Analog Modulation Conventional AM
Analog Modulation Conventional AM
Conventional AM Quite similar to DSB-AM Easy to demodulate by employing envelope detector m(t) Normalize 1+am,(t) u(t)=A[1+am,(t)]cos(2nft) Scaling Add constant c(t)=Acos(2πft) 1 am(t)>0,Always -1≤m(t)≤l:Normalized message signal a:index of modulation
Conventional AM ◼ Quite similar to DSB – AM ◼ Easy to demodulate by employing envelope detector ( ) cos(2 ) c c c t A f t = ( ) [1 ( )]cos(2 ) 1 ( ) + am t n u t A am t f t = + c n c Normalize Scaling Add constant m t( ) 1 + amn (t) > 0, Always -1 mn (t) 1: Normalized message signal a: index of modulation
Generating 1 am(t)>0 Normalizing and Scaling m(t) mp m(t) -mp m(t)=mpmn(t) ·mn()=m(mp
Generating 1 + amn (t) > 0 ◼ Normalizing and Scaling ◼ m(t) = mpmn (t) ◼ mn (t) = m(t)/mp mn (t) 1 -1
Generating 1+am(t)>0 Define index of modulation ■0≤a≤1 Definition of New message signal m-1≤am()≤1 Add 1 to new message signal ■ ■0≤1+am)≤2 1+am.(t) 0
Generating 1 + amn (t) > 0 ◼ Define index of modulation ◼ 0 a 1 ◼ Definition of New message signal ◼ -1 amn (t) 1 ◼ Add 1 to new message signal ◼ 0 1 + amn (t) 2 1+amn (t) 2 0
AM signal and Envelope AM signal Envelope(for Ac=1) 2 Envelope 1+am.(t) 1+am (t) 0
AM signal and Envelope ◼ AM signal Envelope(for Ac=1) 1+amn (t) 2 0 1+amn (t)
Wrong choice of a >1 What happens if 1+am(t)<0 Hard to recover m(t)using envelope detector (1+amn(t)) Envelope |1+amp(t)l (1+amn()
Wrong choice of a > 1 ! ◼ What happens if 1 + amn (t) < 0 ◼ Hard to recover m(t) using envelope detector 0 1 |1+amn (t)| -(1+amn (t)) (1+amn (t))
Spectrum of conventional AM Modulated signal u(t)=A.[1+am,(t)]cos(2nft) ■ =A.cos(2πft)+A.amn(t)cos(2πfct) Carier Sidebands In frequency domain ■U)=26U-f)+f+)+aM,f-)+aM.U+】 M(f) Conventional-AM tU(f) 2W A Ac2/2 a2AAc/2 -W 0 W
Spectrum of conventional AM ◼ Modulated signal ◼ ◼ In frequency domain ◼ ( ) [1 ( )]cos(2 ) cos(2 ) ( ) cos(2 ) c n c c c c n c u t A am t f t A f t A am t f t = + = + Carrier Sidebands ( ) [ ( ) ( ) ( ) ( )] 2 c c c n c n c A U f f f f f aM f f aM f f = − + + + − + + -W 0 W f M(f) f U(f) fc -fc 2W Conventional-AM A Ac2 /2 a 2AAc2 /2
Power of conventional AM From the spectrum Power of modulated signal Power of Carrier Power of Sidebands Cross terms If message signal is zero mean signal (Cross terms =0) ·P=P+P=2+ 2 Useful power to transmit message Waste power by carrier
Power of conventional AM ◼ From the spectrum ◼ Power of modulated signal = Power of Carrier + Power of Sidebands + Cross terms ◼ If message signal is zero mean signal (Cross terms = 0) ◼ 2 2 2 2 2 n c c u c s m A A P P P a P = + = + Useful power to transmit message Waste power by carrier
Modulation efficiency ■Definition ■ 1+d2P% ■n>1asa→o ■Since m,(t)sl,a≤l,we have n≤0.5 "In practice,.n≈0.1 10%of total power is useful power 90%of total power is waste Carrier is filtered out at receiver Efficiency is very low
Modulation efficiency ◼ Definition ◼ ◼ → 1 as a → ◼ Since , we have ◼ In practice, 0.1 ◼ 10% of total power is useful power ◼ 90% of total power is waste ◼ Carrier is filtered out at receiver ◼ Efficiency is very low 2 2 1 n n s m u m P a P P a P = = + m t a n ( ) 1, 1 0.5
SNR of conventional AM SNR is reduced by the factor of n U(f)1 R(f) nAc2Pm/2 Transmit nPR -Distortion -LOSs N(f) White Gaussian Noise N/2 WNo 2W
SNR of conventional AM ◼ SNR is reduced by the factor of ◼ 0 0 ( ) S PR N N W = fc U(f) Ac 2Pm/2 Transmit -Distortion -Loss fc R(f) PR N(f) 2W N0 White Gaussian Noise /2 WN0