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Differential Small-Loop Radiated-Spectrum Estimator

Pass trapezoidal-wave harmonics line by line through a terminated filter network, then use the load-side differential RMS current to estimate the discrete maximum far-field spectrum of an electrically small loop; this is not a site measurement or compliance decision.

FORMULAv1.0.0
INPUT PARAMETERS

Enter the switching source, port network, and differential loop

Calculate load-side RMS differential current and the electrically small loop maximum far field harmonic by harmonic. Parameters must come from the actual circuit and geometry.

THEVENIN SOURCEOpen-circuit trapezoidal excitation
LOADED TWO-PORTFilter network and port

L1 series inductor

C1 load-side shunt capacitor

DIFFERENTIAL SMALL LOOPLoad-Side Differential-Loop Geometry

This page models only the load-side differential loop. Common-mode current must be supplied separately by an imbalance-conversion network, current-clamp spectrum, or measured transfer function; this tool does not invent it.

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 2026-09-01.

4 formulas · 4 references
CORE EQUATIONS

Core equations

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

2
F01

From Source-Voltage Spectrum to Load-Side Differential-Current Spectrum

Vport,n=Vsource,n·H(nf₀)；I_D,n=Vport,n/RL

Pass each RMS harmonic of the trapezoidal Thevenin source through the same complex terminated network, then use the resistive load current as the load-side differential loop current.

Vsource,n
Open-circuit RMS harmonic n of the Thevenin sourceV RMS
H(nf₀)
Complex voltage transfer including source/load terminations1
RL
Purely resistive load-side terminationΩ
I_D,n
Load-side differential RMS loop current of harmonic nA RMS
Applicability
  • Linear time-invariant small-signal network
  • The load is purely resistive
  • The radiating loop is on the network load side
F02

Differential Small-Loop Maximum Far-Field Line

E_DM,n=(η₀π/c²)·(nf₀)²·A·I_D,n/r

Insert each differential RMS current line into the same electrically small loop model to obtain the free-space maximum-direction RMS far-field envelope.

A
Differential-current loop aream²
r
Observation distancem
η₀
Free-space wave impedanceΩ
c
Speed of light in vacuumm/s
Applicability
  • The loop electrical size is much smaller than the wavelength
  • Loop current is approximately uniform in magnitude and phase
  • The observation point is in the radiating far field
DERIVED & CONVERSION

Derived and conversion equations

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

1
F03

Current and Field Spectrum-Line Levels

L_I,n=20log₁₀(I_D,n/1 μA)；L_E,n=20log₁₀(E_DM,n/1 μV/m)

Both right-axis current and left-axis field use RMS values. Theoretical nulls remain zero rather than being assigned fabricated finite logarithmic values.

L_I,n
Differential-current level of harmonic ndBμA RMS
L_E,n
Maximum far-field level of harmonic ndBμV/m RMS
Applicability
  • Convert only non-zero discrete spectrum lines
  • Not equivalent to quasi-peak, average, or peak measuring-receiver readings
BOUNDARIES & RULES

Boundary and rule equations

Check model applicability, measurement conditions, and regulatory rules.

1
F04

Combined Model Applicability Screening

C_loop/λ < 0.1 ∧ f ≤ f_model,max

Both the loop electrical size and circuit-parameter verification range must be satisfied. C_loop/λ=0.1 is only the conservative screening line used by this tool, not a regulatory limit.

C_loop
Circumference of an equal-area circular loopm
λ
Free-space wavelengthm
f_model,max
User-provided circuit parameter/model verification limitHz
Applicability
  • Screening controls only the displayed confidence range
  • Does not replace measurement, full-wave simulation, or near-/far-field analysis
REFERENCES

References

01Wiley · Paul, C.R., 2nd ed., ISBN 978-0-471-75500-5Introduction to Electromagnetic Compatibility2006 · Textbook source for the differential electrically small loop radiation model, variable definitions, and far-field assumptions.
02Honda R&D Technical Review · Vol.26 No.1, equations (1)–(2)Noise-Reduction Design for Printed Circuit Boards2014 · Provides a reproducible SI differential-mode equation and numerical example; the single-frequency core is regression-tested against its 100 MHz result.
03National Bureau of Standards / NIST · Journal of Research of the NBS, Vol.71C No.4The Near-Zone Magnetic Field of a Small Circular-Loop Antenna1967 · Explicitly uses RMS quantities and the uniform-magnitude, uniform-phase current assumption of an electrically small loop, supporting this page’s RMS convention and model boundary.
04IEC / CISPR · CISPR 16-2-3Specification for radio disturbance and immunity measuring apparatus and methods — Radiated disturbance measurementsOfficial publication metadata · Used only to establish that formal radiated-disturbance measurement requires defined site, antenna, setup, scan, and receiver conditions. This page does not reproduce standard text or limits.
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.

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