report in digicom

8/8/2019 Report in Digicom

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Pulse ModulationPulse Modulation


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It is consist of essentially of sampling

analog information signals and then

converting those samples into discrete

pulses and transporting the pulses from

a source to a destination over a physical

transmission medium.


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Sample pulses are pulses that has constant

amplitude, width, and position at every

time (ts)


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Pulse Width Modulation (PWM)

Pulse Amplitude Modulation (PAM)

Pulse Position Modulation (PPM)

Pulse Code Modulation (PCM)


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Sometimes called as Pulse Duration

Modulation (PDM) or Pulse Length Modulation

(PLM)In this method, the width of the constant

amplitude pulse varies proportionally with the

amplitude of the analog signal at time the signalis sampled


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In this method, the position of a constant

width pulse within a prescribed time slot is

varied according to the amplitude of the

sample of the analog signal.


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In this method, the amplitude of a constant

width, constant-position pulse is varied

according to the amplitude of the sample of

the analog signal.


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In this method, the analog signal is sampled

and then converted to a serial n-bit binary

code for transmission. Each code has the

same number of bits and requires the same

length of time for transmission.


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PAM is used to develop other pulse-modulatedwaveforms and as an intermediate form ofmodulation in PSK, QAM, and PCM but seldom

used to itself. PWM and PPM are used in special-purpose

communication systems mainly for military butseldom used for commercial digital communicationsystems.

PCM is by far the most prevalent form of pulsemodulation.


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Alec Reeves was born in Redhill, Surrey in

1902 and was educated at the Reigate

Grammar School, followed by a scholarship tothe City and Guilds Engineering College in

1918, and then postgraduate studies

at Imperial College London in 1921.


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1937 Alex H. Reeves was credited for

inventingPCM while working at AT&T at

its Paris Laboratories.

1960s PCM became prevalent with the

advent of solid-state electronics

Today PCM is the preferred method of

communication within the public

switched telephone network.


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In PCM, it is easy to combine digitized voice

and digital data into a single, high speed

digital signal and propagate it over either

metallic or optical cables.

PCM is the only digitally encoded modulation

technique that is commonly used for digital

transmission.


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The pulse are fixed in amplitude and length.

It is a binary system where a pulse or lack of

a pulse within a prescribed time slotrepresents either a logic 1 or logic 0

condition.

PWM,

PPM and

PAM are digital but seldombinary, as pulse does not represents a single

binary digit.


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Band-pass filter - standard voice-band

frequency range of 300 Hz to 3000 Hz.

Sample and Hold circuit periodically samples

the analog input signal and converts those

samples to a multilevel PAM signal.

Analog-to-Digital converter converts the PAM

samples to parallel PCM codes.

Parallel-to-Serial converter parallel PCM

codes to serial binary data.


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Transmission line repeaters regenerates the

digital pulses

Serial-to-Parallel converter converts serial pulses

to parallel PCM codes.

Digital-to-Analog converter converts parallel PCMcodes to multilevel PAM signals.

Hold circuit PAM signals back to its original analog

form.

Codec is an integrated circuit that performs the

PCM encoding and decoding functions.


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The function of sampling circuit in a PCM

transmitter is to periodically sample the

continually changing analog input voltageand convert those samples to a series of

constant-amplitude pulses that can more

easily be converted to binary PCM code.


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Natural Sampling

Flat-top Sampling


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Natural sampling is when tops of the sample

pulses retain their natural shape during the

sample interval, making it difficult for anADC to convert the sample to a PCM code.


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The common method used for sampling voice

signals in PCM system which is accomplished

in a sample-and-hold circuit.It periodically sample the continuall

changing analog input voltage and convert

those sample to a series of constant

amplitude PAM voltage levels.


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Aperture error is when the amplitude of the

sampled signal changes during the sample

pulse time.The magnitude of the error

depends on how much the analog signal

voltage changes while the sample is being

taken and the width of the sample pulse


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Natural Sampling Flat-top Sampling

Retain the natural shape PAM signal

Higher aperture Less aperrture

Amplitude of frequency

components produced from

narrow, finite-width samples

pulses

Sampled with a narrow pulse

and held relatively constant

Needs an equalizer or

compensation filter

Can operate with a slower ADC


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The FET acts as a simple analog switch.

When turned on, Q1 provides a low-impedance path

to deposit the analog sample voltage across

capacitor C1. The time that Q1 is on is called the

aperture or acquisition time.

Essentially, C1 is the hold circuit. When Q1 is off, C1does not have a complete path to charge through

and therefore, stores the sample voltage.


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The storage time of the capacitor is called A/D

conversion time because it is during this time that

the ADC converts the sample voltage to a PCM

code.

The acquisition time should be very short to ensure

that the minimum change occurs in the analogsignal while it is being deposited across C1.

If the input to the ADC is changing while it is

performing the conversion, aperture distortion

results. So, by having short aperture time and keeping the

input to the ADC relatively constant, the sample-

and-hold circuit can reduce aperture distortion.


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It is important that the output impedance of

voltage follower Z1 and the on resistance of

Q1

be as small as possible.

This ensures that the RC charging time

constant of the capacitor is kept very short,

allowing the capacitor to charge or discharge

rapidly during the short acquisition time.


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Note the gradual discharge across the

capacitor during conversion time, it is called

droop which is caused by the capacitor

discharging through its own leakage

resistance and the input impedance ofvoltage follower Z2.

Therefore, it is important that the input

impedance of Z2 and the leakage resistanceof C1 be as high as possible.


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dv

i= C -----

dtwhere:

C = maximum capacitance in farad

i= maximum ouput current from Z1dv= maximum charge of voltage across C1dt = charge time (aperture time)


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= RC

= one charge time constant

R = output impedance of Z1 plus the

resistance of Q1 in

ohms

C = capacitance value of C1


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Accuracy (%) Charge Time

1.0 2.3

1 4.6

0.1 6.9

0.01 9.2


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Using the Sample-and-Hold Circuit,

determine the

largest value capacitor that can be used.U

sean output

impedance for Z1 of 10, an on resistance

for Q1 of 10,

an acquisition time of 10s, a maximum peak-

to-peak

input voltage of 10V, a maximum output

current from Z1


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The Nyquist sampling theorem establishes

the minimum sampling rate (fs) that can be

used for a given PCM system. For a sample toreproduce accurately in PCM receiver, each

cycle of the analog input signal (fa) must be

sampled least at twice.


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fs > 2fa

fs = minimum Nyquist sample rate in hertz

fa=

maximum analog input frequency inhertz


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The minimum sampling rate is equal to

twice the highest audio input frequency.

Alias is an impairment that occurs when fs isless than two times fa.


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The binary codes use for PCM are n-bit codes,

where nmay be any positive interger greater

than 1.The codes currently used in PCM are

sign-magnitude codes, where the most

significant bits (MSB) is the sign bit and theremaining bits are used for magnitude.


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For a PCM system with maximum audio input

frequency

of 4 Khz, determine the minimum sample rateand the

alias frequency produced if a 5 Khz audio

signal were

allowed to enter the sample-and-hold circuit.


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Sign (MSB) Magnitude ( 2-1) Decimal Value Quantization

Range

1 1 -1 + 3 + 2.5 to + 3.5 V

1 1-0 + 2 + 1.5 to + 2.5 V

1 0-1 + 1 + 0.5 to + 1.5 V

1 0-0 + 0 + 0 to + 0.5 V

0 0-0 - 0 -0 to - 0.5 V

0 0-1 - 1 - 0.5 to - 1.5 V

0 1-0 - 2 - 1.5 to - 2.5 V

o 1-1 - 3 - 2.5 to - 3.5 Vn = 3

1 = positive

0 = negative


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Quantization process of converting an infinitenumber of possibilities to a finite number ofconditions

(rounding off amplitudes) Quantizing - assigningPCM codes to absolute

magnitudes

Resolution magnitude of a quantum, equal tothe voltage of the minimum step size which isequal to the voltage of the least significant bit(Vlsb)


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Quantum/Quantization interval magnitude

difference between adjacent steps

Overload Distortion or peak limiting occurs

when the sample exceeds the highest

quantization interval.

Each code has a quantization range equal to

+ or one-half the magnitude of quantum


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Sign (MSB) Magnitude ( 2-1) Decimal Value Quantization

Range

1 1 -1 + 3 + 2.5 to + 3.5 V

1 1-0 + 2 + 1.5 to + 2.5 V

1 0-1 + 1 + 0.5 to + 1.5 V

1 0-0 + 0 + 0 to + 0.5 V

0 0-0 - 0 -0 to - 0.5 V

0 0-1 - 1 - 0.5 to - 1.5 V

0 1-0 - 2 - 1.5 to - 2.5 V

o 1-1 - 3 - 2.5 to - 3.5 V

Folded Binary Code is characterized as that the codes

on half of a given Coding table is a mirror image of

the another half in the Coding table except for the

sign bit.


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Round-off errors in the transmitted signal thatare reproduced when the code is convertedback to analog

Equivalent to additive white noise that altersthe signal amplitude.

The maximum magnitude for quantization erroris equal to one-half a quantum.

The folded PCM code is: sample voltage

resolution

Qe = Original Sample voltage quantized level


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For the PCM coding scheme shown in the

figure,

determine the quantized voltage, quantization

error

(Qe), and the PCM code for the analog sample

votltage

of +1.07 V.


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Ratio of the largest possible magnitude tothe smallest possible magnitude that can bedecoded by DAC

DR = Vmax (maximum voltage magnitude)

Vmin (quantum value/resolution)

DR expressedindB

DR = 20 log VmaxVmin

Where DR = dynamic range (unitless)


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Number of bits used for PCM code depends

on DR

2n 1 DRwhere n = no. of bits in a PCM code excluding sign

bit

2n

= DR + 1log 2n = log (DR+1)

nlog 2 = log (DR+1)

n = log (3+1) = 0.602 = 2

log 2 0.301For a dynamic range of 3, a PCM code requires 2

bits


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For a PCM system with the following

parameters,

determine:

Minimum sample rate

Minimum no. of bits used in the PCM code

Resolution Quantization error

Maximum analog input frequency = 4 Khz

Maximum decoded voltage at the receiver =


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Numerical indication of how efficiently a

PCM code is utilized

Ratio of the minimum number of bit required

to achieve a certain dynamic range to the

actual number ofPCM bits used


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Coding Effieciency

=minimum no. of bits X 100

actual no. of bits


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Is a measurement of the effect of quantization

errors introduced by analog-to-digital

conversion at the ADC.Worst SQR occurs when the input signal is at

its minimum amplitude (101 or 001).


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SQR = resolution/ Qe

= Vlsb/(Vlsb/2) = 2

SQRmin = 1/0.5 = 2

= 20 log 2 = 6 dB

SQRmax = 3/(0.5) = 6= 20 log 6 = 15.6 dB


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Signal PowerSignal Power--toto--QuantizationQuantization NoiseNoiseRatioRatio

SQR(db)= 10 log V2/ R

(q2 / 12) / R

SQR(db)= 10 log V2/ R

q2 / 12

SQR(db) 20 log Vq

Where:

R = resistance

v = rms signal voltage

q = quantization interval

v2/R = average signal power

(q2/12/R) = average quantization

noise power


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Linear codes magnitude change between

any two successive steps in uniform

Resolution/accuracy is the same for lower

and higher amplitude signal

SQR for low amplitude signal is less than the

SQR for higher amplitude signal


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Nonlinear step size increases with the

amplitude of the input signal

More codes at the bottom

Distance between successive codes is

greater for higher amplitude signals


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The only input to the PAM sampler when

there is no analog input signal

Converted to a PAM sample as if it were asignal, then quantized by the ADC.


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One way to reduce idle noise

First quantization interval is made larger in

Amplitude than the rest of the step

Advantage: less idle channel noise

Disadvantage: larger possible magnitude forQe


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Level-at-a Time Coding

Digit-at-a Time Coding

Word-at-a Time Coding


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Compares the PAM signal to a rampwaveform

while the counter is advanced at a uniform

rate

When the ramp waveform equals or exceeds

the PAM sample, the counter contains thePCM code


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Determines each digit of the PCM code

Sequentially

Feedback coder one common kind of digit

at-a time coder that determines the PCM code

simultaneously because it uses successive

approximation register(SAR)


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Use flash encodersmore complex

Multiple Threshold Circuit common type

of word-at-a time coding where logic

circuit senses the highest threshold circuit

sensed by the PAM input signal and

produce the approximate PCM code.

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