EE104: Lecture 21 Outline Review of Last Lecture Vestigial Sideband Modulation AM Radio Introduction to FM FM Bandwidth and Carson’s Rule Narrowband and Wideband FM

Review of Last Lecture Noise in AM Receivers: DSBSC Single Sideband Modulation USB LSB M(f) 0 fcfc -f c B -B

Coherent Detection of SSB Same as detection of DSBSC s(t) Product Modulator LPF m(t) A c cos(2  f c t+  S(f) for USB 0 fcfc -f c v(t) V(f) 0 fcfc -f c -2f c 2f c 0 fcfc -f c 1.5 M(f)=.5M(f).5

Vestigial Sideband Transmits upper or lower sideband and vestige of other band Reduces bandwidth by roughly a factor of 2 Generated using standard AM or DSBSC modulation, then filtering Standard AM or DSBSC demodulation USB

AM Radio and Superheterodyne Receivers Multiplexes AM radio signals in frequency 10 KHz bandwidth, carrier in Khz Receiver needs tight filtering to remove adjacent signals LO can radiate out receiver front end Fix problems by IF processing (Superheterodyne) f1f1 f2f2 f3f3

Introduction to FM Information signal encoded in carrier frequency (or phase) Modulated signal is s(t)=A c cos(  (t))  (t)=f(m(t)) Standard FM:  (t)=2  f c t+2  k f  m(  )d  Instantaneous frequency: f i =f c +k f m(t) Signal robust to amplitude variations Robust to signal reflections and refractions

FM Bandwidth and Carson’s Rule Frequency Deviation:  f=k f max|m(t)| Maximum deviation of f i from f c : f i =f c +k f m(t) Carson’s Rule: B depends on maximum deviation from f c AND how fast f i changes Narrowband FM:  f<<B m  B  2B m Wideband FM:  f>>B m  B  2  f B  2  f+2B m

Spectral Analysis s(t)=A c cos(2  f c t+2  k f  m(  )d  Nonlinear function of m(t) Very hard to analyze with FTs Let m(t)=cos(2  f m t) Spectrum S(f) is a sequence of delta functions at multiples of f m from f c fcfc fmfm 2f m 3f m 4f m -4f m -3f m -2f m -f m …… f S(f) for m(t)=cos(2  f m t) NBFM B  2B m WBFM B2fB2f

Generating FM Signals NBFM WBFM Direct Method: Modulate a VCO with m(t) Indirect Method: Use a NBFM modulator, followed by a nonlinear device and BPF m(t) Product Modulator A c sin(2  f c t) s(t) 2  k f  (·)dt  (t) -90 o LO + A c cos(2  f c t) + -

Main Points VSB similar to SSB, uses slightly more BW for a lower DC distortion. AM radios and many other systems downconvert to IF before demodulation. FM modulation encodes information in carrier frequency or phase. More robust to channel impairments. FM signal bandwidth depends on information signal amplitude. NBFM is easier to analyze and generate (simple product modulator). WBFM more complicated to analyze and generate.