If the whole earth is to be connected by LOS
Question: If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earths radius? Solution: Let ht be the height of the receiving antenna Then ht = hr where r is the radius of the earth Let dm be the line of sight distance between the transmission and receiving antennas, Then the maximum distance is R = ht....
Read More →A TV transmission tower antenna is at a height of 20 m.
Question: A TV transmission tower antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level, (ii) at a height of 25 m? Calculate the percentage increase in area covered in case (ii) relative to case (i). Solution: (i) Range , it = 16 km Area covered = 803.84 km2 (ii) Height from ground level = 25 m Range = dm = 33.9 km Area covered = 3608.52 km2 Percentage increase in area = 348.9 %...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{(\sin x-2 \cos x)(2 \sin x+\cos x)} d x$ Solution: Given $I=\int \frac{1}{(\sin x-2 \cos x)(2 \sin x+\cos x)} d x$ $\Rightarrow \int \frac{1}{(\sin x-2 \cos x)(2 \sin x+\cos x)} d x$ $=\int \frac{1}{2 \sin ^{2} x+\sin x \cos x-4 \sin x \cos x-2 \cos ^{2} x} d x$ Dividing the numerator and denominator by $\cos ^{2} x$, $\Rightarrow \int \frac{1}{2 \sin ^{2} x+\sin x \cos x-4 \sin x \cos x-2 \cos ^{2} x} d x$ $=\int \frac{\sec ^{2} x}{2 \t...
Read More →Figure 15.3 shows a communication system.
Question: Figure 15.3 shows a communication system. What is the output power when the input signal is of 1.01mW? (gain in dB = 10 log10 (Po /Pi ). Solution: Loss suffered in the path of transmission = 2 dB/km Distance travelled by the signal = 5 km Total loss suffered = -10 dB Totla amplifier gain = 30 dB Overall gain in signal = 20 dB Gain in dB = 2 Input power = 1.01 mW Po = 1.01 100 Output power is 101 mW....
Read More →Why is an AM signal likely to be noisier
Question: Why is an AM signal likely to be noisier than an FM signal upon transmission through a channel? Solution: The instantaneous voltage of the carrier wave varies by the modulating wave voltage in the AM. Therefore, the AM signal is more likely to be noisily than an FM signal....
Read More →From a well-shuffled pack of cards, a card is drawn at random.
Question: From a well-shuffled pack of cards, a card is drawn at random. Find the probability of its being either a queen or a heart. Solution: let A denote the event that the card drawn is queen and B denote the event that card drawn is the heart. In a pack of 52 cards, there are 4 queen cards and 13 heart cards Given: $P(A)=\frac{4}{52}, P(B)=\frac{13}{52}$ To find : Probability that card drawn is either a queen or heart = P(A or B) The formula used : Probability = $P(A$ or $B)=P(A)+P(B)-P(A$ ...
Read More →Compute the LC product of a tuned amplifier
Question: Compute the LC product of a tuned amplifier circuit required to generate a carrier wave of 1 MHz for amplitude modulation. Solution: LC = 2.54 10-14seconds...
Read More →The maximum amplitude of an A.M.
Question: The maximum amplitude of an A.M. wave is found to be 15 V while its minimum amplitude is found to be 3 V. What is the modulation index? Solution: Modulation index is defined as the ratio of change of amplitude of carrier wave to the amplitude of the original carrier wave. The maximum amplitude of AM wave is = Amax = Ac + Am = 15 V The minimum amplitude of the AM wave is = Amin = Ac Am = 3V m = modulation index = Am/Ac = 2/3...
Read More →Two waves A and B of frequencies 2 MHz and 3 MHz,
Question: Two waves A and B of frequencies 2 MHz and 3 MHz, respectively are beamed in the same direction for communication via skywave. Which one of these is likely to travel a longer distance in the ionosphere before suffering total internal reflection? Solution: The refractive index of B would be more than a refractive index of A because the frequency of wave B s more than the frequency of wave A....
Read More →Would sky waves be suitable for transmission
Question: Would sky waves be suitable for transmission of TV signals of 60 MHz frequency? Solution: Skywaves wont be suitable for transmission of TV signals of 60 MHz frequency as the TV signals are beyond 60 MHz. Space wave transmission needs to be used....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{3+2 \cos ^{2} x} d x$ Solution: Given I $=\int \frac{1}{3+2 \cos ^{2} x} d x$ Divide numerator and denominator by $\cos ^{2} x$, $\Rightarrow I=\int \frac{1}{3+2 \cos ^{2} x} d x=\int \frac{\sec ^{2} x}{3 \sec ^{2} x+2} d x$ Replacing $\sec ^{2} x$ in denominator by $1+\tan ^{2} x$, $\Rightarrow \int \frac{\sec ^{2} x}{3 \sec ^{2} x+2} d x=\int \frac{\sec ^{2} x}{3+3 \tan ^{2} x+2} d x$ $=\int \frac{\sec ^{2} x}{5+3 \tan ^{2} x} d x$ Put...
Read More →Which of the following would produce analogue
Question: Which of the following would produce analogue signals and which would produce digital signals? (i) A vibrating tuning fork (ii) Musical sound due to a vibrating sitar string (iii) Light pulse (iv) Output of NAND gate Solution: (i) A vibrating tuning fork and ii) musical sound due to a vibrating sitar string will produce analogue (iii) Light pulse and iv) Output of NAND gate will produce digital signals....
Read More →In amplitude modulation,
Question: In amplitude modulation, the modulation index m, is kept less than or equal to 1 because (a) m 1, will result in interference between the carrier frequency and message frequency, resulting in distortion (b) m 1 will result in overlapping of both sidebands resulting into loss of information (c) m 1 will result in a change in phase between the carrier signal and the message signal (d) m 1 indicates the amplitude of message signal greater than the amplitude of the carrier signal resulting...
Read More →The frequency response curve in the figure
Question: The frequency response curve in the figure for the filter circuit used for production of AM wave should be (a) (i) followed by(ii) (b) (ii) followed by (i) (c) (iii) (d) (iv) Solution: (a) (i) followed by(ii) (b) (ii) followed by (i) (c) (iii)...
Read More →From a well-shuffled pack of 52 cards, a card is drawn at random.
Question: From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of its being a king or a queen Solution: let A denote the event that the card drawn is king and B denote the event that card drawn is queen. In a pack of 52 cards, there are 4 king cards and 4 queen cards Given : $P(A)=\frac{4}{52}, P(B)=\frac{4}{52}$ To find : Probability that card drawn is king or queen $=P(A$ or $B)$ The formula used : Probability = $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$ $P(A)=\frac...
Read More →A TV transmission tower has a height of 240 m.
Question: A TV transmission tower has a height of 240 m. Signals broadcast from this tower will be received by LOS communication at a distance of (assume the radius of the earth to be 6.4 106m) (a) 100 km (b) 24 km (c) 55 km (d) 50 km Solution: (b) 24 km (c) 55 km (d) 50 km...
Read More →Audio sine waves of 3 kHz frequency are used to amplitude
Question: Audio sine waves of 3 kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true? (a) The sideband frequencies are 1506 kHz and 1494 kHz (b) The bandwidth required for amplitude modulation is 6kHz (c) The bandwidth required for amplitude modulation is 3 MHz (d) The sideband frequencies are 1503 kHz and 1497 kHz. Solution: (b) The bandwidth required for amplitude modulation is 6kHz (d) The sideband frequencies are 1503 kHz and 14...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{1+3 \sin ^{2} x} d x$ Solution: Given I $=\int \frac{1}{1+3 \sin ^{2} x} d x$ Divide numerator and denominator by $\cos ^{2} x$, $\Rightarrow I=\int \frac{1}{1+3 \sin ^{2} x} d x=\int \frac{\sec ^{2} x}{\sec ^{2} x+3 \tan ^{2} x} d x$ Replacing $\sec ^{2} x$ in denominator by $1+\tan ^{2} x$, $\Rightarrow \int \frac{\sec ^{2} x}{\sec ^{2} x+3 \tan ^{2} x} d x=\int \frac{\sec ^{2} x}{1+\tan ^{2} x+3 \tan ^{2} x} d x$ $=\int \frac{\sec ^{2...
Read More →An audio signal of 15kHz frequency cannot be transmitted
Question: An audio signal of 15kHz frequency cannot be transmitted over long distances without modulation because (a) the size of the required antenna would be at least 5 km which is not convenient (b) the audio signal can not be transmitted through sky waves (c) the size of the required antenna would be at least 20 km, which is not convenient (d) effective power transmitted would be very low, if the size of the antenna is less than 5 km Solution: (a) the size of the required antenna would be at...
Read More →Identify the mathematical expression for amplitude
Question: Identify the mathematical expression for amplitude modulated wave: (a) Ac sin [{c + k1vm(t)}t + ] (b) Ac sin {c t + + k2 vm(t)} (c) {Ac + k2 vm(t)} sin (c t + ) (d) Ac vm(t) sin (c t + ) Solution: (c) {Ac + k2 vm(t)} sin (c t + )...
Read More →A basic communication system consists of
Question: A basic communication system consists of (A) transmitter (B) information source (C) user of information (D) channel (E) receiver Choose the correct sequence in which these are arranged in a basic communication system: (a) ABCDE (b) BADEC (c) BDACE (d) BEADC Solution: (b) BADEC...
Read More →A male voice after modulation-transmission sounds
Question: A male voice after modulation-transmission sounds like that of a female to the receiver. The problem is due to (a) poor selection of modulation index (selected 0 m 1) (b) poor bandwidth selection of amplifiers (c) poor selection of carrier frequency (d) loss of energy in transmission Solution: (b) poor bandwidth selection of amplifiers...
Read More →I-V characteristics of four devices
Question: I-V characteristics of four devices are shown in the figure. Identify devices that can be used for modulation: (a) i and iii (b) only iii (c) ii and some regions of iv (d) All the devices can be used. Solution: (c) ii and some regions of iv...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\cos x}{\cos 3 x} d x$ Solution: Given $I=\int \frac{\cos x}{\cos 3 x} d x$ $\Rightarrow \int \frac{\cos x}{\cos 3 x} d x=\int \frac{\cos x}{4 \cos ^{3} x-3 \cos x} d x$ $=\int \frac{1}{4 \cos ^{2} x-3} d x$ Dividing numerator and denominator by $\cos ^{2} x$, $\Rightarrow \int \frac{1}{4 \cos ^{2} x-3} d x=\int \frac{\sec ^{2} x}{4-3 \sec ^{2} x} d x$ Replacing $\sec ^{2} x$ by $1+\tan ^{2} x$ in denominator, $\Rightarrow \int \frac{\sec ^...
Read More →The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3).
Question: The probability that a company executive will travel by plane is (2/5) and that he will travel by train is (1/3). Find the probability of his travelling by plane or train. Solution: let A denote the event that a company executive will travel by plane and B denote the event of him travelling by train Given : $P(A)=\frac{2}{5}, P(B)=\frac{1}{3}$ To find : Probability of a company executive will be travelling by plane or train=P(A or B) Formula used: $P(A$ or $B)=P(A)+P(B)-P(A$ and $B)$ P...
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