Transcript SCADA (Supervisory Control And Data Acquisition)

Pulse Code Modulation
Sukiswo
[email protected]
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Outline
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Pulse Code Modulation
Quantizing
Encoding
Analogue to Digital Conversion
Bandwidth of PCM Signals
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PULSE CODE MODULATION
 DEFINITION:
Pulse code modulation (PCM) is essentially
analog-to-digital conversion of a special type
where the information contained in the
instantaneous samples of an analog signal is
represented by digital words in a serial bit
stream.
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PULSE CODE MODULATION
 The advantages of PCM are:
• Relatively inexpensive digital circuitry may be used
extensively.
• PCM signals derived from all types of analog sources
may be merged with data signals and transmitted over a
common high-speed digital communication system.
• In long-distance digital telephone systems requiring
repeaters, a clean PCM waveform can be regenerated at
the output of each repeater, where the input consists of a
noisy PCM waveform.
• The noise performance of a digital system can be superior
to that of an analog system.
• The probability of error for the system output can be
reduced even further by the use of appropriate coding
techniques.
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PULSE CODE MODULATION
 The PCM signal is generated by carrying
out three basic operations:
1. Sampling
2. Quantizing
3. Encoding
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PULSE CODE MODULATION
1.
2.
Sampling operation generates a flat-top PAM
signal.
Quantizing operation approximates the analog
values by using a finite number of levels. This
operation is considered in 3 steps
a) Uniform Quantizer
b) Quantization Error
c) Quantized PAM signal output
3.
PCM signal is obtained from the quantized PAM
signal by encoding each quantized sample value
into a digital word.
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Analog to Digital Conversion
Analog
Input
Signal
Sample
ADC
Quantize
Encode
111
110
101
100
011
010
001
000
Digital Output
Signal
111 111 001 010 011 111 011
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Analog to Digital Conversion
 The Analog-to-digital Converter (ADC) performs three functions:
– Sampling
• Makes the signal discrete in time.
• If the analog input has a bandwidth of W Hz, then the minimum
sample frequency such that the signal can be reconstructed
without distortion.
– Quantization
• Makes the signal discrete in amplitude.
• Round off to one of q discrete levels.
– Encode
• Maps the quantized values to digital words that are  bits long.
 If the (Nyquist) Sampling Theorem is satisfied, then only quantization
introduces distortion to the system.
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Quantization
 The output of a sampler is still continuous in amplitude.
– Each sample can take on any value e.g. 3.752, 0.001,
etc.
– The number of possible values is infinite.
 To transmit as a digital signal we must restrict the number
of possible values.
 Quantization is the process of “rounding off” a sample
according to some rule.
– E.g. suppose we must round to the nearest tenth, then:
3.752 --> 3.8
0.001 --> 0
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Illustration of the Quantization Error
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Uniform Quantization
 Most ADC’s use uniform
Dynamic Range:
(-8, 8)
Output sample
XQ
7
5
3
1
-8
-6
-4
-2
-1 2
4
6
8
Input sample X
-3
-5
-7
Quantization Characteristic
Example: Uniform  =3 bit quantizer
q=8 and XQ = {1,3,5,7}
quantizers.
 The quantization levels of a
uniform quantizer are
equally spaced apart.
 Uniform quantizers are
optimal when the input
distribution is uniform.
When all values within the
Dynamic Range of the
quantizer are equally likely.
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Quantization Example
Analogue signal
Sampling TIMING
Quantization levels.
Quantized to 5-levels
Quantization levels
Quantized 10-levels
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PCM encoding example
Table: Quantization levels with
belonging code words
Levels are encoded
using this table
M=8
Chart 1. Quantization and digitalization of a signal.
Chart 2. Process of restoring a signal.
PCM encoded signal in binary form:
101 111 110 001 010 100 111 100 011 010 101
of 33 bits were used to encode a signal 13
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Signal is quantized in 11 time points & 8 quantization
segments.
Encoding
 The output of the quantizer is one of M
possible signal levels.
– If we want to use a binary transmission system,
then we need to map each quantized sample
into an n bit binary word.
M  2 , n  log2 (M )
n
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Encoding
 Encoding is the process of representing
each quantized sample by an  bit code
word.
– The mapping is one-to-one so there is no
distortion introduced by encoding.
– Some mappings are better than others.
• A Gray code gives the best end-to-end
performance.
• The weakness of Gray codes is poor
performance when the sign bit (MSB) is
received in error.
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Gray Codes
 With gray codes adjacent samples differ only in one bit
position.
 Example (3 bit quantization):
XQ
+7
+5
+3
+1
-1
-3
-5
-7
Natural coding
111
110
101
100
011
010
001
000
Gray Coding
110
111
101
100
000
001
011
010
 With this gray code, a single bit error will result in an
amplitude error of only 2.
– Unless the MSB is in error.
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Waveforms in a PCM system for M=8
M=8
(a) Quantizer Input output characteristics
(b) Analog Signal, PAM Signal, Quantized PAM Signal
M  2n n  log 2 (M )
(c) Error Signal
(d) PCM Signal
M is the number of Quantization levels
n is the number of bits per sample
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PCM Transmission System
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Practical PCM Circuits
 Three popular techniques are used to
implement the analog-to-digital converter
(ADC) encoding operation:
1. The counting or ramp, ( Maxim ICL7126 ADC)
2. Serial or successive approximation, (AD 570)
3. Parallel or flash encoders. ( CA3318)
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Practical PCM Circuits

The objective of these circuits is to generate the
PCM word.
 Parallel digital output obtained (from one of the
above techniques) needs to be serialized before
sending over a 2-wire channel
 This is accomplished by parallel-to-serial
converters [Serial Input-Output (SIO) chip]
 UART,USRT and USART are examples for
SIO’s
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Bandwidth of PCM Signals
 The spectrum of the PCM signal is not directly
related to the spectrum of the input signal.
 The bandwidth of (serial) binary PCM

waveforms depends on the bit rate R and the
waveform pulse shape used to represent the
data.
The Bit Rate R is
R=nfs
Where n is the number of bits in the PCM word
(M=2n) and fs is the sampling rate.
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Bandwidth of PCM Signals
 For no aliasing case (fs≥ 2B), the MINIMUM
Bandwidth of PCM Bpcm(Min) is:
Bpcm(Min) = R/2 = nfs//2
The Minimum Bandwidth of nfs//2 is obtained
only when sin(x)/x pulse is used to generate the
PCM waveform.
 For PCM waveform generated by rectangular
pulses, the First-null Bandwidth is:
Bpcm = R = nfs
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