# Friis Transmission Equation Calculator

### Input

 Power Transmitted $$P_{r}$$ milliwattwattdBmdBW Transmitter Gain $$G_{t}$$ dBidBd Receiver Gain $$G_{r}$$ dBidBd Wavelength* $$\lambda$$ millimetercentimetermeterkilometer Distance $$d$$ millimetercentimetermeterkilometer
*For wavelength from the frequency calcuations use Frequency to Wavelength.

### Output

 Power at receiver antenna $$P_{r}$$ ____ milliwattwattdBmdBW Free Space Path Loss $$FSPL$$ ____ milliwattwattdBmdBW ### Friis Transmission Equation

Consider the RF Transmitting and Receiving system as shown in the figure above. The Friis transmission equation could be used to estimate the ideal power received by the Rx antenna of such communication systems. Antenna alignment, polarization matching, and antennas being in the far-field zone are the optimal conditions needed to be considered. Bandwidth is narrow enough to base the calculations as single wavelength. RF Link Budget calculations is one of the important applications of Friis transmission equation. The relation between EIRP of the transmitting antenna, Effective aperture area of the receiving antenna and the Friis Transmission Equation could be found in EIRP ERP Calculator

## Formula

$$P_{r} = P_{t}G_{t}G_{r}\left (\frac{\lambda }{4 \pi d } \right )^2$$

$$FSPL =\left (\frac{4 \pi d }{\lambda} \right )^2$$

 Where: $$P_{r}$$ = Power Received in watt $$P_{t}$$ = Power Transmitted in watt $$G_{t}$$ = Gain of Transmitter Antenna $$G_{r}$$ = Gain of Receiver Antenna $$\lambda$$ = Wavelength in meter $$d$$ = Distance between TX and RX antenna in meter $$FSPL$$ = Free Space Path Loss
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