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A coherent detector's local carrier is in error by a phase angle \( \phi \). The recovered output is scaled by

  • A.Cosine of phi
  • B.Sine of phi
  • C.Phi itself in radians
  • D.Cosine squared of phi

Answer: A

Multiplying the received signal by a reference at phase error \( \phi \) gives an output proportional to \( \cos\phi \), so a small error costs little but a quarter-cycle error nulls the output completely. That is the quadrature null, and it is what a Costas loop exists to avoid. A sine dependence would null at zero error, which is the reverse of the truth. The angle itself has the wrong form, and a squared cosine would describe a power rather than a voltage.

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