1Lecture 15 Outline Announcements Regular HWs for rest of quarter (2 more HWs after this weeks) 20 MT bonus points for correcting MT mistakes; turn in by 5pm today to Pat with your graded exam (or a copy), 94+ need not do corrections MT regrades: Solns posted tonight, regrade requests with original MT should be in writing: entire exam regraded Introduction to Angle Modulation and FM Relation between PM and FM FM Bandwidth and Carsons Rule FM Spectral Analysis FM Modulation FM DetectionReview of Last Lecture Vestigial Sideband Modulation Quadrature Modulation Coherent Detection: VCOs and PLLs The Costas LoopProductModulatorProductModulatorAccos( ct+ )m(t)LPFLPFPhaseDiscriminatorVCO-90ocos( ct+ (V))sin( ct+ (V))V=sin2( ( ( ( )/8 /8 /8 /8.5Accos( )m(t).5Acsin( )m(t) (V)V 0DSBSCDemodulatorIntroduction to Angle Modulation and FM Information encoded in carrier freq./phase Modulated signal is s(t)=Accos( (t)) (t)=f(m(t)) Standard FM: (t)=2 fct+2 kf m( )d Instantaneous frequency: fi=fc+kfm(t) Signal robust to amplitude variations Robust to signal reflections and refractions Analysis nonlinear Hard to analyzeFM Bandwidth and Carsons Rule Frequency Deviation: f=kf max|m(t)| Maximum deviation of ifrom c: i= c+kfm(t) Carsons Rule: Bsdepends on maximum deviation from cANDhow fast ichanges Narrowband FM: fBm Bs 2 fBs 2 f+2Bm2Spectral Analysis of FM s(t)=Acos( ct+kf m( )d) ) ) ) Very hard to analyze for general m(t). Let m(t)=cos( mt): Bandwidth fm S(f) sequence of functions at f=fcnfm If f fm, significant components up to fc f.S(f) for m(t)=cos(2fmt)NBFMB2BmAc-.5Ac.5Acfcfc+fm fc+2fmfc+3fmfc+ 4fmfc -4fmfc -3fmfc -2fm fc-fmf .5AcJn()B2fWBFM.5AcJn()Generating FM Signals NBFM WBFM Direct Method: Modulate a VCO with m(t) Indirect Method m(t)ProductModulatorAsin( ct)s(t)2kf( )dt (t)-90oLO+Accos( ct)+-ProductModulator(k1,f1)m(t)s1(t)NonlinearDevices2(t)BPF s(t)) ( ... ) ( ) ( ); ) ( 2 2 cos( ) (1 1 201 1 1t s a t s a t s d m k t f A t snntc+ + = + = terms other + + =) ) ( 2 2 cos(01 1td m nk t nf A terms other + + =) ) ( 2 2 ( cos ) (01 1 2tn nc nd m k t f A a t s FM Detection Differentiator and Envelope Detector Zero Crossing Detector Uses rate of zero crossings to estimate i Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t) + + =tf c f cd m k t t m k A t s ] ) ( sin[ )] ( [ ) ( &Main Points FM modulation encodes information in signal frequency. More robust to amplitude errors FM modulation nonlinear. Bandwidth approximate by Carsons rule: Bs 2 f+2Bm Spectral analysis of FM difficult. For a simple cosine information signal, FM spectrum is discrete and infinite. NBFM is easier to analyze and generate (simple product modulator). WBFM more complicated to analyze and generate In theory just need differentiator and envelope detection for FM. Many techniques used in practice (mostly VCO).