Digital Communication

Communication System

Source of Information

Destination Information

Transmitter ReceiverChannel

Communication System

Transmitted Signal

Received Signal

Voice, Video, data

Data Communication Terms Data - entities that convey meaning, or

information Signals - electric or electromagnetic

representations of data Transmission - communication of data by

the propagation and processing of signals

Examples of Analog and Digital Data Analog

Video Audio

Digital Text Integers

Analog Signal

Digital Signal

Analog Signals A continuously varying electromagnetic wave that

may be propagated over a variety of media, depending on frequency

Examples of media: Copper wire media (twisted pair and coaxial cable) Fiber optic cable Atmosphere or space propagation

Analog signals can propagate analog and digital data

Digital Signals A sequence of voltage pulses that may be

transmitted over a copper wire medium Generally cheaper than analog signaling Less susceptible to noise interference Suffer more from attenuation Digital signals can propagate analog and

digital data

Analog Signaling

Digital Signaling

Time-Domain Concepts Analog signal - signal intensity varies in a smooth

fashion over time No breaks or discontinuities in the signal

Digital signal - signal intensity maintains a constant level for some period of time and then changes to another constant level

Periodic signal - analog or digital signal pattern that repeats over time s(t +T ) = s(t ) where T is the period of the signal

Time-Domain Concepts Aperiodic signal - analog or digital signal pattern

that doesn't repeat over time Peak amplitude (A) - maximum value or strength

of the signal over time; typically measured in volts Frequency (f )

Rate, in cycles per second, or Hertz (Hz) at which the signal repeats

Time-Domain Concepts Period (T ) - amount of time it takes for one

repetition of the signal T = 1/f

Phase () - measure of the relative position in time within a single period of a signal

Wavelength () - distance occupied by a single cycle of the signal Or, the distance between two points of corresponding

phase of two consecutive cycles

Sine Wave Parameters General sine wave

s(t ) = A sin(2ft + ) Figure shows the effect of varying each of the

three parameters (a) A = 1, f = 1 Hz, = 0; thus T = 1s (b) Reduced peak amplitude; A=0.5 (c) Increased frequency; f = 2, thus T = ½ (d) Phase shift; = /4 radians (45 degrees)

note: 2 radians = 360° = 1 period

Sine Wave Parameters

Frequency-Domain Concepts Fundamental frequency - when all frequency

components of a signal are integer multiples of one frequency, it’s referred to as the fundamental frequency

Spectrum - range of frequencies that a signal contains

Absolute bandwidth - width of the spectrum of a signal

Effective bandwidth (or just bandwidth) - narrow band of frequencies that most of the signal’s energy is contained in

Frequency-Domain Concepts Any electromagnetic signal can be shown to

consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases

The period of the total signal is equal to the period of the fundamental frequency

Relationship between Data Rate and Bandwidth

The greater the bandwidth, the higher the information-carrying capacity

Conclusions Any digital waveform will have infinite bandwidth BUT the transmission system will limit the bandwidth

that can be transmitted AND, for any given medium, the greater the bandwidth

transmitted, the greater the cost HOWEVER, limiting the bandwidth creates distortions

Reasons for Choosing Data and Signal Combinations Digital data, digital signal

Equipment for encoding is less expensive than digital-to-analog equipment

Analog data, digital signal Conversion permits use of modern digital transmission

and switching equipment Digital data, analog signal

Some transmission media will only propagate analog signals

Examples include optical fiber and satellite Analog data, analog signal

Analog data easily converted to analog signal

Analog Transmission Transmit analog signals without regard to

content Attenuation limits length of transmission

link Cascaded amplifiers boost signal’s energy

for longer distances but cause distortion Analog data can tolerate distortion Introduces errors in digital data

Digital Transmission Concerned with the content of the signal Attenuation endangers integrity of data Digital Signal

Repeaters achieve greater distance Repeaters recover the signal and retransmit

Analog signal carrying digital data Retransmission device recovers the digital data from

analog signal Generates new, clean analog signal

About Channel Capacity Impairments such as noise, limit the data

rates that can be achieved. For digital data, to what extent do

impairments limit data rate? Channel Capacity – the maximum rate at

which data can be transmitted over a given communication path, or channel, under given conditions

Concepts Related to Channel Capacity

Data rate - rate at which data can be communicated (bps)

Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz)

Noise - average level of noise over the communications path

Error rate - Rate at which errors occur Error = transmit 1 and receive 0; transmit 0 and receive

1

Nyquist Bandwidth For binary signals (two voltage levels)

C = 2B With multilevel signaling

C = 2B log2 M M = number of discrete signal or voltage levels

Signal-to-Noise Ratio Ratio of the power in a signal to the power

contained in the noise that’s present at a particular point in the transmission

Typically measured at a receiver Signal-to-noise ratio (SNR, or S/N)

A high SNR means a high-quality signal, low number of required intermediate repeaters

SNR sets upper bound on achievable data rate

power noise

power signallog10)( 10dB SNR

Shannon Capacity Formula Equation:

Represents theoretical maximum that can be achieved

In practice, only much lower rates achieved Formula assumes white noise (thermal noise) Impulse noise is not accounted for Attenuation distortion or delay distortion not accounted

for

SNR1log2 BC

Example of Nyquist and Shannon Formulations Spectrum of a channel between 3 MHz and

4 MHz ; SNRdB = 24 dB

Using Shannon’s formula

251SNR

SNRlog10dB 24SNR

MHz 1MHz 3MHz 4

10dB

B

Mbps88102511log10 62

6 C

Example of Nyquist and Shannon Formulations How many signaling levels are required?

16

log4

log102108

log2

2

266

2

M

M

M

MBC

TRANSMISSION MEDIA

Communication Channels

• Wire line Channels (Copper)

• Microwave Radio

• Satellite communication

• Optical Fibre

Electromagnetic Signal Function of time Can also be expressed as a function of

frequency Signal consists of components of different

frequencies

Electromagnetic Spectrum

Classifications of Transmission Media Transmission Medium

Physical path between transmitter and receiver Guided Media

Waves are guided along a solid medium E.g., copper twisted pair, copper coaxial cable, optical

fiber Unguided Media

Provides means of transmission but does not guide electromagnetic signals

Usually referred to as wireless transmission E.g., atmosphere, outer space

Unguided Media Transmission and reception are achieved by

means of an antenna Configurations for wireless transmission

Directional Omnidirectional

General Frequency Ranges Microwave frequency range

1 GHz to 40 GHz Directional beams possible Suitable for point-to-point transmission Used for satellite communications

Radio frequency range 30 MHz to 1 GHz Suitable for omnidirectional applications

Infrared frequency range Roughly, 3x1011 to 2x1014 Hz Useful in local point-to-point multipoint applications

within confined areas

Terrestrial Microwave Description of common microwave antenna

Parabolic "dish", 3 m in diameter Fixed rigidly and focuses a narrow beam Achieves line-of-sight transmission to receiving

antenna Located at substantial heights above ground level

Applications Long haul telecommunications service Short point-to-point links between buildings

Satellite Microwave Description of communication satellite

Microwave relay station Used to link two or more ground-based microwave

transmitter/receivers Receives transmissions on one frequency band (uplink),

amplifies or repeats the signal, and transmits it on another frequency (downlink)

Applications Television distribution Long-distance telephone transmission Private business networks

Broadcast Radio Description of broadcast radio antennas

Omnidirectional Antennas not required to be dish-shaped Antennas need not be rigidly mounted to a precise

alignment Applications

Broadcast radio VHF and part of the UHF band; 30 MHZ to 1GHz Covers FM radio and UHF and VHF television

MULTIPLEXING TECHNIQUES

Multiplexing Capacity of transmission medium usually

exceeds capacity required for transmission of a single signal

Multiplexing - carrying multiple signals on a single medium More efficient use of transmission medium

Multiplexing

Reasons for Widespread Use of Multiplexing Cost per kbps of transmission facility

declines with an increase in the data rate Cost of transmission and receiving

equipment declines with increased data rate Most individual data communicating

devices require relatively modest data rate support

Multiplexing Techniques Frequency-division multiplexing (FDM)

Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal

Time-division multiplexing (TDM) Takes advantage of the fact that the achievable

bit rate of the medium exceeds the required data rate of a digital signal

Frequency-division Multiplexing

FREQUENCY DIVISION MULTIPLEXING

F

R

E

Q

U

E

N

C

Y

Time-division Multiplexing

30 CHL PCM MUX FRAME & MULTI FRAME

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 MULTI FRMAE (2 m sec)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

FRAME – 125 u sec32 TS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Y 0 0 1 1 0 1 1

Y 1 0 X X X X X

FAW 2

FAW 1

ALTERNATE FRAMES

30 SPCH CHLS

1 = LOSS OF FRAME ALIGNMENT

0 0 0 0 X 0 X X

1 2 3 4 5 6 7 8

FRAMES 1 TO 15

FIRST 4 DIGITS OF FRAME 0 MFAW

DIGIT 1 TO 4 FOR CHL 1 TO 15

SIGNALLING

DIGIT 5 TO 8 FOR CHL 16 TO 30 SIGNALLING 1 = LOSS OF MULTI FRAME

ALIGNMENT

1 2 3 4 5 6 7 8

8 BITS PER CHL

EACH BIT = 488 n sec

Spectrum & Bandwidth

Spectrum range of frequencies contained in signal

Absolute bandwidth width of spectrum

Effective bandwidth Often just bandwidth Narrow band of frequencies containing most of the

energy DC Component

Component of zero frequency

WAVE FORM CODING TECHNIQUES

PULSE CODE MODULATION

DIFFERENTIAL PCM

ADAPTIVE DIFFERENTIAL PCM

DELTA MODULATION

ADAPTIVE DELTA MODULATION

MODULATION TYPES

Modulation is the process of transformation of the message signal (baseband) into a form suitable for transmission over the channel with acceptable degradation.

• PAM (PULSE AMPLITUDE MODULATION). THE AMPLITUDE OF A TRAIN OF PULSE IS VARIED ACCORDING TO THE AMPLITUDE OF THE ANALOG SIGNAL (MODULATING SIGNAL)

• PCM (PULSE CODE MODULATION). THE ANALOG SIGNAL MODULATES A TRAIN OF PULSE (PAM). IN EFFECT THE ANALOG SIGNAL IS SAMPLED AND THE SAMPLES ARE CODED TO A BINARY VALUE WHICH IS A FUNCTION OF THE AMPLITUDE OF THE SAMPLED ANALOG SIGNAL

Digitizing Analog Speech PAM & PCM

PCM = PAM + QUANTIZATION + COMPANDING

PULSE CODE MODULATION

• PCM IS A TYPE OF CODING THAT IS CALLED "WAVEFORM" CODING BECAUSE IT CREATES A CODED FORM OF THE ORIGINAL VOICE WAVEFORM.

• PCM IS A WAVEFORM CODING METHOD DEFINED IN THE ITU-T G.711 SPECIFICATION.

• PCM WAS DEVELOPED BY BELL LABS IN 1937

• PCM (ADPCM) IS THE PREFERRED METHOD OF COMMUNICATION WITHIN THE PSTN

SINGLE CHANNEL SIMPLEX PCM TRANSMISSION SYSTEM

QuantizationCompanding

PCM BLOCK DIAGRAM

SAMPLINGCIRCUIT

QUANTIZERAND

COMPANDER

ANALOG VOICE

SIGNAL

SAMPLINGCLOCK

PULSE AMPLITUDEMODULATED(PAM) SIGNAL

DIGITIZEDVOICE

SIGNAL

PULSE CODEMODULATED

SIGNAL(PCM)

VOICE BAND FILTER

PULSE MODULATION

Signal

PAM

PWM

PPM

SAMPLER QUANTIZER ENCODER

CODEC

Analogsignal

Digitalsignal

• SAMPLING• QUANTIZING• ENCODING

Pulse Code Modulation(PCM) If a signal is sampled at regular

intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal (Proof - Stallings appendix 4A)

Voice data limited to below 4000Hz Require 8000 sample per second Analog samples (Pulse Amplitude

Modulation, PAM) Each sample assigned digital value

SAMPLING THEOREMSTATEMENT :- Any signal with a bandwidth of W can be completely reconstructed if it

is sampled at a rate of 2W.

Original waveform

samples

Capacitor charges

Capacitor discharges

Thus by sampling first at the transmitter and then passing the samples through a LPF the original waveform can be completely reconstructed

EFFECT OF UNDER SAMPLING

THUS WHEN ANY WAVE IS SAMPLED AT A FREQUENCY THAT IS LESS THAN DOUBLE THE MAXIMUM SIGNAL FREQUENCY, THE RECOVERED WAVE WILL NOT BE OF THE SAME FREQUENCY AS THE INPUT WAVEFORM. THIS DISTORTION IS CALLED ALIASING .

THUS, IT IS SEEN THAT THE SAMPLING FREQUENCY HAS TO BE ADJUSTED SUCH THAT fs > 2fm

ORIGINAL SIGNAL AT 3 Hz SAMPLES AT LESS

SAMPLING RATE AT 2 Hz

WRONGLY RECONSTRUCTED

SIGNAL AT 1 Hz

Pulse Code Modulation(PCM) 4 bit system gives 16 levels Quantized

Quantizing error or noise Approximations mean it is impossible to

recover original exactly 8 bit sample gives 256 levels Quality comparable with analog

transmission 8000 samples per second of 8 bits each

gives 64kbps

PULSE CODE MODULATION

IN THIS TYPE OF SOURCE ENCODING THE SPEECH DATA THAT IS SAMPLED IS QUANTISED OR FIXED AT PREDETERMINED LEVELS

IF THE RANGE OF THE INPUT IS -V TO +V THEN, THE ENTIRE RANGE IS DIVIDED INTO STEPS OF 2V/L. THUS THE STEP SIZE IS 2V/L.

IF WE CHOOSE 8 BIT PCM, THEN THE TOTAL No. OF LEVELS ARE 2 = 256 8

IN COMMERCIAL 8 BIT PCM, WE HAVE 256 LEVELS OR 8 BITS PER SAMPLE OF SPEECH DATA. THE SPEECH IS SAMPLED AT THE RATE OF 8 kHz. HENCE THE DATA RATE OF THE COMMUNICATION IS 8 x 8 kHz = 64 kbps

HENCE THE BIT RATE OF EACH SPEECH CHANNEL IN 8 BIT PCM IS 64 kbps

DIAGRAMMATIC REPRESENTATION OF 3 BIT PCM

0

-4

-3

3

2

1

-1

-2

4

CODE No. 0 -3.5

CODE No. 7 3.5

CODE No. 6 2.5

CODE No. 5 1.5

CODE No. 4 0.5

CODE No. 3 -0.5

CODE No. 2 -1.5

CODE No. 1 -2.5

SAMPLE VALUE 0.0 3.35 1.75 - 0.25 -1.4 -2.3 -3.5

NEAREST Q LEVEL 0.5 3.5 1.5 -0.5 -1.5 -2.5 -3.5

QUANT ERROR +0.5 +0.15 -0.25 +0.25 +0.1 +0.2 0.0

CODE NUMBER 4 7 5 3 2 1 0

ENCODED BITS 100 111 101 011 010 001 000

LINEAR QUANTIZATION USE OF EQUAL QUANTIZATION INTERVALS THROUGHOUT THE ENTIRE DYNAMIC RANGE OF AN INPUT ANALOG SIGNAL (FOR LOW & HIGH ENERGY SIGNALS) RESULTS IN

LOW LEVEL SIGNALS HAVE A LOW SNR, HIGH LEVEL SIGNALS HAVE A HIGH SNR (UNDESIRABLE)

MOST VOICE SIGNALS ARE OF LOW LEVELS. THUS,VERY INEFFICIENT WAY OF DIGITIZING VOICE SIGNALS TO IMPROVE VOICE QUALITY AT LOWER SIGNALLEVELS, USE A NON-UNIFORM (NON-LINEAR) QUANTIZATION PROCESS CALLED COMPANDING

NON-LINEAR PCM AND COMPANDING

IT HAS BEEN SEEN THAT SPEECH SIGNALS CONSIST PREDOMINANTLY OF SMALL AMPLITUDE SIGNALS AND THE LARGE AMPLITUDE SIGNALS OCCUR WITH MUCH LESSER PROBABILITY.

HENCE IT IS LOGICAL THAT THE SMALLER AMPLITUDES ARE QUANTISED WITH MORE PRECISION.

THIS MEANS THAT THE STEP SIZE IS MAINTAINED SMALL FOR THE REGION WHERE THE SIGNAL AMPLITUDE IS SMALL. CORRESPONDINGLY, THE STEP SIZE FOR THE LARGE SIGNALS ARE MADE LARGE.

THIS WILL OF COURSE RESULT IN LARGE QUANTISATION ERROR IN CASE OF LARGE SIGNALS. BUT THIS IS TOLERABLE SINCE THE LARGE SIGNAL AMPLITUDES DO NOT OCCUR VERY REGULARLY.

THIS PROCESS OF VARYING THE STEP SIZE DURING THE ENCODING PROCESS IS CALLED COMPRESSING AND THE CORRESPONDING RECEIVER WILL DO EXPANDING TO REVERSE THE DISTORTION INTRODUCED AT THE ENCODER.

THIS PROCESS IS CALLED COMPANDING.

THIS TYPE PCM IS KNOWN AS NON-LINEAR OR LOGRITHMIC PCM

NON-LINEAR QUANTIZATION

• THE VOLTAGE RANGE BETWEEN THE LOWEST LEVEL AND THE HIGHEST LEVEL IS DIVIDED INTO SEGMENTS IN A NON-LINEAR MANNER

LOGARITHMIC

• THE LOWER THE VOLTAGE LEVELS, THE SMALLER THE RANGE OF A SEGMENT. THE RANGE OF A SEGMENT GETS LARGER FOR HIGHER VOLTAGE LEVELS

• THE NUMBER OF STEPS FOR EACH SEGMENT IS THE SAME

COMPANDING

• DURING THE COMPANDING PROCESS, INPUT ANALOG SIGNAL SAMPLES ARE COMPRESSED INTO LOGARITHMIC SEGMENTS AND THEN EACH SEGMENT IS QUANTIZED AND CODED USING UNIFORM QUANTIZATION.

• COMPANDING (COMPRESSION AND EXPANSION) INCREASES SNR PERFORMANCE (MINIMISE QUANTIZATION NOISE) WHILE KEEPING THE NUMBER OF BITS USED FOR QUANTIZATION CONSTANT.

70dB

40dB

30dB

70dB

30dB60dBI/P

60dBO/P

40dB

Compressor Expander80dB

80dB

20dB 20dB

COMPANDOR

A law: Y=Ax /(1+Log A); 0 < V/A

U law: U= log(1+ux) / log(1+u)

DIFFERENTIAL PCM OR DPCM

IN DPCM THE DIFFERENCE BETWEEN THE PREVIOUS SAMPLE AND THE PRESENT SAMPLE IS ENCODED AND TRANSMITTED.

ONE BIT IS THE SIGN BIT WHICH SAYS WETHER THE PREVIOUS SAMPLE IS MORE OR LESS THAN THE PRESENT SAMPLE AND THREE BITS ARE USED TO ENCODE THE ERROR OR THE DIFFERENCE BETWEEN THE PREVIOUS SAMPLE AND THE PRESENT SAMPLE

ERROR

QUANTISER

INTEGRATOR

DE-QUANTISER

DIFF AMP

BLOCK DIAGRAM OF A DPCM SYSTEM

m(t)

m(t)~

THE ADVANTAGE IN THIS SYSTEM IS THAT, THE DIFFERENCE BETWEEN SAMPLES WILL NOT BE AS LARGE AS THE SAMPLE ITSELF. HENCE, WE CAN USE LESSER NUMBER OF BITS FOR ENCODING. THIS IN TURN REDUCES THE REQUIRED BANDWIDTH.

0

-4

-3

3

2

1

-1

-2

CODE No. 0 -3.5

CODE No. 7 3.5

CODE No. 6 2.5

CODE No. 5 1.5

CODE No. 4 0.5

CODE No. 3 -0.5

CODE No. 2 -1.5

CODE No. 1 -2.5

DIFFERENCE VALUE +0.5 + 3.0 -1.5 - 1.0 -0.5 -2.0 -1.5

NEAREST Q LEVEL 0.5 3.5 1.5 -0.5 -1.5 -2.5 -3.5

Tx BITS 1001 1111 0011 0010 0001 0100 0011

TRANSMISSIONS IN DPCM

IT MAY BE NOTED THAT EACH STEP IN THIS DPCM IS 0.5V WHEREAS THE STEP SIZE IN THE CORRESPONDING PCM SYSTEM WAS 1V.

ADAPTIVE DPCM OR ADPCM

IN THIS SYSTEM THE SPEECH WAVEFORM IS PREDICTED AND THE DIFFERENCE BETWEEN THE PREDICTED VALUE AND THE PREVIOUS VALUE IS ENCODED AND SENT.

THE ADVANTAGE OF THIS SYSTEM IS THAT DUE TO PREDICTION THE ERROR MAGNITUDE REDUCES DRASTICALLY AND THUS THE BANDWIDTH ALSO REDUCES CORRESPONDINGLY.

ERROR

QUANTISER

ADAPTIVE PREDICTOR

DE-QUANTISER

DIFF AMP

BLOCK DIAGRAM OF A ADPCM SYSTEM

m(t)~ m(t)

DELTA MODULATIONIN THE DPCM, THE PCM DATA WAS USED TO PREDICT THE NEXT SAMPLE. FOR TRANSMISSION OF SUCH DATA WE USED ONE SIGN BIT AND THREE INFORMATION BITS. WE CAN DEVISE A NEW SPEECH REPRESENTATION SCHEME WHERE WE CAN SEND ONLY THE SIGN BIT.

WHEN SAMPLED VALUE IS GREATER THAN A REFERENCE THEN A SYMBOL ‘1’

IF THE SAMPLE VALUE IS LESS THEN A SYMBOL ‘0’ IS USED

THIS IS DELTA MODULATION.

PULSE

MOD

UP/DN

COUNTER

D/A CONVERTOR

COMPARATOR

BLOCK DIAGRAM OF A DELTA MODULATOR

m(t)

m(t)~

V(n) = +1 if m(t) >= m(t)~

V(n) = -1 if m(t) < m(t)~

GRAPHICAL REPRESENTATION OF DELTA MODULATION

AND THE PROBLEMS THEREIN

m(t)

m(t)~

SLOPE

OVERLOAD

PROBLEM DUE TO SMALL STEP SIZE

time

PROBLEMS IN DELTA MODULATIONTHE MAJOR PROBLEMS OF DELTA MODULATION ARE :-

(a) SLOPE OVERLOAD WHICH RESULTS WHEN THE SLOPE OF THE SIGNAL EXCEEDS THE SLOPE OF THE DELTA MODULATOR. THIS PROBLEM CAN BE OVERCOME BY USE OF A LARGE STEP SIZE.

(b) SMALL SIGNAL VARIATIONS OF THE SIGNAL RESULT IN ALTERNATE 1’s AND 0’s WHICH DURING RECONSTRUCTION, WILL RESULT IN A dc LIKE SIGNAL. THIS PROBLEM CAN BE OVERCOME BY USE OF A SMALL STEP SIZE.

THESE CONFLICTING DEMANDS OF A LARGE STEP SIZE AND SMALL STEP SIZE CAN BE OVERCOME BY USE OF SPECIAL DELTA MODULATOR WHICH

- USES A SMALL STEP SIZE WHEN THE SIGNAL VARIATIONS ARE SMALL

- USES A LARGE STEP SIZE WHEN THE SIGNAL VARIATIONS ARE LARGE

SUCH A SYSTEM IS CALLED THE ADAPTIVE DELTA MODULATOR OR ADM

DIFFERENCE

AMPLIFIERMODULATOR

PULSE

GENERATOR

INTEGRATORVARIABLE GAIN AMP

SQUARE LAW

DEVICE

m(t)~

m(t)

BLOCK DIAGRAM OF ADAPTIVE DELTA MODULATOR

VARIABLE STEP SIZE OF ADM

ACTUAL WAVEFORM

DM OUTPUT

VARIABLE STEP SIZE AT THE INPUT OF THE

INTEGRATOR

THUS IT CAN BE SEEN THAT THE ADM OUTPUT IS ABLE TO FOLLOW THE ACTUAL SPEECH WAVEFORM MUCH MORE CLOSELY THAN THE DM OUTPUT WHICH IS SEVERELY AFFECTED BY SLOPE OVERLOAD

THE ADM OUTPUT IS “ 1 0 1 1 1 1 1 0 1 0 1 0 1 0 ”

1 0

11

1

1

1

1

0 00

Relationship between Data Rate and Bandwidth

The greater the bandwidth, the higher the information-carrying capacity

Conclusions Any digital waveform will have infinite

bandwidth BUT the transmission system will limit the

bandwidth that can be transmitted AND, for any given medium, the greater the

bandwidth transmitted, the greater the cost HOWEVER, limiting the bandwidth creates

distortions

POWER MEASUREMENTS

UNITS OF MEASUREMENT

UNITS OF MEASUREMENT THE POWER LEVEL IN TRANSMISSION

EQUIPMENTS ARE VERY SMALL TO VERY BIG.

IF ALL THE MEASUREMENTS ARE TAKEN HAVING THE SAME IMPEDANCE THE VOLTAGE WILL GIVE DIRECT INDICATION OF THE POWER LEVEL

RIP

REP

*2

2 /

EIP

THE DECIBEL The decibel is widely used in

transmission system The decibel is a unit that

describes a ratio. It is logarithmic with base 10

dB = 10 log (P2/P1)Where P1is input level & P2 is

output level

dB

Gain (dB)=10 log (output/input) = 10 log 2/1

= 10(0.30103) = 3.0103 approximately 3 dB gain

Net work1W 2W

dBRATIO dB2 3

3 5

10 10

4 = 2*2 ?

5 = 10/2 ?

80 = 2*2*2*10

?

500 = 5*1001000/2

?

.001=1/1000 ?0.02 = 2/100 ?

dBRATIO dB

2 3

3 5

10 10

4 = 2*2 3+3 = 6

5 = 10/2 10 – 3 =7

80 = 2*2*2*10 3+3+3+10 = 19

500 = 5*1001000/2

7 +20 = 2730 – 3 =27

.001 = 1/1000 – 30

0.02 = 2/100 3 - 20 =-17

dBRATIO dB10 10100 201000 3010,000 400.1 -100.01 -200.001 -300.0001 -40

BASIC DERIVED DECIBEL UNIT

1. dBm : Power level related to 1 mW

Power (dBm) = 10 log (Power in mW/1mW)

Eg. 20 W power = 10 log (20*1000/1)

= + 43 dBm2. dbw: dBW= 10 log power (w)/1w +30 dBm = 0dBW

-30 dBW = 0dBm dBW = dBm +30 dB

CORRECTION FACTOR Most instrument have internal

impedance of 600 . If the impedance of circuit under test is 600 , then reading will be correct. If the circuit impedance is 150 then,Indicated Power =

Actual power =

Error =Error in dB =

dB

EE

EE

E

E

6)600/150log(10

)150/log(10)600/log(10

)150/()600/(

150/

600/

22

22

2

2

CORRECTION FACTOR Thus the correction factor =

+6 dB

The correction factor for 300 is ?

For 75 impedance it is ?

+3dB

+9dB

EXERCISE

-12dB +35 dB -10dB4 mw ?

Net work 27 dB loss

Network 27 dB gain

1 w ?

10 w ?

ZERO TRANSMISSION LEVEL POINT (ZTLP) ZTLP – it is the point in the system

at which the standard test tone has an absolute power of 1mw or 0 dBm

It is a reference level for the system

Generally situated in the trunk exchange at the transmit end of a long haul system

RELATIVE TRANSMISSION LEVEL(dBr) The level of any point in the

system expressed in dB relative to ZTLP is referred to as dBr of that point

E.g. –33 dBr point in the system will be 33 dB below the ZTLP

RELATIVE POWER LEVEL(dBmo) The term dBmo is a measure of power

at any dBr point with reference to 0 dBm at the ZTLP

dBmo = dBm - dBr E. g. A tone of +36 dBm measured at

+19 dBr transmission level point is equivalent to +17 dBmo

A tone of +17 dBmo is equivalent to +7 dBm measured at – 10 dBr point

NOISE MEASURING UNITS The interfering effect of noise on

speech telephony is a function of response of human ear to specific frequencies in the voice channel

1000Hz tone at –90 dBm was chosen as reference

Any level below -90 is not ordinarily audible

dBrn Western electric 144 hand set used 1KHz at –90 dBm taken as

reference 0 dBrn = -90 dBm at 1000 Hz

+90 dBrn = 0 dBm or 1 mW Weighing net work provides 8 dB

attenuation at 3KHz band of white noise

dBrn = dBm + 82 for white noise of 3 KHz

dBa dBa – stand for dB reference noise

adjusted Western electric w-3 type F1-A hand

set used 1000 Hz at –85 dBm taken as

reference0 dBa = - 85 dBm at 1KHz

Weighing net work provides 3 dB attenuation when subjected to 3 KHz band of white noise

dBa = dBrn – 5 for 1KHz tone= dBm +82 for white noise of 3 KHz band

dBrnc Western electric type 150 hand set used 1000Hz at – 90 dBm taken as reference

0 dBrnc = - 90 dBm at 1000 Hz Weighing net work provides 2 dB

attenuation at 3KHz band, also known as message weighing

dBrnc = dBrn, dBa – 5 for single tone of 1KHz

= dBrn +6, dBa +6, dBm + 88 for white Noise of 3 KHz band

dBmp & pWp It is measured with psophometer &

called psophometrically weighted 800 Hz at 0 dBm taken as reference Provides 2 dB attenuation at 3KHz band

0 dBmp = 0 dBm at 800 Hz

=dBm – 2 for white noise of 3 KHz