# EIRP ERP Calculator

### EIRP

Effective Isotropic Radiated Power (or Equivalent Isotropic Radiated Power) is the power that would have to be radiated by an isotropic antenna to provide same signal level as the actual transmitting antenna in the direction of main lobe. EIRP determines the peak power density transmitted by the tranmsitter.
Note: Cable losses and connector attenuation has to be considered while calculating the EIRP. One could observe EIRP plays important parameter in the link budget calculations using Friis Transmission Equation.

EIRP without account for cable loss and other losses is given by

\(EIRP= P_{Tx} \cdot G_{Tx}\)

### EIRP, Effective Aperture Area and Friis Transmission Equation Relationship

Effective aperture area of receiver antenna is given by

\(A_{e} = \frac{G_{Rx} }{4 \pi } \lambda^2\)
Friis Transmission Equation
\(P_{Rx} = P_{Tx}\cdot G_{Tx} \cdot G_{Rx}\left (\frac{\lambda }{4 \pi d } \right )^2\)
Therefore the relation between EIRP of the transmitting antenna and Effective aperture area of the receiving antenna in the Friis Transmission Equation could be expressed as follows:

\(P_{Rx} = \left (\frac{EIRP \cdot A_{e} }{4 \pi d^2 } \right )\)
### ERP

Effective Radiated Power is the power that would have to be radiated by a dipole antenna to provide same signal level as the actual transmitting antenna in the direction of main lobe. EIRP determines the peak power density transmitted by the tranmsitter.
Note: Cable losses has to be considered while calculating the ERP.

EIRP and ERP is related by:
\(ERP (dBm)= EIRP (dBm) - 2.15 \)

## Formula

\(EIRP (dBm)= P_{Tx}(dBm) - L_{Tx}(dB) + G_{Tx}(dBi)\)

\(ERP (dBm)= P_{Tx}(dBm) - L_{Tx}(dB) + G_{Tx}(dBd)\)

Where: |

\(EIRP\) = Effective Isotropic Radiated Power |

\(ERP\) = Effective Radiated Power |

\(A_{e}\) = Effective Aperture Area in meter^2 |

\(P_{Tx}\) = Power Transmitted in watt |

\(P_{Rx}\) = Power Received in watt |

\(G_{Tx}\) = Gain of Transmitter Antenna with reference to Isotropic Antenna \((dBi)\) or Dipole Antenna \((dBd)\) |

\(G_{Rx}\) = Gain of Receiver Antenna |

\(\lambda \) = Wavelength in meter |

\(d\) = Distance between TX and RX antenna in meter |

\(L_{Tx}\) = Cable Loss |

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