Friis Equation formula |
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| \( P_r \;=\; P_t \cdot G_t \cdot G_r \cdot \left( \dfrac{ \lambda }{ 4 \cdot \pi \cdot R } \right)^2 \) | ||
| Symbol | English | Metric |
| \( P_r \) = Power Available at Receiving Antenna Output Terminals | \(W\) | \(W\) |
| \( P_t \) = Power Fed into the Transmitting Antenna Input Terminal | \(W\) | \(W\) |
| \( G_t \) = Gain of Transmitting Antenna | \(dimensionless\) | \(dimensionless\) |
| \( G_r \) = Gain of Receiver Antenna | \(dimensionless\) | \(dimensionless\) |
| \( \lambda \) (Greek Symbol lambda) = Wavelength of the Radio Frequency | \(ft\) | \(m\) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( R \) = Distance between Antennas | \(ft\) | \(m\) |
Friis equation, abbreviated as \( P_r \), also called Friis transmission formula, is a fundamental equation in telecommunications that relates the power received by one antenna to the power transmitted by another antenna over a line-of-sight path. It helps determine how much power is successfully transmitted from a source to a receiver through free space. The Friis equation assumes ideal conditions with no obstructions, reflections, or atmospheric losses, making it useful for estimating the maximum theoretical power received in free-space communication links such as satellite, microwave, or radio transmissions.
Friis Equation formula |
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| \( P_r \;=\; \dfrac{ P_t \cdot G_t \cdot G_r \cdot \lambda^2 }{ \left( 4 \cdot \pi \cdot R \right)^2 } \) | ||
| Symbol | English | Metric |
| \( P_r \) = Power Available at Receiving Antenna Output Terminals | \(W\) | \(W\) |
| \( P_t \) = Power Fed into the Transmitting Antenna Input Terminal | \(W\) | \(W\) |
| \( G_t \) = Gain of Transmitting Antenna | \(dimensionless\) | \(dimensionless\) |
| \( G_r \) = Gain of Receiver Antenna | \(dimensionless\) | \(dimensionless\) |
| \( \lambda \) (Greek Symbol lambda) = Wavelength of the Radio Frequency | \(ft\) | \(m\) |
| \( \pi \) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( R \) = Distance between Antennas | \(ft\) | \(m\) |
Friis Equation (Simplified Form) formula |
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| \( \dfrac{ P_r }{ P_t } \;=\; \dfrac{ A_t \cdot A_r }{ \lambda^2 \cdot R^2 } \) | ||
| Symbol | English | Metric |
| \( P_r \) = Power Available at Receiving Antenna Output Terminals | \(W\) | \(W\) |
| \( P_t \) = Power Fed into the Transmitting Antenna Input Terminal | \(W\) | \(W\) |
| \( A_t \) = Effective Aperture Area of the Transmitting Antenna | \(ft^2\) | \(m^2\) |
| \( A_r \) = Effective Aperture Area of the Receiving Antenn | \(ft^2\) | \(m^2\) |
| \( \lambda \) (Greek Symbol lambda) = Wavelength of the Radio Frequency | \(ft\) | \(m\) |
| \( R \) = Distance between Antennas | \(ft\) | \(m\) |