Problem 1:

For a particular case of AM using sinusoidal modulating wave, the percentage modulation is 20 percent. Calculate the average power in (a) the carrier and (b) each side frequency, expressing your results as percentages of total transmitted power.

Problem 2:

In AM, spectral overlap is said to occur if the lower sideband for positive frequencies overlaps with its Enrage for negative frequencies. What condition must the modulated wave satisfy if we are to avoid spectral overlap? Assume that the message signal WO is of a low-pass kind with bandwidth W.

Problem 3:

The coherent detector for the demodulation of DSB-SC fails to operate satisfactorily if the modulator experiences spectral overlap. Explain the reason for this failure.

Problem 4:

Throughout the chapter we focused on

c(t) = A_c cos(2Πf_cd)

as the sinusoidal carrier wave. Suppose we choose

c(t) = A_c sin(2Πf_ct)

as the sinusoidal carrier wave. To be consistent, suppose we also define

m(t) = A_m sin(2Πf_mt)

(a) Evaluate the spectrum of the new definition of AM:

s(t) = A_c[1 + k_am(t)] sin(2Πf_ct)

where le, is the amplitude sensitivity.

(b) Compare the result derived in part (a) with that studied in Example 3.1.

(c) What difference does the formulation in this problem make to the formulation of modu)a¬tion theory illustrated in Example 3.1?

Problem 5:
Consider the message signal

m(t) = 20 cos(2Πt) volts

and the carrier wave

c(t) - 50 cos(100Πt) volts

of Sketch (to scale) the resulting AM wave for 75 percent modulation.

(b) Find the power developed across a load of 100 ohms due to this AM wave.

Problem 6:

Consider the DSB-SC modulated wave obtained by using the sinusoidal modulating wave

m(t) = A_m cos(2Πf_mt)

and the carrier wave

c(t) = A_ccos(2Πf_mt + Φ)

The phase angle A Φ, denoting the phase difference between c(t) and m(t) at time t = 0, is variable. Sketch this modulated wave for the following values of Φ:

(a) Φ = 0
(b) Φ = 45°
(c) Φ = 90°
(d) Φ = 135°

Comment on your results.