Question

The quadrature null effect of the coherent detector occur at

• A. \(\phi=0\)
• B. \(\phi=\pm\frac{\pi}{2}\)
• C. \(\phi=\pm\pi\)
• D. \(\phi=2\pi\)

Hint:

Quadrature null occurs when \[ \cos\phi=0 \] i.e. \[ \phi=\pm90^\circ. \]

Answer 1

The Correct Option is B

Concept: In coherent detection, the recovered signal amplitude is proportional to \[ \cos\phi \] where \(\phi\) is the phase error between the received carrier and local oscillator.

Step 1: Apply quadrature condition.
Quadrature null occurs when \[ \cos\phi=0. \]

Step 2: Find phase values.
\[ \phi=\pm\frac{\pi}{2} \] \[ \phi=\pm90^\circ \] At this phase difference, detector output becomes zero.

Step 3: Final Answer.
\[ \boxed{\phi=\pm\frac{\pi}{2}} \] Hence, \[ \boxed{\text{Correct Option (B)}} \]