A DSB-SC signal is being detected synchronously. The phase error in the locally generated carrier will _________.

Explanation:

5Double Sideband Suppressed Carrier (DSB-SC) is a type of amplitude modulation where the carrier is suppressed, and only the sidebands carry the information. In synchronous detection, a locally generated carrier is used at the receiver to demodulate the signal. The phase and frequency of this locally generated carrier must align precisely with the transmitted carrier for accurate demodulation.

Phase Error in Synchronous Detection: A phase error occurs when there is a phase difference between the locally generated carrier at the receiver and the carrier used during transmission. This phase mismatch can significantly affect the demodulated output.

Impact of Phase Error: In the case of a DSB-SC signal, the demodulated output is given by the product of the transmitted signal and the locally generated carrier. When there is a phase error, the output signal gets distorted. Mathematically, the transmitted DSB-SC signal can be expressed as:

Transmitted Signal: s(t) = A × cos(ω_ct) × m(t)

Here:

• A = Amplitude of the signal
• ω_c = Angular frequency of the carrier
• m(t) = Modulating signal

The locally generated carrier at the receiver can be expressed as:

Local Carrier: cos(ω_ct + θ)

Where θ is the phase error. The demodulated output is obtained by multiplying the transmitted signal with the local carrier:

Demodulated Output:

y(t) = s(t) × cos(ω_ct + θ)

Substituting the expression for s(t):

y(t) = [A × cos(ω_ct) × m(t)] × cos(ω_ct + θ)

Using the trigonometric identity:

cos(x) × cos(y) = 0.5 × [cos(x-y) + cos(x+y)]

y(t) = 0.5 × A × m(t) × [cos(θ) + cos(2ω_ct + θ)]

The term cos(2ω_ct + θ) represents a high-frequency component that is filtered out during demodulation, leaving:

y(t) = 0.5 × A × m(t) × cos(θ)

This shows that the amplitude of the demodulated signal is scaled by cos(θ). If there is a phase error θ, the output amplitude is reduced by the factor cos(θ). Additionally, the phase error introduces phase distortion in the demodulated signal.

Correct Option Analysis:

The correct option is:

Option 1: Cause phase distortion and reduce the output also.

This option is correct because a phase error in the locally generated carrier introduces distortion in the output and reduces its amplitude by the factor cos(θ). The demodulated signal's quality depends on the alignment of the local carrier with the transmitted carrier, and any phase mismatch degrades the output.