Zestaw posiada opracowanie teoretyczne z opisami gotowych ćwiczeń

Zestaw posiada opracowanie teoretyczne z opisami gotowych ćwiczeń
Sampling and
Reconstruction Trainer
ST2151
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Learning Material
Ver.1.2
An ISO 9001:2008 company
94, Electronic Complex, Pardesipura
Indore - 452 010 India
Tel: +91-731 4211100
Fax: +91-731-2555643
e mail: [email protected]
Websites: www.caddo.bz
www.scientech.bz
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We request you to use the Learning material in the CD form
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Please remember that each paper manual requires 50-100 sheets of paper
Your CD learning material has
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colourful diagrams,
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plenty of theory,
detailed experiments with observation tables,
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frequently asked questions, etc.
…….. and more so sometimes videos as well.
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ST2151
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Scientech Technologies Pvt. Ltd.
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Sampling and Reconstruction Trainer
ST2151
Table of Contents
1.
Safety instructions
5
2.
Introduction
6
3.
Features
8
4.
Technical Specifications
9
5.
Theory
10
•
•
•
•
•
•
13
14
17
30
31
36
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Experiments
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6.
Nyquist’s Criterion
Sampling Techniques
Types of sampling
Sample and hold circuit
Anti aliasing
Low Pass Filters
46
Experiment 2
• Study the Nyquist Criteria for Sampling and Reconstructing signal.
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Experiment 1
• Study of signal Sampling and Reconstruction techniques.
• Study the effect of II order and IV order LPF on reconstructed signal.
• Study the effect of Sample Amplifier and Sample and Hold Amplifier
on reconstructed signal.
55
Experiment 4
• To study and compare responses of 2nd order and 4th order LPFs.
61
Experiment 5
• To verify sampling and reconstruction data transmission scheme for
a. External sampling signal
b. Audio signal
64
6.
Frequently Asked Questions
69
7.
Warranty
71
8.
List of Accessories
71
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Experiment 3
• Study the effect of Sample /Hold Circuitry on reconstructed waveform
• Effect of sampling pulse duty cycle on the reconstructed
Waveform in sample and sample hold output.
ST2151
Safety Instructions
Read the following safety instructions carefully before operating the instrument. To
avoid any personal injury or damage to the instrument or any product connected to it.
Do not operate the instrument if suspect any damage to it.
The instrument should be serviced by qualified personnel only.
For your safety:
: Use only the mains cord designed for this instrument.
Ensure that the mains cord is suitable for your
country.
Ground the Instrument
: This instrument is grounded through the protective
earth conductor of the mains cord. To avoid electric
shock the grounding conductor must be connected to
the earth ground. Before making connections to the
input terminals, ensure that the instrument is properly
grounded.
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Use proper Mains cord
Use only the proper Fuse
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Observe Terminal Ratings : To avoid fire or shock hazards, observe all ratings and
marks on the instrument.
: Use the fuse type and rating specified for this
instrument.
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1.
Do not operate in wet / damp conditions.
2.
Do not operate in an explosive atmosphere.
3.
Keep the product dust free, clean and dry.
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Use in proper Atmosphere : Please refer to operating conditions given in the
manual.
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ST2151
Introduction
The ST2151, Sampling and Reconstruction Trainer demonstrates the basic scheme
used to transmit an information signal. It covers very basic concepts like Nyquist
criteria, role of sample Amplifier, sample and hold amplifier and duty cycle of
sampling pulse while transmitting a signal. It also demonstrates signal recovery using
low pass filters of different orders.
Know your ST2151 trainer better:
The trainer has built in 1 KHz (5Vp-p) sine wave generator as onboard signal to
demonstrate completely, the sampling and reconstruction technique. To understand
the process for audio signal, an Audio Input and Audio Output Circuit in provided on
board along with mic and built in speaker.
Various test points on the trainer makes user to understand, the complete process that
takes place for sampling and reconstruction of transmitted signal.
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On-board six sampling frequencies (20, 50, 80, 100, 200 and 400 KHz), out of which
user can select any one (when Sampling Signal Selector Switch is on Internal Signal
position), using sampling frequency selector switch. For the selected signal the
corresponding LED will be lightened. When the trainer is switched on, it will
randomly select the sampling frequency. For selecting a particular sampling
frequency a three bit control signal is applied to the Mux unit. This three bit signal
again is indicated by lightening of LEDs. The codes are as follows:
TP18
0
TP20
0
1
1
0
1
1
0
0
1
0
50 KHz
0
80 KHz
1
0
100 KHz
1
200 KHz
0
1
1 (000 only on switch on)
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20 KHZ
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400 KHz
TP19
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The selected frequency then passes through frequency divider circuit and duty cycle
selector unit to generate desired sampling frequency of 2, 5, 8, 10, 20 and 40 KHz
with required duty cycle (from 10% to 50%). The trainer allows user to apply external
sampling signal through External Sampling Signal I/P (when Sampling Signal
Selector Switch is on External Signal position)
Using Duty Cycle selector switch one can vary the duty cycle of the selected sampling
frequency from 10 to 90%. The displayed digit (D) on the switch indicates (Dx10) %
duty cycle of sampling signal. E.g. When displayed 5 it indicates (5x10) = 50% duty
cycle of selected sampling signal (only for the case of internal sampling signal).
Once signal is sampled, user can either send Sample Amplifier output or Sample and
Hold Amplifier output to any of the two LPFs. Thus a comparative study is available
to recover original transmitted signal precisely.
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The manual explains a detailed working of the trainer with the help of complete
theory and set of five experiments. The experimentation alone with its conclusion and
resulting waveforms are covered in the manual.
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ST2151 Front View
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Features
Crystal controlled pulse generator
•
Demonstrates sampling and reconstruction as per Nyquist criterion
•
On-board synchronized analog signal generator
•
Six, switch selectable sampling frequencies
•
Sampling pulse duty-cycle selectable
•
Internal/ External sampling signal selectable
•
Separate sample and sample/hold outputs available
•
On-board second order and fourth order low-pass filters
•
Audio Input and Output links to show the transmission and reception of
real time signal (audio signal)
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•
RoHS Compliance
Scientech Products are RoHS Complied.
RoHS Directive concerns with the restrictive use of Hazardous substances (Pb,
Cd, Cr, Hg, Br compounds) in electric and electronic equipments.
Scientech products are “Lead Free” and “Environment Friendly”.
It is mandatory that service engineers use lead free solder wire and use the
soldering irons upto (25 W) that reach a temperature of 450°C at the tip as the
melting temperature of the unleaded solder is higher than the leaded solder.
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Technical Specifications
Crystal Frequency
:
8 MHz
Sampling Frequency
:
2, 5, 8, 10, 20 & 40 KHz (switch selectable)
On-board Generator
:
Synchronized 1 KHz sine wave (5Vpp)
Duty cycle
:
0 - 90% in decade steps
(Switch Selectable)
Low -Pass Filters
:
Butterworth 2nd & 4th order filters
Cut-off frequency - 3.4 KHz each
Test Points
:
50 in numbers
Interconnections
:
2 mm sockets
Power Supply
:
+ 12V DC (150mA)
:
W325 X H90 X D255
:
1.5 Kgs. (approximately)
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Weight
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Dimensions (mm)
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Theory
The signals which are required to be transmitted as information is known as
information signal and in the case of voice communication this will be a continuously
changing signal containing speech information. The aim of the kit is to transmit the
signals in digital form and is to reproduce this information signal in analog form at the
receiving end of the communication system with the help of sampling and
reconstruction trainer.
In the exercises to follow, you will simulate audio signal by a 1 KHz test signal
provided On-board. The repetitive, non-changing waveform does not contain
information. Provided the frequency of the test-signal lies within the frequency range
which an information signal will occupy, a test signal of this type can be extremely
helpful in system analysis and testing.
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The voice signals are limited to the range 300 Hz to 3.4 KHz, a 1 KHz frequency fits
conveniently in this range and can be used to demonstrate and test many techniques
used in communication system.
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Theory of sampling:
The signals we use in the real world, such as our voice, are called "analog" signals.
To process these signals for digital communication, we need to convert analog signals
to "digital" form. While an analog signal is continuous in both time and amplitude, a
digital signal is discrete in both time and amplitude. To convert continuous time
signal to discrete time signal, a process is used called as sampling. The value of the
signal is measured at certain intervals in time. Each measurement is referred to as a
sample.
Principle of sampling:
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Consider an analogue signal x(t) that can be viewed as a continuous function of time,
as shown in figure1. We can represent this signal as a discrete time signal by using
values of x(t) at intervals of nTs to form x(nTs) as shown in figure 1. We are
"grabbing" points from the function x(t) at regular intervals of time, Ts, called the
sampling period.
Basic Sampling Process
Figure 1
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Sampling of signal at sampling interval (period) Ts
Figure 2
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Figure 2 depicts the sampling of a signal at regular interval (period) t=nTs where n is
an integer. The sampling signal is a regular sequence of narrow pulses δ (t) of
amplitude 1.Figure 3 shows the sampled output of narrow pulses δ (t) at regular
interval of time.
Sampled Output of narrow pulses δ (t)
Figure 3
The time distance Ts is called sampling interval or sampling period, fs=1/Ts is called
as sampling frequency (Hz or samples/sec), also called sampling rate.
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The Sampling Theorem:
The Sampling Theorem states that a signal can be exactly reproduced if it is sampled
at a frequency Fs, where Fs is greater than twice the maximum frequency Fmax in the
signal.
Fs > 2·Fmax
The frequency 2· Fmax is called the Nyquist sampling rate. Half of this value, Fmax, is
sometimes called the Nyquist frequency.
The sampling theorem is considered to have been articulated by Nyquist in 1928 and
mathematically proven by Shannon in 1949. Some books use the term "Nyquist
Sampling Theorem", and others use "Shannon Sampling Theorem". They are in fact
the same sampling theorem.
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The sampling theorem clearly states what the sampling rate should be for a given
range of frequencies. In practice, however, the range of frequencies needed to
faithfully record an analog signal is not always known beforehand. Nevertheless,
engineers often can define the frequency range of interest. As a result, analog filters
are sometimes used to remove frequency components outside the frequency range of
interest before the signal is sampled.
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For example, the human ear can detect sound across the frequency range of 20 Hz to
20 KHz. According to the sampling theorem, one should sample sound signals at least
at 40 KHz in order for the reconstructed sound signal to be acceptable to the human
ear. Components higher than 20 KHz cannot be detected, but they can still pollute the
sampled signal through aliasing. Therefore, frequency components above 20 KHz are
removed from the sound signal before sampling by a band-pass or low-pass analog
filter.
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Nyquist Criterion
As shown-in the figure 4 the lowest sampling frequency that can be used without the
sidebands overlapping is twice the highest frequency component present in the
information signal. If we reduce this sampling frequency even further, the sidebands
and the information signal will overlap and we cannot recover the information signal
simply by low pass filtering. This phenomenon is known as fold-over distortion or
aliasing.
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Nyquist Criterion (Sampling Theorem)
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Figure 4
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The Nyquist criteria states that a continuous signal band limited to Fm Hz can be
completely represented by and reconstructed from the samples taken at a rate greater
than or equal to 2Fm samples/second.
This minimum sampling frequency is called as Nyquist Rate i.e. for faithful
reproduction of information signal fs > 2 fm.
For audio signals the highest frequency component is 3.4 KHz.
So,
Sampling Frequency
≥ 2 fm
≥ 2 x 3.4 KHz
≥ 6.8 KHz
Practically, the sampling frequency is kept slightly more than the required rate. In
telephony the standard sampling rate is 8 KHz. Sample quantifies the instantaneous
value of the analog signal point at sampling point to obtain pulse amplitude output.
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Nyquist’s Uniform Sampling Theorem for Low pass Signal:
Part - I If a signal x(t) does not contain any frequency component beyond W Hz, then
the signal is completely described by its instantaneous uniform samples with sampling
interval (or period ) of Ts < 1/(2W) sec.
Part – II The signal x(t) can be accurately reconstructed (recovered) from the set of
uniform instantaneous samples by passing the samples sequentially through an ideal
(brick-wall) low pass filter with bandwidth B, where W ≤ B < fs – W and fs = 1/(Ts).
As the samples are generated at equal (same) interval (Ts) of time, the process of
sampling is called uniform sampling. Uniform sampling, as compared to any nonuniform sampling, is more extensively used in time-invariant systems as the theory of
uniform sampling (either instantaneous or otherwise) is well developed and the
techniques are easier to implement in practical systems.
Sampling Techniques:
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There are three types of sampling techniques as under:
Ideal sampling or Instantaneous sampling or Impulse sampling
2.
Natural sampling
3.
Flat top sampling
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Ideal sampling or Instantaneous sampling or Impulse sampling:
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For the proof of sampling theorem we use ideal or impulse sampling.
{x(nTs)} = Σ x(t).δ(t- nTs)
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The concept of ‘instantaneous’ sampling is more of a mathematical abstraction as no
practical sampling device can actually generate truly instantaneous samples (a
sampling pulse should have non-zero energy). However, this is not a deterrent in
using the theory of instantaneous sampling, as a fairly close approximation of
instantaneous sampling is sufficient for most practical systems. To contain our
discussion on Nyquist’s theorems, we will introduce some mathematical expressions.
If x(t) represents a continuous-time signal, the equivalent set of instantaneous uniform
samples {x(nTs)} may be represented as:
where x(nTs) = x(t) =nTs , δ(t) is a unit pulse singularity function and ‘n’ is an
integer
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Ideal sampling process
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2. Natural sampling:
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In the analogue-to-digital conversion process an analogue waveform is sampled to
form a series of pulses whose amplitude is the amplitude of the sampled waveform at
the time the sample was taken. In natural sampling the pulse amplitude takes the
shape of the analogue waveform for the period of the sampling pulse as shown in
figure 6.
Figure 6
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3.
Flat Top sampling:
After an analogue waveform is sampled in the analogue-to-digital conversion process,
the continuous analogue waveform is converted into a series of pulses whose
amplitude is equal to the amplitude of the analogue signal at the start of the sampling
process. Since the sampled pulses have uniform amplitude, the process is called flat
top sampling as shown in figure 7.
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Figure 7
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Note that due to the flat-top pulses, the spectrum of the sampled signal is distorted.
The narrower the pulse width, the less distortion.
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The original signal may be obtained by using a low-pass filter with a characteristic
which inverts the distortion.
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Types of sampling:
Over Sampling:
Graphically, if the sampling rate is sufficiently high, i.e., greater than the Nyquist rate,
there will be no overlapped frequency components in the frequency domain. A
"cleaner" signal can be obtained to reconstruct the original signal. This argument is
shown graphically in the frequency-domain figure 8(a) and time-domain figure 8(b).
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Over sampling in Frequency Domain
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Figure 8(a)
Over sampling in Time Domain
Figure 8(b)
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Under Sampling:
When the sampling rate is lower than or equal to the Nyquist rate, a condition defined
as under sampling, it is impossible to rebuild the original signal according to the
sampling theorem.
An example is illustrated below, where the reconstructed signal built from data
sampled at the Nyquist rate is way off from the original signal. This argument is
shown graphically in the frequency-domain figure 9(a) and time-domain figure 9(b).
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Under sampling in frequency domain
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Figure 9(a)
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Under sampling in Time domain
Figure 9(b)
In practice, the continuous signal is sampled using an analog or digital converter
(ADC), a non-ideal device with various physical limitations. This result in deviations
from the theoretically perfect reconstruction capabilities collectively referred to as
distortion.
Various types of distortion can occur, including:
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1.
Aliasing:
A precondition of the sampling theorem is that the signal to be band limited.
However, in practice, no time-limited signal can be band limited. Since signals of
interest are almost always time-limited (e.g., at most spanning the lifetime of the
sampling device in question), it follows that they are not band limited. However, by
designing a sampler with an appropriate guard band, it is possible to obtain output that
is as accurate as necessary.
Aliasing is the presence of unwanted components in the reconstructed signal. These
components were not present when the original signal was sampled. In addition,
some of the frequencies in the original signal may be lost in the reconstructed signal.
Aliasing occurs because signal frequencies can overlap if the sampling frequency is
too low. As a result, the higher frequency components roll into the reconstructed
signal and cause distortion of the signal Frequencies "fold" around half the sampling
frequency. This type of signal distortion is called aliasing.
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We only sample the signal at intervals.
We don't know what happened between the samples.
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A crude example is to consider a 'glitch' that happened to fall between adjacent
samples. Since we don't measure it, we have no way of knowing the glitch was there
at all.
Example of aliasing
Figure 10
In a less obvious case, we might have signal components that are varying rapidly in
between samples. Again, we could not track these rapid inter-sample variations. We
must sample fast enough to see the most rapid changes in the signal. Sometimes we
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may have some a prior knowledge of the signal, or be able to make some assumptions
about how the signal behaves in between samples. If we do not sample fast enough,
we cannot track completely the most rapid changes in the signal.
Some higher frequencies can be incorrectly interpreted as lower ones.
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Example of High frequency signal
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Figure 11
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In the diagram, the high frequency signal is sampled just under twice every cycle. The
result is that each sample is taken at a slightly later part of the cycle. If we draw a
smooth connecting line between the samples, the resulting curve looks like a lower
frequency. This is called 'aliasing' because one frequency looks like another.
Note that the problem of aliasing is that we cannot tell which frequency we have - a
high frequency looks like a low one so we cannot tell the two apart. But sometimes
we may have some a prior knowledge of the signal, or be able to make some
assumptions about how the signal behaves in between samples, that will allow us to
tell unambiguously what we have.
Nyquist showed that to distinguish unambiguously between all signal frequencies
components we must sample faster than twice the frequency of the highest frequency
component.
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Sampling process as per the Nyquist criteria
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Figure 12
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In the diagram, the high frequency signal is sampled twice every cycle. If we draw a
smooth connecting line between the samples, the resulting curve looks like the
original signal. But if the samples happened to fall at the zero crossings, we would see
no signal at all - this is why the sampling theorem demands we sample faster than
twice the highest signal frequency.
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The highest signal frequency allowed for a given sample rate is called the Nyquist
frequency.
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1. Integration effect or aperture effect:
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Actually, Nyquist says that we have to sample faster than the signal bandwidth, not
the highest frequency. But this leads us into multi rate signal processing which is a
more advanced subject.
This results from the fact that the sample is obtained as a time average within a
sampling region, rather than just being equal to the signal value at the sampling
instant. The integration effect is readily noticeable in photography when the exposure
is too long and creates a blur in the image. An ideal camera would have an exposure
time of zero. In a capacitor-based sample and hold circuit, the integration effect is
introduced because the capacitor cannot instantly change voltage thus requiring the
sample to have non-zero width.
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2. Jitter:
Jitter is the time variation of a periodic signal in electronics and telecommunications,
often in relation to a reference clock source. Jitter may be observed in characteristics
such as the frequency of successive pulses, the signal amplitude, phase of periodic
signals. Jitter is a significant, and usually undesired, factor in the design of almost all
communications links applications it is called timing jitter
Jitter can be quantified in the same terms as all time-varying signals, or peak-to-peak
displacement. Also like other time-varying signals, jitter can be expressed in terms of
spectral density (frequency content).
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Jitter period is the interval between two times of maximum effect (or minimum effect)
of a signal characteristic that varies regularly with time. Jitter frequency, the more
commonly quoted figure, is its inverse. Generally, very low jitter frequency is not of
interest in designing systems, and the low-frequency cutoff for jitter is typically
specified at 1 Hz.
3. Noise:
In communication system noise is fluctuations in and the addition of external factors
to the stream of target information being received at a detector. In communications, it
may be deliberate as for instance jamming of a radio or TV signal, but in most cases it
is assumed to be merely undesired interference with intended operations. Natural and
deliberate noise sources can provide both or either of random interference or patterned
interference. Only the latter can be cancelled effectively in analog systems; however,
digital systems are usually constructed in such a way that their quantized signals can
be reconstructed perfectly, as long as the noise level remains below a defined
maximum, which varies from application to application. In communication, the term
noise has the following meanings:
a. An undesired disturbance within the frequency band of interest; the summation
of unwanted or disturbing energy introduced into a communication system from
man-made and natural sources.
b. A disturbance that affects a signal and that may distort the information carried
by the signal.
c. Random variations of one or more characteristics of any entity such as voltage,
current, or data.
d. A random signal of known statistical properties of amplitude, distribution, and
spectral density.
e. Loosely, any disturbance tending to interfere with the normal operation of a
device or system.
Noise and what can be done about it has long been studied. Shannon established
information technology and in so doing clarified the essential nature of noise and the
limits it places on the operation of electronic equipment.
In some cases a little noise may be considered advantageous, allowing a Dithered
representation of signals below the minimum strength, or between two quantization
levels.
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Slew rate:
The slew rate is a fairly subtle specification. It is the time an amplifier needs to go
from 10% to 90% of the total output voltage in response to a step in voltage at the
input (Fig. 13). It is given in V/µs, the number of volts that the output can rise (or fall)
in one microsecond. This spec obviously limits the capability of an amplifier to
generate high voltage pulses with sharp rising and falling edges (Fig. 14), but is also a
bandwidth limiting factor for sine-wave or arbitrary signals. This can be seen as
follows. The highest rate of change in the output voltage of a sine wave is at the 0Vcrossing (Fig. 15). The higher the frequency, the faster the voltage has to rise there to
prevent distortion of the sine wave. If the high voltage amplifier cannot follow due to
its limited slew rate, the sine wave will be distorted and its amplitude is lower than at
low frequencies. The maximum peak to peak sine wave output voltage Vpp is related
to the slew rate S by Vpp = S/pi*f, where f is the frequency of the sine wave.
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The slew rate is the voltage step divided by time required to change the output
from 10% to 90 % amplitude
Figure 13
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Depending on the slew rate a set of pulses can either be amplified undistorted
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Figure 14
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If the slew rate is not sufficient sine waves are distorted
Figure 15
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5
Quantization:
In quantization the levels are assigned a binary codeword. All sample values falling
between two quantization levels are considered to be located at the centre of the
quantization interval. In this manner the quantization process introduces a certain
amount of error or distortion into the signal samples. This error known as quantization
noise is minimized by establishing a large number of small quantization intervals. Of
course, as the number of quantization intervals increase, so must the number or bits
increase to uniquely identify the quantization intervals. For example, if an analogue
voltage level is to be converted to a digital system with 8 discrete levels or
quantization steps three bits are required. In the ITU-T version there are 256
quantization steps, 128 positive and 128 negative, requiring 8 bits. A positive level is
represented by having bit 8 (MSB) at 0 and for a negative level the MSB is 1.
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This is the process of setting the sample amplitude, which can be continuously
variable to a discrete value. Look at Uniform Quantization first, where the discrete
values are evenly spaced.
Uniform Quantization
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We assume that the amplitude of the signal m(t) is confined to the range (-mp, +mp ).
This range (2mp) is divided into L levels, each of step size δ, given by
δ = 2 mp / L
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A sample amplitude value is approximated by the midpoint of the interval in which it
lies. The input/output characteristic of a uniform quantizer is shown figure 16.
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Error due to other non-linear effects of the mapping of input voltage to
converted output value (in addition to the effects of quantization).
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Figure 16
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The conventional, practical digital-to-analog converter (DAC) does not output a
sequence of impulses (such that, if ideally low-pass filtered, result in the original
signal before sampling) but instead output a sequence of piecewise constant values or
rectangular pulses. This means that there is an inherent effect of the zero-order hold
on the effective frequency response of the DAC resulting in a mild roll-off of gain at
the higher frequencies (a 3.9224 dB loss at the Nyquist frequency). This zero-order
hold effect is a consequence of the hold action of the DAC and is not due to the
sample and hold that might precede a conventional ADC as is often misunderstood.
The DAC can also suffer errors from jitter, noise, slewing, and non-linear mapping of
input value to output voltage.
Jitter, noise, and quantization are often analyzed by modeling them as random errors
added to the sample values. Integration and zero-order hold effects can be analyzed as
a form of low-pass filtering. The non-linearity of either ADC or DAC are analyzed by
replacing the ideal linear function mapping with a proposed nonlinear function.
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Sample & Hold circuit:
In electronics, a sample and hold circuit is used to interface real-world signals, by
changing analogue signals to a subsequent system. The purpose of this circuit is to
hold the analogue value steady for a short time while the converter or other following
system performs some operation that takes a little time.
Sampling mode:
In this mode, the switch is in the closed position and the capacitor charges to the
instantaneous input voltage.
Hold mode:
In this mode, the switch is in the open position. The capacitor is now disconnected
from the input. As there is no path for the capacitor to discharge, it will hold the
voltage on it just before opening the switch. The capacitor will hold this voltage till
the next sampling instant.
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Sample and Hold Waveform
Figure 17
Now, from figure 17 the area under the curve (which is equivalent to the signal
power) is greater and so the filter output amplitude and quality of reproduced signal is
improved.
In most circuits, a capacitor is used to store the analogue voltage and an electronic
switch or gate is used to alternately connect and disconnect the capacitor from the
analogue input. The rate at which this switch is operated is the sampling rate of the
system.
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In a sample and hold circuit the switch opens for a very short duration. The sample
and hold circuit integrates for a short duration charge into a capacitor.
The 'hold' facility can be provided by a capacitor, when the switch connects the
capacitor to PAM output it charges to the instantaneous value.
A buffered sample and hold circuit consists of unit gain buffer preceding and
succeeding the charging capacitor. The high input impedance of the preceding buffer
prevents the loading of the message source and also ensures that the capacitor charges
by a constant rate irrespective of the source impedance see figure 18(a).
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Sample Hold Circuit
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Figure 18(a)
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The high input impedance of the succeeding buffer prevents the charging from the
capacitor due to loading and hence the capacitor can hold the charge for infinite time,
at least theoretically. However, small leakage current through the capacitor dielectric
into '+'ve input of second buffer is always present which causes gradual charge loss.
The rate of change of voltage with respect to time dv / dt is called as droop rate and is
important parameter in sample and Hold circuit design. The sample and hold
waveform is shown in figure 18(b).
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Sample and hold wave form
Figure 18(b)
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Important Parameters of Sample & Hold Circuit
1.
Aperture time:
The aperture time is defined as the delay time between the beginnings of the hold
command to the time the capacitor voltage ceases to follow the information signal.
Hence the hold value is different from the true sample value. The aperture time cannot
be reducing to zero because on application of finite time taken by a switch to close &
open on application of the hold signal. Therefore a small value of aperture time is
sought after.
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Timing Diagram for Sample and Hold Circuit
Acquisition Time:
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2.
Figure 18(c)
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In sample mode, it takes finite time for the capacitor to charge to the information
signal value depending on the RC time constant. This is called as the acquisition time.
The acquisition time is dependent on the current flowing from the input buffer
through switch and hence on RC time constant. The maximum acquisition time occurs
when the capacitor voltage has to change by the full amplitude of the information
signal.
3.
Droop Rate:
As it has been discussed earlier, the presence of leakage current through capacitor
dielectric to +ve input of succeeding buffer causes charge loss of capacitor. Hence the
voltage level at the output falls with in time. This rate of change of voltage with
respect to time dv/dt is known as droop rate. Over value of droop rate is desirable as
the circuit should be able to maintain the sample at a relatively constant level until the
next sample.
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4.
Feed Through:
At high frequencies, the stray capacitance within the switch causes some of the input
signal to appear at the output during the hold state (switch open). The fraction of input
signal appearing at the output of sample and hold circuit is called feed through.
The sample and hold feature provides both problem and benefit will be seen
afterwards.
Anti-aliasing:
Nyquist showed that to distinguish unambiguously between all signal frequencies
components we must sample at least twice the frequency of the highest frequency
component. To avoid aliasing, we simply filter out all the high frequency components
before sampling.
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Example of anti-aliasing
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Figure 19
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Note that anti-alias filters must be analogue – it is too late once you have done the
sampling.
This simple brute force method avoids the problem of aliasing. But it does remove
information – if the signal had high frequency components, we cannot now know
anything about them.
Although Nyquist showed that provide we sample at least twice the highest signal
frequency we have all the information needed to reconstruct the signal, the sampling
theorem does not say the samples will look like the signal as shown in figure 20.
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Example of sampling theorem
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Figure 20
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The diagram shows a high frequency sine wave that is nevertheless sampled fast
enough according to Nyquist sampling theorem – just more than twice per cycle.
When straight lines are drawn between the samples, the signal’s frequency is indeed
evident – but it looks as though the signal is amplitude modulated. This effect arises
because each sample is taken at a slightly earlier part of the cycle. Unlike aliasing, the
effect does not change the apparent signal frequency. The answer lies in the fact that
the sampling theorem says there is enough information to reconstruct the signal – and
the correct reconstruction is not just to draw straight lines between samples.
The signal is properly reconstructed from the samples by low pass filtering: the low
pass filter should be the same as the original anti-alias filter.
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Example of anti-aliasing
Figure 21
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The reconstruction filter interpolates between the samples to make a smoothly varying
analogue signal. In the example, the reconstruction filter interpolates between samples
in a ‘peaky’ way that seems at first sight to be strange. The explanation lies in the
shape of the reconstruction filter’s impulse response.
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Low pass filter response
Figure 22
The impulse response of the reconstruction filter has a classic 'sin(x)/x shape. The
stimulus fed to this filter is the series of discrete impulses which are the samples.
Every time an impulse hits the filter, we get 'ringing' - and it is the superposition of all
these peaky rings that reconstructs the proper signal. If the signal contains frequency
components that are close to the Nyquist, then the reconstruction filter has to be very
sharp indeed. This means it will have a very long impulse response - and so the long
'memory' needed to fill in the signal even in region of the low amplitude samples.
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To avoid the aliasing there are two approaches:
1.
To raise the sampling frequency to satisfy the sampling theorem,
2.
The other is to filter off the unnecessary high-frequency component from the
continuous-time signal. We limit the signal frequency by an effective low pass
filter, called anti aliasing pre filter, so that the remained highest frequency is less
than half of the intended sampling rate. If the filter is not perfect we must give
some allowance.
The schematic below repeats the above aliasing argument in the frequency domain.
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Spectrum of Under Sampled Signal
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Reason for aliasing & its preventation:
1.
Aliasing due to Under-Sampling:
If the signal is sampled at rate lower than 2Fm then it causes aliasing. Let us assume a
sinusoidal waveform of frequency FIN which is being sampled at rate Fs < 2Fm. In the
figure 24 dots represents the sample points.
The low-pass filter at demodulator effectively 'joins' the sample causing an unwanted
frequency component to appear at the output. This unwanted component has
frequency equal to (FS-FM)
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Aliasing due to wide Band Signal:
Figure 24
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2.
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Aliasing due to Under - Sampling
The system is designed to take samples at frequency slightly greater than that stated
by Nyquist rate. If higher frequencies are ever present in the information signal or it is
affected by high frequency noise then the aliasing will occur.
This does not generally happen in properly designed telephone network where speech
channels are band-limited by filters before sampling.
In control engineering and telemetry, however, out of band high frequencies either
from source or due to noise pick-up can be present. In this case band-limiting filters,
generally known as anti-aliasing filters are usually installed prior to sampling to
prevent aliasing.
As a principle, the system is designed to sample at rate higher than the rate to take
into account the equipment tolerances, aging and filter response.
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3.
Aliasing Due to Filter Roll-off:
Roll-off is a term applied to the cut-off gradient of a filter. No filter is ideal and
therefore frequencies above the nominal cut-off frequency may still have significant
amplitudes at a filter's output. If proper sampling rate and appropriate filter response
is not chosen, aliasing will occur.
4.
Aliasing due to Noise:
If very small duty cycle is used in sample-and-hold circuit aliasing may occur if the
signal has been affected by noise. High frequency noise generally ‘mixes’ with the
high frequency component of the signal and hence causes undesirable frequency
components to be present at the output.
Low Pass Filter
Filter Basic:
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Reconstruction of the message signal is done with the help of Low pass filter. Low
pass filter pass the message signal as low frequency signals and higher frequency
signals are attenuated.
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The simplest type of filter is a resistance-capacitance (RC) filter. The high pass and
low pass RC filters are as shown in figure 25 (a) & 25 (b).
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The analysis of these filters becomes easier if we think of them as A.C. potential
dividers. The reactance of the capacitor is frequency dependent with a high value at
low frequencies and a low value at high frequencies.
Passive High Pass Filter
Figure 25 (a)
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Passive Low Pass Filter
Figure 25 (b)
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In case of high pass filter, the series capacitance has high reactance at low frequencies
and hence results in reduction in output voltage. An increase in frequency causes an
increase in output voltage with VOUT approaching input voltage VIN.
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The effect of capacitance is just opposite as the case of low pass filter. Here, the
capacitance is in short and hence VOUT reduces as frequency increases thereby
decreasing its reactance.
So,
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The ratio of VOUT to VIN is known as Transfer function for the circuit. For RC low pass
filter, the transfer function can be derived by using potential divider resistance.
This is the half-power point of the filter i.e. at frequency ω = RC, the output power
decreases to half of the input power. This is also known as the cut-off frequency (Fc).
The filter not only causes amplitude change but a change in phase is also experienced.
A typical response of a low pass filter is as shown below:
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Gain Response of Passive Filter
Figure 26(a)
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Phase Response of Passive Filter
Figure 26(b)
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The RC filter is a passive filter and does not give a steeper fall-off. Cascading many
such RC Filters give a steeper full-off but at a price of successive attenuation of the
signal.
Active filter gives much flatter response in the pass band and they also have a steeper
cut-off gradient. The following figure shows a comparison between two types of filter
responses.
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Amplitude Response of Active & Passive Filters
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Figure 27
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The other advantages offered by Active Filters are:
1.
Gain frequency adjustment flexibility (i.e. easy tuning).
2.
No loading problem between sources, load or successive stages.
3.
They are economical than passive filters.
The active filters employ transistors or op-amps in addition to resistors and capacitors.
The resistors at the output of the op-amp create a non-inverting voltage amplifier of
voltage gain K while other resistor and capacitor sets the frequency response
properties of the filter.
An ideal filter should have zero loss in pass band and infinite loss in stop band. In
practice no ideal response exists, but there are many responses which approximate the
ideal response namely, Butter worth, Chebyshev, Bessel etc. the comparison of these
filter responses are as shown in figure 28.
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Comparison of Filter Responses
Figure 28
The voltage controlled voltage source (VCVS) can be arranged in the following
manner to get the Butterworth response.
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Second Order Butterworth Low Pass Filter
Figure 29
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The n order filter has a rate of fall off of 6n dB/octave or 20n dB/decade and one
capacitor or inductor is required for each pulse (order).
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The following table summaries the effect of fall-off gradient-on a signal such-as
square wave.
6
Second
12
Fourth
14
Phase at cut-off
Frequency
20
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First
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fall-off Octave
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Filter order
40
- 90
80
- 180
See figure 30.
The amplitude response of a Butterworth filter is given by;
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Figure 30
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Frequency Response of a Second Order Butter worth Low Pass Filter:
The arrangement shown in figure 29 can be used as second order butter worth filter
with cut-off frequency.
The amplitude and phase response of second order butter worth low pass filter with
respect to frequency is as shown in figure 31.
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Frequency (Normalized)
Amplitude Vs Frequency & Phase Vs Frequency
Response of Second Order Butterworth Low Pass Filter
Figure 31
For this circuit, the voltage gain has been set equal to 1.586.
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Fourth Order Butter worth Low Pass Filter:
The fourth order Butter worth filter can be formed by cascading two second order
Butter worth filters. As can be seen from figure 30 the components R, and C are
identical in both filter stages and they determine the cut-off frequency. In our circuit
the gain of first stage has been set to 1.152 and that of other is set at 2.235.
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Fourth Order Butter worth Low Pass Filter
Figure 32
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The amplitude/frequency and phase/frequency responses of fourth order Butterworth
low pass filters are as shown in figure 33.
Amplitude Vs Frequency & Phase Vs Frequency
Response of Second Order Butterworth Low Pass Filter
Figure 33
The filter design should be done critically so that any unwanted frequency
components existing close to the desired frequency components are attenuated
sufficiently to save the output from getting corrupted.
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Though increasing order of filter is desirable, there is a price that we have to pay for
steeper fall-off.
1.
Additional circuitry increases complexity and cost
2.
Increase in order increases phase lag, though it is not so critical in audio circuits.
Testing Instruments required for Experiments
1.
Scientech Oscilloscope Model ST201 20 MHz, Dual Trace, ALT Trigger or
equivalent
2.
Oscilloscope Probes X1 – X 10 etc.
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Experiment 1
Objective:
1.
Study of Sampling and Reconstruction of signal.
2.
Study the effect of II order and IV order Low Pass Filter on reconstructed signal.
3.
Study the effect of Sample Amplifier and Sample and Hold Amplifier on
reconstructed signal.
Equipment Required:
1.
ST2151 trainer with power cords
2.
CRO with oscilloscope probe
3.
Connecting cords
Connection Diagram:
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Figure 1.1
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Procedure:
Figure 1.2
A. Set up for Sampling and reconstruction of signal.
Duty cycle selector switch position : Position 5
Sampling selector switch
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Initial set up of trainer:
: Internal position
1.
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect 1 KHz Sine wave to signal Input as shown in figure 1.1.
3.
Switch ‘On’ the trainer's power supply & Oscilloscope.
4.
Connect BNC connector to the CRO and to the trainer’s output port.
You can observe the process of step-by-step generating sine wave signal from square
wave of 1 KHz at TP3, TP4, TP5 and TP6 respectively.
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Time/Div. = 500u
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Volt/Div.= 1
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B. Set up for effect of Sample Amplifier and Sample and Hold Amplifier on
reconstructed signal.
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Set up for effect of II order and IV order Low Pass Filter on reconstructed
signal.
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Initial set up of trainer:
Duty cycle selector switch position : Position 5
: Internal position
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Sampling selector switch
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect 1 KHz Sine wave to signal Input.
3.
Switch ‘On’ the trainer's power supply & Oscilloscope.
4.
Connect BNC connector to the CRO and to the trainer’s output port.
5.
Select sampling frequency of 8 KHz by Sampling Frequency Selector Switch
pressed till 80 KHz signal LED glows.
6.
Observe 1 KHz sine wave and Sample Output (TP39) on oscilloscope. The
display shows 1 KHz sine wave being sampled at 8 KHz, so there are 8 samples
for every cycle of the sine wave.
7.
Connect Sample Output to Fourth Order low pass filter Input as shown in figure
1.2. Observe the filtered output (TP48) on the oscilloscope. The display shows
the reconstructed 1 KHz sine wave.
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8.
Similarly observe the sampled 1 KHz sine wave at and Sample and Hold Output
(TP41) on oscilloscope. The display shows 1 KHz sine wave being sampled and
hold signal at 8 KHz.
9.
Connect Sample and Hold Output to Second Order low pass filter Input and
observe the filtered output (TP44) on oscilloscope. The display shows the
reconstructed
1 KHz sine wave.
Time/Div. = 50u
Volt/Div. = 1
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Conclusion:
For transmitting the signal if a sample and hold amplifier is used just before the
transmission channel, the signal will be less suffered from distortion as
compared to when only sample amplifier is used.
2.
As the order of low pass filter is increased at output, the recovered signal will be
reconstructed more like the transmitted signal. To further verify this you can
connect output of either sample amplifier or sample and hold amplifier to II
order LPF Input and the output of II order LPF to the input of IV order LPF. The
order of LPF is now VI. Observe the output of IV order LPF and compare it
with previously obtained waveforms.
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1.
Questions:
1.
Why Continuous Time signals are represented by samples.
2.
What is meant by sampling?
3.
State Sampling theorem.
4.
Define Nyquist rate and Nyquist interval.
5.
Explain the working principle of sample and hold circuit.
6.
What is the significance of using sample and hold circuit?
7.
What do you understand by duty cycle? Explain it.
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Experiment 2
Objective:
Study the Nyquist Criteria for Sampling and Reconstruction of signal.
Equipment required:
1.
ST2151 trainer with power cords
2.
CRO with oscilloscope probe
3.
Connecting cords
Connection Diagram:
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Figure 2.1
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Procedure:
Setup for Nyquist Criteria for Sampling and reconstruction of signal
Initial set up of trainer:
Duty cycle selector switch position : Position 5
Sampling selector switch
: Internal position
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect 1 KHz Sine wave to signal Input.
3.
Connect BNC connector to the CRO and to the trainer’s output port.
4.
Connect Sample Output to fourth order low pass filter Input and Sample and
Hold Output to second order low pass filter Input. Observe the output wave
form (on TP44 and TP48 respectively) as shown in figure2.1.
5.
Switch ‘On’ the trainer's power supply & Oscilloscope. (Turning ‘On’ the
supply will randomly select the sampling frequency).
6.
By pressing Sampling Frequency Selector Switch, change the sampling
frequency from 2 KHz, 5 KHz, 10 KHz, 20 KHz up to 40 KHz (Sampling
frequency is 1/10th of the frequency indicated by the illuminated LED). Observe
how Sample output (TP39) and Sample and Hold Output (TP41) changes in
each case.
7.
Also observe output of second order low pass filter (TP44) and fourth order low
pass filter (TP48).
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Time/Div. = 500u
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To study Nyquist criteria follow the steps
1.
Set sampling rate of 2 KHz with 50% duty cycle.
2.
Instead of on board 1 KHz Sine Wave on board signal, apply a 3 KHz (2Vp-p)
sine wave from external source (Function generator) to the Signal Input of
Sampling Circuit.
3.
Observe the output waveform of the two low pass filters.
4.
Increase the sampling rate from 2 KHz gradually up to 40 KHz. Observe the
output waveform recovered at low pass filters output (TP44 and TP48).
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Conclusion:
1.
The lower sampling frequencies introduce distortion into the filter output
waveform. This is due to the fact that the filter does not attenuate the unwanted
next frequency component significantly. Use of higher order filter would
improve the output waveform.
2.
Testing for validity of Nyquist criteria it has been found that if the signal is
sampled at the rate equal to or lower than that of the signal frequency, the
recovered signal will get distorted and improves gradually with increasing
sampling frequency rate. This is due to the fact that we under-sampled the input
waveform overlooking the Nyquist criteria and thus the output was distorted
even though the signal lie below the cut-off frequency of the filter. This also
describes the phenomenon of Aliasing.
Questions:
Why Continuous Time signals are represented by samples.
2.
Define Nyquist rate and Nyquist interval.
3.
What is the effect of choosing low sampling rate with respect to applied signal?
4.
Explain the importance of sample and hold circuit?
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Experiment 3
Objective:
1. Study the effect of Sample /Hold Circuit on reconstructed signal
2.
Effect of sampling pulse duty cycle on the reconstructed signal in sample and
sample hold output.
Equipment Required:
1.
ST2151 trainer with power cords
2.
CRO with oscilloscope probe
3.
Connecting cords
Connection diagram:
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Figure 3.1
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Procedure:
Setup for Sample /Hold Circuit on reconstructed signal
Initial set up of trainer:
Duty cycle selector switch position : Position 5
Sampling selector switch
: Internal position
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect 1 KHz Sine wave to signal Input.
3.
Connect BNC connector to the CRO and to the trainer’s output port.
4.
Connect Sample Output to fourth Order low pass filter Input and Sample and
Hold Output to second Order low pass filter Input as shown in figure 3.1.
5.
Switch ‘On’ the trainer's power supply & Oscilloscope. (Turning ‘On’ the
supply will randomly select the sampling frequency).
6.
Select sampling frequency of 8 KHz by Sampling Frequency Selector Switch
pressed till 80 KHz signal LED glows.
7.
Vary the position of Duty Cycle Selector Switch from 0% to 90% (position 0 to
9) and observe the Sample Output (TP39) and Sample and hold Output (TP41).
8.
Also observe variation of output signal with the change in duty cycle at low pass
filter outputs (TP44 and TP48). Compare the output of the two low pass filters
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Time/Div. = 100u
Volt/Div. = 2
Duty Cycle = 10%
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Conclusion:
When varied the sampling pulse duty cycle from 10% to 90%,
The sampling signal width increase and thus more and more signal will be
coupled in a single sampling pulse. This leads to better recovery of transmitted
signal.
2.
The chances of channel distortion in received signal increases.
3.
Number of TDM signal reduces.
4.
The II order LPFs output amplitude is independent of the sampling duty cycle
and is equal to the amplitude of the original signal input; whereas the IV order’s
output amplitude gradually increases with the increase in sampling signal’s duty
cycle. This is an important result - with Sample And Hold Output, the
proportion of sampling time to holding time has no effect on reconstructed
waveform provided that Nyquist criteria has been followed. In practical digital
communication, this result is very useful as the use of narrow pulses let many
channels to be multiplexed with maximum amplitude of reconstructed signal if
sample/hold feature is utilized in communication system.
Questions:
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1.
Explain the working principle of sample and hold circuit.
2.
What is the significance of using sample and hold circuit?
3.
What is the effect takes place due to changing the duty cycle on reconstructed
signal.
4.
What is the effect takes place due to changing the sampling frequency on
reconstructed signal.
5.
What do you understand by duty cycle? Explain it.
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Experiment 4
Objective: Study and comparison responses of 2nd order and 4th order LPFs.
Equipment Required:
1.
ST2151 trainer with power cords
2.
CRO with oscilloscope probe
3.
Connecting cords
Connection Diagram:
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Figure 4.1
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Initial set up of trainer:
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Procedure:
Figure 4.2
Duty cycle selector switch position : Position 5
: Internal position
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Sampling selector switch
1.
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect 1 KHz Sine wave to signal Input.
3.
Connect BNC connector to the CRO and to the trainer’s output port.
4.
Switch ‘On’ the trainer's power supply & Oscilloscope. (Turning ‘On’ the
supply will randomly select the sampling frequency).
5.
Select sampling frequency of 8 KHz by Sampling Frequency Selector Switch
press it till 80 KHz signal LED glows.
6.
Connect Sample Output to input of the Second Order low pass filter and to the
input of Fourth Order low pass filter. Observe the outputs of two filters (TP44
and TP48) on the oscilloscope. Vary the sampling frequency from 2 KHz to 40
KHz gradually and compare the output of filter in each case.
Time/Div. = 500u
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Volt/Div. = 1
Also compare the phase lag between input and output for each filter.
2.
Repeat the above procedure with Sample and Hold Output connected to the
Second Order low pass filter and Fourth Order low pass filter input as shown in
figure 4.2.
3.
Using a function generator of 600 ohms impedance, apply sine wave of 2V peak
at 100Hz output to Second Order Filter Input. Note the peak output value (at
tp42) and the phase difference between input and output. Vary the frequency at
steps of 200Hz /s500Hz to 35 KHz. sketch the amplitude/frequency and
phase/frequency response of the second order filter. What is the cut-off gradient
of the filter/decade? What is the phase lag at filter's cut-off frequency?
Repeat the above steps with fourth order filter. Find out which one of the two
filter's cut-off has more gradient? What is the phase lag input and output?
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4.
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Conclusion:
The output of fourth order filter always exhibits less distortion than second order
filter. This is because fourth order filter has a sharper roll-off and thus rejects
(attenuates) more unwanted frequency components caused by sampling.
Questions:
1.
What are active and passive filter?
2.
What is the importance of using low and high pass filter?
3.
Why high order low pass filters are preferred for reconstruction of signals.
4.
Give the comparison of second order and fourth order filter.
5.
Draw the circuit diagram of passive filter.
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Experiment 5
Objective:
Verification sampling and reconstruction data transmission scheme for
a.
External sampling signal
b.
Audio signal
Equipment Required:
1.
ST2151 trainer with power cords
2.
CRO with oscilloscope probe
3.
Connecting cords
Connection Diagram:
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Figure 5.1
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Procedure:
Figure 5.2
A. Initial set up of trainer for External Sampling Signal:
: External position
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Sampling selector switch
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Duty cycle selector switch position : Position 5
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect BNC connector to the CRO and to the trainer’s output port.
3.
Apply a 5Vp-p pulse signal to the External Sampling Signal I/P socket.
4.
Connect 1 KHz Sine wave output (TP6) to Signal Input socket in Sampling
Circuit or you can apply sine wave of amplitude from 0-5Vp-p and frequency up
to 3 KHz to the Signal Input socket of Sampling Circuit from any external
source (Function Generator).
5.
Switch ‘On’ the trainer's power supply & Oscilloscope.
6.
Connect Sample Output to IV order low pass filter Input and Sample and Hold
Output to II order low pass filter Input. Observe the output wave form (on TP44
and TP48).
7.
Verify the Nyquist criteria as described in experiment 2 for the signal applied,
by varying frequency of externally applied sampling signal.
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8.
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B. Initial set up of trainer for Audio Signal: as shown in figure 5.2
Duty cycle selector switch position : Position 5
Sampling selector switch
: Internal position
Connect the power cord to the trainer. Keep the power switch in ‘Off’ position.
2.
Connect BNC connector to the CRO and to the trainer’s output port.
3.
Apply a 5Vp-p pulse signal to the External Sampling Signal I/P socket.
4.
Select sampling frequency of 8 KHz by Sampling Frequency Selector Switch
pressed till 80 KHz signal LED glows.
5.
Connect Mic to the Mic Input socket of Audio Input Circuit.
6.
Connect Audio Input Circuit Output to second Order low pass filter Input.
7.
Connect second Order low pass filter Output to Signal Input socket of Sampling
Circuit.
8.
Connect Sample Output to fourth order low pass filter Input.
9.
Connect IV Order low pass filter Output to Audio Output Circuit Input.
10.
Turn on the speaker ‘On/Off’ switch ‘On’.
11.
Observe the processing of audio signal transmitted through mic up to the
speaker on TP8, TP42, TP44, TP39 TP48 and TP50.
12.
Now instead of connecting Sample Output to fourth Order low pass filter Input
connect Sample and Hold Output to fourth Order low pass filter Input and
compare two results (reconstructed voice signals through will clearly show the
difference).
13.
Follow the above procedure for other sampling frequencies (2 KHz, 5 KHz,
10 KHz, 20 KHz and 40 KHz) available on board.
14.
Note the difference in all the cases by varying duty cycle of the sampling
frequency.
15.
Repeat the above procedure for externally applied sampling signal (as explained
above).
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Conclusion:
The audio signal reconstructed and output through speaker get better in quality as the
sampling frequency increases from 2 KHz to 40 KHz; also when the duty cycle of the
sampling signal is increased from 10% to 90%. The reconstructed signal is better in
quality when sample and hold amplifier is used.
Maximum distortion in reconstructed signal is obtained when signal is sampled at 2
KHz 10% duty cycle pulse and sample amplifier is used. Minimum distortion in
reconstructed signal is obtained when signal is sampled at 40 KHz 90% duty cycle
pulse and sample and hold amplifier is used.
At audio input circuit output and audio output circuit input it is required to use LPF to
minimize the channel distortion. To verify this connect audio input circuit output
directly to the signal input socket of sampling circuit and output of either sample
amplifier or sample and hold amplifier to audio output circuit input and check the
quality of reconstructed signal.
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Questions:
What are active and passive filter?
2.
What is the importance of using low and high pass filter?
3.
Why high order low pass filters are preferred for reconstruction of signals.
4.
Give the comparison of second order and fourth order filter.
6.
Draw the circuit diagram of passive filter.
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Frequently Asked Questions
1.
What do you mean by sampling?
Ans: To convert continuous time signal to discrete time signal, a process is used
called as sampling.
2.
What is sampling theorem?
Ans: The Sampling Theorem states that a signal can be exactly reproduced if it is
sampled at a frequency Fs, where Fs is greater than twice the maximum frequency
Fmax in the signal.
Fs > 2· Fmax
3.
What is Nyquist frequency?
4.
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Ans: The frequency 2· Fmax is called the Nyquist sampling rate. Half of this
value, Fmax, is sometimes called the Nyquist frequency.
List different sampling techniques?
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Ans: There are three types of sampling, which are as follows:
2. Natural sampling
5.
What is under sampling?
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3. Flat top sampling
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1. Ideal sampling or Instantaneous sampling or Impulse sampling
6.
What do you mean by aliasing?
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Ans: When the sampling rate is lower than or equal to the Nyquist rate, a condition
defined as under sampling, it is impossible to rebuild the original signal according
to the sampling theorem.
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Ans: Aliasing is the presence of unwanted components in the reconstructed signal.
These components were not present when the original signal was sampled. In
addition, some of the frequencies in the original signal may be lost in the
reconstructed signal. Aliasing occurs because signal frequencies can overlap if the
sampling frequency is too low. As a result, the higher frequency components roll into
the reconstructed signal and cause distortion of the signal Frequencies "fold" around
half the sampling frequency. This type of signal distortion is called aliasing.
7.
Explain the process of sample and hold?
Ans: In electronics, a sample and hold circuit is used to interface real-world signals,
by changing analogue signals to a subsequent system. The purpose of this circuit is to
hold the analogue value steady for a short time while the converter or other following
system performs some operation that takes a little time.
Sampling mode:
In this mode, the switch is in the closed position and the capacitor charges to the
instantaneous input voltage.
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Hold mode:
In this mode, the switch is in the open position. The capacitor is now disconnected
from the input. As there is no path for the capacitor to discharge, it will hold the
voltage on it just before opening the switch. The capacitor will hold this voltage till
the next sampling instant.
7.
How aliasing is removed?
Ans: Aliasing is removed by simply filtering out all the high frequency components
before sampling.
8.
List methods to avoid aliasing?
Ans: To avoid the aliasing there are two approaches:
1. To raise the sampling frequency to satisfy the sampling theorem,
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2. The other is to filter off the unnecessary high-frequency component from the
continuous-time signal. We limit the signal frequency by an effective low
pass filter, called anti aliasing pre filter, so that the remained highest
frequency is less than half of the intended sampling rate. If the filter is not
perfect we must give some allowance.
What are active and passive filter?
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Ans: Filter is a network designed to pass signals having frequencies within certain
bands (called pass bands) with little attenuation, but greatly attenuates signals within
other bands (called attenuation bands or stop bands).
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A filter network containing no source of power is termed passive, and one containing
one or more power sources is known as an active filter network.
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How many types of sampling techniques are there, Draw the related
waveforms?
Ans: There are three types of sampling techniques as under:
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1.
Ideal sampling or Instantaneous sampling or Impulse sampling
2.
Natural sampling
3.
Flat top sampling
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Ideal sampling or Instantaneous sampling or Impulse sampling:
3.
Natural sampling:
4. Flat Top sampling:
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Warranty
1
We guarantee this product against all manufacturing defects for 24 months from
the date of sale by us or through our dealers. Consumables like dry cell etc. are
not covered under warranty.
2
The guarantee will become void, if
a)
The product is not operated as per the instruction given in the Learning
Material.
b)
The agreed payment terms and other conditions of sale are not followed.
c)
The customer resells the instrument to another party.
d)
Any attempt is made to service and modify the instrument.
The non-working of the product is to be communicated to us immediately giving
full details of the complaints and defects noticed specifically mentioning the
type, serial number of the product and date of purchase etc.
4
The repair work will be carried out, provided the product is dispatched securely
packed and insured. The transportation charges shall be borne by the customer.
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List of Accessories
1.
2mm Patch Cord 16"(Red) ......................................................................... 2 Nos.
2.
2mm Patch Cord 16"(Black) ...................................................................... 4 Nos.
3.
2mm Patch Cord 16" (Blue) ....................................................................... 6 Nos.
4.
Microphone ............................................................................................... 1 No.
5.
Learning Material (CD) ............................................................................. 1 No.
6.
DC Power Supply for DCT ........................................................................ 1 No.
7.
DIN Cable for DC Supply .......................................................................... 1 No.
8.
Mains Cord ................................................................................................ 1 No.
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