chapter 6 digital transmission.pdf

8/10/2019 CHAPTER 6 DIGITAL TRANSMISSION.pdf

1/45

A

Digital

Transmission

:TEFI

OUTLINE

-

rduction

.e

\4odu

larion

\t

\l

Sanrpling

-:rul-to

Quantization

Noise

Ratio

-'iLt-\'crsus Nonlinear

pCM

Codcs

:

Channc'l

Noise

-:ing

l

e

lhods

()

()

Compandino

l,

lr)

Vocoder\

()

ll

PCN{

Line

Specd

r,

ll

Della

\,[odularion

pCM

6-

I

.i

Aclaprir

e Dclla

N,lodularion

pC\,I

(,

l+

Ditlerentiai

pCM

(r

l.

Pulse

Tritnsrnission

()

i(r

Si-snal

Pou.er

in

Binarv

Digital

Si-unals

.:TIVES

:

:

i:lle d i

i I

e

I

I

rLt t.t t t

t

i.t \

i

otl

.:

and

dcrcribe

the

rd\

artage\

and disiLdYantnges

0f

digital

transmission

jtl

de\cribe

pulse

N

idth

nroduiatirrn_

pul,,e

pl,,ition

,"n.f"f,ri,,n.

,,nJ

prlsc

anrplitude

nrodulittion

'rc

ll),1

Ll(.(rihr prrlse

c,rJr,

rnoJul:rtiun

:litin

flat-top

and

narural

sanrplin-sl

-..ribe

the Nrquisl

sanrpling

lheorcnr

..

ribc

lirlde'd

binary

codes

i

:oe

and

e\plain

dttttttttic

ntn.qc

:-i.rin

PCNI

coding

c

iciencv

.

.-

rihc sir:rrrl-r,r

qulnli,/Jltol)

D,,i\c

rJtt(r

i.rin

the

dit'lerence

betteen

linerr

and

nonlinear

pCM

codcs

..-

ribe

idle

channel

noisc

:'i.Lin

several

comnton coding

ntethods

.

.ne

utrttlturtling

itnd

expiain

analog

and di-uital

cornpanding

'

trc

d

i

gita

I

rrtn

p

re

ss

ion

273

PT


2/45

t

I

T

I

I

I

I

T

T

Dc.crihc

r

ocodcrs

Erplain

hou

ro

determine PCM line

speed

De..ribc'

d.ltr

modulation PCM

De.eribc aJaptir.-

delta

modulation

Dciine

rnJ describe dit.ferential

pulse

codc modulation

lle.rribe

the composition ol di-sital

pulses

Erpl"in intc-r's)

mbol

interf

er-elce

Erl.llin

eve

patterns

Erplain

the signal

po\\cr

dishibution in

binar),digital

signals

6.1

INTRODUCTION

A\ stirted

previousl)

. digitol

trunsntis.\iolr is the transmittal of di-uital signals

betuee

-r"

otnrorepointsiniicolnrrunicationssystcm.Thcsignalscanbebinaryoranyothertir-:

discrete levcl digital

pulses.

The

original source information may be in digital forn:

-:

could

be

anriog signnis

that have

been

converted

to

digital

pulses prior

to

trun\mi\s1..

-a

converted

back

to

anakrg signals in thc rcccivcr. With digital

transmission

systems.

ii:-

-

ical facilitl. such

as a

pair

of

wires.

coaxial

cable. or an

optical fiber

cable. is

requr:.-

:

intcrconnect the larioLr\

points

within

the system. The

pulses

are

contained

in

and

p

:r-

gate

doun tire cable. Digital

pulses

cannot be

plopagated

through a wireless transn..-

r

slslem.

such

as

Earth's atmosphele

or

tiee space

(vacuum).

,AT&T

de\

eloped

the

ti

rst

digital

transmission

system

fbr

the

purpose of

canl

ir: :--

itrll) encoded

irnalog signals. such as

the

human

rrrice.

over metallic wire cables

be:.

telephone

ollices.

Todal'.

digital

transmission systems are used to cirry not

only

di-i

-r"

encoded

r

oice

and

Yideo

signals

but also

digital

source infonnation

directly between

-

putcrs

and

corlputer

networks.

Digital

transmission systems

use

both metallic and

(.:-

flber cables tbl their transnrission

medium.

6-''l-1

Advantages

of

Digital Transmission

The

plinrarl

atlr antage

ol digital tron\mission

over analog transmission is noise

ini .

'

-

Digital

signals are inherently

less

susceptible than analog signals

to interference

cau:::

noise because

rith

di-uital signals

it

is not

necessary

to

evaluate the

precise

amplitudl

quenc].

or

phase

1o Isccrtain its logic

condition. Instead.

pulses

are evaluated

during.:

cise tinle inter\al.

rnd

a

simple determination is

made

whether

the

pulse

is

above

or

-

r

prescribed

reter-ence

Ievel.

Digital signals

are

also better suited

than analog signals tbr

processing

and cor::

ing using a technique

calJed

nultiple.ring.

Digital

signal

processing

(DSP)

is the

pr..,:

ing

of

analos signals

using digital methods and includes

bandlimiting

the signal

\\

ii

tels.

amplitude equalization. and

phase

shifiing.

It

is

much

simpler to

store

digital

sL--

thiin analog signals.

and

the trunsmission

rate of

digital

signals can

be easily chang.,

ldapt to dillerent

envilonments

and to

intedhce with dilferent

types of equipmenr.

In

addition. digital

transmission systems

are

more resistant to analog

systems rr

djtive

noise because

they

use

signal regetlerution rather than signal

amplification.

\

produccd

in

electronic

circuits is

additive

(i.e..

it

accumulates):

therefore. the sign.

noi\e

rrtio

deteliorates

each

time an analog signal is

amplified. Consequently,

the

nu:

olcircuits

the

si-cnal

musl

pass

through iimits

the

total distance analog signals

can

be t:.

pofied.

Ho\c cr'.

digital

regenerators

sanrple

noisy

signals and then reproduce

an en:

ne\\

digital

signal uith

the same signal{o-noise ratio

as the original transmitted ::

Therefirre.

digital

signals

crn be

transported longer

distances than analog signals.

Finally.

digitai signals

are simpler

ro

measure and evaluate

than analog

Thelefbre. it is

easier to

compare

the

error

perfbrmance

of

one

digital

system to

another

ital

system. Also. \\'ith

digital signals. trrnsmission

errors can be detected and corr:-

nrure

easilv and nrore accurttcly than is possible with

analog signals.

274

Chapter

6


3/45

e3:

-b

:-: -

to::-:

.r

r

:.8

:

:'rl

"

Ieqi.:i:

I

an.j

::.'--

1:.:

j :-

:e:;:-

;::

:.rb

ee:

:

:c_

an;

,:

l:rr

irrrr.-lIn

a]'-


4/45

(a)

(e)

Pu se

modulation:

[a]

analog

signal;

[b]

sample

pulse;

[c]

PWM;

[d]

PPM;

CM

the standard

voice-band

frequency

range

of 300

Hz to 3000

Hz

The sample-and-ho':

PCM

is the

only digitally

encoded

modulation

technique

shown

in

Figure

6-1

r-'

I

commonly

used

for

digital

transmission.

The

tetm

pulse

code

zodalaliort

is someuh;:

rI

misnomer.

as

it is nc,t

really

a

type of

modulation

but

rather a

form of digitally

codins

--:.

log

signals.

With PCM,

the

pulses

are

of fixed

length

and

fixed amplitude

PCM

is

a

cr:"'"

sy,stem

where

a

pulse or

lack

of a

pulse

within

a

prescribed time

slot represents

either

;

''s

I or a

logic 0

condition.

PwM,

PPM.

and PAM

are

digital but

seldom

binary'

as :

:

-'c

does

not

represent

a single

binary

digit

(bit)

(b)

P

l,Jt'A

(c)

PPH

(d)

?^^

Fctl

(f)

Figure

6 2 shows

a simplified

block diagram

of

a

single-channel,

simplex

(on'-

'7

only)

PCM

system.

The bandpass

tilter

limits

the tiequency

of

the analog

input

sig:'

r

276

Chapter

6

,"

8-bit

word

FIGURE 6,

[e]

PAM;

[f)


5/45

PCNI-fransmittcr

Analog

1'r

31;;x,

"""'*

Lino spd

clock

PC\,1

Rcce

ir

cr

:

3URE

6-2 Simplified

block diagram of a single-channel,

simplex PCM transmrsston system

Parallel

data

J\*

*,J

$

.v'

,

.d,

^\

,d'

11/

SerialPCM

code

An log

Output

signal

-

PPMI

6-l

thr

>

somewhat

':

I:

coding

r:

PCM

is

a

bir''-'

either

a

li;

as

a

(one-s:'

inPut

sign'

cuit

periodically

samples the analog input signal

and converts those samples to

a

multilevel

PAM signal.

The analog-to-digital

converrer

(ADC)

convens the PAM samples

to

parallel

PCM codes, which are

converted to serial binary data in the

p.trullel-to-se

rial

cotNe

rter and

then outputted

onto

the transmission

line

as

serial

digital

pulses.

The transmission

line

/.e-

peaters 'are placed

at

prescribed

distances to regenerate the digital

pulses.

In the receiver, the

serial-to-parallel convefier colyerls serial pulses

received

from

the transmission line

to

parallel

PCM codes. The

digittrl-to-analog converter

(DAC)

con-

verts the parallel

PCM codes to multilevei PAM

signals. The hold

circuit

is

basically a

lou-

pass

filter that converts the PAM

signals back

to its odginal

analog form.

Figure 6-2 also

shows several

clock

signals and sample pulses

that

will

be explained

in later sections

of this chapter An integrated

circuit that

performs

the PCM

encoding

and

decoding functions

is

called

a

codec

(coder/decoder),

which is

also described in a later sec-

tion of this chapter.

SAMPLING

The function of a sampling

circuit in

a

PCM transmitter is to

periodically

sample the con-

tinually changing

analog input voltage and convert those

samples to a

series

of

constant-

amplitude pulses

that can more easily

be converted to binary PCM code. For the ADC

to ac-

curately convefi a voltage to

a binary code. the

yoltage

must be relatively

constant so that the

ADC can complete the

conversion before the voltage

level

changes.

If not. the ADC would

be continually attempting

to

follow

the changes and may never

stabilize on any PCM code.

I

::l

Transmission


6/45

(a)

Input.

tb)

Sample

'

pulse

tc)

OutpLrt

FIGURE 6-3

Naturai sampling:

[a]

input

analog

signall

[b)

sample

pulse;

Ic]

sampled output

Essentially, there arc two basic techniques

used

to

perform

the sampling

funcr:tr

natural sampling and flat-top sampling.

Nalrral

.rumpling

is

shown

in Figure

6-3.

Nar--r

sampling is when tops of the sample

pulses

retain their natural shape during the sample

*-

terval, making

it

difficult

for

an

ADC

to conveft

the sample to a PCM code. With

nar-a

sampling, the ftequency spectrum of the sampled output

is

different

from

that of

an ia

sample. The amplitude

of

the frequency conponents

produced

tiom

narrow finite-u:g

sample

pulses

decreases

for

the

higher harmonics in a

(sin

r)/r manner. This alters the -:-

formation frequency spectrum requiring

the use

of frequency equalizers

(compensatior

-1-

ters) before

recovery by

a

low-pass filter.

The most common method used for sampling

voice signals in PCM systems is

-:r-

top sampling,which is accomplished in a sample-and-hold

circrlt.

The

purpose

ofa

sarn:,e..

and-hold circuit

is

to

periodically

sample the continually changing analog input voltage::r

convert those samples to a

series

of constant-amplitude

PAM voltage levels. With flat-:r

sampling,

the

input

voltage is

sampled

with

a

narrow

pulse and then

held

relativell

;

,r-

stant

until

the next sample

is

taken. Figure 6-4 shows flat-top sampling. As the

fiS-=

shows, the

sampling

process

alters the

frequency spectrum and introduces an error

cL.=

ttperture error, which is

when

the amplitude ofthe sampled signal changes during

the :,=-

ple pulse

time. This

prevents

the recoverl, circuit in the PCM receiver from exactly

re5-

ducing the original

analog signal voltage. The magnitude of error depends on how rr--.,:

the analog signal voltage changes

while

the sample is being taken and the

width

(durat:..r

of

the sample

pulse.

Flartop

sampling, however, introduces less aperture distortion

::a

natural sampling

and

can operate with a slower analogto-digital converter

Figure 6-5a shows the schematic diagram of a sample-and-hold

circuit. The FET l-

as

a

simple analog switch. When tumed on,

Q1

provides

a

low-impedance

path

to deposii

=

analog sample

voltage across capacitor

Cq.

The time that

Q1

is on is called the apefiuft

acquisition

time. Essentially,

C1

is the

hold

circuit.

When

Q,

is

off,

C,

does

not

have

a

c.:,:-

plete path

to discharge through

and,

therefore,

stores

the sampled

voltage.

The storoge

i-'E

ofthe

capacitor is called

the

A./D conversior /lr?e because it is during this time that

the

-{:t:

converts the sample voltage to a PCM code. The acquisition

time should

be

very short to

:,1-

sure that a minimum change occurs

in

the analog signal

while

it is being deposited ac:-=i

Cr.

If the input to

the ADC is

changing while

it

is

performing

the conversion.

aprr--

274 Chapter 6


7/45

functior'

6-3.

Natur.

the

sample

it-

With

naturi

of

an

ide-

finite-widr

alters

the

in'

fij

systems

is/c:'

of

a

samPle'

voltage

an:

With

flat{o:

relatiYely

cor-

As

the

figur.

an

enor

calle:

during

the

sarr-

exactly

repri-

on

how

mu;:

(duratio.

distortion

th.

The

FET

ac:'

tlE

the

aPerture

it

not

have

a

cori-

storage

tit"

that

the

AX

very

short

to

er-

deposited

acro..

aPerllr?

(u)

Input.

1g;

SamPle

pulse

(c)

OutPUi

FIGURE

6-4

Flat-top sampling:

{al

input analog signal;

(bl

sample

pulse;

[c]

sampled ouiput

lv

t'r

Inptd

'#

[11

Sample

AFturc

ol

Outpst

FIGURE

6-5

(a)

Sample-and-hold

circuitt

[b]

input

and

output wavefo.ms

279


8/45

distortion

results. Thus,

by having

a short aperture

time

and keeping

the

input

to the

-{ir:

relatively

constant.

the sample-and-hold

circuit can

reduce aperture

distortion.

Flat-top

s;j:-

pling introduces less

aperture distortion

than

natural sampling

and

requires a slower

anal

;

to-digital

converter

Figure 6-5b

shows

the input analog

signal.

the sampling

pulse'

and

the wavef.=

developed

across C

r.

lt

is important

that the

output

impedance

of voltage

follower

Z,

--c

the

on

resistance

of

Q1

be as small

as

possible. This ensures

that the RC

charging time

'

:-

stant of the capacitor

is

kept very shon.

allowing

the capacitor

to charge

or discharge

:---

idly

during the

short acquisition

time.

The rapid

drop

in the capacitor

Yoltage

immedia::

-

following

each

sample pulse is due to the

redistribution of

the

charge

across C1.

The

in:--

electrode

capacitance

between

the

gate and drain

of

the FET

is

placed

in series

witi:

--

when

the

FET is

olf,

thus acting

as a capacitive

voltage-divider

network. Also.

note

=

gradual

discharge

across

the capacitor

during the conversion

time. This

is

called droop

':ti

is caused by the

capacitor discharging

through its

own leakage

resistance and

the

input

:-

pedance of voltage

follower

2,.

Therefore.

it

is important

that the

inpur impedance

t"

--

and the

leakage resistance

of C1 be

as high as

possible

Essentially,

voltage

follo*er'

I

and

Zr

isolate

the sample-and-hold

circuit

(Q1

and C1)

from the

input

and output

circL::'

Example 6-1

For the sample-and

hold circuit

shown in Figure

6

5a, determine

the largest-value

capacitor

th;:

'

be used. Use

an output

impedance tbr Z

1

ofl0O.anonresistanceforQ1

of10Q'anacquisitiot

a

of lO

us,

a maximum

peak-to-peak input

voltage

of

l0

V,

a maximum

output

current

from

zr

i:

i

mA.

and an accuracy

of

I

7..

Solution

The expression

for the current

through a capacitor

is

i: C

Reirranging

and solving

for

C

yields

C=,+

where

C

=

maximum capacitance

(tarads)

i

=

maximum

output current

from

Zl,

l0 mA

dv

=

maximum

change

in voltage across

Cr,

which equals

l0 V

./t

:

charge

time.

which equals the

aperture time,

l0

us

(10

mA)(10 ps)

Thercfore.

Accuracy

(7.)

Charge

Time

:

I0

nF

r0v

The charge

time constant

fbr

C

when

Qr

is on

is

r:RC

where

1

=

one charge

time constant

(seconds)

R

=

output

impedance

of 21

plus

the

on resistance

of

Qr

(ohms.)

C

=

capacitance

value of Cr

(tarads)

Reananging

and solving

for C

gives

us

The charge time

ofcapacilor

Cr is also dependent

on

the accuracy

desired from

fhe

device' Tl:

:F

cent accuracy

and its

required RC

time constant

are summarized

as tbllows:

-l

t0

I

0.1

0.0r

2.3r

6.9r

9.2r

280

Chapter

6


9/45

to

the

ADC

sam-

analos-

wavefofl:

Zr

an;

time

cor'

raF-

immediatei;

The

inte:'

with

C

note

ih:

draoP

an:

the

input

ir-'

of

Z-

tbllowers

Z

circuitl

that

aj

acquisition

ti=t

from

Zl

oi

device.

The

:s

For an accuracy of l%.

c=

r9'{

=

ro87nF

.1.6(20

)

To satisfi the output current

limitations

ofZr.

a maximum cipacitance

of l0

nF was rcquired. To saF

isfy

the

accuracy requircments. 108.7 nF was required. To satisfy borh requirements. the

smaller-

value

capacitor

must

be used.

Theretbre.

Cr

can be no larger than l0 nF.

5-4-1 Sampling

Rate

q

The

Nyquist

sampling

theorem establishes

the minimum sanpling rate

(f,)

that can be used

for

a

given

PCM system. For

a

sample to

be

reproduced accurately

in

a

PCM receiver, each

cycle

of

the

analog input signal

(f,,)

must

be

sampled

at Ieast

twice. Consequently.

the

min-

imum sampling rate is

equal to tu,ice the

highest audio input tiequency. Iff, is less than two

timesr,.

an impairment called rrlirrs orfi dowr

tlistortion

occurs. Mathematically. the

min-

imum Nyquist sampling rate is

(6-l

)

ma\imLrm .lnalng input lrequen()

rhcrr/r

A sample-and-hold circuit is a nonlinear device

(mixer)

with

two

inputs: the sampling

pulse

and the analog input signal. Consequently. nonlinear

mixing

(heterodyning)

occurs be-

tween these two signals.

Figure 6-6a shows the frequency-domain

representation

of the output

spectrum

from

a sample-and-hold circuit. The output includes the two

o

ginal

inputs

(the

audio and

the fundamental frequencl, of the sampling

pulse).

their sum and difference frequencies

f,

a.l").

all the

harmonics

ofl"

andL,

(21

.

2L,,

31..

3/,.

and

w

on), and

their associated cross

products

(2/,

:t

.f,,.

3^

:l1,,

and so on).

Because the sampling

pulse

is a repetitive waveform. it is made up of a series of har-

monically

related

sine waves.

Each

of

these

sine u'aves is

ampJitr.rde

modulated by the ana-

Iog signal and

produces

sum and difference frequencies symmetrical around each

of

the

harmonics

off,.

Each sum and difference frequency

generated

is separated from its respec

tive

center tiequency by

L,.

As

Jong

as

L

is

at

least twice

1,,.

none

of

the side fiequencies

from

one

harmonic

will

spill into

the sidebands

of

another

harmonic.

and aliasing does not

31"

+

l"

Freqle.:y

+

Output spectrum

for a

sample-and hold circuit:

[a]

no

3 as-:

.:.

"

==-=

2e1

2f"- t" 3fs

-

f.

1b)

FIGURE

6.6

distortion

::

Transmission

21,-

L


10/45


11/45

than

/.:

of

ar:-

(hence

th'

the

llrst

har-

or

anl

minimum

sar-

the

samPl''

\hoNn

in

Figur'

3

kHz

that

hr'

or

anti|ol(b\'.'

one-half

th'

the

Possl-

binary

cod.

original

ana-

anY

Positive

in-

codes,

wher:

for

magnitude

bit

is

used

ti

The

two

re'

codes

Possi

ble for

positive

numbers and

four codes

possible

tirr

negativc numbers. Consequently, there

is

a

total of eight

possible

codes

(23

:

ti).

6-4-2

Guantization

and

the

Folded

Binary Code

Quonti:tttiott

is the

process

ol converting

an

infinite

nunrber ol

possibilities

to

a

finite

nunrber of conditions. Analog

signals contain an infinite number

of

amplitude

possibili-

ties. Thus. converting

an analog signal to a PCM code

with a limited number of combina-

tions requires

quantization.

In essence.

quantization

is the

process

of

rounding off the ant-

plitudes

of

flat-top samples to a rranageable

numbcr

of

levels. For example. a sine

wave

with

a

peak

amplitude

ef

5

V

varies

betueen

+5

V

and

5

V

passing

through

e\er)

pos

sible

amplitude in

betueen. APCM code couJd

have only eight bits. which equates to onl)

28. or

256 combinations. Obviously. to convert samples

of

a sine wave to PCN{ tequiles

some rounding ofT.

With

quantization.

the total

voltage range is subdivided into a smaller

number ol

subranges. as

shown in Table

6

2. The

PCM

code

shown in Table 6-2 is a three-bit sign-

magnitude code

with

eight

possible

combinations

(four

positive

and

tbur negative). The

le ftmost bit is the sign bit

(

I

:

*and0=

).

and the

two rightmost bits repre\ent

mugni-

tude.

This type of code is called a

lbldr

cl bintrv cotle

because thc codes on the

bottom

half

of the table are a

miror

imagc of the codes on the top half. except tbr the

sign

bit.

If

the

negative codes were folded over on

top ol the

positive

codes. they would match

perfectly.

With

a

folded

binary

code. each r oltage level has one code

assigncd to it except zero volts.

which has two codes,

I

00

(

+

0)

and

000

(

-

0

).

The rnagninrde diflercnce between

adjacent

steps is called the

qtloltia.ttion

inter\\i ot clud

tufir. For the code shorvn in

Table

6-2.

the

quantization interval

is

I V Therefore. fbr this code.

the nraximum signal magnitude that

can be encoded

is

+3

V

(lll)

or

-3

V

(011),

and the minimum signal

magnitude is

*

I

V

(

101)

or

-l

V

(001).

If

the

magnitude

ofthe

sample exceeds the highe't

qulntizutit,n

in-

terval,

overload

disaol

Ii./r

(also

called

perrl

//atltirtg)

occurs.

Assigning

PCM

codes

to absolute magnitudes is called

quantizing.

The ma-snitude

of

a

quantum

is

also called the rcsolutiotl.

The resolution

is

equal

to

the

\oltage

of the

nlininun

step

si:.e.

which

is

equal

to the

voltage of

the /r,.r.ra. i

gnificati

bit

(V

t,)

oi the PCM

code. The resolution is the minirnum

voltage other than 0

V

that can be decoded

by the

digital-to-analog

converter in the

receiver

The resolution

tbr

the PCM code

shown in

Table 6-2

is

I V

The smaller the magnitude

of

a

quantunr. the

better

(smaller.)

the resolu-

tion and the more accurateiy

the

quanlircd

signal will resemble the

original

analog

sample.

ln

Table 6-2,

each

three-bit

code

has

a

rangc

of input

voltages that

will

be

converted

to that code.

For example, any voltage between

+0.5

and

+

1.5 will be

converted to

the

code l0l

(+

I

V). Each code

has

a

quonti:utiott

rtirr.gc equal to

i

or one-half

the mag

nitude

of

a

quantum

except the codes

tbr

f0

and

0. The 0-V codes each have an

input

range equaJ to only

one-half a

quantum

(0.5

V).

Table

6'2

Three Bit PCM Code

I

Sub

,

ranges

-

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