# TRP vs EIRP

Total radiated power (TRP) is the total power radiated by an antenna. It is a function of the output power from the transmitter and the antenna efficiency. As the antenna efficiency decreases, the amount of radiated power decreases. The most efficient antenna will radiate all the power that’s provided at its input.

Effective Isotropic Radiated Power (EIRP) [1] is the power that would have to be radiated by an isotropic antenna [2] to provide the same signal level as the actual source antenna in the direction of the antenna’s strongest beam.

## Formula

Total radiated power in dBm is given by

TRPdBm = PTxdBm + ηdB

where,

• PTxdBm is the power output from the transmitter
• ηdB is the antenna efficiency

The antenna efficiency in linear terms is η = G/D where

• G is the antenna gain
• D is the directivity

The Total radiated power is then given by

TRPdBm = EIRPdBm – DdB

EIRP is always greater than TRP.

## Example Calculation

The directivity of an Omni Directional antenna is 0 dB. For this antenna the Total Radiated Power is equal to the Effective Isotropic Radiated Power.

For EIRP = 10 dBm and D = 5 dB, TRP = 5 dBm.

## Background

### What is EIRP?

Effective Isotropic Radiated Power (EIRP) is the power that would have to be radiated by an isotropic antenna to provide the same signal level as the actual source antenna in the direction of the antenna’s strongest beam.

The mathematical expression for EIRP is

EIRP = PTx – LC + GAnt

where

• PTx is the Transmit Power (dBm)
• GAnt is the Antenna gain (dBi)
• LC is the Cable Loss (dB)

### What is Directivity?

Directivity is an antenna parameter of an which measures the degree to which the radiation emitted is concentrated in a single direction [3].

According to the IEEE, Directivity is the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

The directivity of an isotropic antenna is therefore 0 dBi as it is an ideal antenna that radiates equally in all directions.

???? In the units for directivity, if the unit is dB instead of dBi, it’s important to verify what the reference antenna is. This could be isotropic or a dipole for instance. In this case dBi or dBd should be used to differentiate between the two.

A dish antenna is highly directive with a gain of 50 dBi. In this case, the TRP is significantly lower than the EIRP as according to the formula

TRPdBm = EIRPdBm – DdB

In this case if the EIRP is +10 dBm, the TRP is -40 dBm.

## References

[1] Wikipedia article on EIRP and how it relates to transmit power

[2] Wikipedia article on Isotropic Antennas

[3] Wikipedia article on Directivity