CBSE Class 12 Physics Communication Systems Formulae

1. A TV tower has a height of 71 m. what is the maximum distance up to which TV transmission can be received? Given that the radius of the earth = 6.4 x 104 m. 

2. What is the length of a dipole antenna to transmit signals of frequency 200 MHz? 

3. A 100 kHz bandwidth is to accommodate 10 A. M. broadcasts simultaneously. What is the maximum modulating frequency permissible for each station? 

4. Calculate the number of TV channels which can be accommodated in a band width of 4700 GHz.

5. What should be the height of a transmitting antenna if the TV telecast is to cover a radius of 128 km? 

6. For amplitude modulated wave the maximum amplitude is found to be 15 V while the minimum amplitude is 3 V. Calculate the modulation index. Why modulation index is generally kept less than one?

7. A carrier wave of peak voltage 18 V is used to transmit a signal. Calculate the peak voltage of the modulating signal in order to have a modulation index of 50%. 

8. A message signal of frequency 10 kHz and peak voltage of 10 V is used to modulate frequency of 1 MHz and peak voltage of 20 V. Determine (i) modulation index (ii) the side bands produced. 

9. A TV tower has a height of 100 m. how much population is covered by the TV broad cast if the average population density around the tower is 1000 km-2. 

10. A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them for satisfactory communication in the line of sight mode? (Radius of the earth = 6400 km) 

Level-II:-

1.A TV tower has a height of 300m. What is the maximum distance upto which this TV transmission can be received?

2. A carrier wave of peak voltage 20 V is used to transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index of 80%?

3. The TV signal have a bandwidth of 4.7 MHz.What is the number of channels that can be Accommodated in a bandwidth of 4700Ghz/

4. Calculate the length of half wave dipole antenna at 30 MHz?

5. What should be the height of a transmitting antenna if the TV telecast is to cover a radius Of 128 Km?

6. The tuned circuit of oscillator in a single AM transmitter employs 50 uH coil and 1nF capacitor. The oscillator output is modulated by audio frequency up to 10KHz. Determine the range of AM wave.

7. What is the population covered by the transmission, if the average Population density around the tower is 1200km-2?

8.. A transmitting antenna at the top of tower has a height of 36m and the height of the receiving antenna is 49m. What is the maximum distance between them, for the satisfactory communication in the LOS mode? (Radius of the earth =6400km)

9. Frequencies higher than 10MHz are found not to be reflected by the ionosphere on a particular day at a place. Calculate the maximum electrons density of the ionosphere.

10. A message signal of frequency 10 kHz and peak value of 8 volts is used to modulate a carrier Of frequency 1MHz and peak voltage of 20 volts.

Calculate: (i) Modulation index

(ii) The side bands produced.

LEVEL- 3

1. A carrier wave of frequency 10MHz and peak value 10V is amplitude modulated by a 5KHz sine wave of amplitude 6V.Calculate the frequency and amplitude of the two sidebands.

2. A sinusoidal carrier voltage is amplitude modulated by a sinusoidal voltage of 10 KHz to a depth of 30%. Calculate the frequency and amplitude of the two sidebands if the carrier frequency is 10 MHz and its amplitude is 40 V.

3. A sinusoidal carrier voltage of frequency 1200 KHz is amplitude modulated by a sinusoidal voltage of frequency 20 KHz resulting in maximum and minimum modulated carrier amplitudes of 110 V and 90 V respectively. Calculate

(i) the frequency of lower and upper sidebands

(ii) the unmodulated carrier amplitude

(iii) the modulation and

(iv) the amplitude of each sideband.

4. . An amplitude modulated wave is represented as cm (t) = 5 ( 1 + 0.6 cos + 6280 t ) sin 211 × 104 t, volts.

(i)What are the minimum and maximum amplitudes of the A.M wave?

(ii)What frequency components are contained in the modulated wave?

(iii)What are the amplitudes of the compounds?

5. Assume that light of frequency 4.5 × 1014 Hz is used in an optical communication system. If 2% of the frequency bandwidth is used, how many T.V. channels can be accommodated in this bandwidth? The bandwidth needed for T.V. transmission is 4.5 × 106 Hz / channel.

6. . A ground receiver station is receiving a signal at (a) 5 MHz and (b) 100 MHz, transmitted from a ground transmitter at a height of 3000 m located at a distance of 100 km. identify whether it is coming via space wave or sky wave propagation or satellite transponder. (given the value of radius of earth is 6400 km and maximum electron density, N_max = 1023 m-3 ).

7. On a particular day, the maximum frequency reflected from the ionosphere is 10 MHz. on another day, it was found to increase to 11 MHz. calculate the ratio of the maximum electron densities of the ionosphere on the two days. Point out a possible explanation for this.

8. . What will be the required height of a T.V tower which can cover the population of 60.3 lakhs if average population density around the tower is 1000km-2 ?
[ radius of earth = 6.4 × 10⁶m ]

9. The T.V transmission tower at a particular stationhas a height of 160 m. (a) what is its coverage range ?(b) how much population is covered by the transmission, if the average density around the tower is 1200km-2? (c) by how much should the height be increased to double its coverage range? Given radius of earth = 6400 km.

10. A transmitting antenna at the top of a tower has a height 32 m and that of the receiving antenna is 100 m. what is the maximum distance between them for satisfactory communication in LOS mode? given radius of earth 6.4 × 10 6 m.

SOME QUESTION BASED ON DIAGRAM

1.A modulating signal is a square wave as shown in figure.The carrier wave is given by

C(t) = 2 Sin(8Πt)volt

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