chapter1 noise
TRANSCRIPT
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CHAPTER-1
NETWORK NOISE
AND
INTERMODULATION DISTORTION
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Basic Communication Model
Main purpose of an electronic communications system is totransfer information from one place to another.
Electronic communications can be viewed as the transmission,reception and processing of information between two or
more locations using electronic circuit/device.
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What are we going to discuss ? Types of Noise
Sources of noise
Parameters related to noise
Signal to Noise Ratio
Noise Figure Noise Factor
Noise Temperature
Friss formula
Designing of Low noise amplifiers Intermodulation Distortion
- Different terms related to intermodulation distortion
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How do you characterize a receiver performance?
Sensitivity : (Minimum detectable signal)
That is the minimum power level at the point of transmission
that will ensure a final receiver output signal with acceptable
SNR
Signal-to-Noise Ratio
S/N ratio : average signal power
average noise power
The signal-to-noise (S/N) ratio indicates the relative
strengths of the signal and the noise in a communication
system.
The stronger the signal and the weaker the noise, the
higher the S/N ratio.
4
Why should we study noise?
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NoiseRepresentation, types & source
5
Noise is an unwanted electrical signal that gets added to the
information signal as it is transmitted from one place to another.
It is notthe same as interference from other information signals.
It modifies the electrical nature of the transmitted signal
Noise produces Hiss in the loudspeakers when you tune any AM or
FM receiver to any position between stations.It is also the snow or confetti that is visible on a TV screen.
In pulse communication it may produce unwanted pulse which may
perhaps cancel out the wanted ones or which may cause some
serious mathematical errors
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Effects of Noise?
Limits the range of communication
6
Places a limit on the weakest signal that can be
received and amplified by the receiver( affects the sensitivity of the receiver)
Introduction of noise may also lead to reduction
of bandwidth of the system.
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Classification of Noise
Depends upon the sources producing it
External noise
Internal noise
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External noise
a. Atmospheric noise
b. Extraterrestrial noise
c. Industrial noise
Internal noise
a. Thermal noise
b. Shot noise
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External Noise :Noise created outside the receiver/ the communication
system
9
External noise comes from sources over which we have little or
no control, such as:
Atmospheric sources
The naturally occurring electrical disturbances in the
earths atmosphere tends to interfere with the reception
program
Example: Lighting discharges in the thunderstorms or
other electrical disturbances occurring in nature
These spurious signals induces voltages in antenna.
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10
Extraterrestrial noisealso called as SPACE NOISE
-consists of electrical signal that originate from outside earths
atmosphere and therefore also known as deep-space noise.-2 categories of extraterrestrial noise.isolar noisenoise that generated directly from the suns heat.iicosmic noise noise that is distributed throughout the galaxies.
The sun , stars, and other planets in the galaxy are at high
temperature and hence radiate RF noise which interferes with thereceived signal. (GLACTIC NOISE)
Industrial noise (Man made noise)source : automobile, aircraft ignition system.
Electric motors
Switching equipmentsLeakage from high voltage linesHeavy electric machines/motorsFluorescent light
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Frequency Ranges:
Atmospheric noise becomes less severe above about 30 MHz
Space noise is observable in the range from about 8MHz to
somewhat above 1.43 MHz
Industrial noise between 1 to 600 MHz.
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Internal Noise
12
Electronic components in a receiver such as resistors,
diodes, and transistors are major sources ofinternal
noise.
Noise that generated within the device or circuit.
Types of internal noise include:
Thermal noise
Semiconductor noise(Shot Noise)
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Thermal Noise / Resistor Noise
13
The noise created due to random motion of the electrons in a
conductor due to heat ( i.e. at any temperature above absolute
zero i.e. 0 Kelvin or -273 o C.
Noise arises due to thermal cause hence called as THERMAL
NOISE
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The rms value of the thermal noise generated in an impedance
Z(f) is given as
Thermal Noise / Resistor Noise Formula
Instantaneous Value is unpredictable.
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Representation of Resistor Noise
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Equivalent circuit of a noisy resistor
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Available Thermal noise Power
KTB
R
V
R
VP
NN
4
2/ 22
How much amount of noise power will be given to the
load the noisy resistor
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Analysis of a noisy resistor connected
to a linear network with frequency
dependent transfer function G(f)
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G(f) is the transfer function of the network
It is the magnitude squared of the frequency dependent transfer
function between the input and the output voltages.
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The total noise at the output of the network will begiven as.
Where, Is referred to as the
noise bandwidth Bn of the
system
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Problem: Find the total output noise for the parallel
combination of R and C given below
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Hints:
21
Find:
(1)
(2)
We get :
Substituting in (2) we get
Since standard form of noise voltage
is
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Shot Noise / Active Device Noise
22
Is a phenomenon associated with the flow of current across asemiconductor junction.
If Id is the average current, then the total diode
current i(t) will be given asi(t) = Id + in (t)
Where, in (t) represents the noise/ fluctuating
component of the current.
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Representation of shot noise in a diode
23
Represented by a appropriate current source in parallel with the
dynamic resistance of the barrier across which the noiseoriginated
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Shot Noise Formula
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Shot noise current spectral density :
Where, q is the charge on electron = 1.6 x 10 -12 C
Io is the direct current
k is a constant which varies from device to device
and also depends on how the junction is biased.For junction transistor k=2
For junction diode/ transistor :
Total noise current over the given bandwidth :
Where, f is the bandwidth
N i i T i t A lifi
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Noise in Transistor Amplifiers
25
Transistor Amplifier
in1 is the shot noise current density due to the i/p bias currentin2 is the shot noise current density due to the bias current on the
o/p of the device.
en is the noise due to the load resistor RL
in1 = 2qIB A2/Hz , in2 = 2qIc A2/Hz, en = 4kTRL V2/Hz
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Representation model of transistor amplifier with
the noise sources referenced to the input side of the
amplifer
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Values of e2, e3
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Derivation
Assuming RL is much less than the transistor output impedance
Amplifier Voltage Gain is
(1) (2)
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Model or transistor amplifier with all
noise sources on the input side
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Noise Parameters
Signal to Noise Ratio
Noise Figure
Noise Factor
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Noise Parameters
1. Signal-to-noise Power Ratio
signal-to-noise power ratio (S/N) is the ratio of the average signal
power level to the average noise power level and can be expressedas
in logarithmic function
in terms of voltages and resistance
30
n
s
P
P
N
S
n
s
P
PdB
N
Slog10)(
RVRVdB
NS
n
s
//log10)(
2
2
n
s
V
VdB
N
Slog20)(
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2. Noise Factor
Noise factoris the ratio of input signal-to-
noise ratio to output signal-to-noise ratio
Receiver noise figure is a measure of how
much noise is added by the system
31
out
in
NS
NSF
)/(
)/(
A low noise figure is always desirable.
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out
in
NS
NSFNF)/()/(log10log10
Noise figure is the noise factor stated in dB and is a
parameter to indicate the quality of a receiver.
3. Noise Figure
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Noise Factor IEEE definition of noise factor
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Noiseless Network
Minimum value of Noise factor ,F =1 (noiseless n/w)
i.e. No=Ni
The noise figure of a ideal noise less network = 0 db.
However, F is always greater than unity
A low noise figure is always desirable.
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Noise added by the amplifier in terms
of noise factor ( F )
If Ni is the input noise ( noise due to source resistance)
If Si is the input signal (i/p s/g power due to source voltage)
If No is the noise at the o/p of the amplifier
If So is the signal at the output of the amplifier
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Formula for Noise added by amplifier
Na = (F-1)KTB
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Derivation ?
Noise factor of the amplifier
Gain of the amplifier
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Value of
Substituting in Pno we get
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It is seen that the noise power at the output of the
amplifier is increased by F over what it would have
been if the amplifier was noiseless
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Noise added by the amplifier (referred to the i/p)
Noise added by the amplifier as
referred on the i/p side.
Noise Factor and Noise Figure of cascade Amplifier
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Noise Factor and Noise Figure of cascade Amplifier
- when two or more amplifiers are cascaded as shown in the following figure,
the total noise factor is the accumulation of the individual noise factors.
- Friss formula is used to calculate the total noise factor of several cascade
amplifiers
40
N
N
T
AAA
F
AA
F
A
FFF
...
1...
11
2121
3
1
21
Derivation?
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Derivation
Pno = G2 [ G1 F1 KTB + ( F21)KTB] ?
F1 is the noise factor of amplifier A1
G1 is the Gain of amplifier A1
F2 is the noise factor of amplifier A2
G2 is the Gain of amplifier A2
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We shall first see the derivation for Pno
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Total Noise referred the input of the amp A2 = O/p noise of amp. A1 + noise added by amp A2
Pni2 = G1 F1 KTB + ( F21)KTB
Output noise of Amplifier A2 will be
Pno = G2 [ G1 F1 KTB + ( F21)KTB]
O ll N i F t f th d d
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Overall Noise Factor of the cascaded
Network F
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Overall Noise Factor
Overall Gain
Where.
Therefore
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Where,
44
Pno
= G2
[ G1
F1
KTB + ( F2
1)KTB]
And Pni = KTB , G= G1 G2
Substituting all in
We get, the total noise factor of two cascaded
amplifiers as :
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This argument can be extended to any number of amplifiers in
cascade which gives a total noise factor of :
45
N
N
T
GGG
F
GG
F
G
FFF
...
1...
11
2121
3
1
21
FRISS Formula
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Note:
- the Total Noise Figure
where,
47
TT FNF log10
N
N
T
AAA
F
AA
F
A
FFF
...
1...
11
2121
3
1
21
When using Friss formula, the noise figures mustbe converted to noise factors !!!
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Problem 1
48
Ans:
Noise Factor F = 1.779
Noise Figure NF = 2.5dB
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Problem 2
49
For problem 1 what will be the total noisepower of the cascaded system in a 3-kHz
bandwidth? The opeating temperature is
290o
K
Ans:
Total output noise power = 337 x 10 -17 W
N i T t
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Noise Temperature
50
Noise added by amplifier is considered to be the
noise added by a resistor which is as a fictious
temperature Tr, and the amplifier is now
considered to be noiseless.
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4. Noise Temperature
Noise added by amplifier is
given by
51
Where T is the reference noise temperature
Tr is referre to as system noise temperature
Formula
Derivation
Pn a =(F1)KTB
Where the resistor noise equation is Pn = KTB
Resistor now being at fictious temp. Tr the eqn is Pn = KTrB
Therefore, KTrB =(F1)KTB
Tr =(F-1)KT
O ll N i T t f d d
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Overall Noise Temperature of cascaded
network
Friss Formula can be expressed in terms of
equivalent temp. Tr
Overall noise temp. of a cascaded network is
given by :
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Problem What is the variation in noise temperature as
the noise factor varies from 1 to 1.6 ( I,e NF
caries from 0 to 2 dB)? Assume the reference
temperature is 290K
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Ans:Tr= ( 1.6 -1) 290 = 174K
Note: The change is noise temperature is much greater than thechange in noise factor. This is the prime reason why noise
temperature is used to describe the system noise
5. Sensitivity
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5. SensitivityDenoted as Si and is also called as MINIMUM DETECTABLE SIGNAL/ SYSTEM SENSITIVITY
/ NOISE FLOOR
Definition:
For a given output Signal to Noise ratio (S/N)o ,the available input signal level is
referred to as system sensitivity
54
Formula:
where, No is the total noise power at the output
So is the total signal power at the output
Note:
Sensitivity is always specified for a given signal-to-noise ratio
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Derivation for Sensitivity
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Problem:
What minimum input signal will give an output signalto noise ratio of 0dB in a system that has an input
impedance equal to 50 , a noise figure (NF) of 8 dB,
and a bandwidth of 2.1kHz?
56
Ans:
10 log Si = NF -144+10 log B+10log(S/N)o
Si = -133 dBm
Si= (Ei2
/ 4 Rs) =5.02 x 10-17
WEi=0.10V
That is, for the specifications given the noise floor for
an output signal to noise ratio of 1 is 0.10V.
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Problem: What is the minimum detectable signal or the
noise floor of the system in the previousexample for a output signal to noise ratio of10 dB
57
Ans:Given data: (S/N)o= 10 dB
B=2.1kHz
10 log Si = NF -144+10 log B+10log(S/N)o
Si = -123dBmSi= (Ei2 / 4 Rs)
Ei=0.32V
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Problem What is the minimum detectable signal level
of a communication receiver with a 50 inputimpedance, ofB of 3 kHz, and a 4dB noisefigure at an output signal to noise ratio of 10
dB
58
Ans:
Si = -125dBm = 3 x 10-16 W
Ei=0.245V
That is an input signal of 0.245 V will produce a 10 dB
output signal to noise ratio.
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Design of Low Noise Network
59
Transistor amplifier
noise model.
Transistor amplifier
noise model with voltage source
D i D i ti
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Design Derivation
60
Total Noise referred to the input side in a unit bandwidth B=1, is
N = en2 + in2Rs2 + 4KTRs (1)
Na = en2 + in
2Rs2 (2)
Noise added by the network/amplifier
Amplifier equivalent
noise voltage sources
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Design Derivation
Overall noise Factor of the network
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F = Available input noise power + noise added
available input noise power
Network noise factor depends upon the source resistance Rs
Value of Rs that minimizes the noise factor can be found as
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Contd:
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Rs is chosen to minimize the spot noise factor at a specified
frequency.
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Problem:
63
What will be the minimum noise figure for 741 operational
amplifier with a 10 kHz source resistance at 1kHz , the inputnoise voltages are en
2 = 8 x 10-16 V2/Hz, in2 = 9 x 10-25 A2/Hz
Formula:
Minimum noise factor F = 4.35
Minimum noise figure NF = 6.4 dB
Ans:
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Problem
64
Find the noise factor for an 741 operational amplifier with a
10 kHz source resistance at 1kHz , the input noise voltages areen
2 = 8 x 10-16 V2/Hz, in2 = 9 x 10-25 A2/Hz
Formula:
Ans: F = 6.6
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For Rs = 30 K, Minimum noise factor F = 4.35
For Rs = 10 K, F = 6.6
Noise Factor minimizes when the Rs increases
from 10K to 30 K
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Another aspect of low noise design
Noise Factor
Signal to Noise ratio
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By selecting high Rs
F is minimized (which is desirable)S/N also has minimized(which is undesirable)
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There fore ,
Minimizing the noise factor does not necessarilymaximize the S/N ratio
Solution:
Value of Rs should be such that it
simultaneously
1. minimizes noise factor and2. maximizes the S/N ratio
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Design
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Source is transformer coupled to the amplifier i/p
In this case, Reflected source resistance
Equivalent source voltage
Output Signal to Noise Ratio
Contd:
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The resistor value Rs which maximizes the S/N ratio and
minimizes the noise factor is found as follows:
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gives:
This is the value of source resistance Rs which minimizes
the noise factor as well as maximizes the signal to noise
ratio Noiseless transformer coupling can be used to match the
source to amplifier input, then the turn ratio that
minimizes the noise factor will also maximize the o/p s/n
ratio
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Intermodulation Distortion
70
Effects of nonlinearity?
Harmonic distortion
Intermodulation distortion
Gain Compression
Terms related to IMD
IMR (Intermodulation Distortion Ratio)
Intercept point Dynamic Range
SINAD
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Explanation for IMD A network nonlinearity can be described by the following
expression
71
f(x) is the input signal to the circuit
y(x) is the output signal to the circuitLet the inputf(x) consist of two sinusoids
Then the output y(x) will be
Ignoring the higher order terms
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Contd.Expanding the given eqn.
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Contd: Effects of Nonlinearity
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y Amplitude ofcos1tterm which wasA1 now becomes
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Gain Compression ?
Normally K3 will be negative
If A2cos
2t is of large amplitude
1.It will mask a smaller signalA1cos1t
2. It results in a reduced gain because of the third order
term coefficient K3.( This effect is known as GAIN
COMPRESSION)
How to avoid Gain Compression ?
The third order coefficient K3 must be reduced.
Multiple signals at the input must be avoided as it leads to
further reduction of gain
1 dB Compression Point
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1 dB Compression Point
The K3 term causes gain to deviate
from the idealized linear curve
The point at which the power gain is
down by 1dB from the ideal is
referred to as 1-dB compression
point.
Significance
Receivers must be operated below
their gain compression point if the
nonlinear gain region is to beavoided
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If only one signal is present at the input the
reduction in gain from amplitudeA1 to A1 is known
as the SINGLE TONE GAIN COMPRESSION FACTOR
given by
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Single Tone Gain Compression Factor
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Harmonic Distortion
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Harmonic Distortion occurs when unwanted harmonics of
signal are produced through nonlinear amplification.Harmonics are integer multiples of the original signal.
The original signal is thefirst harmonic (fundamental
harmonic), a frequency two times the fundamental
frequency is thesecond harmonic, three times is the third
harmonic and so on.
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Second Harmonic Distortion
The receiver output due to k2term
If a single signal is present at the receiverinput, then the amplitude of the second
harmonic is
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Intermodulation Distortion
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Intermodulation Distortion
Distortion caused due to cubic term
Cubic term creates INTERMODULATION FREQUENCIES
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The frequencies which lie within the system
passband and appear at the output as signal
distortion are
Intermodulation Distortion Ratio (IMR)
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Intermodulation Distortion Ratio (IMR)
Desired Output: K1A1
Intermodulation distortion terms are
79
Amplitude of Intermodulation distortion terms are
Definition:
IMR is defined as the ratio of the amplitude of one of the
intermodulation terms to the amplitude of the desiredoutput signal
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Intercept Point Intermodulation Power
(IMD):
80
Rearranging,
Intermodulation Power Pd:
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Therefore
IMD power varies as cube of the input power.
i.e. for every 1 dB increase in the input power there
is a 3 dB increase in the power of the
intermodulation terms
On Log scale the IMD power increases 3 times as fast
as the expected output power.
Intermodulation Distortion Power is given as
Pi is the power in one signal component
Kd is called the scale factor where, Kd = (3/4 ) (K3/K1)
Significance
IMD P i i
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IMD Power is given as
Out put Power contributed by
linear term is given as
Plot of outputpower
v/s
input power
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What is INTERCEPT POINT(Pi )?
The value of input power for which the IMDpower Pd is equal to the output power Po
contributed by the linear term
83
At intercept point Pi,Pd = Po
Significance ofINTERCEPT POINT(Pi )?
A measure of the distortion created in the receiver.
Ability to reject large amplitude signals that lie in the
close frequency proximity to a weak signal targeted
for reception.
Formula for INTERCEPT POINT(Pi )?
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( i )
84
IMD power (PIMR ) is defined as
Substituting PdandPo
We get ,
At Pi, Pd=Po and PIMR= 1
That is,
Since, At this signal level
Where,Ki = (Kd / K12) and Kd = (3/4 ) (K3/K1)
Problem :
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Problem :
If the intercept point of a system is +20dBm, whatis the IMR for an input signal power of 0dBm?
85
Formula :
In dB : PIMR =2 x (Pi dB PI dB)
Ans : PIMR = - 40 dBm
Dynamic Range:
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Dynamic Range:
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SINAD:
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87
SINAD:
Equivalent Noise Bandwidth, Bn
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n
88
When noise is passed through a filter having a frequency
response, some of the noise power is rejected by the filter and
some is passed through to the output
The noise bandwidth of a non-ideal filter is defined as the
bandwidth of an ideal (rectangular) filter which will pass
the same noise power as the non-ideal filter.
Definition
Equivalent Noise Bandwidth f
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Equivalent Noise Bandwidth f
89
The relationship between f and f3dB, the 3dB
frequency of the system,
The NBW is the frequency such that a rectangle defined by
H(max)2 and Bn has an area equal to the area under|H()|2.
D i ti f N i B d idth
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Derivation of Noise Bandwidth
90
The relationship between f and f3dB, the 3dBfrequency of the system, depends on the number of
poles in the transfer function.
The noise bandwidth for a single pole filter
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The noise bandwidth for a single pole filterExample: A RC filter
Questions:
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Q
Define noise factor, noise figure, and sensitivity. State and explain the sources of noise.
Explain the concept of equivalent noise bandwidth
What is intermodulation distortion? Discuss in detail the different
parameters that are related with intermodulation distortion.
Explain the noises that occur in active devices.
Derive the expression of the noise factor of n cascaded stages. What is the
significance of the first stage.
Explain the significance of 1dB compression point.
A receiver has 10 dB noise figure, 50 input impedance, a 5dBm two toneintercept point (PI), and a 3.5 KHz bandwidth. What is the minimum
detectable signal for a 0 dB output signal to noise ratio? What is the
receivers dynamic range.