ECE 5233 Satellite Communications
Prepared by:
Dr. Ivica Kostanic
Lecture 9: Satellite link design
(Section 4.3)
Spring 2014
Outline
Thermal noise in satellite systems
Noise temperature and noise figure of a device
System level noise figure and noise temperature
Examples
Important note: Slides present summary of the results. Detailed
derivations are given in notes.
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Thermal noise
 Power spectrum density of thermal noise
form a black body (one sided):
 Generated as a consequence of random
electron motion at non zero temperature
 Dominant source of noise in microwaveportion of spectrum
S f  
 Other types of noise in electronic circuits
hf
 hf 
exp    1
 kT 
o
Shot noise – random motion of charge in solid
state devices and tubes
h  6.626068 ×10-34 m 2 kg / s
o
Flicker noise – low frequency noise in solid
state circuits
k  1.3806503 ×10-23 m 2 kg s -2 K -1
o
Quantum noise – consequence of discrete
nature of charge
o
Plasma noise – random motion of charge in
ionized plasma
Radio spectrum extends up to
300GHz
PSD of the thermal noise
4.5
4
3.5
PSD [W/Hz]
 Different noise types have different origins
but similar power spectral density -> they
can all be treated as thermal noise
-21
x 10
3
2.5
2
1.5
1
Satellite
service
0.5
Note: PSD graph is generated for
T=300K
0
0
10
1
2
10
10
f [GHz]
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Thermal noise in RF communication
Consider
hf 6.62 10 34

f  1.655 10 13 f
 21
kT
4 10
 1.655 10  4 f GHz 
Since frequency smaller than
40GHz, hf/kT is small.
hf
hf
 hf 
exp    1  1 
1 
kT
kT
 kT 
hf
hf
S f  

 kT
hf / kT
 hf 
exp    1
 kT 
Note 1: T is temperature in K
PDF of thermal noise in amplitude domain
Fn n  
 n2 
1

exp  
2 
2

2 


 2  kTBe
Note 1: noise has normal
distribution in amplitude
domain (CLT)
Note 2: filter noise is also
Gaussian (i.e. normally
distributed)
Note 3. power of the noise is
limited by the equivalent
bandwidth of the system
Note 2: The noise if flat in
spectral domain – “white
noise”
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Equivalent noise temperature of a device
 Noise temperature of the device – used to
characterize noise sources internal to the device
 Measurement of equivalent noise temperature – Y
factor method
 Each device is characterized either by noise
temperature or noise figure
 In satellite communication – noise temperature more
convenient
N1  GkT1 B  GkTe B
N 2  GkT2 B  GkTe B
N1 T1  Te

Y
N 2 T2  Te
Te 
T1  YT2
Y 1
Note: accuracy dependant on size of Y
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Noise temperature of waveguides
 Waveguides are part of RF front end
 Waveguides have associated losses
 Losses attenuate both signal and
noise that enter the waveguide
All components on the same
temperature – thermal equilibrium
Solving for equivalent noise temperature
Te  1 / GS  1T  LS  1T
Available input noise
N i  kTBn
Note: Two ways of minimizing equivalent
noise temperature of a waveguide
Available output noise
N o  kTBn  Gs k T  Te Bn
1.
Reduce losses
2.
Reduce physical temperature
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Noise figure
One may write
N 0  GFkT0 B
System may be modeled as a noise free
but one assumes that the PSD of the
input is increased by the factor of F
relative to the PSD on the room
temperature
Available power at the input
Ni  kT0 B,
T0  290K
If the network were noise free
N o  G  N i  GkT0 B
Due to sources internal to network
N 0  GN i
N 0  GFN i
Noise figure/Noise temperature
N 0  k T0  Te BG
N 0  kT0 BFG
Te  T0  FT0
Te  F  1T0 ; F  1 
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Te
T0
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Noise temperature of cascaded devices
 At the Rx signal travels through multiple components
 Each component has associate noise temperature
One may extend the process to arbitrary
number of components
 Of great interest is to determine equivalent “end to
end” noise temperature – system temperature
Te  Te1 
Te 2
T
 e3  
G1 G1G2
Using relationship between noise
temperature and noise figure:
F  F1 
F2  1 F3  1


G1
G1G2
N1  G1kTi B  G1kTe1 B  G1k Ti  Te1 B
Note 1: System noise figure depends
most heavily on the first component in Rx
chain
N 0  Gk Ti  Te1  Te 2 / G1 B
Note 2: Noise figure values in above
equations are in linear domain
N 0  G2 N1  G2 kTe 2 B  G1G2 k Ti  T1 B  G2 kTe 2 B
Ts  Te1 
Te 2
G1
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G/T ratio for earth stations
Signal to noise ration at the output of the RX
antenna
Signal
S
PT  GT  GR
4R /  2
 GR 
 
 TK 
Depends on the RX only
 G/T ratio – figure of merit for the RX
Noise
 Usually given in dB/K
N  kTs Be
 Small satellite terminals may have
negative G/T value
Signal to noise
S PT GT   



N
kBe  4R 
2
 GR 
 
 Ts 
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Example
Consider the system shown in the figure
a)
Compute the overall noise figure of the
system.
b)
If the noise power from the antenna is kTaB
where Ta = 15K, find the output noise power
in dBm.
c)
What is the two sided PSD of the thermal
noise?
d)
If the required SNR at the output is 20dB,
what is the minimum signal power at the
input?
Assume that the system is at the temperature of
290K and with bandwidth of B=10MHz
Answers:
a)
2.55
b)
-98.7dBm
c)
6.8e-18mW/Hz
d)
-84.66dBm
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Examples
Example 4.3.4. Earth station has a
diameter of 30m, overall efficiency of 68%
and it is used for reception of a signal at
4150MHz. The system noise temperature
is 79K when the antenna points at 28
degrees above horizon.
a) What is the G/T ratio under these
conditions?
b) If heavy rain causes system
temperature to increase to 88K, what is
the new G/T value?
Answer:
a) G/T = 41.6dB/K
b) G/T = 41.2dB/K
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