Compare the power contained in the sidebands to the total

Question

Q1: Repeat (a) and (b) for s₂(t) = cos(600Πt)sin(1800Πt).

The message signal s(t) = 2cos(6Πt) + 0.5sin(10Πt) modulates the carrier signal c(t) = A_ccos(100Πt) using DSB-SC AM scheme.

a. Write an expression for the modulated signal x(t).

b. Determine and sketch the spectrum of the modulated signal x(t).

c. Calculate the average power contained in the modulated signal x(t).

Q2: A message signal s(t) = 2cos(6Πt) + 5sin(10Πt) modulates the carrier signal c(t) = 100cos(1000Πt) using convention AM scheme. The modulator operates with a modulation index of 0.7.

a. Write an expression for the modulated signal x(t).

b. Determine and sketch the spectrum of the modulated signal x(t).

c. Compare the power contained in the sidebands to the total power in the modulated signal. What is the power efficiency in this AM scheme?

d. Calculate the PEP supplied by the AM transmitter.

Q3: The output of an AM modulator is given by

x(t) = A_ccos(2000Πt) + 50cos(2100Πt + 50cos(1900Πt) The carrier power is 5 kW.

a. Determine the modulation index m_a.

b. Write an expression for the normalized modulating signal.

c. Calculate the power efficiency.

d. Calculate the PEP supplied by the AM transmitter and compare it with the normalized average power and the carrier power.

e envelope detector shown in Figure 4.16(a) is used to demodulate the message signal s(t) from the conventional AM signal x(t) = A_c [1 + s(t)]cos(2Πf_ct) where s(t) is a square wave taking on the values 1 and -1 and having a period T_o >> 1/f_c. Sketch the demodulated signal if R_LC = T_o/40 and T_o/4.