1
QUESTION 1
• Define electrical noise
Solution
Electrical noise is defined as any undesirable
electrical energy that falls within the pass
band of the signal.
QUESTION 2
• Convert the following temperatures to Kelvin
Solution
a)17⁰C
17 ⁰C +273⁰ = 290K The formula T= ⁰C+273
is used to convert ⁰C to
b)27 ⁰C Kelvin
27 ⁰C +273⁰ =300K
c)-17 ⁰C
-17 ⁰C +273⁰ =256K
d)-50 ⁰C
-50 ⁰C+273⁰ =223K
QUESTION 3
• Calculate the thermal noise power in watts and
dBm for the following bandwidth and
temperatures
Solution
a)B=100Hz, T=17 ⁰C
N(dBm) = 10 log KTB T=17⁰C+273=290K
0.001
= 10 log (1.38x10-23)(290)(100)
0.001
= 10 log 4.002x10-16
= -153.98dBm
b) B=100Hz, T=100⁰C
N(dBm) = 10 log KTB
0.001 T=100⁰C+273=373K
= 10 log (1.38x10-23)(373)(100)
0.001
= 10 log 5.1474x10-16
= -122.88dBm
c) B=1MHz, T=500⁰C
N(dBm) = 10 log KTB
0.001 T=500⁰C+273=773K
= 10 log (1.38x10-23)(773)(100)
0.001
= 10 log 1.06674x10-15
= -149.72dBm
QUESTION 4
• For a nonideal amplifier and the following
parameters,
Input signal power = 2x10-10W
Input noise power = 2x10-18W
Power gain = 1,000,000
Internal noise (Nd) = 6x10-12W
a) Input S/N ratio (dB)
b) Output S/N ratio (dB)
c) Noise factor and noise figure
Solution 4
a) Input S/N ratio (dB)
S = 2x10-10W =100,000,000
N 2x10-18W
10 log (100,000,000) = 80 dB
b) Output S/N ratio (dB)
Nout = 1,000,000 ( 2 x 10-18 ) + 6 x 10-12
= 8 x 10-12W= 8pW
Pout = 1,000,000 ( 2 x 10-10 ) = 200μW
S = 200x10-6W
=25,000,000
N 8x10-12W
10 log (25,000,000) = 74 dB
c) Noise factor and noise figure
Noise factor, F = input signal-to-noise power ratio
output signal-to-noise power ratio
= 100,000,000
25,000,000
=4
Noise figure, NF = 10 log F
= 10 log 4
= 6dB
5. What is meant by the terms external
noise and internal noise ?
• External noise :
- noise that is generated outside the device or
circuit. The three primary sources of external noise
are atmospheric, extraterrestrial and man – made.
• Internal noise :
- Internal noise is electrical interference generated
within a device or circuit. There are three primary
kinds of internally generated noise : shot, transit
time and thermal.
6. Determine the bandwidth necessary to
produce 8x10-17 watts of thermal power
at a temperature of 17oC.
N = noise power (watts) = 8x10-17
T = absolute temperature (Kelvin) = 17oC
T = 273o + oC = 273o + 17o = 290K
K = boltzmannls constant (1.38x10-23 joules/Kelvin)
N = KTB
B = N/KT
= 20kHz
7. Determine the second, third and total harmonic
distortion for a repetitive wave with a fundamental
frequency amplitude of 10Vrms, a second harmonic
amplitude of 0.2Vrms and a third harmonic amplitude
of 0.1Vrms.
8. Noise generate in an amplifier with bandwidth 5MHz
can be represented by internal noise power
0.082pW. Calculate noise factor and noise figure for
the amplifier if:
a) a signal with 300k
b) a signal with 100k
a) a signal with 300k
b) a signal with 100k
11. What is the most significant form of
internal noise?
• Noise Classification
– Correlated Noise
– Uncorrelated Noise
• Uncorrelated Noise
– External Noise
– Internal Noise
• Thermal Noise
• Shot Noise
• Flicker
Thermal noise is most significant form of internal noise
13. If an amplifier has a bandwidth B=20kHz and a total
noise power N=2x10-17W,determine the total noise
power if bandwidth increases to 40kHz.Decrease to
10kHz.
14. For an amplifier operating at a
temperature of 270 C with a bandwidth of 20
kHz, determine :
a) the total noise power in watts and dBm
Amplifier 2700 C , BW=20kHz
Noise power, N=KTB
N=1.38x10-23 x (27+273) x20k
N=1.38x10-23x300x20k
N=8.28x10-17W
NdBm=10log(N/1m)
NdBm=-130.82dBm
b) The rms noise voltage Vn for a 50Ω internal
resistance and a 50Ω load resistor VN=?, Ri=R=50Ω
VN = √(4RKTB)
VN2 = 4RKTB=4RN
VN2 = 4x50x8.28x10-17
VN2 = 1.656x10-14
VN = 1.3x10-7
VN = 130nV
13. Explain the difference between correlated
and uncorrelated noise.
Correlated noise Uncorrelated noise
A form of internal noise that Present regardless of whether
correlated to the signal and there is a signal present or not,
cannot be present in a circuit can be further subdivided into two
unless there is no signal. general categories, external and
internal.
Produced by nonlinear External noise generate outside
amplification and includes the device or circuit.
harmonic and inter-modulation
distortion
Nonlinear distortion creates Internal noise is electrical
unwanted frequencies that interference generated within a
interfere with the signal and device or circuit.
degrade performance.
14. Describe the signal-to-noise ratio.
• Signal-to-noise ratio (S/N) is the ratio of the
signal power level to the noise power level.
S/N = Ps / Pn
15. For three cascaded amplifier stage , given noise figure and
gain for each stage as below, each amplifier operates at a
temperature of 27⁰C with a bandwidth of 20 kHz, determine :
-
Amplifier A : GA = 20 dB NFA = 3dB
Amplifier B : GB = 10dB NFB = 5dB
Amplifier C : GC = 5dB NFC = 10dB
a) The rms noise voltage VN for a 50 Ω internal
resistance and a 5oΩ load resistor.
VN = √4KTBRL with load resistance of 50Ω
= √4(K)(27+273)(20000)(50)
= 1.287 x 10-7 Vrms
b) Total noise factor and total noise figure
• Total noise figure :
NFT = NFA+NFB+NFC
= 3 + 5 + 10
= 18 dB
• Total noise factor :
FT = F1 + (F2-1/G1) + (F3-1/G1G2)
= 2 + (3.16 -1 /100) + (10-1 /100x10)
= 2.03
16. An input signal for a receiver with input signal power 100μ W and noise power 1μ W.
The gain of the receiver given is 20 dB with internal noise as much 80μ W. Determine
input S/ N ratio, output S/N ratio and noise factor of the receiver.
Input S/ N ratio = Si/Ni = 100μ/ 1μ
= 100
Gain, G = 20 dB = 10 2/10 = 100
Output signal power, So = Gsi
= 100μx100
= 0.01 w
Output noise power, No = GNi + Na
= 100 (1μ) + 80μ
= 180μw
Output S/N ratio =So/No
= 0.01/180μ
= 55.56
Noise factor, F = SNRi/ SNRo
= 100/ 55.56
= 1.8
• The noise factor of a system is the ratio of
output noise power (Pno) to input noise power
(Pni):
• The noise figure is the noise factor converted
to decibel notation:
NF = 10 LOG Fn
• The noise factor is always measured at the
standard temperature (To) 290°K
(standardized room temperature).
The input noise power Pni is defined as the
product of the source noise at standard
temperature (To) and the amplifier gain (G):
Pni = GKBT0
• The noise figure of a system can be defined as
• where SNRin and SNRout are the input and
output signal-to-noise ratios, respectively.
Alternatively, noise figure may be defined in
terms of dB units
• where SNRin,dB and SNRout,dB are in dB.
Sni = 30 dB, Sno = 24 dB
Fn = 1.25
NF = 10logFn
= 0.969dB
• NF=5.4dB, Sno =16dB
, NF = 10logFn
Fn = 10 5.4/10
= 3.467
Sni = 16 x 3.467
= 55.48dB
• NF = 3.9dB, Pi = 65μW, Po = 20mW, Pno =1mW
a. Gain = Po/Pi
= 20m/65μ
= 333.33
b. Fn = Pno / Pni
Fn = 103.9/10
= 2.45
Pni = 2.45 x 1m
= 2.45mW
Give examples of external and internal noise. Give some explanation
on it.
a) External noise – generated outside the device or circuit.
Atmosphere noise
- naturally occurring electrical disturbances that originate within Earth’s
atmosphere such as lightning.
– - also known as static electricity.
Extraterrestrial noise
– - consists of electrical signal that originate from outside Earth’s
atmosphere and therefore also known as deep-space noise.
– - subdivided into two categories :
– ~ solar noise that is generated directly from the sun’s heat
– ~ cosmic noise / black-body noise that is distributed throughout the
galaxies.
• b) Internal noise – generated within a device or circuit
• Shot noise
– - caused by the random arrival of carriers (holes and
electrons) at the output element of an electronic device
– - shot noise is randomly varying and is superimposed onto
any signal present.
• Transit – time noise
– - irregular, random variation due to any modification to a
stream of carriers as they pass from the input to the output
of a device.
– - This noise become a noticeable when the time delay takes
for a carrier to propagate through a device is excessive.
