Question 2 - Antenna. Data: Transmitter distance d = 2000m, Receiver height hr = 20m, Transmitter height ht…

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Question 2 - Antenna. Data: Transmitter distance d = 2000m, Receiver height hr = 20m, Transmitter height ht = 1a, Transmitter Gain Gf = 10Gnts (1×103), Receiver Gain Gr = 10, Power transmitted Pt = 5, Power Received Pr = 3/4 of 2W. Solution using a) PR=...

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Here's the solution for calculating the received power based on your image:

The problem asks to calculate the received power ( $P_R$ ) under two conditions using the provided data.

Given Data:

Distance $d = 2000 \text{ m}$
Transmitter height $h_t = 20 \text{ m}$
Receiver height $h_r = 1 \text{ m}$
Transmission Frequency $F = 1 \text{ GHz} = 1 \times 10^9 \text{ Hz}$
Transmitter Gain $G_t = 10$
Receiver Gain $G_r = 5$
Power transmitted $P_t = 2 \text{ W}$

Calculate the wavelength ( $\lambda$ ).
The speed of light $c = 3 \times 10^8 \text{ m/s}$ .
$\lambda = \frac{c}{F}$ $\lambda = \frac{3 \times 10^8 \text{ m/s}}{1 \times 10^9 \text{ Hz}}$ $\lambda = 0.3 \text{ m}$
Calculate the received power ( $P_R$ ) neglecting reflections (using the Friis transmission formula).
The formula is:
$P_R = P_t G_t G_r \left(\frac{\lambda}{4\pi d}\right)^2$
Substitute the given values:
$P_R = (2 \text{ W}) \times 10 \times 5 \times \left(\frac{0.3 \text{ m}}{4\pi \times 2000 \text{ m}}\right)^2$ $P_R = 100 \text{ W} \times \left(\frac{0.3}{25132.74}\right)^2$ $P_R = 100 \text{ W} \times (1.19366 \times 10^{-5})^2$ $P_R = 100 \text{ W} \times (1.4248 \times 10^{-10})$ $P_R = 1.4248 \times 10^{-8} \text{ W}$
Converting to nanowatts (nW):
$P_R = 1.4248 \times 10^{-8} \text{ W} \times \frac{10^9 \text{ nW}}{1 \text{ W}}$ $P_R = 14.248 \text{ nW}$
The received power neglecting reflections is $\boxed{\text{14.2 nW}}$ .
Calculate the received power ( $P_R$ ) including reflections (using the two-ray ground reflection model).
The formula is:
$P_R = P_t G_t G_r \left(\frac{h_t h_r}{d^2}\right)^2$
Substitute the given values:
$P_R = (2 \text{ W}) \times 10 \times 5 \times \left(\frac{20 \text{ m} \times 1 \text{ m}}{(2000 \text{ m})^2}\right)^2$ $P_R = 100 \text{ W} \times \left(\frac{20}{4000000}\right)^2$ $P_R = 100 \text{ W} \times \left(5 \times 10^{-6}\right)^2$ $P_R = 100 \text{ W} \times (25 \times 10^{-12})$ $P_R = 2500 \times 10^{-12} \text{ W}$ $P_R = 2.5 \times 10^{-9} \text{ W}$
Converting to nanowatts (nW):
$P_R = 2.5 \times 10^{-9} \text{ W} \times \frac{10^9 \text{ nW}}{1 \text{ W}}$ $P_R = 2.5 \text{ nW}$
The received power including reflections is $\boxed{\text{2.5 nW}}$ .

Question 2 - Antenna. Data: Transmitter distance d = 2000m, Receiver height hr = 20m, Transmitter height ht = 1a, Transmitter Gain Gf = 10Gnts (1x103), Receiver Gain Gr = 10, Power transmitted Pt = 5, Power Received Pr = 3/4 of 2W. Solution using a) PR=...

Step-by-step solution

Calculate the wavelength ( $\lambda$ ).

Calculate the received power ( $P_R$ ) neglecting reflections (using the Friis transmission formula).

Calculate the received power ( $P_R$ ) including reflections (using the two-ray ground reflection model).

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