JNTU B.Tech III ANALOG COMMUNICATIONS Previous Question Paper (September - 2021 - R16)

Coherent detection of a DSBSC wave involves multiplying the received signal with a locally generated carrier that is perfectly synchronized in both frequency and phase with the original carrier. The received DSBSC signal is s(t) = A_cm(t)cos(2πf_ct). This signal is multiplied by a local oscillator output c(t) = cos(2πf_ct), resulting in v(t) = A_cm(t)cos²(2πf_ct). Using the trigonometric identity cos²(θ) = (1 + cos(2θ))/2, this becomes v(t) = (A_cm(t)/2) + (A_cm(t)/2)cos(4πf_ct). Passing v(t) through a low-pass filter with cutoff frequency f_m removes the high-frequency component, leaving the baseband signal m(t) scaled by a constant. The primary disadvantage is the requirement for a complex synchronization circuit (such as a Costas loop or PLL) to maintain phase and frequency coherence, and the system is highly sensitive to phase errors, which can cause significant distortion in the recovered message signal.

A square-law modulator generates an AM signal using a non-linear device, such as a diode, operating in its square-law region. The input to the non-linear device is the sum of the carrier signal c(t) = A_ccos(2πf_ct) and the message signal m(t). The output of the non-linear device is expressed as v_o(t) = a₁v_i(t) + a₂v_i²(t), where v_i(t) = m(t) + A_ccos(2πf_ct). Expanding this, the squared term produces a component 2a₂A_cm(t)cos(2πf_ct), which represents the desired AM wave. A band-pass filter centered at the carrier frequency f_c is then used to extract this term while suppressing the baseband message signal and the second harmonic of the carrier frequency.