Tele3113 wk3tue

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Tele3113 wk3tue

  1. 1. TELE3113 Analogue and Digital Communications Amplitude Modulation Wei Zhang w.zhang@unsw.edu.au School of Electrical Engineering and Telecommunications The University of New South Wales
  2. 2. Modulation Modulation is defined as the process by which some characteristics of a carrier wave is varied in accordance with an information-bearing signal. amplitude modulation (AM) (varying amplitude) angle modulation (varying phase or frequency) AM family: amplitude modulation double sideband-suppressed carrier (DSB-SC) single sideband (SSB) vestigial sideband (VSB) TELE3113 - Amplitude Modulation. August 4, 2009. – p.1/1
  3. 3. Amplitude Modulation (1) Consider a sinusoidal carrier wave c(t) defined by c(t) = Ac cos(2πfct), where Ac is the carrier amplitude and fc is the carrier frequency. Amplitude modulation (AM) is a process in which the amplitude of the carrier wave c(t) is varied linearly with the message signal m(t). An AM wave is: s(t) = Ac[1 + kam(t)] cos(2πfct). where ka is a constant called the amplitude sensitivity. TELE3113 - Amplitude Modulation. August 4, 2009. – p.2/1
  4. 4. Amplitude Modulation (2) In AM, information resides solely in the envelop, i.e., Ac|1 + kam(t)|, which has the same shape as the message signal m(t). In order to properly detect the information, the shape of the envelop of the modulated signal should be unchanged in the modulation. Specifically, 1. The amplitude of kam(t) < 1 for all t; 2. The carrier frequency fc >> W, where W is the message bandwidth. TELE3113 - Amplitude Modulation. August 4, 2009. – p.3/1
  5. 5. Amplitude Modulation (3) AM wave for kam(t) < 1. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 −20 0 20 Carrier Wave c(t) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 −1 0 1 Message Signal m(t) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 −40 −20 0 20 40 Amplitude Modulated Wave s(t) TELE3113 - Amplitude Modulation. August 4, 2009. – p.4/1
  6. 6. Amplitude Modulation (4) AM wave for |kam(t)| > 1. Over modulated. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 −20 −10 0 10 20 Carrier Wave c(t) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 −0.5 0 0.5 1 Message Signal m(t) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 −200 −100 0 100 200 Amplitude Modualted Signal s(t) Phase reversal TELE3113 - Amplitude Modulation. August 4, 2009. – p.5/1
  7. 7. FT of AM (1) Consider the AM signal, s(t) = Ac[1 + kam(t)] cos(2πfct). The Fourier transform of s(t) is given by S(f) = Ac 2 [δ(f − fc) + δ(f + fc)] + kaAc 2 [M(f − fc) + M(f + fc)]. We used the relations: exp(j2πfct) ⇔ δ(f − fc) m(t) exp(j2πfct) ⇔ M(f − fc) (Shifting Property) TELE3113 - Amplitude Modulation. August 4, 2009. – p.6/1
  8. 8. FT of AM (2) )( fS )( fM WW− 0 0 Wfc −− Wfc +−cf− Wfc − Wfc +cf )( 2 c c ff A −δ)( 2 c c ff A +δ )0( 2 M Ak ca )0(M f f Upper sideband Lower sideband Spectrum of message signal Spectrum of AM wave signal TELE3113 - Amplitude Modulation. August 4, 2009. – p.7/1
  9. 9. Example: Single-Tone AM (1) Consider a message signal with a single tone, m(t) = Am cos(2πfmt). The corresponding AM wave is therefore given by s(t) = Ac[1 + µ cos(2πfmt)] cos(2πfct), where µ is called the modulation factor or percentage modulation, as µ = kaAm. TELE3113 - Amplitude Modulation. August 4, 2009. – p.8/1
  10. 10. Example: Single-Tone AM (2) Let Amax and Amin denote the maximum and minimum values of the envelope of the modulated wave, respectively. Then, Amax = Ac(1 + µ), Amin = Ac(1 − µ). Rearranging the equation, we may express the modulation factor as µ = Amax − Amin Amax + Amin . TELE3113 - Amplitude Modulation. August 4, 2009. – p.9/1
  11. 11. Example: Single-Tone AM (3) 0 0.5 1 1.5 −20 0 20 Carrier wave 0 0.5 1 1.5 −1 0 1 Message signal 0 0.5 1 1.5 −50 0 50 µ=0.5 0 0.5 1 1.5 −50 0 50 µ=1 0 0.5 1 1.5 −50 0 50 µ=1.5 TELE3113 - Amplitude Modulation. August 4, 2009. – p.10/1
  12. 12. Example: Single-Tone AM (4) For the single-tone signal, we may express it as s(t) = Ac cos(2πfct)+ µAc 2 cos[2π(fc+fm)t]+ µAc 2 cos[2π(fc−fm)t]. The Fourier transform of s(t) is therefore S(f) = Ac 2 [δ(f − fc) + δ(f + fc)] + µAc 4 [δ(f − fc − fm) + δ(f + fc + fm)] + µAc 4 [δ(f − fc + fm) + δ(f + fc − fm)]. TELE3113 - Amplitude Modulation. August 4, 2009. – p.11/1
  13. 13. Example: Single-Tone AM (5) Carrier power = 1 2 A2 c Upper sideband power = 1 8 µ2A2 c Lower sideband power = 1 8 µ2 A2 c Total sideband power Total sideband power+Carrier power = µ2 2+µ2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Percentage modulation factor µ Ratiooftotaltransmittedpower Sidebands Carrier TELE3113 - Amplitude Modulation. August 4, 2009. – p.12/1
  14. 14. Envelop Detection Envelope detection is a demodulation process which is responsible for extracting the message signal m(t) from the modulated signal s(t). Output AM wave )(ts sR C lR TELE3113 - Amplitude Modulation. August 4, 2009. – p.13/1
  15. 15. Pros and Cons of AM Pros: Easily generated and inexpensive to build. Cons: Waste of transmitted power. The carrier power is useless. Waste of channel bandwidth. Due to the symmetry, only upper or lower sideband is needed. Modifications of AM: Double sideband-suppressed carrier (DSB-SC) modulation Single sideband (SSB) modulation Vestigial sideband (VSB) modulation TELE3113 - Amplitude Modulation. August 4, 2009. – p.14/1

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