Tele3113 wk3tue

TELE3113 Analogue and Digital Communications Amplitude Modulation Wei Zhang w.zhang@unsw.edu.auSchool of Electrical Engineering and Telecommunications The University of New South Wales

ModulationModulation is deﬁned as the process by which somecharacteristics of a carrier wave is varied in accordance with aninformation-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

Amplitude Modulation (1) Consider a sinusoidal carrier wave c(t) deﬁned by c(t) = Ac cos(2πfc t), 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 + ka m(t)] cos(2πfc t). where ka is a constant called the amplitude sensitivity. TELE3113 - Amplitude Modulation. August 4, 2009. – p.2/1

Amplitude Modulation (2) In AM, information resides solely in the envelop, i.e., Ac |1 + ka m(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 ka m(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

Amplitude Modulation (3)AM wave for ka m(t) < 1. Carrier Wave c(t) 20 0 −20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Message Signal m(t) 1 0 −1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Amplitude Modulated Wave s(t) 40 20 0 −20 −40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 TELE3113 - Amplitude Modulation. August 4, 2009. – p.4/1

Amplitude Modulation (4)AM wave for |ka m(t)| > 1. Over modulated. Carrier Wave c(t) 20 10 0 −10 −20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Message Signal m(t) 1 0.5 0 −0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Amplitude Modualted Signal s(t) 200 Phase reversal 100 0 −100 −200 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 TELE3113 - Amplitude Modulation. August 4, 2009. – p.5/1

FT of AM (1)Consider the AM signal, s(t) = Ac [1 + ka m(t)] cos(2πfc t).The Fourier transform of s(t) is given by Ac ka AcS(f ) = [δ(f − fc ) + δ(f + fc )] + [M (f − fc ) + M (f + fc )]. 2 2We used the relations: exp(j2πfc t) ⇔ δ(f − fc ) m(t) exp(j2πfc t) ⇔ M (f − fc ) (Shifting Property) TELE3113 - Amplitude Modulation. August 4, 2009. – p.6/1

FT of AM (2) Spectrum of message signal M ( f ) M (0) f −W 0 W Spectrum of AM wave signal S ( f ) Ac Ac δ ( f + fc ) k a Ac δ ( f − fc ) 2 M (0) 2 2 Lower Upper sideband sideband − fc − W − fc − fc + W fc − W fc fc + W f 0 TELE3113 - Amplitude Modulation. August 4, 2009. – p.7/1

Example: Single-Tone AM (1)Consider a message signal with a single tone, m(t) = Am cos(2πfm t).The corresponding AM wave is therefore given by s(t) = Ac [1 + µ cos(2πfm t)] cos(2πfc t),where µ is called the modulation factor or percentagemodulation, as µ = k a Am . TELE3113 - Amplitude Modulation. August 4, 2009. – p.8/1

Example: Single-Tone AM (2)Let Amax and Amin denote the maximum and minimum values ofthe envelope of the modulated wave, respectively. Then, Amax = Ac (1 + µ), Amin = Ac (1 − µ).Rearranging the equation, we may express the modulation factoras Amax − Amin µ= . Amax + Amin TELE3113 - Amplitude Modulation. August 4, 2009. – p.9/1

Example: Single-Tone AM (3) Carrier wave µ=0.5 20 50 0 0 −20 −50 0 0.5 1 1.5 0 0.5 1 1.5 Message signal µ=1 1 50 0 0 −1 −50 0 0.5 1 1.5 0 0.5 1 1.5 µ=1.5 50 0 −50 0 0.5 1 1.5 TELE3113 - Amplitude Modulation. August 4, 2009. – p.10/1

Example: Single-Tone AM (4)For the single-tone signal, we may express it as µAc µAcs(t) = Ac cos(2πfc t)+ cos[2π(fc +fm )t]+ cos[2π(fc −fm )t]. 2 2The Fourier transform of s(t) is therefore Ac S(f ) = [δ(f − fc ) + δ(f + fc )] 2 µAc + [δ(f − fc − fm ) + δ(f + fc + fm )] 4 µAc + [δ(f − fc + fm ) + δ(f + fc − fm )]. 4 TELE3113 - Amplitude Modulation. August 4, 2009. – p.11/1

Example: Single-Tone AM (5) Carrier power = 1 A2 2 c Upper sideband power = 1 µ2 A2 8 c Lower sideband power = 1 µ2 A2 8 c Total sideband power µ2 Total sideband power+Carrier power = 2+µ2 1 0.9 0.8 Ratio of total transmitted power 0.7 Carrier 0.6 0.5 0.4 0.3 Sidebands 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 TELE3113 - Amplitude Modulation. August 4, 2009. – p.12/1 Percentage modulation factor µ

Envelop DetectionEnvelope detection is a demodulation process which isresponsible for extracting the message signal m(t) from themodulated signal s(t). Rs Rl C Output AM wave s(t ) TELE3113 - Amplitude Modulation. August 4, 2009. – p.13/1

Pros and Cons of AMPros: 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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