Free space propagation is assumed,$G_t = 1 \ and \ G_r = 2$

Find:-

a) Power at receiver

b) Magnitude of E field at receiving antenna

c) The RMS voltage applied to Receiver input assuming that receiving antenna has purely real impedance of 50 ohms and is matched to the receiver.

Mumbai University > Electronics and Telecommunication > Sem 7 > Mobile Communication

Marks: 10 M

Year: May 2015

Given:

Transmitter power $p_t =50 watts$

Carrier frequency $f_c=900 MHz$

Transmitter antenna gain $G_t = 1$

Receiver antenna gain $G_r = 2$

Power received at distance d=10 km is

1. Power at receiver $$ p_r (d)=10 log⁡(\frac{p_t G_t G_r λ^2}{((4π)^2 d^2 ) }$$

$$p_r (d)=10 log⁡ \left(\frac{50×1×2× (1/3)^2}{4π×10000^2}\right)$$

$$p_r (d) = -91.5dBw = -61.5dBm$$

1. Magnitude of E field at receiving antenna $$|E| = \sqrt[2]{\frac{p_r (d)120π}{A_e }}$$ $$|E| = \sqrt[2]{\frac{p_r (d)120π}{G_r \frac{λ^2}{4π}}}$$

$$|E |=\sqrt[2]{\frac{7×10^{-10} × 120π}{2× 0.33^2/4π}} = 0.0039 V/m$$

1. Open circuit RMS voltage at receiver input:

$$v_ant = \sqrt{p_r(d) × 4R_ant} = \sqrt{7×10^{-10} × 4 × 50} = 0.374mV$$