-field reading alone does not supply those internal quantities; see RF and ELF distinctions for that change of assessment question.

Record what the instrument actually measures or calculates, its calibration, usable frequency and dynamic ranges, detector mode and averaging interval, the locations and heights sampled, how maxima were sought, source configuration and uncertainty. Keep these details with the result so another person can reconstruct the comparison. If multiple frequencies are present, retain the frequency information needed for the adopted summation rule; a broadband total alone may be insufficient.

Further reading

• ICNIRP 2020 RF guidelines, including the definitions and scenario-specific reference-level rules.
• The adopted IEEE C95.1 edition and IEC 62232 assessment method where applicable.
• ITU RF measurement guidance and the actual instrument’s detector, bandwidth and calibration documentation.

Knowledge check

Exercises