Friis Transmission Calculator
Enter the Tx Power, Tx Gain, Rx Gain, Wavelength and the Distance to calculate the power received at the antenna.
Calculate the Power Received by the Receiver
![Frequency to Wavelength Calc.](http://cdn.everythingrf.com/live/calculator.png)
Result
Power Received (dBm):
Power Received (W):
Formula for Friis Transmission Calculator
The Friis transmission equation gives the power received by an antenna from another antenna that is transmitting a known amount of power at a distance under ideal conditions. The formula was derived by Herald T. Friis at Bell Labs in 1945.
The Derivation of the Formula can be seen below:
Assumption: Assume that the Transmitting antenna sends out a power (Pt). We assume that the transmit antenna is omni-directional, lossless and that the receive antenna is in the far field.
Step 1: The Power Density of the plane wave incident on the receive antenna which is at a distance ® from the transmitting antenna, can be calculated by:
![power density](http://cdn.everythingrf.com/live/power_density.PNG)
Step 2: We assume that the transmit antenna has a gain (Gt), then the power density becomes:
![Power Density with Gain](http://cdn.everythingrf.com/live/power_density_gain.PNG)
Step 3: We assume that the receive antenna has an effective aperture of Ae. Then the power received by the receive antenna is (Pr):
![Power Received](http://cdn.everythingrf.com/live/power_received.PNG)
Step 4: The Effective Antenna Aperture Ae, can also be defined as:
![Antenna Aperture](http://cdn.everythingrf.com/live/antenna_aperture.PNG)
Step 5: The Final formula for the power received at the antenna can be denoted by the Friis Transmission Equation:
![Friis Equation Wavelength](http://cdn.everythingrf.com/live/power_rec_wavelength.PNG)
OR – If you prefer to use frequency over wavelength
![Friis Equation Frequency](http://cdn.everythingrf.com/live/power_rec_freq.PNG)
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