Linear and non-linear modulation systems: All bandpass modulated waveform can be represented by'v(t)=Re(g(t)ejoct? The desired type of modulated waveform,s(t), is defined bythe mapping function g[.]Linear modulation----Amplitude Modulation (AM)Mapping function: gAM[.]=Ac[1+.]Modulated waveform:s(t)=Re(Ac[1+m(t)] ejoct)= Ac[1+m(t)]cos0ctSpectrum:S(f)=1/2Ac[8(f+f.)+M(f+f)+s(f-fo))+M(f-f)): Normalized average power of s(t):<s2(t)>=1/2A.2+1/2 A.2<m2(t)>
• All bandpass modulated waveform can be represented by: v(t)=Re{g(t)ejωc t} • The desired type of modulated waveform,s(t), is defined by the mapping function g[.]. • Linear modulation-Amplitude Modulation (AM) • Mapping function: gAM[.]=Ac[1+.] • Modulated waveform: s(t)=Re{Ac[1+m(t)] ejωc t}= Ac[1+m(t)]cosωc t • Spectrum:S(f)=1/2Ac[δ(f+fc)+M(f+fc)+δ(f-f0)]+M(f-fc)] • Normalized average power of s(t): <s2 (t)>=1/2Ac 2+1/2Ac 2<m2 (t)> Linear and non-linear modulation systems
AM system diagram----modulation:m(t)A[1+m(t)]cosoctLocaloscillatorAccosoctdemodulation:EnvelopeBPFdetectorNoisy s(t)m'(t)LPFBPFNoisy s(t)m'(t)cosoct
• AM system diagram-modulation: • demodulation: Local oscillator m(t) Accosωct Ac[1+m(t)]cosωct BPF Envelope Noisy s(t) detector m’(t) BPF Noisy s(t) m’(t) cosωct LPF
Spectrum ofAM waveformM(f)f-BBS(f)41/28(f-fo)1/21/2M(f-f)ff.WhereA.-l
• Spectrum of AM waveform: f M(f) -B B 1 fc f S(f) 1/2 1/2δ(f-f0) 1/2M(f-fc) Where Ac=1
Some definitions:AM modulation: A[1+m(t)]coso;where | m(t) |≤1The percentage of positive modulation on an AM signal is%positive modulation=(Amax-A.)/A.*100=max ( m(t)}*100The percentage of negative modulation is:%negative modulation=(Ac-Amin)/A。*100=-min( m(t)) *100The overall modulation percentage is:%modulation= (Amax-Amin)/2 A={ max[m(t)]-min[m(t)])/2* 100Where Amax and Amin is Ac[1+m(t)]'s maximum andminimum values, is the level of the AM envelope whenm(t)=0.The modulation efficiency is the percentage of the totalpower of the modulated signal that convoys information
• Some definitions: • AM modulation: Ac[1+m(t)]cosω;where │m(t)│≤1 • The percentage of positive modulation on an AM signal is: %positive modulation=(Amax-Ac)/Ac*100=max{m(t)}*100 • The percentage of negative modulation is: %negative modulation=(Ac-Amin)/Ac*100=-min{m(t)}*100 • The overall modulation percentage is: %modulation= (Amax-Amin)/2Ac={max[m(t)]-min[m(t)]}/2*100 • Where Amax and Amin is Ac[1+m(t)]’s maximum and minimum values, is the level of the AM envelope when m(t)=0. • The modulation efficiency is the percentage of the total power of the modulated signal that convoys information
In AM signaling,we have:E=<m?(t)>/[1+ <m2(t)>1*100%m(t) 1Ac[1+m(t)]Amaxs(tAcAmint
• In AM signaling,we have: E=<m2 (t)>/[1+ <m2 (t)>]*100% m(t) t t s(t) Amax Amin Ac s(t) Ac[1+m(t)]