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A message signal m(t) = Am sin (2πfmt) is used to modulate the phase of a carrier Ac cos (2πfct) to get the modulated signal y(t) = Ac cos (2πfct + m(t)). The bandwidth of y(t)
  • a)
    depends on Am but not on fm
  • b)
    depends on fm but not on Am
  • c)
    depends on both Am and fm
  • d)
    does not depends on Am or fm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A message signal m(t) = Am sin (2πfmt) is used to modulate the phas...
Concept:
If m(t) is the message single & c(t) = Ac cos(ωct) is the Carrier signal, then the General expression for a Phase modulated signal is:
SPM(t) = Ac cos[ωct + kpm(t)]
Where kp = Phase Sensitivity (rad/Volts)
Analysis:
SPM(t) = Accos[ωct + kpm(t)] = Ac cos(θi)
Instantaneous Phase θi(t) = ωc(t) + kpm(t)
Instantaneous frequency ωi(t) = 
  • Phase deviation Δϕ = kp m(t)
  • Frequency deviation Δω = 
  • Deviation ratio 
According to Carson formula, the Bandwidth of a phase-modulated signal is:
BW = 2(β + 1) ωm = 2(kpAm + 1)ωm
Hence the Bandwidth depends on both Am & ωm
So, Option (3) is Correct.
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A message signal m(t) = Am sin (2πfmt) is used to modulate the phas...
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A message signal m(t) = Am sin (2πfmt) is used to modulate the phase of a carrier Ac cos (2πfct) to get the modulated signal y(t) = Ac cos (2πfct + m(t)). The bandwidth of y(t)a)depends on Am but not on fmb)depends on fm but not on Amc)depends on both Am and fmd)does not depends on Am or fmCorrect answer is option 'C'. Can you explain this answer?
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