What is Total Radiated Power (TRP)?

Total Radiated Power (TRP) is a fundamental metric in RF engineering used to quantify the total amount of power an antenna radiates into free space when it is driven by a transmitter. Instead of looking at how much power the transmitter delivers to the antenna, TRP focuses entirely on how much of that power ultimately leaves the antenna as useful radiation. It consolidates the antenna’s performance in all directions and across all polarizations, giving engineers a complete picture of its radiated output. TRP is one of the most critical measurements in modern RF design and product validation.

The formal equation for Total Radiated Power (TRP) comes directly from its physical definition - the sum of radiated power in all directions, giving the total power the antenna sends into free space. 

Where:

• P_rad (θ,ϕ) = radiated power density (W/sr) at direction (θ,ϕ)(\theta, \phi)(θ,ϕ)
• The integration covers the entire sphere around the antenna
• sin⁡θ dθ dϕ = differential solid angle dΩ
  
  

A simplified version of TRP can be computed from discrete samples using the following equation:

Where:

• P_i= measured power at sample point iii
• ΔΩ_i = solid angle weight for that sample
• N = number of angular samples

This is the equation used in CTIA/Wi-Fi OTA certification.

Relation of Antenna Efficiency and TRP

TRP is also directly linked to antenna efficiency. Efficiency represents how effectively an antenna converts input electrical power into radiated electromagnetic power.

Where:

• P_in is the power delivered to the antenna
• P_out is the total radiated power (TRP)

TRP is expressed in terms of power: Watts (W), milliwatts (mW), or the logarithmic terms for W and mW (dBW and dBm). Antenna efficiency is expressed either in percentage or dB. A higher TRP indicates that a greater portion of the transmitter’s power is successfully radiated, implying better antenna efficiency.

How do you measure TRP?

TRP measurements are carried out on an antenna test range, most commonly inside an anechoic chamber, which provides a controlled RF environment free from reflections and external interference.

Step 1: Stimulating the Device - The transmitter under test (e.g., a cellular module or WLAN chipset) is activated so that it delivers RF power to the antenna.

Step 2: Sampling Radiation in All Directions - The measurement system captures radiated power at many points surrounding the device - Typically every 5° to 30° in elevation and azimuth. Measurements include both vertical and horizontal polarization components. This creates a dense spherical sampling grid around the antenna.

Step 3: Integrating the Data - All measured power values around the sphere are mathematically combined to estimate the total power radiated in all directions and the device’s omnidirectional performance, independent of orientation.

TRP is a mandatory requirement in many wireless certification programs. It is thoroughly defined in the CTIA Over-the-Air (OTA) Certification Test Plan.