(a) A modulation signal 2 cos(2π103 t) V is used to amplitude modulate a carrier wave 10 cos(2π104 t) V. (i) Determine the carrier and modulating frequencies. (ii) Determine the transmission bandwidth. (iii) Determine the percentage modulation. (iv) Determine the carrier and sideband powers if the AM wave is dropped across a 50 Ω load. (b) Explain the operation of the Costas receiver, shown in Fig. 2, when used to demodulate a double-sideband suppressed carrier AM signal. In your answer show equations for the signals at A, B, C, D and E. Fig. 2. Costas receiver.
![An amplitude modulated wave is given by s(t) = [1 + kam(t)]c(t), where ka is the modulator sensitivity, m(t) is the message wave and c(t) is the carrier wave. Assume that a sinusoidal signal is chosen as the carrier wave; c(t) = cos(2πfct), where fc is the carrier frequency. Let the message signal m(t) be a periodic triangular pulse wave shown in Fig. 1 Figure 1: Message signal m(t) (a). Find ka for 50% modulation. [hint: Percentage modulation is defined as max|kam(t)| × 100% ] (b). Sketch the amplitude modulated signal s(t) for 50% modulation.](https://www.doubtrix.com/uploads/editor/0778063553RLzvMpgLmL.jpeg)
