EEEE2044:Analogue AM, FM and PM Modulation and Demodulation

Question 1

State two applications of AM modulation

Answer 1

• Broadcasting (AM Radio)
• Communicating between aircraft

Question 2

State when modulation occurs

Answer 2

• When the modulation index < 1

Question 3

State what happens as the modulation index increases in the time domain

Answer 3

• The trough of the top wave and the peak of the bottom wave get closer together

Question 4

State the equation for the modulation index, μ

Answer 4

• μ = (Modulating or sideband amplitude)/Carrier Amplitude
• μ = Am/Ac

Question 5

State the equations used to find the modulation index from frequency domain spectrum

Answer 5

• 𝑁𝑑𝐵 = 20 𝑙𝑜𝑔(μ/2)
• 𝑁𝑑𝐵 = Carrier Amplitude - Lower Side Band Amplitude
• μ = 2 x 10^(𝑁𝑑𝐵/20)

Question 6

State the formula for Power used by the carrier

Answer 6

• Pcarrier = Ac²/2R

Question 7

State the formula for Power used by one sideband

Answer 7

• Psideband = (Am²/2R) x 1/R = Am²/8R = (μ² x Ac²)/8R

Question 8

State the formula for total power in an AM Modulated Signal

Answer 8

• Ptotal = Pcarrier + 2(Psideband) = Ac²/2R(1 + μ²/2)

Question 9

State the equation for Power efficiency of AM Modulation, η

Answer 9

• η = 2(Psideband)/Ptotal = 2μ²Ac²/8R x 2R/Ac²(1 + μ²/2)
• η = μ²/2 x (2/2+μ²)
• η = μ²/2+μ²

Question 10

State the advantages of SSB-SC compared to DSB-AM

Answer 10

• Uses less Bandwidth
• Saves more power
• Reduces amount of noise in signal
• SSB transmitters can be made smaller and lighter

Question 11

Explain the difference in bandwidth content between DSB-SC and DSB-SC AM modulations?

Answer 11

• DSB-AM transmits the carrier and lower sidebands
• DSB-SC AM has no carrier in spectrum, only upper and lower sidebands

Question 12

State the expression of a DSB-AM signal over time

Answer 12

• Xam(t) = Am/2 x (cos(ω𝑐 ± ω𝑚)t) + A𝑐cosω𝑐t

Question 13

State the equation for frequencies of the Carrier, Lower Sideband and Upper Sideband

Answer 13

• Carrier = ω𝑐 = 2πf𝑐
• Lower Sideband = ω𝑐 - ω𝑚
• Upper Sideband =
  ω𝑐 + ω𝑚

Question 14

State the equation for Bandwidth of a modulated signal

Answer 14

• Bandwidth = 2 x fm = Upper Sideband - Lower Sideband

Question 15

In FM Modulation, when is the frequency of the modulated signal highest?

Answer 15

• Frequency highest when modulated signal amplitude is highest

Question 16

In FM Modulation, when does the frequency of the modulated signal match the carrier frequency?

Answer 16

• When the modulating voltage is 0

Question 17

State the expression of a PM signal over time

Answer 17

• Xpm(t) = Acos[ω𝑐t + kpm(t)]

Question 18

State the expression of a FM signal over time

Answer 18

• Xfm(t) = Acos[ω𝑐t + βsin(ω𝑚t)]

Question 19

State the equation for the FM modulation index, β

Answer 19

• ∆𝜔 = 𝑘𝑓Am
• β = 𝑘𝑓Am/ω𝑚 =
  ∆𝜔/ω𝑚 = ∆𝑓/𝑓𝑚

Question 20

State the equation for the series of a FM signal with sinusoidal input

Answer 20

• Xfm(t)= A x Σ(∞ to -∞)
  Jn(β )cos(ω𝑐 + nω𝑚)t

Question 21

State the equation for the Bessel Function

Answer 21

• Jn(β)= 1/π x ∫(π to 0)
  cos(βsint - nt)dt

Question 22

Should the calculator be in Degrees or Radians when using the Bessel function equation?

Answer 22

• Radians