Question

Assume an isotropic antenna operating at 10 GHz, find the effective area and antenna gain.

Answer 1

The effective area 

$A_e=k \frac{\pi D^2}{4}\\ 46=10 \log_{10} k(\frac{\pi D^2}{\lambda})^2\\ \frac{\pi D^2}{\lambda}=269.04\\ D=\frac{269.04* \lambda}{\pi}=\frac{269.04* 0.025}{3.14}=2.14\\ \therefore A_e=k \frac{\pi D^2}{4}= \frac{0.55*3.14*2.14^2}{4}=1.98 m^2\\$

Antenna gain

$G=10 \log_{10} k(\frac{\pi D^2}{\lambda})^2\\ G=10 \log_{10} *0.55*(\frac{3.14* 30}{0.075})^2\\ G=59.38dB$