Question

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away having radar cross-section of 3 m². If it transmits 100 kW, then the received power (in μW) is __________

Answer 1

Concept:

Form the radar equation, the received power is given by:

\({{\rm{P}}_{\rm{r}}} = \frac{{{{\left( {{\rm{\lambda }}{{\rm{G}}_{\rm{d}}}} \right)}^2}{\rm{\sigma }}{{\rm{P}}_{{\rm{rad}}}}}}{{{{\left( {4{\rm{\pi }}} \right)}^3}{\rm{\;}}{{\rm{r}}^4}}}\)

where λ is the signal wavelength,

G_d is receiver gain,

σ is radar scattering cross-section or radar cross-section

P_rad is radiated power, and

r is target distance.

Calculation:

Substituting the given values in \({{\rm{P}}_{\rm{r}}} = \frac{{{{\left( {{\rm{\lambda }}{{\rm{G}}_{\rm{d}}}} \right)}^2}{\rm{\sigma }}{{\rm{P}}_{{\rm{rad}}}}}}{{{{\left( {4{\rm{\pi }}} \right)}^3}{\rm{\;}}{{\rm{r}}^4}}}\)

\(\begin{array}{l} {{\rm{P}}_{\rm{r}}} = \frac{{{{\left( {3 \times {{10}^8} \times 150} \right)}^2} \times \left( 3 \right) \times 100 \times {{10}^3}}}{{{{\left( {5 \times {{10}^9}} \right)}^2}{{\left( {4{\rm{\pi }}} \right)}^3}{{\left( {{{10}^3}} \right)}^4}}}\\ {{\rm{P}}_{\rm{r}}}{\rm{\;}} = 0.012{\rm{\mu W}} \end{array}\)