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Link Budgets and Outage CalculationsDr Costas Constantinou
School of Electronic, Electrical & Computer EngineeringUniversity of Birmingham
W: www.eee.bham.ac.uk/ConstantinouCC/E: [email protected]
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Decibels
• Logarithmic units of measurement suitable for describing both very large and very small numbers conveniently
• Named by telephone engineers in honour of Alexander Graham Bell
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Why work with Decibels
1. Decibels can be used to express a set of values having a very large dynamic range without losing the fine detail
2. They allow gain and signal strengths to be added and subtracted in a link budget calculation
• The American mathematician Edward Kasner once asked his nine-year-old nephew Milton Sirotta to invent a name for a very large number, ten to the power of one hundred; and the boy called it a googol. He thought this was a number to overflow people's minds, being bigger than anything that can ever be put into words …
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1 googol = 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
1 googol = 10100 10 log1010100 = 10 x 100
= 1000 dB
dBs are easier to write down!
Why work with Decibels
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The figure shows a large carrier and also something else higher up the frequency band which is hardly visible
If we plot the result in dBm (decibels relative to 1mW – see later) we can see all of the information clearly
Why work with Decibels
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Decibels
• A power P can be expressed in decibels by
where Pref is the power (unit) to which P is compared
10ref
10 logdB
PP
P
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DecibelsIf for example
P = 20 WattsPref = 1 Watt
thenP dB = 13 dBW
where the W after the dB denotes a reference value of 1 W.
IfPref = 1 milliWatt
thenP dB = 43 dBm
where the m after the dB refers to a mW.
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• The decibel can also be used to refer to the power gain or power loss of a component
1010 log outdB
in
PG
P
Pin Pout
Decibels
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DecibelsThus for an amplifier with
Pin = 0.1 WPout = 1 W
G dB = 10 dB
Similarly if the component is a long cable with
Pin = 1 WPout = 0.1 W
then G = –10 dB
which represents a loss of 10dB.
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Decibels
• If the input and output signals are known in voltage or current terms, then
assuming that the impedances at the input and output are the same (Zout = Zin).
2
10 10 2
10
210log 10log
2
20 log
out out outdB
in in in
out
in
P V ZG
P V Z
V
V
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Decibels
Decibels 1000
number
100
10
1
0.1
30
dB
20
10
0
-10
10
number
8
4
2
1
10
dB
9
6
3
0
0.1
number
0.125
0.25
0.5
1
-10
dB
-9
-6
-3
0
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Decibels• Previous chart is useful for converting from numbers to dBs
• Examples
Pout/Pin = 103 30 dB = 8 x 102 29 dB = 4 6 dB
= 10-1 –10 dB • Memorising the chart will help you perform most
conversions in your head to an accuracy necessary for estimation purposes.
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Cascaded amplifiers
• What happens if we have two amplifiers in series?
Conclusion – we add gains in dB.
int10 10
int
10 1 2
10 1 10 2
1 2
10 log 10 log
10 log
10 log 10 log
out outdB
in in
dB dB
P P PG
P P P
G G
G G
G G
PinPoutPint
G1 G2
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Cascaded amplifiers
ExamplePin = 10 mW, Pint = 1 W, Pout = 100 W
So G1 = 1/10x10-3 = 100 = 20 dB
G2 = 100/1 = 100 = 20 dB
AndG = 100/10x10-3 = 10,000 = 40 dB
G = G1 + G2
PinPoutPint
G1 G2
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Cascaded attenuators
int10 10
int
10 1 2
10 1 10 2
1 2
10 log 10 log
10 log
10 log 10 log
out outdB
in in
dB dB
P P PG
P P P
G G
G G
G G
PinPoutPint
G1 G2
• What happens if we have two attenuators in series?
• Conclusion – losses are negative gains in dB• Conclusion – can add losses in dBs.
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Cascaded attenuators
ExamplePin = 10 W, Pint = 1 W, Pout = 1 mW
So G1 = 1/10 = 0.1 = –10 dB
G2 = 10–3/1 = 10–3 = – 30 dB
AndG = 10–3/10 = 10–4 = – 40 dB
G = G1 + G2
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Cascaded amplifier & attenuator
• What happens if we have an amplifier followed by a loss, such as a long cable?
• Conclusion – now we can proceed to do real systems
int10 10
int
10 1 2
10 1 10 2
1 2
10 log 10 log
10 log
10 log 10 log
out outdB
in in
dB dB
P P PG
P P P
G G
G G
G G
PinPoutPint
G1 G2
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Cascaded amplifier & attenuatorExample
Pin = 1 mW, Pint = 1 W, Pout = 1 mW
So G1 = 1/10–3 = 1000 = 30 dBG2 = 10–3/1 = 10–3 = –30 dB
AndG = 10–3/10–3 = 1 = 0 dBG = G1 + G2
PinPoutPint
G1 G2
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Link budgets
• G = G1 + G2 is a rudimentary system link budget
• Link budgets are used in all RF systems– to get rough feel for viability– to fine tune actual design
PinPoutPint
G1 G2
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Example – submarine cable communications
• Birmingham to Beijing– Distance = 8171 km– Cable attenuation = 0.3 dB/km– Velocity of electromagnetic wave in cable = c/1.46
• Delay = 1.46 x 8191 x 103 / (3 x 108) s• Attenuation = 0.3 x 8171 dB = 2451 dB
• Attenuation is bigger than a googol – it will never work!
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Want a zero gain system, so they can be cascaded to cover long distance
Amp to get input signal power big enough to drive diodegain = 20 dB 20
Laser converts digital signal to lightconversion gain = –20 dB, (or loss = 20 dB) –20
Fibre 100 km long gives 100 x 0.3 = 30 dBso gain = –30 dB –30
Diode converts light back to digital signal conversion gain = –20 dB, (or loss = 20 dB) –20
Amp to bring signal back to input levelgain = 50 dB 50
Overall gain 0 dB
Pin PoutP1
G1 L2L1
P2 P3 P4
amp amplaser diode
detector diodefibre
Simple link budget example
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• Birmingham to Beijing(assuming single satellite trip, up and down)
• Delay = 2 x 35,855 x 103 / 3 x 108 s= 0.23 s
• But what is link budget?
83 10 /g
dc m s
d
35,855 km
Example – geosynchronous satellite link
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Link budgets – satellite downlink model
Transponder
Earth station Rx
Σ
Free space + other losses
antenna
noise
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Link budgets – downlink model
• Satellite transponder output power = Pt
• Antenna gain = Gt
• Effective isotropic radiated power = EIRP = PtGt
• Free space path loss = (λ/4πd)2 = Lp
• Atmospheric loss = La
• Antenna loss (feeder loss, pointing error, etc) = Lat, Lar
• Clear air margin = Mp
• Coverage contour margin = Mc
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Link budgets – downlink model
• Power at receiverS = EIRP + Gr – Lp – La – Lat – Lar (dBW)
(all terms in dBs)
• Noise at receiverN = kTsB = k(Ta + Te)B (dBW)
• Note that Ts = Noise temperature of system in Kelvin
Ta = Noise temperature of antenna in K
Te = Noise temperature of receiver in K
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up link down link
Pt tx power 25 20 dBW
Gt tx ant gain 46 44 dB
Lat tx ant loss -1 -1 dB
Lp free space loss -208 -206 dB
La atmos loss -0.5 -0.6 dB
Gr rx ant gain 46 44 dB
Lar rx ant loss -1 -1 dB
Pr rx power -93.5 -100.6 dBW
Note – up/down link values different due to different frequencies
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12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth station
Typical link budgets
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Typical link budgets
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mm/hr
Typical link budgetsRain loss
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Rain distribution
Typical link budgets
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Noise
• Electromagnetic noise is produced by all bodies above absolute zero temperature (0 K)
• Examples– Earth– Sky– Atmosphere– Sun– Galaxy– Universe– Man-made noise– Interference
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ant i i i ii
T g x T L
Antenna temperature
• The summation is taken over all bodies in the field of view of the antenna
– gi = fraction of total antenna sensitivity (gain) in direction of body i.
– xi = greyness of body i (xi = 1 for a black body)
– Ti = temperature of body i (K)
– Li = transmission factor from body i to antenna
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Source gi xi Li Ti (K) gxTL
sky 0.7 0.99 1.0 50 34.6
earth 0.3 0.3 1.0 300 27.0
sun 0.005 0.99 0.01 7000 0.4
sky-earth
0.3 0.99.(1.0 – 0.3) 1.0 50 10.4
sun-earth
0.3 0.99.(1.0 – 0.3) 0.01 7000 14.5
Tant 86.9
Sample noise calculation for typical satellite earth station at 20 GHz
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• Assuming no loss in the connection between antenna and receiver, the total noise temperature (at input to receiver)
where Te, F = effective noise temp and noise figure of receiver
T0 = reference temp for noise figure (normally 290 K)• Noise power (at input to receiver)
where k = Boltzmann’s constant = 1.38 x 10-23 JK–1
B = receiver bandwidth
Receiver noise temperature
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0( 1)ant e
ant
T T T
T F T
N kTB
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La atmospheric loss in bad storm
10 10 dB
S/N at rx 20.5 12.4 dB
S/N required 10.0 10.0 dB
Mp margin 10.5 2.4 dB
up link down link
Pr rx power -93.5 -100.6 dBW
T noise temp 800 1000 K
B bandwidth 36 36 MHz
N noise power -124 -123 dBW
S/N at rx 30.5 22.4 dB
S/N required 10.0 10.0 dB
Mp clear air margin 20.5 12.4 dB
Note – down link margin only just acceptable in storm
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Typical link budgets
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Outage calculations
• In the case of mobile radio the path loss is not known fully; it is described by– a deterministic component and– a stochastic (randomly varying) component
• The overall link budget is then computed from a desirable BER as
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10 0min
( ) 10log ( ( 1) )r ant
SEIRP G L d X k T F T B
N
min
S S SBER f
N N N
L d L d X
L d
X
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Area mean path loss model example
• The Hata-Okumura model, derives from extensive measurements made by Okumura in 1968 in and around Tokyo between 200 MHz and 2 GHz
• The measurements were approximated in a set of simple median path loss formulae by Hata
• The model has been standardised by the ITU as recommendation ITU-R P.529-2
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Area mean path loss model example
• The model applies to three clutter and terrain categories– Urban area: built-up city or large town with large buildings
and houses with two or more storeys, or larger villages with closely built houses and tall, thickly grown trees
– Suburban area: village or highway scattered with trees and houses, some obstacles being near the mobile, but not very congested
– Open area: open space, no tall trees or buildings in path, plot of land cleared for 300 – 400 m ahead, e.g. farmland, rice fields, open fields
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Area mean path loss model example
where
cities small tomediumfor 8.0log56.17.0log1.1
MHz300 cities, largefor 1.154.1log29.8
MHz300 cities, largefor 97.475.11log2.3
94.40log33.18log78.4
4.528log2
log55.69.44
log82.13log16.2655.69
2
2
2
2
cmc
cm
cm
cc
c
b
bc
fhfE
fhE
fhE
ffD
fC
hB
hfA
urban areas: dB log
suburban areas: dB log
open areas: dB log
L A B R E
L A B R C
L A B R D
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Area mean path loss model example
• The Hata-Okumura model is only valid for:– Carrier frequencies: 150 MHz fc 1500 MHz
– Base station/transmitter heights: 30 m hb 200 m
– Mobile station/receiver heights: 1 m hm 10 m
– Communication range: R > 1 km– A large city is defined as having an average building height
in excess of 15 m
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Local mean model• The departure of the local mean received power from the
area mean prediction is given by a multiplicative factor which is found empirically to be described by a log-normal distribution
• This is the same as an additive deviation in dB from the area mean model being described by a normal distribution
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Local mean model• Working in logarithmic units (decibels, dB), the total path loss is
given by
where Xs is a random variable obeying a lognormal distribution with standard deviation s (again measured in dB)
• If x is measured in linear units (e.g. Volts)
where mx is the mean value of the signal given by the area mean model
L d L d X
2 2dB
dB
1exp 2
2p X X
2dBdB 2
lnlnexp
2
1
xmx
xxp
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Outage calculations
• Cumulative probability density function
• Xmax plays the role of the link margin that you can afford to lose and still maintain an acceptable BER - This is called an outage calculation
max
2 2dB
dB
max
1exp 2
2
11 erfc
2 2
X
P BER Threshold X dX
X
10 0min
max
( ) 10log ( ( 1) )r ant
SX EIRP G L d k T F T B
N
X X
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What next?
• Attempt tutorial questions on link budgets