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Test & Measurement

Radiated Field-Strength Distance Extrapolation

Convert field strength to a target distance using FCC 20/40 dB-per-decade rules or a documented custom basis.

FORMULAv1.0.0
INPUT PARAMETERS

Convert test distance using a regulatory rule

This normalizes distance under the selected rule; it does not show that the device meets a limit.

CALCULATION RESULT

Calculation result

Calculated locally
∿

Enter the parameters and run the calculation to see results and model assumptions here.

FORMULA & TRACEABILITY

Formulas and applicability

Formulas, variables, and model boundaries are published. References last reviewed on 2026-08-30.

3 formulas · 2 references
CORE EQUATIONS

Core equations

These equations directly produce the primary results and define the tool’s core model.

1
F01

Log-domain distance extrapolation

E₂ = E₁ + N log₁₀(d₁ / d₂)

Converts measured field strength to a target distance using an N dB-per-decade rule.

E₁
Measured field strengthdBμV/m
E₂
Field strength at target distancedBμV/m
d₁
Measurement distancem
d₂
Target distancem
N
Correction per decade of distancedB/decade
Applicability
  • Extrapolation method is supported by the applicable regulation or measured regression
  • Avoid near-field measurements for which the model is not applicable
DERIVED & CONVERSION

Derived and conversion equations

Derive units, levels, and supporting engineering quantities from the core values.

1
F02

Linear-domain distance model

E₂ / E₁ = (d₁ / d₂)^(N/20)

20 dB/decade corresponds to inverse-distance field decay; 40 dB/decade corresponds to inverse-square decay.

N/20
Linear distance exponent1
Applicability
  • Compare the same physical field quantity at the same frequency
BOUNDARIES & RULES

Boundary and rule equations

Check model applicability, measurement conditions, and regulatory rules.

1
F03

FCC Part 15 prescribed modes

N = 20 dB/decade (f ≥ 30 MHz); N = 40 dB/decade or measured factor (f < 30 MHz*)

The starred mode applies only from a closer measured distance to the specified farther distance; 40 dB/decade is an allowed alternative, and an applicable factor may also be determined from measurements at two or more distances.

f
Measured emission frequencyMHz
Applicability
  • Only for the applicable FCC Part 15 provision; not for Access BPL
  • For f < 30 MHz, extrapolate only from a closer measured distance to the specified farther distance
  • Alternative measurements for f ≥ 30 MHz must also meet the field-region, detectability, and no-more-than-30-m conditions; a distance beyond 30 m requires further demonstration
  • Application records must document the extrapolation method actually used
REFERENCES

References

01FCC / eCFR · 47 CFR § 15.31(f)Measurement standardsCurrent electronic edition · 规定 ≥30 MHz 的 20 dB/decade，以及 <30 MHz 时从较近距离向规定的更远距离外推的实测或 40 dB/decade 方法；含 Access BPL 例外。
02FCC · FCC 03-100Carrier Current Systems, including Broadband over Power Line Systems2003 · Explains 20/40 dB-per-decade extrapolation and a 3 m-to-30 m correction example.
STANDARD EVIDENCE

Standard excerpt

Only necessary short quotations or factual data are shown according to the source rights; verify context and current status at the source.

Necessary short quote47 CFR Part 15§ 15.31(f)(1)

Measurement-distance extrapolation at or above 30 MHz

The results shall be extrapolated to the specified distance using an extrapolation factor of 20 dB/decade.

For measurements at or above 30 MHz made at an allowed alternate distance, extrapolate to the specified distance at 20 dB per decade, subject to the field-region and detectability conditions in the same paragraph.

Source information · eCFR current consolidated textAccessed 2026-08-28
Only one sentence necessary to support the calculation rule is reproduced; use the standard and clause identifiers to verify context and current status in the official source.
Necessary short quote47 CFR Part 15§ 15.31(f)(2)

Measurement-distance extrapolation below 30 MHz

The results shall be extrapolated to the specified distance using an extrapolation factor of 40 dB/decade.

This sentence is the below-30-MHz alternative method. The same paragraph also permits a factor determined from measurements at two or more distances and excludes Access BPL. This page uses the fixed 40 dB/decade method only from a closer measurement distance to the specified farther distance.

Source information · eCFR current consolidated textAccessed 2026-08-30
Only one sentence necessary to support the calculation rule is reproduced; use the standard and clause identifiers to verify context and current status in the official source.
Engineering use notice

Results use the models and assumptions shown on this page for design estimates and pre-compliance risk review. Complex structures, dispersion, near-field coupling, and test setup can cause significant deviation.

FAQ

Frequently asked questions

What is the FCC test-distance extrapolation rule?

Per 47 CFR 15.31(f): 20 dB/decade of distance at or above 30 MHz (inverse-distance field decay) and 40 dB/decade below 30 MHz (inverse-square). Scope and alternatives are governed by that provision.

How do I convert a 10 m limit to a 3 m measurement?

From 10 m to 3 m in the 30–230 MHz band, the distance ratio is 0.3, so add about 10.46 dB to the measured field under the 20 dB/decade rule before comparing with the limit.

When is a custom extrapolation slope used?

When measured regression or an applicable provision gives a slope other than 20/40 dB per decade. A custom slope cannot directly support a compliance conclusion unless its basis is documented.

STANDARD TEXT

Regulatory text excerpt

FCC distance extrapolation provision47 CFR § 15.31(f)

“…measurements of the radiated emissions may be performed at a distance other than that specified… provided it is shown that the results… can be extrapolated to the specified distance using… 20 dB/decade of distance (for frequencies at or above 30 MHz) or 40 dB/decade (below 30 MHz)…”

eCFR — Code of Federal Regulations, Title 47, Part 15 ↗
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