An amplitude modulated wave is as shown in Fig. 15.4. Calculate (i) the percentage modulation, (ii) peak carrier voltage and, (iii) peak value of information voltage.

(i) The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation I = I_oe^–αx, where I_o is the intensity at x = 0 and α is the attenuation constant.

Show that the intensity reduces by 75 per cent after a distance of

(ii) Attenuation of a signal can be expressed in decibel (dB) according to the relation . What is the attenuation in dB/km for an optical fiber in which the intensity falls by 50 per cent over a distance of 50 km?

A 50 MHz sky wave takes 4.04 ms- to reach a receiver via re-transmission from a satellite 600 km above earth’s surface. Assuming re-transmission time by satellite negligible, find the distance between source and receiver. If communication between the two was to be done by Line of Sight (LOS) method, what should size and placement of receiving and transmitting antenna be?

(i) Draw the plot of amplitude versus ‘ω’ for an amplitude modulated wave whose carrier wave (ω_c) is carrying two modulating signals, ω₁ and ω₂ (ω₂ > ω₁). [Hint: Follow derivation from Eq 15.6 of NCERT Textbook of XII]

(ii) Is the plot symmetrical about ω_c? Comment especially about plot in region ω < ω_c.

(iii) Extrapolate and predict the problems one can expect if more waves are to be modulated.

(iv) Suggest solutions to the above problem. In the process can one understand another advantage of modulation in terms of bandwidth?

An audio signal is modulated by a carrier wave of 20MHz such that the bandwidth required for modulation is 3kHz. Could this wave be demodulated by a diode detector which has the values of R and C as

(i) R = 1 kΩ, C = 0.01μF.

(ii) R = 10 kΩ, C = 0.01μF.

(iii) R = 10 kΩ, C = 0.1μF.