ECE 2C, notes set 11: Mixing, Modulation, Demodulation and ...

class notes, M. Rodwell, copyrighted 2013

ECE 2C, notes set 11: Mixing, Modulation, Demodulation and Radio

Mark Rodwell

University of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax


Goals of this note set

bandwidthn informatio ofconcept Rough

Receiverr / Transmitte Radio of Structure Basic

(AM) Modulation

Mixing


The Radio Spectrum

109

1010

1011

1012

1013

1014

1015

Frequency (Hz)

microwave

SHF*

3-30 GHz

10-1 cm

mm-wave

EHF*

30-300 GHz

10-1 mm

op

tica

l

38

5-7

90

TH

z

sub-mm-wave

THF*

0.3-3THz

1-0.1 mm

far-IR: 0.3-6 THz

ne

ar-IR

10

0-3

85

TH

z

3-0

.78

m

mid-IR

6-100 THz

50-3 m

104

105

106

107

108

109

1010

Frequency (Hz)

MF*

0.3-3 MHz

1000-100 m

HF*

3-30 MHz

100-10 m

VHF*

30-300 MHz

10-1 m

UHF*

0.3-3 GHz

1 m-10 cm

microwave

SHF*

3-30 GHz

10-1 cm

10-1

100

101

102

103

104

Wavelength (meters)

10-6

10-5

10-4

10-3

10-2

10-1

Wavelength (meters)

*ITU band designations ** IR bands as per ISO 20473


Frequencies of a Few Services (Rough #s)

109

1010

1011

1012

1013

1014

1015

Frequency (Hz)

radar sa

tellite

TV

sa

tellite

links

wire

less H

DM

I

ima

gin

g

104

105

106

107

108

109

1010

Frequency (Hz)

AM

rad

io

FM

rad

io

TV

TV

cell phones

WiFi

10-1

100

101

102

103

104

Wavelength (meters)

10-6

10-5

10-4

10-3

10-2

10-1

Wavelength (meters)


Choice of Transmission Frequency

earth theof Curvature

beam. blocking of Ease

size. antenna Required

bad. and weather good :nattenuatio cAtmospheri

.allocationfrequency Government


Nearly Isotropic Antennas

/2~ islenght y when effectivel radiates :antenna Dipole

antenna" wave-quarter"

plane. ground wideusingby

length in 1:2 reduced becan Antenna

plane lin vertica )cos(~ as variesand

plane, lin vertica isotropic ispattern radiation

http://en.wikipedia.org/wiki/File:Elem-doub-rad-pat-pers.jpg


Directional Antennas

Uda-Yagi

http://en.wikipedia.org/wiki/File:Two_meter_yagi.jpg http://en.wikipedia.org/wiki/Log-periodic_antenna

http://en.wikipedia.org/wiki/File:SuperDISH121.jpg

periodic-log

reflector

parabolic

patternradiation

ofplot Typical

http://en.wikipedia.org/wiki/Radiation_pattern


Signals we might want to transmit by radio

kb/s 320-32 :audio compressed MP3

Mb/s 100 ~ :WiFi

Mb/s 15about : HDTV Compressed

Gb/sec 1.5about :HDTV edUncompress

20kHz-20Hz :c)(optimisti hearinghuman of Range

kHz 4-0.4 :ion transmisssoundquality -Voice

waves.radioby them transmit toare weif

frequency in d translatebemust signals These

pattern eye


Spectra of Digital Signals

ece2c of scope thebeyond is

thisExplaining

rate.bit theis where

2/ to2/ from

extends train pulse a of spectrum the

period,bit a than lesssomewhat are

risetimes that so filteringAfter

B

BB


Frequency Conversion / Modulation

ation).(multiplic mixingby done isit ;modulation called is This

carrier.frequency -high on the signalour imposemust we this,do To

105

106

107

108

109

1010

1011

Frequency (Hz)

DCat centered is spectrum The

bandwidth. some occupying spectrum a has signalOur

GHz. 100 toMHz few perhapsbetween sfrequencie radio using signal the transmit We


Signal representation in this note set

spectra continuous haveusually and

n,informatio randomcarry signals Real

waves).(sine

lines spectral discrete as

signals theserepresent weif

easier be on willpresentati But the


Multiplying sinewaves easily (1)

? How easily. thisdo learn to should We

)cos()( and )cos()(

where

/)()()(

calculate toneed willWe

0

tVtVtVtV

VtVtVtV

MMMLOLOLO

MLORF



! s)'(1/ and s' into scosinewave and sinewaves * turnedhave We

sin2/1 :And

cos2/1 :So

write

.frequency at signal some have wesuppose : trickThe

zz

tjeezz

teezz

ez

M

tjtj

MM

M

tjtj

MM

tj

M

M

MM

MM

M

transform.- theinto ansformFourier tr econvert th to thisuse you willyear Next * z



tt

eeeeeeee

eeeeeeee

zzzzzzzz

zzzz

tt

zzeet

zzeet

MLOMLO

tjtjtjtjtjtjtjtj

tjtjtjtjtjtjtjtj

LOMLOMMLOLOM

LOLOMM

LOM

LOLO

tjtj

LO

MM

tjtj

M

LOMMLOLOMLOM

LOMLOMMLOLOM

LOLO

MM

)(cos2)(cos2

)()(

))((

)cos()cos(4

so

)cos(2

)cos(2

11111111

1111

11

11



tttt MLOMLOLOM )(cos2

1)(cos

2

1)cos()cos(

:Summarize


Multiplication of two signals in a mixer (1)

)cos()(

Message

tVtV MMM

)cos()(

Oscillator Local from Sinewave

tVtV LOLOLO

0/)()()( VtVtVtV LOMRF

0/)cos()cos()( VtVtVtV LOLOMMRF

0/)()()(

ed transmittbe tosignalFrequency -Radio

VtVtVtV LOMRF

)(tVM

)(tVLO


Multiplication of two signals in a mixer (2)

)(tVRF)(tVM

)(tVLO

tV

VVt

V

VVtV MLO

o

LOMMLO

o

LOMRF )(cos

2)(cos

2)(

0/)cos()cos()( VtVtVtV LOLOMMRF

so

)(cos2

1)(cos

2

1)cos()cos(

but

tttt MLOMLOLOM


(Suppressed Carrier) Amplitude Modulation Transmitter

tV

VVt

V

VVtV MLO

o

LOMMLO

o

LOMRF )(cos

2)(cos

2)(

0/)cos()()( VtVtVtV LOLOMRF

radiated and amplified, filtered,then

,oscillator localagainst multiplied is signal Message

then),cos()( if So tVtV MMM


(Suppressed Carrier) AM Waveforms

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

Message

Oscillator Local

Signal dTransmitte


(Suppressed Carrier) AM Waveforms

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

biggerdrawn :Signal dTransmitte


(Suppressed Carrier) AM Fourier Spectra

tjLOtjLOLOLOLO

LOLO eV

eV

tVtV

22

)cos()(

tjMtjMMMM

MM eV

eV

tVtV

22

)cos()(

tjtjtjtj

o

LOM

MLO

o

LOMMLO

o

LOMRF

MLOMLOMLOMLO eeeeV

VV

tV

VVt

V

VVtV

)()()()(

4

)(cos2

)(cos2

)(


(Suppressed Carrier) AM Receiver

)2cos(2

)(2

)(

)2cos(121)/()(

)(cos)/()(

/)cos()()(

/)cos()cos()(

2

0

2

2

0

2

2

0

22

0

0

0

tV

VtV

V

VtV

tVVtV

tVVtV

VtVtVtV

VtVtVtV

LOLO

MLO

M

LOLOM

LOLOM

LOLORFREC

LOLOMMRF

LOat wavesine aagainst multiplied is signal received The

0/)cos()()( VtVtVtV LOLORFREC

)(tVRF

scopeour beyond is This ion.configurat *odynesuperheter* a use receivers Typical


(Suppressed Carrier) AM Receiver

)2cos(2

)(

2)()(

2

0

2

2

0

2

tV

VtV

V

VtVtV

LOLO

M

LOMREC

message ed transmittThe

filterby removed

.2at wavesine a

modulating message thePlus

LO

etc. losses,n propagatio gains, amplifier by changed are amplitudes signal absolute The

)(tVRF0/)cos()()( VtVtVtV LOLORFREC


Suppressed Carrier AM: Comments

AM"" : techniquemodified a used systems radioEarly

1970~ untildifficult radio, of daysearly in theDifficult

loop.-locked-phase using ,Easy today

receiver. in the LO edsynchroniz requiresRecovery Signal

format modulation digital usedWidely

keying"shift phaseBinary "

BPSK. asknown is AMcarrier suppressed

pulses, digital of series a is message theIf


Amplitude Modulation Transmitter

tV

VV

tV

VVt

V

VVtV

LO

o

LODC

MLO

o

LOMMLO

o

LOMRF

cos

)(cos2

)(cos2

)(

0/)cos()()( VtVVtVtV LOLODCMRF

modulation before message the toadded is level DC

then),cos()( if So tVtV MMM


AM Waveforms

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.5 1 1.5 2

VR

F(t

)

time

Message

Oscillator Local

Signal dTransmitte

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.5 1 1.5 2

VR

F(t

)

time


AM Waveforms

biggerdrawn :Signal dTransmitte

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.5 1 1.5 2

VR

F(t

)

time


AM Fourier Spectra

LOat power carries signal ed transmitthein that t differs AM

easy.on demodulati Makes

power. RF ed transmittof Wasteful


AM Receiver

detector-peak diode awith

detected is signal received theof amplitude The

)(tVRF

amplitude waveformRF ofpeak tochargesCapacitor

period. veformcarrier wan longer thamuch :constant timeRC

period. waveformsignalan shorter thmuch :constant timeRC

radio of daysearly since feasible :circuitreceiver Simple

scopeour beyond is This ion.configurat *odynesuperheter* a use receivers Typical


Superheterodyne Receiver (Amstrong, 1918)

selection. channelfor used are filters IF tuned-fixed Sharp

frequency. LO theby varying tunedis frequency signal Received

detection. before

frequency teintermediaan toconverted is signal radio Receive


Spectral Requirements: AM

bandwidth 10kHz occupies signal ed transmittthen the

5kHz,-DC (say) toedresistrict is signal ic voice/mus theIf

10kHz. by spaced bemust

signals AM then music, 5kHz-DC want weIf :So


Mixers and Modulators are Usually Switches

LOfrequency at on/off turnedswitches simple :mixersMost

enough.usually isswitch a :necessarynot are smultiplier True

effort. but take---possible are smultiplier True

? signals twomultipliesich circuit wh aconstruct wedo How

)(tVRF)(tVM

)(tVLO


Mixing with a Switch

)( squarewave a with )( signalmultiply We tStVRF

input

alDifferenti

output

alDifferenti

)(tS

closed. is open when is

:switchesfour with done is This

21


Mixing with a Switch

termsmixing mixing undesired etc. )5cos( ),3cos(

)(... termsmixing desired )cos(4

....5

)5cos(

3

)3cos()cos(

4)(

)()()(

tt

t

ttttS

tVtStV

LOLO

LORFLO

LOLOLO

RFIF

input

alDifferenti

output

alDifferenti

)(tS


Diode Double Balanced Mixer

connection IF-RF negative on, diodes crossedLO Negative

connection IF-RF PositiveLO Positive

diodes. (Schottky) with dimplemente are switches 4 The

)(tS


FET Unbalanced Mixer

currents. RF and LO strong has alsoport IF

wave.squareby dmulitiplie form waveRF iscurrent IF

off. ispath ....signal

zero. to reducing zero, toreduced is Q1 of low, is LOWhen

on. ispath ....signal

signal... RFfor stage gate-common as operates Q2 high, is LOWhen

1mds gV

)(tS


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ECE 2C, notes set 11: Mixing, Modulation, Demodulation and ...

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