# 1. (10 pts) A mobile receiver communicates with the transmitter at an operating frequency of 550 MHz at a distance of 3 km. Calculate the path loss in the system.

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1. (10 pts) A mobile receiver communicates with the transmitter at an operating frequency of 550 MHz at a distance of 3 km. Calculate the path loss in the system.

2. (15 pts) Assume that two antennas are half-wave dipoles and each has a gain of 3 dB. If the transmitted power is 1 W and the two antennas are separated by a distance of 10 km, what is the received power? Assume that the frequency is 100 MHz.

3. (10 pts) Show that doubling the transmission frequency or doubling the distance between transmitting antenna and receiving antenna reduces the received power by 6 dB.

Solution:-

=>1) Here we have Calculated the path loss in dB as shown below, by substituting the given values in the free space path loss or path loss formula.

2). The received power of an Antenna is calculated by using the Friis Transmission Equation. The received power is calculated in mW and dBm as shown below

3)Here we consider the Friis Transmission Equation in dB and as per the question, we first double the frequency and then double the distance. The solution is shown below. When we double the frequency or double the distance we can see that the equation gets divided by 2 and when we solve it further we can see that there is a reduction of 6dB in received power.

In equation 2, we can see mathematical expression which shows that there is a reduction of 6dB.

Now, distance is doubled and the remaining parameters are same.

In equation 3, we can see mathematical expression which shows that there is a reduction of 6dB.

Hence, by doubling the transmission frequency or doubling the distance between transmitting antenna and receiving antenna reduces the received power by 6 dB.