noise and snr calculation
TRANSCRIPT
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CHAPTER 6NOISE
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INTRODUCTION
Noise is random energy that interferewith the information signal.
Noise may be defined as any unwantedintroduction of energy tending to
interfere with the proper reception andreproduction of transmitted signal.
In radio receiver, noise may produce hissin the loudspeaker output.
Noise can limit the range of systems. It affects the sensitivity of the receiver.
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NOISE
Electrical noise any undesirable that falls withinthe passband of the signal.
Figure 4 show the effect of noise on electricalnoise.
2 general categories
Correlated noise implies relationship betweenthe signal and the noise, exist only when signalis present.
Uncorrelated noise present at all time,whether there is signal or not.
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Classification ofUncorrelated Noise
NOISE
EXTERNAL INTERNAL
ATMOSPHERIC
NOISE
EXTRATERRESTRIALNOISE
INDUSTRIAL
NOISE
THERMAL
NOISE
SHOT
NOISE
Figure 6.1
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ATMOSPHERIC NOISE Caused by lightning discharges in thunderstorms and other
natural electric disturbances occurring in the atmosphere. Consist of spurious radio signal with components distributed
over a wide range of frequencies. It propagates over the earth in the same way as ordinary
radio waves of the same frequencies. Become less severe at frequencies above 30MHz because: The higher frequencies are limited to line-of-sight
propagation. Nature of the mechanism generating this noise is such
that very little of it is created in the VHF range and
above.
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EXTRATERRESTRIAL NOISE
SOLAR NOISE: Normal condition, there is a constant noise radiation
from the sun, simply because large body at a very highfrequency.
Radiates over a very broad frequency spectrum.
COSMIC NOISE: Stars radiate RF noise in the same manner of sun. The noise received is called thermal noise and
distributed fairly uniformly over the entire sky.
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INDUSTRIAL NOISE
Between 1 to 600 MHz, the intensity noisemade by humans easily outstrips thatcreated by any other source to the
receiver.Sources such as: automobile, aircraft,
electric motors and other heavy machine.
The nature of industrial noise is sovariable that it is difficult to analyze.
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SHOT NOISE
Caused by the random arrival of carriersat the output element of an electronicdevice.
First observed in the anode current of a
vacuum-tube amplifier.The current carriers are not moving in
continuous steady flow.Randomly varying and superimposed onto
any signal present.Sometimes called transistor noise.
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Thermal noise power is proportional to theproduct of bandwidth and temperature.
Mathematically, noise power is
N=KTB
N = noise power,K=Boltzmanns constant (1.38x10-23J/K)B = bandwidth,T = absolute temperature (Kelvin)(17oCor290K)
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NOISEVOLTAGE
4N
V RkTB
VN/2
VN/2VN R
RI
Noise Source
Figure 4.2 shows the equivalentcircuit for a thermal noise source.
Internal resistanceRIin series
with the rms noise voltage VN
.
For the worst condition, the loadresistanceR = R
I, noise voltage
dropped acrossR =half the noise
source (VR
=VN/2) and
From the final equation The
noise powerPN , developed acrossthe load resistor = KTB
The mathematical expression :
RKTBV
RKTBV
RV
RVKTBN
N
N
NN
4
4
42/
2
22
Figure 6.2 : Noise source
equivalent circuit
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Example 1
Convert the following temperaturesto kelvin:a) 100C
b) 0Cc) -10C
T=aC+273C
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Example 2
Calculate the thermal noise poweravailable from any resistor at roomtemperature (290K) for a bandwidth of1 MHz. Calculate also thecorresponding noise voltage, given that
R = 50.
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Example 3
For an electronic device operating ata temperature of 17oC with abandwidth of 10 kHz, determine
a)Thermal noise power in watts and dBmb)rms noise noise voltage for a 100
internal resistance and 100 load
resistance.
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Example 4
Two resistor of 20k and 50 kareat room temperature (290K). For abandwidth of 100kHz, calculate thethermal noise voltagegenerated by
1.each resistor
2.the two resistor in series
3.the two resistor in parallel
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Correlated Noise
Form of internal noise that is correlatedto the signal and cannot be present in acircuit unless there is a signal.
Produced by nonlinear amplification.All circuits are nonlinear therefore, theyall produce nonlinear distortion.
Nonlinear distortion creates unwanted
frequencies that interfere with the signaland degrade performance.
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Intermodulation DistortionGeneration of unwanted sum and
difference frequencies produced when twoor more signals mix in a nonlinear device.
The sum and difference frequencies are
called cross products.Unwanted cross products can interfere
with the information signal.Cross products are produced when
harmonics as well as fundamentalfrequency mix in a nonlinear device.
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Cont..
Cross products = mf1nf2.
F1 and f2 are fundamental frequency.
F1>f2
M and n are positive integer.
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Correlated Noise-Intermodulation Distortion
f1 f2
V1 V2
f1 f2f1-f2 f1+f2
V1 V2
Vdifference Vsum
Input frequency spectrum Output frequency spectrum
Figure 6.4
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Example 6
For a nonlinear amplifier with 2 inputfrequencies, 3kHz and 8kHz,determine:
a) First 3 harmonics present in theoutput for each input frequency.
b) Cross-product frequencies
produced for values of m and n of 1and 2.
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InterferenceForm of external noise.Means to disturb or detract from.Electrical interference is when
information signals from one sourceproduce frequencies that fall outside theirallocated bandwidth and interfere withinformation signals form another source.
Most interference occur when harmonics
frequencies from one source fall into thepassband of a neighboring channel.
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Review Notes
Gain
Attenuation Both has the ratio output to the input.
in
out
VV
V
input
outputA
Figure 6.5
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Gain
Ratio output to the input.
Output has greater amplitude than theinput
Most amplifiers are power amplifier, thesame procedure can be used to calculatepower gain, Ap.
Ap= P
out/P
in
Figure 6.6
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Attenuation
Refers to loss introducedby a circuit.
Output is less than input.
For cascade circuit, totalattenuation is,
AT=A1x A2x A3..
Voltage divider network
may introduce
attenuation.
in
out
V
VAnAttenuatio
Figure 4.7 Voltage divider
introduces attenuation
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Attenuation can be offset byintroducing gain.
Figure 6.8 Total attenuation in cascaded network
Figure 6.9 Gain offsets theattenuation
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Figure 6.10 Total gain is the product of the individual stage gains and attenuation
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Example 7
What is the gain of an amplifier that
produces an output of 750 mV for 30 Vinput?
Example 8
The power output of an amplifier is 6 W. Thepower gain is 80. What is the input power?
Example 9Three cascade amplifier have power gains of5,2, and 17. The input power is 40 mW. What
is the output power?
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Signal to Noise Ratio (SNR)
Ratio of the signal power level to thenoise power level.
Express in logarithmic function:
n
sP
PSNR
n
s
P
PdBSNR log10)(
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Example 10
1 For an amplifier with an output signalpower of 10W and an output noise powerof 0.01W, determine the SNR.
2 For an amplifier with an output signalvoltage of 4V, an output noise voltage of0.005V and an input and outputresistance of 50, determine the SNR.
( ) d
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Noise Factor (F) and NoiseFigure (NF)
Figures of merit used to indicate howmuch the SNR deteriorates as a signalpasses through a circuit.
Noise factor is simply a ratio of inputSNR to output SNR.
SNRoutput
SNRinputF
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Cont..
NF is noise factor stated in dB.
Used to indicate the quality of a receiver.
SNRoutputSNRinputdBNF log10)(
FdBNF log10)(
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Ideal Noiseless Amplifier
i
i
N
S
inpowerNoise
inpowerSignal
Ideal Noiseless AmplifierAp=power gain
i
i
ip
ip
N
S
NA
SA
inpowerSignal
outpowerSignal
Figure 6.11
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Non ideal amplifier
i
i
N
S
inpowerNoise
inpowerSignal
Nonideal amplifierAp=power gain
Nd=internally generated noise
p
d
i
i
dip
ip
A
N
N
S
NNA
SA
inpowerSignal
outpowerSignal
Figure 6.12
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Example 11For a nonlinear amplifier and the following
parameter, determine:a) Input SNR(dB)b) Output SNR(dB)c) Noise Factor and Noise Figure
Input signal power=2x10-10WInput Noise power=2x10-18W
Power gain=1,000,000Internal noise (Nd)=6x10-12W
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Noise Figure of Cascaded
Amplifier
i
i
N
S
T
i
i
o
o NFN
S
N
S
Ap1NF1
Ap2NF2
Ap3NF3
Input Output
i
i
N
S
Figure 6.13
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Cont..
Total noise factor is the accumulation ofthe individual noise factor.
Friisss formula is used to calculate thetotal noise factor of several cascadedamplifiers.
n
nT
AAA
F
AA
F
A
FFF
2121
3
1
21
111
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Example 12
For 3 cascaded amplifier stages,each with noise figure of 3 dB andpower gain of 10 dB, determine the
total noise figure.
E l
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Equivalent NoiseTemperature (Te)
Hypothetical value that cannot be directlymeasured.
To indicates the reduction in the SNR a signal
undergoes as it propagates through a receiver. The lower Te is the better quality of a receiver.
1 FTTeT
TF e1
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Example 13
Determine:
a) Noise Figure for an equivalent noisetemperature of 75K.
b) Equivalent noise temperature for anoise figure of 6dB.
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Example 14
A voltage divider shown in Figure 6.9hasvalues of R1= 10kand R2= 47k.
1. What is the attenuation?2.What amplifier gain would you need to
offset the loss for an overall gain of 1?
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Example 15
An amplifier has gain of 45,000, which is toomuch for the amplification. With an input
voltage of 20 V, what attenuation factor isneeded to keep the output voltage fromexceeding 100mV?. Let A1= amplifier gain =45,000; A2= attenuation factor; AT= total
gain.
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Example 16A RF sine wave generator whose output impedance is50 is connected to a 50 load using 50 coaxialcable. The generators output amplitude level is setto + 3 dBm. An rms voltmeter is used to measure the
effective voltage, and an oscilloscope is used todisplay the sine wave. Compute the following:
1. The rms voltage measure by the rms voltmeter2. The peak voltage, Vpof the sine wave that should be
displayed on the oscilloscope.3. The peak-to-peak voltage, Vp-pof the sine wave that
should be displayed on the oscilloscope
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Example 17
The input signal to a telecommunicationsreceiver consists of 100W of signal power
and 1W of noise power. The receivercontributes an additional 80W of noise, ND,and has a power gain of 20 dB. Compute theinput SNR, the output SNR and the
receivers noise figure.