1 satellite link design – part ii joe montana it 488 – fall 2003
TRANSCRIPT
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Satellite Link Design – Part II
Joe MontanaIT 488 – Fall 2003
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Agenda
• System Noise Power (Part II)
• Numerical Examples
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Acknowledgements:
• Dr. James W. LaPean course notes• Dr. Jeremy Allnutt course notes
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System Noise Power
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System Noise Power - 1Performance of system is determined by C/N ratio.Direct relation between C/N and BER for digital systems.Usually: C > N + 10 dBWe need to know the noise temperature of our receiver so that we can calculate N, the noise power (N = Pn).
Tn (noise temperature) is in Kelvins (symbol K):
2739
5320 FTKT 2730 CTKT
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System Noise Power - 2System noise is caused by thermal noise sources
External to RX system• Transmitted noise on link• Scene noise observed by antenna
Internal to RX system
The power available from thermal noise is:
where k = Boltzmann’s constant = 1.38x10-23 J/K(-228.6 dBW/HzK),
Ts is the effective system noise temperature, andB is the effective system bandwidth
(dBW) BkTN s
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Noise Spectral DensityN = K.T.B N/B = N0 is the noise spectral density (density of noise power per hertz):
N0 = noise spectral density is constant up to 300GHz.All bodies with Tp >0K radiate microwave energy.
(dBW/Hz) 0 ss kT
B
BkT
B
NN
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System Noise Temperature1) System noise power is proportional to
system noise temperature2) Noise from different sources is
uncorrelated (AWGN)Therefore, we can
Add up noise powers from different contributionsWork with noise temperature directly
So:
But, we must:Calculate the effective noise temperature of each contributionReference these noise temperatures to the same location
Additive White Gaussian Noise (AWGN)
RXlinelossLNAantennadtransmittes TTTTTT
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Typical Receiver
(Source: Pratt & Bostian Chapter 4, p115)
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Noise Model
(Source: Pratt & Bostian Chapter 4, p115)
Noise is added and then multiplied by the gain of the device (which is now assumed to be noiseless since the noise was already added prior to the device)
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Equivalent Noise Model of Receiver
(Source: Pratt & Bostian Chapter 4, p115)
Equivalent model: Equivalent noise Ts is added and then multiplied by the equivalent gain of the device, GRFGmGIF
(noiseless).
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Calculating System Noise Temperature - 1
Receiver noise comes from several sources.We need a method which reduces several sources to a single equivalent noise source at the receiver input.Using model in Fig. 4.5.a gives:
End)-(Front
(Mixer)
(IF)
inRFRFmIF
mmIF
IFIFn
TTkBGGG
BkTGG
BkTGP
(Eqn. 4.15)
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Calculating System Noise Temperature - 2
Divide equation 4.15 by GIFGmGRFkB:
If we replace the model in Fig. 4.5.a by that in Fig. 4.5b
RFm
IF
RF
minRFRFmIFn GG
T
G
TTTkBGGGP
(Eqn. 4.16)
BkTGGGP sRFmIFn (Eqn. 4.17)
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Calculating System Noise Temperature - 3
Equate Pn in Eqns 4.16 and 4.17:
Since C is invariably small, N must be minimized.How can we make N as small as possible?
RFm
IF
RF
minRF GG
T
G
TTTT S (Eqn. 4.18)
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Reducing Noise Power
Make B as small as possible – just enough bandwidth to accept all of the signal power (C ).Make TS as small as possible
Lowest TRF
Lowest Tin (How?)
High GRF
If we have a good low noise amplifier (LNA), i.e., low TRF, high GRF, then rest of receiver does not matter that much.
inRFRFm
IF
RF
minRF TT
GG
T
G
TTTT
S
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Reducing Noise Power Low Noise Amplifier
Parametric amplifier (older technology, complex and expensive):Cooled (thermo-electrically or liquid nitrogen or helium):
- 4 GHz : 30 K- 11 GHz: 90 K
Uncooled:- 4 GHz : 40 K- 11 GHz: 100 K
Ga AS FET (Galium Arsenide Field-Effect Transistor): Cooled (thermo-electrically):
- 4 GHz : 50 K- 11 GHz: 125 K
Uncooled:- 4 GHz : 50 K- 11 GHz: 125 K
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Reducing Noise Power Discussion on Tin
Earth Stations: Antennas looking at space which appears cold and produces little thermal noise power (about 50K).Satellites: antennas beaming towards earth (about 300 K):
Making the LNA noise temperature much less gives diminishing returns. Improvements aim reduction of size and weight.
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Antenna Noise Temperature
Contributes for Tin Natural Sources (sky noise):
Cosmic noise (star and inter-stellar matter), decreases with frequency, (negligible above 1GHz). Certain parts of the sky have punctual “hot sources” (hot sky).Sun (T 12000 f-0.75 K): point earth-station antennas away from it.Moon (black body radiator): 200 to 300K if pointed directly to it.Earth (satellite)Propagation medium (e.g. rain, oxygen, water vapor): noise reduced as elevation angle increases.
Man-made sources:Vehicles, industrial machineryOther terrestrial and satellite systems operating at the same frequency of interest.
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Antenna Noise Temperature
Useful approximation for Earth Station antenna temperature on clear sky (no rain): Earth Station Antenna - Noise Temperature
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70 80 90 100
Elevation Angle (degrees)
Ta
(K)
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Noise from Active Devices
Active devices produce noise from:Dissipative losses in the active deviceDissipative losses in the supporting circuitsElectrical noise caused by the active device
The effective temperature of active devices is specified by the manufacturer
Can be measured by a couple of methodsCan be (somewhat laboriously) calculatedAssumes specific impedance matches
The effective temperature is (almost) always specified at the input of the deviceThe noise is often given as a noise figure (see later)
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Noise from Lossy Elements -1All lossy elements reduce the amount of power transmitted through them
Carrier or signal powerNoise power
The noise temperature contribution of a loss is:
G = 1/Loss
where G is the “gain” (smaller than unit) of the lossy element, also called transmissivity (Pout /Pin) and T0 is the physical temperature of the loss.Note the temperature is at the output of the loss.
[K] G)-(1TT 0N
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Noise from Lossy Elements –2Assume lossy element has gain = GL=1/LNotes: GL <0 dB (because 0 < GL < 1)
T0= physical temperature
G
Noisy, Lossy
S SxG+N
G
Noiseless
S SxG+
N=kTNB+
TN Noise Source at output:
TN=T0(1-G) [K]
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Noise from Lossy Elements –2
G
Noisy, Lossy
S SxG+N
G
Noiseless
S SxG+
N=kTNB+
TN
Noise Source at input:
T’N = TN/G = T0(1/G-1) [K]
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Noise FigureNoise Figure:
Relates the noise temperature to a referenceEasily used in dB scale
Definition:
Convert to Noise Temperature:
T0 = standard noise temperature = 290 K
G = gain of network
)1(0 ne FTT
GBkT
N
NS
NSF
N
out
out
inN
0/
/
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Translating NoiseWe need to have all of the noise referenced to a common pointThe output flange of a lossless antenna is the standard referenceNoise temperature can be moved through components just like power is since the two are linearly related
This is only valid if the system is linearNote that the RX bandwidth must still be wide enough for the signal!
If the temperatures T2 and T3 are referenced to the input (T1 at the output of L1) of the respective component, then:
L1 T3
Tin
G2, T2
Ta Tb Tc
321122122
32111
2
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11
111
11
1 1
1
TTTTGGTGGTGTG
TTTGTGTT
G
TT
GG
TTTTGT
LG
insysasysbsyscinsysasysb
insysaphys
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Multi-bounce link budgets
If the C/N ratios for each of the linear bent pipe transponder links are available:
so long as the noise is uncorrelated between the linksFor baseband processing links:
111
2
1
1
...
ntotal N
C
N
C
N
C
N
C
ntotal BERBERBERBER ...21
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So many trade-offs !!!
rotherpolrataap
rttr LLLLLLL
GGPP
BKT
P
N
C
s
r
RFm
IF
RF
minRF GG
T
G
TTTT S
2D
G
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R
LpFLa
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Numerical Examples
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Noise TemperatureExample – 4.2.1
4GHz ReceiverTin =Ta =50 K
TRF =50 K GRF =23 dB (=200)
Tm =500 K Gm =0 dB (=1)
TIF =1000 K GIF =50 dB (=1000)
Tin=50 KGRF=200 Gm=1 GIF=1000
TRF=50 K Tm=500 K TIF=1000 K
System Temperature referred to this point
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Noise TemperatureExample – 4.2.1
K
GG
T
G
TTTT
RFm
IF
RF
minRF
5.10755.25050
1 x 200
1000
200
5005050
S
Solution:
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Noise TemperatureExample – 4.2.1
If mixer had 10 dB lossGm = -10 dB (=0.1)
Comment: GRFGm is too small here, so the IF amplifier contribution is large.
If we made GRF = 50 dB (=105)
KT 5.15220
1000
200
5005050 S
KT 1.100000,10
1000
000,100
5005050 S
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Noise Temperature – Lossy ElementsExample – 4.2.2
In original problem, insert lossy waveguide with 2 dB attenuation between antenna and LNA
Tin=50 KGRF=200 Gm=1 GIF=1000
TRF=50 K Tm=500 K TIF=1000 K
System Temperature referred to this point
GL
TL
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Noise Temperature – Lossy ElementsExample – 4.2.2
Loss of 2 dB, obtain GL and TL:
K
GT
dBG
LL
L
3.107
)63.01(290
)1(290
63.058.1
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K 8.138
K 3.0710.63 x 05
TG LLain
TT
•Input noise power is attenuated by 2 dB:New Tin:
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Noise Temperature – Lossy ElementsExample – 4.2.2
K
GG
T
G
TTTT
RFm
IF
RF
mRFin
3.19655.2508.138
1 x 200
1000
200
500508.138
S
Increased from 107.5 to 196.3 K at the same reference point:
dBT
T
BKT
BKT
N
N
s
s
s
s 6.282.1 1
2
1
2
1
2
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Noise Temperature – Lossy ElementsExample – 4.2.2
Inserting 2 dB loss in the front end of the received carrier power (C ) by 2 dB and increased noise temperature by 88.8 K, from 107.5 K to 196.3 K (comparing at the same reference point).N has increased by 2.6 dB.C has decreased by 2 dB.Result: C/N has been reduced by 4.6 dB!
Moral:Losses before LNA must be kept very small.
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Antenna Example - 13.7.1 Earth subtends an angle of 17 degrees when
viewed from geostationary orbit. a. What should be the dimensions of a reflector antenna
to provide global coverage at 4 GHz?b. What will be the antenna gain if efficiency =0.55?
a. 3dB = 17 degrees
b. =0.55
mD
D
dB
dB
33.017
075.0x7575
75
3
3
dBGain
EdB
23.2065.10517
7555.0
752
22
3
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Antenna Example - 23.7.1 Continental US subtends a “rectangle” of 6 x 3 degrees.Find gain and dimensions of a reflector antenna to provide global coverage at 11 GHz? a. Using 2 antennas (3 x3 degrees)
b. Using only 1 antenna (3 x 6 degrees)a. 3dB = 3 degrees
b. 3dBA = 6 degrees
3dBE = 3 degrees
mDdB
68.03
0273.0x7575
3
dBGaindB
2.357.33923
7555.0
7522
3
dBGain
EdBAdB
3.323.16963x6
7555.0
75 2
33
2
mD
D
dBA
E
34.06
0273.0x7575
0.68m
3
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Power Budget Example - 14.1.1 Satellite at 40,000 km (range)
Transmits 2WAntenna gain Gt = 17 dB (global beam)
Calculate: a. Flux density on earth’s surface b. Power received by antenna with effective aperture of 10m2
c. Gain of receiving antenna. d. Received C/N assuming Ts =152 K, and Bw =500 MHz
a. Using Eqn. 4.3: (Gt = 17 dB = 50)
2215-
2722
dBW/m 143W/m10 x 4.97
) x(4x104
50 x 2
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R
GP
R
EIRPF tt
(Solving in dB…)
dBW/m2 1431521120
114
dB[meter] )10x4(log x 2 R
dBW 20173)(27
102
F
dB
GtPtEIRP
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Power Budget Example - 1b. Received Power
dBWW 13310 x 4.97 P
10 x )(4.97x10 A x FP14-
r
-15r
(Solving in dB…)
dBW 133
10)143(
r
r
P
AFP
c. Gain given Ae = 10 m2 and Frequency = 11GHz ( eqn. 4.7)
dBA
G er 3.52
0273.010 x 4π4
2
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Power Budget Example - 1b. System Noise Temperature
dBNC
NCNC
dBWW
dBW
BTKor
KTB
dBdBdB
2.13/
)79.119(133/
13310 x 4.97 PC
97.119
99.8682.21 6.228
10 x 500 x 152x 01 x 38.1PN
14-r
623n
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Power Budget Example - 2Generic DBS-TV:
Received PowerTransponder output power , 160 W 22.0 dBWAntenna beam on-axis gain 34.3 dBPath loss at 12 GHz, 38,500 km path -205.7 dBReceiving antenna gain, on axis 33.5 dBEdge of beam -3.0 dBMiscellaneous losses -0.8 dBReceived power, C -119.7 dBW
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Power Budget Example - 2Noise powerBoltzmann’s constant, k -228.6
dBW/K/HzSystem noise temperature, clear air, 143 K 21.6
dBKReceiver noise bandwidth, 20MHz 73.0
dBHzNoise power, N -134.0 dBW C/N in clear air 14.3 dBLink margin over 8.6 dB threshold 5.7
dBLink availability throughout US Better than
99.7 %