EE104: Lecture 22 Outline

AnnouncementsHW due, final HW posted (due Monday, 3/17)Final exam Thursday, 3/20, 8:30-11:30amMore details next week

Review of Last Lecture Spectral Analysis of FM FM Bandwidth and Carson’s Rule Narrowband FM Modulation Wideband FM Modulation FM Detection

Review of Last Lecture

Vestigial Sideband ModulationTransmits a small part of unwanted sidebandDoes not cause distortion at basebandCan use a carrier or suppress the carrierStandard envelope detection or DSBSC

demod.

AM Radio Superheterodyne Receivers

Use IF downconversion and processingGets around reradiation and processing at fc.

Introduction to FM

Introduction to FMInformation signal encoded in carrier

frequency (or phase): s(t)=Accos((t))(t)=f(m(t))

Standard FM: (t)=2fct+2kf m()dSignal robust to amplitude variationsRobust to signal reflections and

refractionsInstantaneous frequency: fi=fc+kfm(t)Maximum Deviation: f=fc+kf|m(t)|

Bandwidth of S(f) depends on f.

Spectral Analysis of FM

s(t)=Accos(2fct+2kf m()dNonlinear function of m(t)Very hard to analyze for general m(t).

Let m(t)=cos(2fmt): Bandwidth fm

Spectrum S(f) is a sequence of delta functions at multiples of fm from fc

fcfc+fm fc+2fm fc+3fm fc+ 4fm

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

……f

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

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

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)+

-

FM Detection

Differentiator and Envelope Detector

Zero Crossing DetectorUses rate of zero crossings to estimate fi

Phase Lock Loop (PLL)Uses VCO and feedback to extract m(t)

t

fcfcc dmktftmkfAts0

])(22sin[)](22[)(

Main Points

Spectral analysis of FM difficult. For a simple cosine information signal, FM spectrum is discrete and infinite.

FM signal bandwidth depends on information signal amplitude. Carson’s rule yields B=2Bm+2f.

NBFM easy to analyze and is generated with a simple product modulator. WBFM harder to generate and to analyze.

In theory just need a differentiator and envelope detector for FM demodulation. Multiple methods used in practice