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Differential / Common-Mode Radiation Estimator

Estimate differential- and common-mode maximum far fields with Paul’s electrically small loop and two-conductor models, then compare the dominant radiation mode.

FORMULAv2.0.0
INPUT PARAMETERS

Select a radiation mode and enter single-frequency parameters

Estimate maximum far field using Paul’s electrically small loop and two-conductor models. Defaults reproduce a published example; results are neither an EMI sweep nor a compliance conclusion.

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 2026-08-28.

5 formulas · 3 references
CORE EQUATIONS

Core equations

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

2
F01

Differential-mode small-loop maximum far field

E_DM,max = η₀k²I_DA/(4πr) = (η₀π/c²)·f²I_DA/r

Treat the equal-and-opposite differential-current loop as an electrically small loop and calculate the far-zone electric-field envelope in the maximum-radiation direction. The SI coefficient is derived from η₀π/c² and is approximately 1.316×10⁻¹⁴.

I_D
Differential-mode frequency-component amplitude in one conductorA
A
Differential-current loop aream²
f
FrequencyHz
r
Observation distancem
η₀
Free-space wave impedanceΩ
Applicability
  • Loop dimensions are much smaller than the wavelength
  • Maximum-radiation direction in the free-space far field
  • Current is approximately uniform in magnitude and phase around the electrically small loop
F02

Common-mode two-conductor maximum far field

E_CM,max = (η₀/c)·fI_CL/r = μ₀·fI_CL/r

Use Paul’s model of two adjacent conductors carrying equal in-phase currents to calculate the maximum far-zone electric field. The SI coefficient η₀/c=μ₀ is approximately 1.257×10⁻⁶.

I_C
In-phase common-mode current in each conductorA
L
Effective radiating length of the two conductorsm
f
FrequencyHz
r
Observation distancem
μ₀
Vacuum permeabilityH/m
Applicability
  • L is much smaller than the wavelength
  • The two conductor currents are equal, in phase, and approximately uniform along their length
  • Maximum-radiation direction in the free-space far field
DERIVED & CONVERSION

Derived and conversion equations

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

2
F03

Cable-bundle clamp-current conversion

I_sum = I₁ + I₂ = 2I_C ⇒ I_C = I_sum/2

When the clamp surrounds both modeled conductors, its reading is the algebraic sum of the two in-phase currents; the core equation requires per-conductor current I_C.

I_sum
Two-conductor bundle-sum current measured by the clampA
I_C
In-phase common-mode current in each conductorA
Applicability
  • Exactly two conductors are represented by the model
  • Current directions use the same reference and are equal and in phase
  • Do not divide by 2 when per-conductor current is already known
F04

Electric-field level conversion

L_E = 20·log₁₀(E / 1 μV/m) = 20·log₁₀(E[V/m]) + 120

Convert linear electric-field strength to dBμV/m referenced to 1 μV/m.

L_E
Electric-field strength leveldBμV/m
E
Linear electric-field strengthV/m
Applicability
  • E > 0
  • Use the same amplitude convention for the linear field and logarithmic result
BOUNDARIES & RULES

Boundary and rule equations

Check model applicability, measurement conditions, and regulatory rules.

1
F05

Electrical-size applicability screening

λ = c/f； C_loop/λ ≪ 1； L/λ ≪ 1

The sources require the loop and conductor length to be sufficiently small relative to wavelength. This tool gives a conservative warning at a ratio of 0.1, but 0.1 is not a standards limit and does not replace a complete near-/far-field assessment.

C_loop
Circumference of an equal-area circular loopm
L
Effective common-mode conductor lengthm
λ
Free-space wavelengthm
Applicability
  • For model-applicability guidance, not pass/fail assessment
  • Use simulation or measurement near resonance or when current distribution is nonuniform
REFERENCES

References

01Wiley · Paul, C.R., 2nd ed., ISBN 978-0-471-75500-5Introduction to Electromagnetic Compatibility2006 · Textbook source for the differential-mode small-loop and common-mode two-conductor radiation models, including derivations, variable definitions, and assumptions.
02IEEE Standards Association · IEEE SA technical presentation, p.5Navigating EMC Challenges in Automotive Ethernet2024 · Publicly lists the differential-mode 1.32×10⁻¹⁴ and common-mode 1.257×10⁻⁶ SI forms and states the electrically short and far-field assumptions.
03Honda R&D Technical Review · Vol.26 No.1, equations (1)–(2)Noise-Reduction Design for Printed Circuit Boards2014 · Provides SI equations and reproducible examples; this project’s automated tests reproduce its 100 MHz differential- and common-mode results.
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 difference between common-mode and differential-mode radiation?

Differential-mode current flows in small signal loops whose fields largely cancel; common-mode current flows along the whole cable against ground, forming a long effective antenna—usually the dominant cause of failures.

Why can tiny common-mode currents cause failures?

The CM loop area spans the entire cable against ground with no cancelling return, so microamps of CM current can exceed limits at 30–230 MHz, while DM would need milliamps for the same effect.

How is cable common-mode radiation suppressed?

Common-mode chokes/ferrites, shorter and tidier cables, routing near ground planes, Y-capacitors for a low-impedance return path, and 360° shield bonding to the chassis.

PRE-COMPLIANCE SUPPORT

Need accredited testing or pre-compliance support?

These tools support design-stage estimates. For accredited EMC testing, compliance decisions, and troubleshooting, contact us.

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