bawdsey

034

The power Pr returning to the receiving antenna is given by the equation:

P_r = {{P_t G_t A_r \sigma F^4}\over{{(4\pi)}^2 R_t^2R_r^2}}

where

  • Pt = transmitter power
  • Gt = gain of the transmitting antenna
  • Ar = effective aperture (area) of the receiving antenna; this can also be expressed as {G_r\lambda^2}\over{4\pi}, where
  • \lambda = transmitted wavelength
  • Gr = gain of receiving antenna
  • σ = radar cross section, or scattering coefficient, of the target
  • F = pattern propagation factor
  • Rt = distance from the transmitter to the target
  • Rr = distance from the target to the receiver.

In the common case where the transmitter and the receiver are at the same location, Rt = Rr and the term Rt² Rr² can be replaced by R4, where R is the range. This yields:

P_r = {{P_t G_t A_r \sigma F^4}\over{{(4\pi)}^2 R^4}}.

This shows that the received power declines as the fourth power of the range, which means that the received power from distant targets is relatively very small.

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