JNTU B.Tech III ANALOG COMMUNICATIONS Previous Question Paper (August - 2022 - R13)

A square law modulator consists of a non-linear device, such as a diode, operating in its square-law region, followed by a bandpass filter. The input to the non-linear device is the sum of the carrier signal c(t) = A_c cos(2πf_ct) and the message signal m(t). The output of the non-linear device is represented by the power series v_o(t) = a₁v_i(t) + a₂v_i(t)², where v_i(t) = m(t) + A_c cos(2πf_ct).

Expanding the squared term produces components including m(t)², A_c² cos²(2πf_ct), and 2a₂A_cm(t) cos(2πf_ct). The bandpass filter is tuned to the carrier frequency f_c with a bandwidth sufficient to pass the modulated signal while rejecting the low-frequency m(t)² and high-frequency harmonic components. The resulting output is the AM wave: s(t) = a₁A_c[1 + (2a₂/a₁)m(t)] cos(2πf_ct), which represents the amplitude-modulated signal.

In a DSB-SC system, the modulated signal is s(t) = A_cm(t) cos(2πf_ct). Assuming a sinusoidal message m(t) = A_m cos(2πf_mt), the signal becomes s(t) = A_cA_m cos(2πf_mt) cos(2πf_ct). Using the trigonometric identity, s(t) = (A_cA_m/2) [cos(2π(f_c+f_m)t) + cos(2π(f_c-f_m)t)]. The total power P_DSB-SC is the sum of the powers of the two sidebands: P_DSB-SC = (A_c²A_m²/8) + (A_c²A_m²/8) = A_c²A_m²/4.

For standard AM, the total power is P_AM = P_c(1 + μ²/2), where P_c = A_c²/2 is the carrier power and μ is the modulation index. The power ratio of DSB (standard AM) to DSB-SC is given by the ratio of P_AM to P_DSB-SC. Since DSB-SC transmits only the sidebands, it is more power-efficient than standard AM, which wastes power in the carrier component.