16.2 Safe Separation Distances, Power Density, and Duty Cycles

ACMA Amateur Radio Advanced Recognition Certificate - Theory Exam

Track your progress as you read

Finished sections get a check mark.

1 Chapter 1: DC Theory, Circuit Laws & Passive Components

1.1 DC Circuit Analysis, Ohm's Law, and Kirchhoff's Laws 1.2 AC Fundamentals, Sine Waves, Peak, RMS, and Phase Relationships 1.3 Inductance, Capacitance, Reactance, and Time Constants

2 Chapter 2: Impedance, Resonance & Passive Filters

2.1 Complex Impedance, Phasors, and AC Circuit Analysis 2.2 Series and Parallel LC Resonance and Q Factor 2.3 Passive Filters, Cutoff Frequency, and Attenuator Pads

3 Chapter 3: Semiconductor Devices & Power Supplies

3.1 Semiconductor Diodes, Zener Regulators, and Rectifier Circuits 3.2 Bipolar Junction Transistors, FETs, and Operational Amplifiers 3.3 Thermionic Valves (Vacuum Tubes) and High-Power Linear Amplifiers 3.4 DC Power Supplies, Filter Networks, and Voltage Regulators

4 Chapter 4: Oscillators & Frequency Synthesis

4.1 RF Oscillators, LC Tank Topologies, and Frequency Stability 4.2 Phase-Locked Loops (PLLs) and Frequency Synthesisers 4.3 Direct Digital Synthesis (DDS), SDR Architectures, and Digital Filter Topologies

5 Chapter 5: RF Amplifiers & Linearity

5.1 Classes of Amplification, Conduction Angles, and Operating Efficiency 5.2 RF Power Amplifiers, Push-Pull Topologies, and Output Matching 5.3 Amplifier Stability, Neutralisation, and Intermodulation Distortion

6 Chapter 6: Modulation & Demodulation

6.1 Amplitude Modulation, Double Sideband, and Single Sideband (SSB) 6.2 Frequency Modulation, Phase Modulation, and FM Detectors 6.3 Digital Modulation Modes, Spectral Efficiency, and Weak-Signal Protocols

7 Chapter 7: Transmitters, Mixers & Receivers

7.1 RF Mixers, Frequency Translation, and Intermodulation 7.2 Transmitter Architectures, CW Keying, and Output Filtering 7.3 Superheterodyne Receiver Design, IF Selection, and Image Rejection 7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

8 Chapter 8: Transmission Lines & Waveguides

8.1 Transmission Line Characteristics, Impedance, and Velocity Factor 8.2 Standing Waves, Reflection Coefficient, SWR, and Return Loss 8.3 Resonant Line Sections, Quarter-Wave Transformers, and Stubs

9 Chapter 9: Impedance Matching & Baluns

9.1 Lumped-Element Matching Networks and Antenna Tuning Units 9.2 Baluns, Ununs, and Common-Mode Current Choking 9.3 Feedline Losses, High-SWR Stress, and Coaxial Installation Practice

10 Chapter 10: Practical Antennas & Arrays

10.1 Resonant Dipoles, Inverted-Vs, and Multiband Wire Antennas 10.2 Quarter-Wave Verticals, Ground Systems, and Radiation Efficiency 10.3 Parasitic Arrays, Yagi-Uda Antennas, and Quad Arrays 10.4 Antenna Gain, Aperture Antennas & Horns, ERP/EIRP, Radiation Patterns

11 Chapter 11: Radio Wave Propagation & Ionospheric Mechanics

11.1 Electromagnetic Wave Fundamentals, Polarisation, and Ground Waves 11.2 The Ionosphere, Solar Radiation, and Solar Cycles 11.3 Critical Frequency, Maximum Usable Frequency, and HF Propagation Paths

12 Chapter 12: VHF/UHF Propagation & Space Communications

12.1 Line-of-Sight, Tropospheric Ducting, and Diffraction 12.2 Sporadic-E, Auroral Scatter, and Trans-Equatorial Propagation 12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

13 Chapter 13: Test Equipment & RF Measurements

13.1 Decibels, Power Ratios, and Cascaded Stage Calculations 13.2 RF Power Meters, Directional Couplers, and Dummy Loads 13.3 Multirange Meters, Waveform Diagnostics, Oscilloscopes, and Frequency Counters

14 Chapter 14: Advanced RF Analysis & Diagnostics

14.1 Spectrum Analyser Architecture, Operation, and Spectral Purity 14.2 Antenna Analysers, Vector Network Analysers, and Smith Charts 14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

15 Chapter 15: Electromagnetic Compatibility & Interference

15.1 Sources of Interference, Coupling Mechanisms, and Audio Rectification 15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation 15.3 Practical RFI Suppression, Filter Design, and Bonding Techniques

16 Chapter 16: Electrical, RF & Station Safety

16.1 Biological Effects of RF Energy and ARPANSA Exposure Standards 16.2 Safe Separation Distances, Power Density, and Duty Cycles 16.3 Station Electrical Safety, Battery Hazards, and Safe Headphone Use 16.4 Mast and Tower Construction, Power Line Clearance, and Lightning Protection

16.2 Safe Separation Distances, Power Density, and Duty Cycles

Key Takeaways Explain This Topic AI

Reactive near-field, radiating near-field and far-field regions require different assessment methods. Aperture formulas give approximate boundaries; the amateur class licence defines far field beyond the larger of 2 D²/λ and 0.5λ. Check the region before using an inverse-square power-density model.

Ground reflections can increase or decrease the local field. If a model assumes an in-phase reflected field 0.60 times the direct field, total E increases 1.6 times and equivalent power density 2.56 times. Those factors are assumptions, not universal maxima.

Compliance with ARPANSA thermal exposure limits is determined by time-averaged power ( P avg P_{\text{avg}} P avg ​ ), which is calculated as the product of transmitter Peak Envelope Power (PEP), mode duty factor ( D mode D_{\text{mode}} D mode ​ ), and operational transmit-to-receive factor ( D op D_{\text{op}} D op ​ ).

Duty factors must match the actual waveform and timing. Illustrative values are 20% for unprocessed SSB and 40% for processed SSB or CW; constant-envelope FM/RTTY is 100% during transmission. FT8 keying for 12.6 seconds in alternating 15 second slots gives 42% overall, without another receive-time reduction.

RF contact currents can produce severe localized heating and burns. At HF/VHF, heating is the principal contact hazard; lower RF frequencies also require protection against electrostimulation. Avoid energized conductors and do not rely on pain as a warning.

Last updated: November 2026

16.2 Safe Separation Distances, Power Density, and Duty Cycles

Accurate assessment of radiofrequency exposure requires applying electromagnetic field equations tailored to the antenna's geometry and operating frequency. In amateur installations, antennas are rarely isolated in infinite free space; they operate in proximity to the ground, structures, and human occupants. Calculating compliant safe separation distances demands understanding field regions, ground reflection amplification, modulation duty cycles, and the unique physical mechanism of radiofrequency burns.

Field Regions Surrounding Antennas

The space surrounding any radiating antenna is partitioned into three distinct electromagnetic regions characterized by differing wave impedances, field geometries, and radial power decay rates. Electromagnetic Field Regions Around an Antenna

• Reactive Near-Field Radiating Near-Field Far-Field
• (Storage Field) (Fresnel Zone) (Fraunhofer Zone)
• ◄──────────────────────►◄────────────────────────►◄────────────────────────►
• R1 R2
• True Plane Wave
• E and H in time phase
• Z0 = E/H ≈ 377 Ω
• S = EIRP / (4 π R²)
• Inverse-Square Law (1/R²)

• Boundary R1 = 0.62 √(D³ / λ) or λ / (2π)
• Boundary R2 ≈ 2 D² / λ; class-licence far field also requires R > 0.5 λ
• 1. Reactive Near-Field

The reactive near-field is the region immediately adjacent to the antenna conductors ( R < R 1 R < R_1 R < R 1 ​ ): R 1 = 0.62 D 3 λ R_1 = 0.62 \sqrt{\frac{D^3}{\lambda}} R 1 ​ = 0.62 λ D 3 ​ ​

where D D D is the largest linear aperture dimension of the antenna and λ \lambda λ is the wavelength. For electrically small antennas ( D < λ / 2 D < \lambda/2 D < λ /2 , such as small loops or short dipoles), this boundary is commonly approximated by the radiansphere radius: R 1 ≈ λ 2 π ≈ 0.159 λ R_1 \approx \frac{\lambda}{2\pi} \approx 0.159 \lambda R 1 ​ ≈ 2 π λ ​ ≈ 0.159 λ

Within this zone, stored inductive (magnetic B ⃗ \vec{B} B ) and capacitive (electric E ⃗ \vec{E} E ) energy dominates over radiated energy. Reactive field components are out of phase, but the phase relationship and ratio of the total electric and magnetic fields vary with position. Do not assume the free-space wave impedance ( 377 Ω 377\ \Omega 377 Ω ). Energy sloshes back and forth between the antenna and surrounding reactive space without propagating away. Crucially, plane-wave power density equations cannot be used here. Use an appropriate near-field calculation or calibrated E/H measurement method. At higher frequencies the standard requires assessment of basic restrictions in the reactive near field; measuring one field and converting it to power density does not suffice.

2. Radiating Near-Field (Fresnel Region)

The radiating near-field , or Fresnel region, extends from R 1 R_1 R 1 ​ to the Fraunhofer boundary R 2 R_2 R 2 ​ : R 1 ≤ R < R 2 where R 2 = 2 D 2 λ R_1 \le R < R_2 \quad \text{where} \quad R_2 = \frac{2 D^2}{\lambda} R 1 ​ ≤ R < R 2 ​ where R 2 ​ = λ 2 D 2 ​

In this region, radiation fields predominate over reactive fields, but the angular distribution of radiated power varies with distance from the antenna. The spherical wavefronts originating from different sections of the antenna aperture have not yet coalesced into a unified, parallel plane wave. Field maxima and nulls depend on position. Catalog far-field gain and the inverse-square equation do not, by themselves, establish exposure here.

3. Far-Field (Fraunhofer Zone)

The far-field region begins at distances where the path length difference between rays arriving from the center and edges of the antenna aperture is less than λ / 16 \lambda/16 λ /16 ( 22.5 ∘ 22.5^\circ 22. 5 ∘ phase error): R ≥ R 2 = 2 D 2 λ with R ≫ D and R ≫ λ R \ge R_2 = \frac{2 D^2}{\lambda} \quad \text{with} \quad R \gg D \quad \text{and} \quad R \gg \lambda R ≥ R 2 ​ = λ 2 D 2 ​ with R ≫ D and R ≫ λ

For the amateur class-licence assessment, the far field is beyond the larger of 2 D 2 / λ 2D^2/\lambda 2 D 2 / λ and 0.5 λ 0.5\lambda 0.5 λ . This legal boundary is an assessment definition, not a sharp physical transition. In an unobstructed far-field model:

The wavefront is locally planar (transverse electromagnetic, TEM).

The electric field vector E ⃗ \vec{E} E and magnetic field vector H ⃗ \vec{H} H are in time phase, orthogonal to each other, and perpendicular to the direction of propagation.

The wave impedance is constant and equal to the intrinsic impedance of free space: Z 0 = E H = μ 0 ε 0 ≈ 120 π ≈ 376.73 Ω ≈ 377 Ω Z_0 = \frac{E}{H} = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 120\pi \approx 376.73\ \Omega \approx 377\ \Omega Z 0 ​ = H E ​ = ε 0 ​ μ 0 ​ ​ ​ ≈ 120 π ≈ 376.73 Ω ≈ 377 Ω

Power density obeys the inverse-square law , decaying strictly as 1 / R 2 1/R^2 1/ R 2 .

Power Density and Ground Reflection Enhancement

In ideal free space, the power density S S S at a distance R R R in the far-field along the antenna's main beam is formulated from the transmitter's average time-weighted power ( P avg P_{\text{avg}} P avg ​ ) and isotropic antenna gain ( G tx G_{\text{tx}} G tx ​ ): S free = EIRP avg 4 π R 2 = P avg G tx 4 π R 2 S_{\text{free}} = \frac{\text{EIRP}_{\text{avg}}}{4\pi R^2} = \frac{P_{\text{avg}} G_{\text{tx}}}{4\pi R^2} S free ​ = 4 π R 2 EIRP avg ​ ​ = 4 π R 2 P avg ​ G tx ​ ​

where G tx G_{\text{tx}} G tx ​ is the numeric power gain relative to an isotropic radiator ( dBi = 10 log ⁡ 10 G tx \text{dBi} = 10 \log_{10} G_{\text{tx}} dBi = 10 lo g 10 ​ G tx ​ ). Ground Reflection Multipath Enhancement

• Antenna
• [X]───────────── Direct Ray (E_dir) ─────────────► Receiver /
• │ Human Target

│ ╲ ▲ (Total Field:

• │ ╲ │ Assumed in-phase E_total = 1.6 E_dir)
• │ ╲ Reflected Ray (E_refl = 0.6 E_dir) │
• │ ╲ │
• ────────┴─────────▼─────────────────────────────────────┴───
• Conductive Ground Surface
• The Ground Reflection Multiplication Factor

Amateur antennas are erected over real earth. At ground level or boundary fences, the total field incident upon a person is the vector sum of the direct radiated wave and one or more waves reflected from the ground plane: E ⃗ total = E ⃗ direct + E ⃗ reflected \vec{E}_{\text{total}} = \vec{E}_{\text{direct}} + \vec{E}_{\text{reflected}} E total ​ = E direct ​ + E reflected ​

In a theoretical worst-case over an infinite, perfectly conducting ground plane, the reflected wave adds in phase with the direct wave, doubling the total electric field: E total = 2.0 E direct E_{\text{total}} = 2.0 E_{\text{direct}} E total ​ = 2.0 E direct ​ .

A calculation may assume an in-phase reflected field ρ g = 0.60 \rho_g=0.60 ρ g ​ = 0.60 times the direct field. Under that assumption: E total = ( 1 + 0.60 ) E direct = 1.60 E direct E_{\text{total}}=(1+0.60)E_{\text{direct}}=1.60E_{\text{direct}} E total ​ = ( 1 + 0.60 ) E direct ​ = 1.60 E direct ​ Actual reflection magnitude and phase depend on polarization, ground and geometry. This illustrative factor does not bound every site. The free-space antenna gain must also be used consistently, without counting the same ground effect twice.

Because power density is proportional to the square of electric field strength ( S = E 2 / Z 0 S = E^2 / Z_0 S = E 2 / Z 0 ​ ): S ground = E total 2 Z 0 = ( 1.60 E direct ) 2 Z 0 = 2.56 × E direct 2 Z 0 = 2.56 × S free S_{\text{ground}} = \frac{E_{\text{total}}^2}{Z_0} = \frac{(1.60 E_{\text{direct}})^2}{Z_0} = 2.56 \times \frac{E_{\text{direct}}^2}{Z_0} = 2.56 \times S_{\text{free}} S ground ​ = Z 0 ​ E total 2 ​ ​ = Z 0 ​ ( 1.60 E direct ​ ) 2 ​ = 2.56 × Z 0 ​ E direct 2 ​ ​ = 2.56 × S free ​

Substituting the free-space power density equation yields the ground-enhanced power density formula : S ground = 2.56 × EIRP avg 4 π R 2 = 0.64 × EIRP avg π R 2 S_{\text{ground}} = 2.56 \times \frac{\text{EIRP}_{\text{avg}}}{4\pi R^2} = \frac{0.64 \times \text{EIRP}_{\text{avg}}}{\pi R^2} S ground ​ = 2.56 × 4 π R 2 EIRP avg ​ ​ = π R 2 0.64 × EIRP avg ​ ​

Formulating the Safe Separation Distance ( R safe R_{\text{safe}} R safe ​ )

To find the minimum safe boundary distance ( R safe R_{\text{safe}} R safe ​ ) where power density equals the statutory ARPANSA reference limit ( S limit S_{\text{limit}} S limit ​ ), rearrange the ground-enhanced equation: S limit = 0.64 × EIRP avg π R safe 2 ⟹ R safe = 0.64 × EIRP avg π S limit S_{\text{limit}} = \frac{0.64 \times \text{EIRP}_{\text{avg}}}{\pi R_{\text{safe}}^2} \implies R_{\text{safe}} = \sqrt{\frac{0.64 \times \text{EIRP}_{\text{avg}}}{\pi S_{\text{limit}}}} S limit ​ = π R safe 2 ​ 0.64 × EIRP avg ​ ​ ⟹ R safe ​ = π S limit ​ 0.64 × EIRP avg ​ ​ ​

Important

Under the assumed 1.6 field multiplier, power density increases 2.56 times and the modelled distance for the same limit increases 1.6 times. Check the field region and the suitability of the reflection model before treating a calculated distance as a compliance boundary.

Duty Cycle Corrections and Time-Averaged Power

Amateur radio transmitters are rated by their Peak Envelope Power (PEP) —the average power supplied to the transmission line during one radiofrequency cycle at the crest of the modulation envelope. For thermal assessment, use time-averaged power ( P avg P_{\text{avg}} P avg ​ ) over the applicable interval:30 minutes for whole-body exposure and 6 minutes for local exposure, for both occupational and public categories. Brief-exposure and instantaneous limits may also need checking.

Time-averaged power incorporates two distinct scaling factors: P avg = P PEP × D mode × D operational P_{\text{avg}} = P_{\text{PEP}} \times D_{\text{mode}} \times D_{\text{operational}} P avg ​ = P PEP ​ × D mode ​ × D operational ​

1. Mode Duty Factor ( D mode D_{\text{mode}} D mode ​ )

The mode duty factor represents the ratio of the average RF power contained in the modulated waveform to its peak envelope power:

Single Sideband (SSB) Voice (Normal / Unprocessed): Human speech consists of vowel peaks, consonants, and frequent pauses. Unprocessed conversational voice has a duty factor of approximately 20 % 20\% 20% ( 0.20 0.20 0.20 ).

SSB Voice (Heavily Processed): Utilizing aggressive RF speech clipping or digital dynamic range compression raises average syllabic power, increasing the duty factor to approximately 40 % 40\% 40% ( 0.40 0.40 0.40 ).

Continuous Wave (CW / Morse Code): A40% factor is an illustrative estimate for manual operation. Exact PARIS timing has 22 keyed units in 50 total units, giving 44%; actual messages, keying and pauses change the result.

FT8: The constant-envelope message lasts 12.6 seconds within a 15 second transmit slot, so the slot factor is 12.6/15=0.84. Alternating transmit and receive slots gives a scheduling factor 0.50 and overall duty 0.84×0.50=0.42. Do not include the receive slot in both factors. FT4 uses different timing and requires its own calculation.

Constant-Carrier Modes (FM, RTTY, SSTV, AM Carrier): Frequency modulation (FM) and radioteletype (RTTY) generate continuous, unvarying RF envelopes during key-down. Their mode duty factor is 100 % 100\% 100% ( 1.00 1.00 1.00 ).

2. Operational Transmitting-to-Listening Factor ( D operational D_{\text{operational}} D operational ​ )

During any 6 -minute 6\text{-minute} 6 -minute or 30 -minute 30\text{-minute} 30 -minute regulatory window, an operator spends time listening and transmitting. If an operator transmits for 3 minutes 3\text{ minutes} 3 minutes and listens for 3 minutes 3\text{ minutes} 3 minutes during a 6 -minute 6\text{-minute} 6 -minute averaging window: D operational = t transmit t averaging = 3 min 6 min = 0.50 ( 50 % ) D_{\text{operational}} = \frac{t_{\text{transmit}}}{t_{\text{averaging}}} = \frac{3\text{ min}}{6\text{ min}} = 0.50\quad (50\%) D operational ​ = t averaging ​ t transmit ​ ​ = 6 min 3 min ​ = 0.50 ( 50% )

Summary Table: Duty Factors and Average Power (100 W Illustration)

Emission Mode Typical Modulation Envelope Mode Duty Factor ( D mode D_{\text{mode}} D mode ​ ) Transmit/Receive Ratio (50% Tx) Net Duty Cycle ( D total D_{\text{total}} D total ​ ) Time-Averaged Power ( P avg P_{\text{avg}} P avg ​ ) for 100 W 100\text{ W} 100 W PEP

SSB Voice (Normal) Dynamic speech peaks 0.20 0.20 0.20 ( 20 % 20\% 20% ) 0.50 0.50 0.50 0.10 0.10 0.10 ( 10 % 10\% 10% ) 10 W 10\text{ W} 10 W

SSB Voice (Compressed) Clipped speech peaks 0.40 0.40 0.40 ( 40 % 40\% 40% ) 0.50 0.50 0.50 0.20 0.20 0.20 ( 20 % 20\% 20% ) 20 W 20\text{ W} 20 W

CW (Morse Code) On-off keying 0.40 0.40 0.40 ( 40 % 40\% 40% ) 0.50 0.50 0.50 0.20 0.20 0.20 ( 20 % 20\% 20% ) 20 W 20\text{ W} 20 W

FT8 Digital Mode Constant-envelope 8-GFSK in a 15 s slot 0.84 0.84 0.84 ( 84 % 84\% 84% ) 0.50 0.50 0.50 0.42 0.42 0.42 ( 42 % 42\% 42% ) 42 W 42\text{ W} 42 W

RTTY (FSK) Continuous carrier 1.00 1.00 1.00 ( 100 % 100\% 100% ) 0.50 0.50 0.50 0.50 0.50 0.50 ( 50 % 50\% 50% ) 50 W 50\text{ W} 50 W

FM Telephony Continuous carrier 1.00 1.00 1.00 ( 100 % 100\% 100% ) 0.50 0.50 0.50 0.50 0.50 0.50 ( 50 % 50\% 50% ) 50 W 50\text{ W} 50 W

Caution

This table compares waveforms at an illustrative 100 W setting. For Australian Advanced operation on the relevant ordinary bands, specified SSB emissions have a 400 W PEP limit and other emissions a 120 W mean-power limit; consult TableC for the actual band and emission.

Notice that transmitting on FM or RTTY generates 5 times greater average thermal power than uncompressed SSB voice at the same PEP setting. A station safely compliant on SSB may severely exceed ARPANSA limits if switched to FM or continuous carrier data without adjusting power or physical clearance.

Pathophysiology of Radiofrequency Burns and Induced Currents

In addition to whole-body radiated exposure, operators face direct physical hazards from high RF voltages and induced currents on metallic conductors. Resonant Half-Wave Dipole: Relative Distributions

• Open tip Centre feed Open tip
• Current minimum Current maximum Current minimum
• Voltage maximum Voltage minimum Voltage maximum
• o──────────────────────┬──────────────────────────o
• │ Feedline

A voltage minimum is not necessarily zero or safe to touch.

Keep the entire energized antenna inaccessible.

1. Standing-Wave Voltage and Feedpoint Impedance

A resonant half-wave dipole has relatively high current and low voltage near its centre, and high voltage near its open ends. These are relative distributions, not a claim that the feedpoint voltage is zero. For example, 400 W delivered to a resistive 50 ohm input gives V rms = 400 × 50 ≈ 141 V V_{\text{rms}}=\sqrt{400\times50}\approx141\text{ V} V rms ​ = 400 × 50 ​ ≈ 141 V .

At a finite, resistive end-fed input, voltage can be estimated from V rms = P R V_{\text{rms}}=\sqrt{PR} V rms ​ = PR ​ . A400 W envelope crest into 3000 ohms gives about 1095 V rms and 1550 V peak. The open tip of a centre-fed dipole is not a 3000 ohm load absorbing all transmitter power, so that calculation must not be assigned to the tip. Both low- and high-impedance parts can present contact hazards.

2. RF Contact Burns and Electrical Shock

At 50 Hz, current through the body can stimulate nerves and muscles and disrupt heart rhythm. At HF and VHF the principal RF contact hazard is localized heating. This does not make all radiofrequency contact safe: RPS S-1 also sets restrictions against electrostimulation from 100 kHz to 10 MHz.

Contact with an energized antenna, feedline or metal object can concentrate current into a small area. Current density is J = I / A J=I/A J = I / A , and resistive heating increases with I 2 R I^2R I 2 R . High local absorption can cause serious burns; arcing may also occur. Severity depends on the current path, contact area, exposure duration and frequency, rather than a fixed voltage or a guaranteed painless onset.

Prevent access to energized antennas and exposed RF connections, isolate transmitters before work, and control induced currents on nearby metalwork. Do not test safety by touching a conductor or waiting for pain. RF exposure assessment and prevention of contact burns are complementary precautions.

• Step-by-Step Worked Calculations
• Worked Example 1: Check a Far-Field Calculation Before Using Its Distance

An Advanced station operates compressed SSB at 400 W 400\text{ W} 400 W PEP on 14.150 MHz 14.150\text{ MHz} 14.150 MHz . Assume mode factor 0.40 0.40 0.40 , transmit/listen factor 0.50 0.50 0.50 , negligible feedline loss and Yagi gain 7.5 dBi 7.5\text{ dBi} 7.5 dBi . Its largest dimension is D = 11 m D=11\text{ m} D = 11 m . For illustration, assume an in-phase reflected field 0.60 0.60 0.60 times the direct field; this gives a 1.6 1.6 1.6 field multiplier, not a universal site bound.

Calculate average power and EIRP.

Find the applicable whole-body public E/H reference levels.

Calculate the distance suggested by the assumed plane-wave model, then check whether that distance is in the far field.

Step 1: Average power and EIRP G = 10 7.5 / 10 ≈ 5.623 , P avg = 400 × 0.40 × 0.50 = 80 W G=10^{7.5/10}\approx5.623,\qquad P_{\text{avg}}=400\times0.40\times0.50=80\text{ W} G = 1 0 7.5/10 ≈ 5.623 , P avg ​ = 400 × 0.40 × 0.50 = 80 W EIRP avg = 80 × 5.623 ≈ 449.84 W \text{EIRP}_{\text{avg}}=80\times5.623\approx449.84\text{ W} EIRP avg ​ = 80 × 5.623 ≈ 449.84 W

Use the maximum relevant 30-minute whole-body average. The 6-minute local and other applicable conditions also need checking.

Step 2: Current HF reference levels

From RPS S-1 Table 4, with f M = 14.15 f_M=14.15 f M ​ = 14.15 : E public = 300 14.15 0.7 ≈ 46.95 V/m , H public = 2.2 14.15 ≈ 0.1555 A/m E_{\text{public}}=\frac{300}{14.15^{0.7}}\approx46.95\text{ V/m},\qquad

H_{\text{public}}=\frac{2.2}{14.15}\approx0.1555\text{ A/m} E public ​ = 14.1 5 0.7 300 ​ ≈ 46.95 V/m , H public ​ = 14.15 2.2 ​ ≈ 0.1555 A/m

There is no incident-power-density reference level in this HF row. In a valid plane-wave model only, one may convert an E-field calculation using S eq = E 2 / 377 S_{\text{eq}}=E^2/377 S eq ​ = E 2 /377 .

Step 3: Calculate a candidate distance and test the method

With the assumed reflection multiplier, the model gives: E ( R ) = 1.6 30 EIRP avg R E(R)=\frac{1.6\sqrt{30\,\text{EIRP}_{\text{avg}}}}{R} E ( R ) = R 1.6 30 EIRP avg ​ ​ ​

Setting E ( R ) = 46.95 V/m E(R)=46.95\text{ V/m} E ( R ) = 46.95 V/m suggests R ≈ 3.96 m R\approx3.96\text{ m} R ≈ 3.96 m . This is a model output, not yet a safe separation distance. λ = 300 14.15 ≈ 21.20 m , 2 D 2 λ = 2 × 11 2 21.20 ≈ 11.41 m , 0.5 λ ≈ 10.60 m \lambda=\frac{300}{14.15}\approx21.20\text{ m},\qquad

\frac{2D^2}{\lambda}=\frac{2\times11^2}{21.20}\approx11.41\text{ m},\qquad

0.5\lambda\approx10.60\text{ m} λ = 14.15 300 ​ ≈ 21.20 m , λ 2 D 2 ​ = 21.20 2 × 1 1 2 ​ ≈ 11.41 m , 0.5 λ ≈ 10.60 m

The suggested 3.96 m is inside the class-licence far-field boundary of 11.41 m. Therefore this inverse-square calculation cannot establish the required separation there. Use a suitable near-field assessment or change the installation and reassess; do not declare 3.96 m safe.

For comparison, at 30 m the stated geometry is in the far field. The assumed model gives E ≈ 6.20 V/m E\approx6.20\text{ V/m} E ≈ 6.20 V/m and H = E / 377 ≈ 0.0164 A/m H=E/377\approx0.0164\text{ A/m} H = E /377 ≈ 0.0164 A/m , below the whole-body public values. That conclusion depends on the stated operating pattern, gain and reflection model; a real station assessment must cover accessible locations, other applicable limits and simultaneous sources.

Worked Example 2: RF Voltage at an End-Fed Half-Wave Feedpoint

An amateur uses SSB on 7.100 MHz 7.100\text{ MHz} 7.100 MHz ( 40 -metre 40\text{-metre} 40 -metre band) at 400 W 400\text{ W} 400 W PEP into an end-fed half-wave antenna. Calculate the RF-cycle rms voltage at the crest of the modulation envelope, where P = 400 W P=400\text{ W} P = 400 W . The impedance matching transformer presents an impedance of R end = 3200 Ω R_{\text{end}} = 3200\ \Omega R end ​ = 3200 Ω at the antenna wire feedpoint.

Calculate the RMS RF voltage present at the wire feedpoint.

Calculate the peak RF voltage ( V peak V_{\text{peak}} V peak ​ ).

Assess the physical contact burn hazard.

Step 1: Calculate RMS voltage: V RMS = P × R end = 400 W × 3200 Ω = 1 , 280 , 000 ≈ 1131.4 V V_{\text{RMS}} = \sqrt{P \times R_{\text{end}}} = \sqrt{400\text{ W} \times 3200\ \Omega} = \sqrt{1,280,000} \approx 1131.4\text{ V} V RMS ​ = P × R end ​ ​ = 400 W × 3200 Ω ​ = 1 , 280 , 000 ​ ≈ 1131.4 V

Step 2: Calculate peak voltage: V peak = V RMS × 2 = 1131.4 V × 1.4142 ≈ 1600 V V_{\text{peak}} = V_{\text{RMS}} \times \sqrt{2} = 1131.4\text{ V} \times 1.4142 \approx 1600\text{ V} V peak ​ = V RMS ​ × 2 ​ = 1131.4 V × 1.4142 ≈ 1600 V

Step 3: Hazard assessment:

The calculated 1600 V peak indicates a serious contact and possible arcing hazard. It does not determine a universal spark distance or burn depth. Keep the wire, transformer and all energized connections inaccessible during operation, isolate the transmitter before work, and assess radiated exposure separately. A single mounting height does not establish safety for every installation.