Chapter 6

4/17/2014
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Communication Systems
Instructor: Engr. Dr. Sarmad Ullah Khan
Assistant ProfessorAssistant Professor
Electrical Engineering Department
CECOS University of IT and Emerging Sciences
Sarmad@cecos.edu.pk
Chapter 6
Dr. Sarmad Ullah Khan
Sampling and Analog to Digital
Conversion
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Outlines
• Sampling Theorem
P l C d M d l ti (PCM)
• Pulse Code Modulation (PCM)
• Noise
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Outlines
• Noise
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Sampling Theorem
• A signal g(t) whose spectrum is band limited to B
Hz can be represented as
Hz can be represented as
G(f) = 0 if |f| > B
• Signal reconstruction requires that sampling rate
should beshould be
R > 2B
Sampling frequency = fs > 2B Hz
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Sampling Theorem
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Sampling Theorem
• Mathematically it can be represented as
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Sampling Theorem
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Sampling Theorem
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Sampling Theorem
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Sampling Theorem
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Sampling Theorem
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Sampling Theorem
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Outlines
• Noise
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Pulse Code Modulation
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Outlines
• Noise
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Noise
• In any real physical system, when the signal voltage
arise at the demodulator it will be accompanied by
arise at the demodulator, it will be accompanied by
a voltage waveform which varies with time in an
entirely unpredictable manner. This unpredictable
voltage wave form is a random process called noise
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Noise
• Types of Noise
Most man made electro magnetic noise occurs at
Most man made electro-magnetic noise occurs at
frequencies below 500 MHz. The most significant of
these include:
• Hydro lines
• Ignition systems
• Fluorescent lightsFluorescent lights
• Electric motors
Therefore deep space networks are placed out in the
desert, far from these sources of interference.
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Noise
• There are also a wide range of natural noise sources
which cannot be so easily avoided, namely:
y , y
• Atmospheric noise - lighting < 20 MHz
• Solar noise - sun - 11 year sunspot cycle
• Cosmic noise - 8 MHz to 1.5 GHz
• Thermal or Johnson noise. Due to free electrons
striking vibrating ions.
• White noise white noise has a constant spectral• White noise - white noise has a constant spectral
density over a specified range of frequencies.
Johnson noise is an example of white noise.
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Noise
• Gaussian noise - Gaussian noise is completely
random in nature however, the probability of
, p y
any particular amplitude value follows the
normal distribution curve. Johnson noise is
Gaussian in nature.
• Shot noise - bipolar transistors (caused by
random variations in the arrival of electrons or
holes at the output electrodes of an amplifying
device)device)
• Transit time noise - occurs when the electron
transit time across a junction is the same period
as the signal.
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Noise
• The noise power is given by:
P kTB
Pn = kTB
• Where:
• k = Boltzman's constant (1.38 x 10-23 J/K)
• T = temperature in degrees Kelvin
• B = bandwidth in Hz
• If the two signals are completely random with respect
to each other, such as Johnson noise sources, the total
power is the sum of all of the individual powers:
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Noise
• A Johnson noise of power P = kTB, can be thought of
as a noise voltage applied through a resistor
as a noise voltage applied through a resistor,
Thevenin equivalent.
• An example of such a noise source may be a cable or
transmission line. The amount of noise power
transferred from the source to a load, such as an
amplifier input is a function of the source and loadamplifier input, is a function of the source and load
impedances
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Noise
• The rms noise voltage at maximum power transfer is
• Observe what happens if the noise resistance is
resolved into two components
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Noise
• The terms used to quantify noise :
Si l t i ti I i i h i l
• Signal to noise ratio: It is either unit-less or
specified in dB. The S/N ratio may be specified
anywhere within a system.
• Noise Factor (or Noise Ratio):
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Noise
• This parameter (i.e. Noise Figure ) is specified in all
high performance amplifiers and is measure of how
high performance amplifiers and is measure of how
much noise the amplifier itself contributes to the total
noise. In a perfect amplifier or system, NF = 0 dB.
This discussion does not take into account any noise
reduction techniques such as filtering or dynamic
emphasisp
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Noise
• Friiss' Formula & Amplifier Cascades
It i i t ti t i lifi d t h
– It is interesting to examine an amplifier cascade to see how
noise builds up in a large communication system
– Amplifier gain can be defined asp g
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Noise
A d th i f t ( ti ) b itt
– And the noise factor (ratio) can be rewritten as
– The output noise power can now be written
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Noise
F thi b th t th i t i i i d b
– From this we observe that the input noise is increased by
the noise ratio and amplifier gain as it passes through the
amplifier. A noiseless amplifier would have a noise ratio
(factor) of 1 or noise figure of 0 dB. In this case, the input
noise would only be amplified by the gain since the
amplifier would not contribute noise
31
Friiss' Formula

Chapter 6

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Chapter 6