# Antenna Parameters Questions and Answers – Friis Transmission Equation

This set of Antenna Parameters Questions and Answers for Experienced people focuses on “Friis Transmission Equation”.

1. Friss transmission is applicable when same antenna is used for both transmission and reception.
a) True
b) False

Explanation: Friss transmission is used to find the receiver power in antenna when power is transmitted from another antenna. These are separated by a far zone distance.

2. What is the distance between antennas to apply the Friss transmission equation in terms of antennas largest dimension?
a) R » 2D2
b) R « 2D2
c) R » 2λ2/D
d) R « 2λ2/D

Explanation: The transmitting and receiving antennas are in a far zone to each other. So the separation distance between them is R » 2D2/λ.

3. Free space loss factor is given by _____
a) $$\frac{\lambda}{4\pi R}$$
b) $$(\frac{\lambda}{4\pi R})^2$$
c) $$\frac{4\pi R}{\lambda}$$
d) $$(\frac{4\pi R}{\lambda})^2$$

Explanation: The free space loss factor is given by $$(\frac{\lambda}{4\pi R})^2$$. It is used to know the amount of losses occurred due to the spreading of energy by an antenna.

4. Which of the following is the Friss transmission equation for the matched polarization of antennas?
a) $$\frac{P_r}{P_t} = \frac{G_t G_r\lambda^2}{(4πR)^2}$$
b) $$\frac{P_t}{P_r} = \frac{G_t G_r\lambda^2}{(4πR)^2}$$
c) $$\frac{P_r}{P_t} = \frac{G_t G_r\lambda^2}{4πR^2}$$
d) $$\frac{P_t}{P_r} = \frac{G_t G_r\lambda^2}{4πR^2}$$

Explanation: Friss transmission equation is used to calculate the power received by the receiving antenna when transmitted from other antenna separated by a distance R. the equation is given by $$\frac{P_r}{P_t} = \frac{G_t G_r \lambda^2}{(4πR)^2}.$$

5. If the operating frequency increases, powers received by the receiving antenna ______
a) will decrease
b) will Increase
c) is Independent of frequency
d) is not predictable

Explanation: From the Friss transmission equation, the received power depends on the wavelength which is inversely proportional to the frequency. So the power decreases as the frequency increases.
$$\frac{P_r}{P_t} = \frac{G_t G_r λ^2}{(4πR)^2} = \frac{G_t G_r c^2}{(4πRf)^2}$$

6. Power received by the antenna when one antenna is horizontally polarized and the other is vertically polarized is _______
a) 1
b) 0
c) $$\frac{P_r}{P_t} = \frac{G_t G_r λ^2}{(4πR)^2}$$
d) $$\frac{P_r}{P_t} = \frac{G_t G_r λ^2}{2(4πR)^2}$$

Explanation: When the receiving and transmitting antennas polarization is not matched, the Friss transmission equation includes a polarization loss factor given by cos2θ. Since one is vertically polarized and other is horizontally polarized, the angle difference is 900. PLF=cos2θ=0
∴ $$\frac{P_r}{P_t} = PLF\frac{G_t G_r \lambda^2}{(4\pi R)^2} =0$$

7. Find the power received by the receiving antenna if it is placed at a distance of 20m from the transmitting antenna which is radiating 50W power at a frequency 900MHz and are made-up of half-wave dipoles.
a) 23.65μW
b) 2.365μW
c) 236.5μW
d) 4.73μW

Explanation: given d=20m, Pt=50W and f=900MHz
Gain of half-wave dipoles is 1.64
$$λ = \frac{c}{f} = \frac{3×10^8}{900Mhz} = \frac{1}{3} m$$
$$\frac{P_r}{P_t} = \frac{G_t G_r \lambda^2}{(4\pi R)^2} = \frac{1.64×1.64×1/3^2}{(4\pi ×20)^2}$$
Pr=236.5μW

8. Let’s assume a transmitting antenna having gain 10dB is placed at a distance of 100m from the receiving antenna and radiates a power of 5W. Find the gain of the receiving antenna in dB when the received power is 150μW and transmitter frequency 500MHz?
a) 1.31dB
b) 1.19dB
c) 11.19dB
d) 13.16dB

Explanation:
Given Pt=5W, Pr=150μW, f=500MHz, R=100m and Gt in dB=10dB
Gt in dB=10log10 Gt=10dB
Gt=10
⇨ $$\lambda = \frac{c}{f} = \frac{3×10^8}{500Mhz} = 0.6m$$
From Friss transmission equation, $$\frac{P_r}{P_t} = \frac{G_t G_r \lambda^2}{(4\pi R)^2}$$
⇨ $$G_r=\frac{P_r (4\pi R)^2}{P_t G_t \lambda^2} = \frac{150\mu(4\pi ×100)^2}{5×10×0.6^2}=13.16$$
⇨ Gr in dB=10log10 Gr=10log10 13.16=11.19dB

9. If the distance between the transmitting and receiving antenna is decreased by a factor 2 while other factors remain same, then the new power received by the antenna _______
a) increases by factor 2
b) decreases by factor 2
c) increases by factor 4
d) decreases by factor 4

Explanation: From Friss transmission equation, $$P_r=P_t\frac{G_t G_r \lambda^2}{(4πR)^2}$$
$$\frac{P_{r1}}{P_{r2}} = \frac{R_2^2}{R_1^2} = \frac{(R/2)^2}{R^2} = \frac{1}{4}$$
Pr2=4Pr1.

10. Assume two similar antennas for transmitting and receiving. If the operating frequency gets reduced by 3 times then the received power gets _______
a) increases by factor 3
b) decreases by factor 3
c) increases by factor 9
d) decreases by factor 9

Explanation: From Friss transmission equation,
$$\frac{P_r}{P_t} = \frac{G_t G_r λ^2}{(4\pi R)^2} = \frac{G_t G_r c^2}{(4\pi Rf)^2}$$
$$\frac{P_{r1}}{P_{r2}} = \frac{f_2^2}{f_1^2} = \frac{(f/3)^2}{f^2} = \frac{1}{9}$$
Pr2=9Pr1

Sanfoundry Global Education & Learning Series – Antennas.

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