EIRP / ERP and Field Strength (with Antenna Gain)

EIRP and ERP from transmitter power, cable loss and antenna gain, plus the free-space field strength at a chosen distance.

Worked example

Input: Transmitter output 30 dBm, Cable and connector loss 2 dB, Antenna gain 6 dB, Gain reference dBi (isotropic), Distance 3 m
Result: EIRP 34 dBm, EIRP 2.51189 W, ERP 31.85 dBm, Field strength E (free space) 2.89361 V/m, Field strength E 129.229 dBµV/m

Formula

EIRP [dBm] = transmitter output − loss + antenna gain [dBi]

dBi = dBd + 2.15, ERP = EIRP − 2.15 dB (half-wave dipole gain is 2.15 dBi)

E [V/m] = √(30 · EIRP[W]) / r (free space, no reflections)

How it works

EIRP is the effective radiated power referenced to an isotropic antenna: transmitter output minus losses plus the antenna gain in dBi. ERP is referenced to a half-wave dipole and is therefore 2.15 dB lower, which is the same reason dBi = dBd + 2.15. In free space the field strength at distance r is E = √(30·EIRP[W])/r. With the example values (30 dBm, 2 dB loss, 6 dBi, 3 m) the EIRP is 34 dBm (2.51 W) and the field strength about 2.89 V/m (129.2 dBµV/m).

Practical tipThe field strength is the free-space value with no reflections. On a test site with a ground plane the direct and reflected waves can add to twice the amplitude (+6 dB). Use this to size the power needed for a radiated immunity level, then calibrate the actual level with a field probe. With 80 % AM the amplifier needs 3.24 times the peak power (+5.1 dB).

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Results and summaries are for reference. For certification and test reports use the latest official standard text and calibrated instrument data. Last updated: 2026-10-10