Friis Transmission Equation - Modifications To The Basic Equation

Modifications To The Basic Equation

The effects of impedance mismatch, misalignment of the antenna pointing and polarization, and absorption can be included by adding additional factors; for example:

\frac{P_r}{P_t} = G_t(\theta_t,\phi_t) G_r(\theta_r,\phi_r) \left( \frac{\lambda}{4 \pi R} \right)^2 (1-|\Gamma_t|^2) (1-|\Gamma_r|^2) |\mathbf{a}_t \cdot \mathbf{a}_r^*|^2 e^{-\alpha R}

where

  • is the gain of the transmit antenna in the direction in which it "sees" the receive antenna.
  • is the gain of the receive antenna in the direction in which it "sees" the transmit antenna.
  • and are the reflection coefficients of the transmit and receive antennas, respectively
  • and are the polarization vectors of the transmit and receive antennas, respectively, taken in the appropriate directions.
  • is the absorption coefficient of the intervening medium.

Empirical adjustments are also sometimes made to the basic Friis equation. For example, in urban situations where there are strong multipath effects and there is frequently not a clear line-of-sight available, a formula of the following 'general' form can be used to estimate the 'average' ratio of the received to transmitted power:

where is experimentally determined, and is typically in the range of 3 to 5, and and are taken to be the mean effective gain of the antennas. However, to get useful results further adjustments are usually necessary resulting in much more complex relations, such the Hata Model for Urban Areas.

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