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

BN

PA

BN

PSNR mcs

0

2

0 2

USB LSB

)]2sin()()2cos()([)( tftmtftmAts chcc

M(f)

0 fc-fc

B-B

Coherent Detection of SSB

Same as detection of DSBSC

s(t) ProductModulator LPF

m(t)

Accos(2fct+

S(f) for USB

0 fc-fc

v(t)

V(f)

0 fc-fc-2fc 2fc

0 fc-fc

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 frequency10 KHz bandwidth, carrier in 530-1610 Khz

Receiver needs tight filtering to remove adjacent signals

LO can radiate out receiver front end Fix problems by IF processing

(Superheterodyne)

f1 f2 f3

Introduction to FMInformation signal encoded in

carrier frequency (or phase)

Modulated signal is s(t)=Accos((t))(t)=f(m(t))

Standard FM: (t)=2fct+2kfm()dInstantaneous frequency: fi=fc+kfm(t)Signal robust to amplitude variationsRobust to signal reflections and

refractions

FM Bandwidth and Carson’s Rule

Frequency Deviation: f=kf max|m(t)|Maximum deviation of fi from fc: fi=fc+kfm(t)

Carson’s Rule:

B depends on maximum deviation from fc AND how fast fi changes

Narrowband FM: f<<BmB2Bm

Wideband FM: f>>Bm B2f

B2f+2Bm

Spectral Analysis

s(t)=Accos(2fct+2kfm()dNonlinear function of m(t)Very hard to analyze with FTs

Let m(t)=cos(2fmt)Spectrum S(f) is a sequence of

delta functions at multiples of fm from fc

fc fm 2fm 3fm 4fm-4fm -3fm -2fm -fm

……f

S(f) for m(t)=cos(2fmt) NBFMB2Bm WBFMB2f

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

Acsin(2fct)

s(t)2kf(·)dt

(t)

-90o LO

+

Accos(2fct)+

-

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.