E9A

Gain, ERP and antenna efficiency

Convert dBi and dBd, calculate ERP and EIRP, and explain what makes an antenna efficient.

12 pool questions1 on the exam

Syllabus: Basic antenna parameters: radiation resistance, gain, beamwidth, efficiency; effective radiated power (ERP) and effective isotropic radiated power (EIRP)

dBi and dBd differ by 2.15 dB

An isotropic radiator is a hypothetical, lossless antenna with equal radiation intensity in all directions. It is the zero point of dBi. dBd uses a half-wave dipole as zero instead, and a dipole is already +2.15 dBi.

Same antenna, same point on the line. The dBd ruler is just the dBi ruler slid by 2.15 dB.

Antenna gain (dBi)6 dBi

ConvertdBi = dBd + 2.15 dBd = dBi − 2.15

RememberThe dBd number is always the smaller one: 6 dBi = 3.85 dBd.

ERP and EIRP: add the dB, then convert once

Effective radiated power is the power actually radiated in the beam direction, counting all gains and losses between transmitter and antenna. Gain referenced to a dipole (dBd) gives ERP. Gain referenced to isotropic (dBi) gives EIRP.

Total the dB first (gain +, loss −), then multiply power by 10^(dB ÷ 10).

Add every gain and loss in dB first. Convert to watts once, at the end.

Example

Gain reference

Transmitter power150 WFeed line loss2.0 dBDuplexer loss2.2 dBCirculator loss0.0 dBAntenna gain7 dBd

Example	Net dB	Result
150 W; −2, −2.2, +7 dBd	+2.8	×1.905 = 286 W ERP
200 W; −4, −3.2, −0.8, +10 dBd	+2.0	×1.585 = 317 W ERP
200 W; −2, −2.8, −1.2, +7 dBi	+1.0	×1.259 = 252 W EIRP

RememberNet dB → ×ratio. dBd → ERP. dBi → EIRP.

Efficiency is the share of resistance that radiates

Current in an antenna meets two resistances in series: radiation resistance (power that leaves as radio waves) and loss resistance (wire, coil, ground: heat). Power splits in proportion.

The same current flows through both resistances, so power splits in proportion to resistance.

Ground-mounted ¼ wave vertical

Radiation resistance36 ΩLoss resistance12 Ω

Efficiencyradiation resistance ÷ (radiation + loss) = radiation resistance ÷ total resistance

For a ground-mounted vertical the biggest loss is the ground. A radial system lowers that loss, and soil conductivity sets how much there is. Shortening the element lowers radiation resistance, so it hurts efficiency.

RememberRaise radiation resistance, cut loss resistance: radials help, shortening hurts.

The ground is part of the antenna

Ground reflections add to the direct signal. That increase in signal strength is ground gain. The same nearby ground also changes the feed point impedance: it depends on antenna height, not on the feed line length, tuner or power.

Ground is part of the antenna: its reflection adds signal, and its distance changes the feed point impedance.

RememberGround gain = reflections adding. Height changes feed point impedance.

Higher frequency, thinner Fresnel zone

The first Fresnel zone is the football-shaped volume around the line of sight that should stay clear for a good link. Its radius grows with wavelength, so the highest frequency has the smallest zone.

Fresnel zone radius at mid-path = ½ √(λ × distance). Shorter wavelength, thinner zone.

RememberShortest wavelength, smallest zone: 5.8 GHz of the choices.

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Compendium articles on the ideas in this lesson, beyond what the exam asks.

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Practise the 12 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".

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