Calculating EIRP (Effective Isotropic Radiated Power)

EIRP (Effective Isotropic Radiated Power) is the measured radiated power of an antenna in a specific direction. It is also called Equivalent Isotropic Radiated Power. It is the output power when a signal is concentrated into a smaller area by the Antenna. The EIRP can take into account the losses in transmission line, connectors and includes the gain of the antenna. It is represented in dB. Enter the transmitted power, cable loss and antenna gain to calculate the EIRP (Effective Isotropic Radiated Power).

Radio communication systems must comply with specific rules established by regulatory bodies, such as the Federal Communications Commission (FCC) in the US or the European Telecommunications Standards Institute (ETSI) in Europe. One rule is that radio equipment must not exceed certain EIRP values.

The effective isotropic radiated power is calculated according to the following EIRP calculation formula:

The formula for EIRP is:

EIRP = T_{x} - L_{c} + G_{a}

Where:

T_x is the output power of the transmitter (in dBmW).
L_c is the sum of cable and connector losses (if present) (in dB).
G_a is the antenna gain (in dBi).

As you can see from the formula, EIRP considers the losses in the transmission cables and connectors and includes the antenna gain. It is often expressed in decibels relative to a reference power emitted by an isotropic antenna with equivalent signal power.

Example

Calculating EIRP

EIRP (Effective Isotropic Radiated Power) is a measure of the power radiated by an antenna, accounting for both the transmitter power and antenna gain. It is an essential parameter in determining the signal strength and coverage area in radio communications.

The general approach to calculating EIRP includes:

Identifying the transmitter power and antenna gain.
Knowing the units of power and gain (e.g., watts and dBi).
Applying the formula for EIRP to calculate the result.

EIRP Formula

The general formula for EIRP is:

EIRP = P_{t} \times G_{t}

Where:

P_t is the transmitter power (in watts, W).
G_t is the antenna gain (in dBi, decibels relative to an isotropic radiator).

Example:

If a transmitter has a power of 10 W and an antenna gain of 15 dBi, the EIRP is:

Step 1: Identify the transmitter power and antenna gain: $P_{t} = 10 W$ , $G_{t} = 15 dBi$ .
Step 2: Multiply the power by the gain: $EIRP = 10 \times 15 = 150 W$ .

EIRP with Power in dBm

If the transmitter power is given in dBm (decibels milliwatt), it must be converted to watts before applying the EIRP formula.

Example:

If the transmitter power is 40 dBm and the antenna gain is 20 dBi, the steps are:

Step 1: Convert the transmitter power from dBm to watts: $P_{t} (W) = 10^{(40 - 30) / 10} = 100 W$ .
Step 2: Multiply by the antenna gain: $EIRP = 100 \times 20 = 2000 W$ .

Real-life Applications of EIRP

Calculating EIRP is crucial in many real-life scenarios such as:

Optimizing signal coverage and reach in wireless networks (e.g., Wi-Fi and cellular networks).
Designing satellite communications to ensure proper signal strength.
Radio broadcasting and determining the strength of broadcasted signals.

Common Units for EIRP

SI Unit: The standard unit for EIRP is watts (W), though dBm is often used in radio communications to express power levels.

Common Operations with EIRP

Amplifying EIRP: Increasing the power or gain increases the EIRP, resulting in a stronger signal.

Reducing EIRP: Decreasing the power or antenna gain will reduce the EIRP, limiting the signal coverage.

Calculating Maximum EIRP: Ensuring that the EIRP does not exceed regulatory limits for safe radiofrequency exposure.

Calculating EIRP Examples Table
Problem Type	Description	Steps to Solve	Example
Calculating EIRP from Transmitter Power	Finding the EIRP when given the transmitter power and antenna gain.	Identify the transmitter power ( $P_{t}$ ) in watts and the antenna gain ( $G_{t}$ ) in dBi. Use the formula for EIRP: $EIRP = P_{t} \times G_{t}$ .	For a transmitter with $P_{t} = 10 W$ and $G_{t} = 15 dBi$ , the EIRP is $EIRP = 10 \times 15 = 150 W$ .
Calculating EIRP from Power in dBm	Converting the transmitter power from dBm to watts and then calculating the EIRP.	Convert the transmitter power from dBm to watts using the formula $P_{t} (W) = 10^{(P_{t} (dBm) - 30) / 10}$ . Use the formula for EIRP: $EIRP = P_{t} \times G_{t}$ .	If the transmitter power is $P_{t} = 40 dBm$ and the antenna gain is $G_{t} = 20 dBi$ , first convert $P_{t} = 40 dBm$ to watts, then calculate EIRP as $EIRP = P_{t} (W) \times G_{t}$ .
Calculating EIRP with Antenna Gain Adjustment	Finding the EIRP when adjusting the antenna gain or input power.	Identify the transmitter power ( $P_{t}$ ) and the antenna gain ( $G_{t}$ ). Adjust the antenna gain and recalculate EIRP accordingly.	If the transmitter power is $P_{t} = 5 W$ and the antenna gain is $G_{t} = 10 dBi$ , the EIRP will change with an increase in gain. For example, increasing $G_{t}$ to $15 dBi$ will result in a higher EIRP value.
Real-life Applications	Applying EIRP in practical situations like radio communication, satellite transmission, and network design.	To calculate signal strength in radio waves. To determine transmission power for optimizing signal reach.	If a radio station transmits with a power of $P_{t} = 100 W$ and an antenna gain of $G_{t} = 30 dBi$ , use the EIRP formula to estimate the effective radiated power in the station's broadcast area.