Effective Isotropic Radiated Power

Effective isotropic radiated power, usually written EIRP, is the power an ideal isotropic antenna would need to radiate to produce the same power density in the direction of maximum radiation as the real transmitting system. It folds together conducted transmitter power, losses before the antenna and transmit antenna gain.

The important boundary is the antenna radiation reference. EIRP is not the radio output power printed in a configuration screen. It is not received power at the far end. It is not link margin. It is a transmitter-side quantity used to connect the physical installation to path loss, interference risk, coordination limits and regulatory approval.

Decibel Formula

In the common dB convention:

where:

• P_t is conducted transmitter output power at the chosen reference plane;
• L_t includes cable, connector, filter, waveguide, lightning-arrestor, combiner or implementation losses before radiation;
• G_t is transmit antenna gain relative to an isotropic radiator.

For satellite or high-power link budgets, the same value may be expressed in dBW:

The gain unit matters. Antenna gain in dBi is referenced to an isotropic radiator. Gain in dBd is referenced to a half-wave dipole and must not be inserted as if it were dBi without conversion.

Linear Form

In linear units:

This form makes the physical meaning visible: losses reduce radiated equivalent power, while directional antenna gain concentrates radiation in the main direction. The antenna does not create power. It redistributes radiation spatially, so EIRP is also tied to pointing, polarization, installation effects and the direction being evaluated.

Regulatory Headroom

Many wireless systems have an EIRP limit set by a license, standard, site coordination agreement or national regulation. A simple headroom check is:

A positive margin means the calculated configuration is below the reviewed EIRP limit. That does not prove good engineering performance. It only says the transmitter-side radiated-power quantity is inside the stated boundary. The link may still fail because of path loss, Fresnel obstruction, receiver sensitivity, interference, fading or insufficient service margin.

Worked Example

A microwave radio is configured for:

• transmitter output power P_t=23 dBm;
• feeder, connector and protection losses L_t=2.5 dB;
• directional antenna gain G_t=14 dBi;
• reviewed EIRP limit 36 dBm.

The EIRP is:

The regulatory headroom is:

The configuration is below the stated EIRP limit, but the margin is small. A later firmware power increase, replacement antenna, shorter cable run or lower-loss lightning protector could push the installation over the limit unless the calculation is repeated.

If the same link has receive antenna gain 18 dBi, path loss 129.3 dB and receiver-side implementation loss 1.5 dB, the predicted received power is:

If receiver sensitivity for the selected mode is -91 dBm, the sensitivity margin is:

This shows why EIRP is only one part of the review. The transmitter is legal under the stated limit, and the link closes against sensitivity in this simplified screen, but the result still needs fade, interference, Fresnel, availability and measurement allowances.

Relation To Link Budgets

EIRP usually enters a link budget as the starting transmitter-side term:

For satellite or long-range links, it may also feed a carrier-to-noise-density calculation:

These equations are useful only when the reference planes are explicit. A vendor transmitter setting, a radio-management RSSI value and a regulatory EIRP limit do not share the same boundary. Mixing them without loss accounting creates false link margins and compliance errors.

Validation Evidence

A defensible EIRP record states transmitter model, configured output power, measured or specified conducted output, cable type and length, connector losses, filters, lightning arrestors, waveguide or combiner losses, antenna model, antenna gain reference, polarization, alignment state, frequency, channel bandwidth, regulatory limit and uncertainty allowance. For critical systems, keep the configuration export, antenna data sheet, installed cable loss estimate, field photos and any conducted or radiated measurement record.

The evidence should also say whether the limit applies to peak power, average power, occupied bandwidth, duty cycle, antenna sector, polarization or spatial direction. Without that boundary, an EIRP number can look precise while failing the actual coordination rule.

Common Mistakes

Common mistakes include using transmitter output power as EIRP, forgetting feeder loss, adding antenna gain with the wrong reference, mixing dBm and dBW, treating a legal EIRP as proof of link reliability, ignoring antenna misalignment or polarization mismatch, increasing power to fix interference, and failing to repeat the calculation after hardware substitutions.

The practical rule is to calculate EIRP at the transmitter boundary, compare it with the correct limit, then pass the value into the path, receiver and service-margin calculations. It should be auditable enough that another engineer can reproduce both the compliance result and the link-budget result.