Presentation on theme: "Link Budgets and Outage Calculations"— Presentation transcript:

Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: E:

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

Why work with Decibels Decibels can be used to express a set of values having a very large dynamic range without losing the fine detail 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 …

Why work with Decibels 1 googol = 1 googol = log = 10 x 100 = 1000 dB dBs are easier to write down!

Why work with Decibels 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

Decibels A power P can be expressed in decibels by
where Pref is the power (unit) to which P is compared

Decibels If for example P = 20 Watts Pref = 1 Watt then P dB = 13 dBW where the W after the dB denotes a reference value of 1 W. If Pref = 1 milliWatt P dB = 43 dBm where the m after the dB refers to a mW.

Decibels The decibel can also be used to refer to the power gain or power loss of a component Pin Pout

Decibels Thus for an amplifier with Pin = 0.1 W Pout = 1 W G dB = 10 dB Similarly if the component is a long cable with Pin = 1 W Pout = 0.1 W then G = –10 dB which represents a loss of 10dB.

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).

Decibels

Decibels Previous chart is useful for converting from numbers to dBs
Examples Pout/Pin =  30 dB = 8 x 102  29 dB =  6 dB =  –10 dB Memorising the chart will help you perform most conversions in your head to an accuracy necessary for estimation purposes.

Cascaded amplifiers What happens if we have two amplifiers in series?
Conclusion – we add gains in dB. Pin Pout Pint G1 G2

Cascaded amplifiers Example Pin = 10 mW, Pint = 1 W, Pout = 100 W So G1 = 1/10x10-3 = 100 = 20 dB G2 = 100/1 = 100 = 20 dB And G = 100/10x10-3 = 10,000 = 40 dB G = G1 + G2 Pin Pout Pint G1 G2

Cascaded attenuators What happens if we have two attenuators in series? Conclusion – losses are negative gains in dB Conclusion – can add losses in dBs. Pin Pout Pint G1 G2

Cascaded attenuators Example Pin = 10 W, Pint = 1 W, Pout = 1 mW So G1 = 1/10 = 0.1 = –10 dB G2 = 10–3/1 = 10–3 = – 30 dB And G = 10–3/10 = 10–4 = – 40 dB G = G1 + G2

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 Pin Pout Pint G1 G2

Pin Pout Pint G1 G2 Example Pin = 1 mW, Pint = 1 W, Pout = 1 mW So G1 = 1/10–3 = 1000 = 30 dB G2 = 10–3/1 = 10–3 = –30 dB And G = 10–3/10–3 = 1 = 0 dB G = G1 + G2

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 Pin Pout Pint G1 G2

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!

Pin Pout P1 G1 L2 L1 P2 P3 P4 amp laser diode detector diode fibre Want a zero gain system, so they can be cascaded to cover long distance Amp to get input signal power big enough to drive diode gain = 20 dB Laser converts digital signal to light conversion gain = –20 dB, (or loss = 20 dB) –20 Fibre 100 km long gives 100 x 0.3 = 30 dB so gain = –30 dB –30 Diode converts light back to digital signal Amp to bring signal back to input level gain = 50 dB Overall gain dB

35,855 km 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?

Transponder Earth station Rx Σ Free space + other losses antenna noise

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

Power at receiver S = EIRP + Gr – Lp – La – Lat – Lar (dBW) (all terms in dBs) Noise at receiver N = 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

Typical link budgets 12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth station up link down link Pt tx power 25 20 dBW Gt tx ant gain 46 44 dB Lat tx ant loss -1 Lp free space loss -208 -206 La atmos loss -0.5 -0.6 Gr rx ant gain Lar rx ant loss Pr rx power -93.5 -100.6 Note – up/down link values different due to different frequencies

Typical link budgets Rain loss mm/hr

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

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

Sample noise calculation for typical satellite earth station at 20 GHz
Source gi xi Li Ti (K) gxTL sky 0.7 0.99 1.0 50 34.6 earth 0.3 300 27.0 sun 0.005 0.01 7000 0.4 sky-earth 0.99.(1.0 – 0.3) 10.4 sun-earth 14.5 Tant 86.9

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 JK–1 B = receiver bandwidth

Typical link budgets up link down link Pr rx power -93.5 -100.6 dBW T noise temp 800 1000 K B bandwidth 36 MHz N noise power -124 -123 S/N at rx 30.5 22.4 dB S/N required 10.0 Mp clear air margin 20.5 12.4 La atmospheric loss in bad storm 10 dB S/N at rx 20.5 12.4 S/N required 10.0 Mp margin 10.5 2.4 Note – down link margin only just acceptable in storm

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

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

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

Area mean path loss model example
where

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

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

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

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

What next? Attempt tutorial questions on link budgets