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.