Link Budget Study Notes
Study Notes for Link Budget Workshop
by Dan Glover 1 and Bill Cowley 2
Goals:
The Link Budget Workshop, provides background information, software tools and typical examples
to allow students to gain a working knowledge of satellite link design fundamentals. This an
introductory workshop designed for students with little technical background.
Key Concepts:
The “Link Budget”
A communications “link” refers to the transmission of a signal from a transmitter and its reception
by a receiver. When the transmitter is located in a ground station and the receiver is on a satellite,
the link is referred to as an “uplink.” When the transmitter is on the satellite and the receiver is on
the ground, the link is referred to as a “downlink.” We will consider these two links (uplink and
downlink) separately.
In summary, the ability to communicate depends on the strength of the signal and the amount of
thermal noise that makes its way into the system. An accounting of signal strength and noise is an
important part of system design and is known as a “link budget.” In this budget, the effective
transmit power is calculated, losses are subtracted, noise is accounted for, and a link margin is
determined which determines whether the link will work properly or not. The margin should be
positive; if this isn’t the case it’s usually possible to adjust some of the parameters until the margin
becomes slightly positive.
These notes are set out as follows. First we review the basic units used for link budgets. Then we
briefly discuss each of the main components of the link budget, defining terms where required but
without full technical details. Finally we discuss the calculation of the link margin and give some
brief examples. More examples can be loaded into the java LinkBudget 3 software
Decibels
Communications engineers work in units called decibels, abbreviated dB. The decibel equivalent
for a power ratio (N1/N2) is defined as
R(dB) = 10 log10 (N1/N2)
For example, because log10 2 = 0.30103, a ratio of 2/1 is expressed in dB as 10 log10 2 ≈ 3 dB.
A ratio expressed in decibels (dB) has logarithmic properties. Multiplying ratios is the same as
adding decibels while dividing ratios is the same as subtracting decibels. This makes decibels
useful for dealing with multiple multiplications and divisions (as found in link budgets).
1
Dan Glover, Nasa Glenn Research Centre
2
Bill Cowley, University of South Australia, Bill.Cowley@unisa.edu.au
3
see http://www.itr.unisa.edu.au/rd/asp/software
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Another useful property of decibels is that they can easily handle a large range of values. For
powers of ten, the decibel value is the number of zeros in the ratio followed by a zero. Thus a ratio
of 1 000 000 to 1 is 60dB. Often the ratio has an associated unit, which is carried through to the
dB value. For example, 100 Watts of power (100W) maybe expressed relative to 1W, giving a
power of 10 log10 (100/1) or 20dBW.
We now consider various components of the link budget, before combining all terms into one
overall result.
Antenna Gain
Antenna gain is a measure of the focusing ability of a given antenna. The maximum gain is in the
direction of maximum radiation, the electromagnetic axis of the antenna called boresight:
G = η (π D / λ)2
Where: D is diameter of an antenna with a circular aperture,
η is the antenna efficiency, often around 0.5
λ = wavelength = c / f
c is the velocity of light, 3 x 108 m/s,
f is the frequency of the wave (in Hz)
An isotropic antenna has the same radiated power in any direction. Simple mobile terminals have
almost isotropic antennas with ~ 0 dBi gain. Antenna gain (in dBi) is measured relative to an
isotropic radiator. For example, LEO satellites often use an antenna pattern covering one
hemisphere below them with gain ~3dBi gain.
Notice in the formula above that the gain is proportional to the antenna area and to the square of
the frequency. Large parabolic antennas used in some satellite links can therefore have gains of
many tens of dBs. The gain of an antenna is inversely proportional to the width of the antenna
beam (its beamwidth). The penalty of high gain antennas is that their beamwidth is small and so
accurate antenna pointing is needed.
GEO satellites use antennas of various beamwidths to cover the required portion of the earth. For
example from GEO, a global beam uses a beamwidth of about 170 whereas a spot beam of 1000
km diameter requires a beamwidth of slightly over 10
E.I.R.P.
The overall effectiveness of the transmitter depends on its power and antenna gain. The so-called
equivalent isotropic radiated power, EIRP, of a transmitter is the product of the transmitted power
and the antenna gain. This is the equivalent power that would be transmitted through an ideal
isotropic antenna to produce the same amount of power at the receiver as the actual transmitter.
In dBs:
[EIRP] = [Ptx] + [Gtx]
Ptx=transmit power in dBW.
Gtx=antenna gain, in dBi.
Noise
Noise is accounted for in terms of an equivalent temperature of a black body that would radiate the
same amount of noise over the relevant frequency range. This is known as the noise temperature.
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The source of most natural noise is thermal. A satellite antenna looking at the Earth would see
noise from thermal sources as well as man-made noise. The noise temperature of the Earth
averages 254K. For an Earth Station antenna looking into cold space the noise temperature is
much lower. Other sources of noise include the Sun, Jupiter, cosmic and galactic noise, and the
atmosphere.
G/T
Just as EIRP is a handy way to characterize a transmitter/antenna combination, it is nice to have a
way to characterize receiver/antenna combinations. At the receiver, when we know the antenna
gain and the system noise temperature it’s useful to form a single figure of merit, called G/T. The
G/T of a receiver is the ratio of the gain of the antenna at the receiving frequency to the equivalent
noise temperature of the station . In logarithmic units
[G/T] =[Grx] - [Ts]
where [Grx] is the receive antenna gain in dBi and [Ts] is the system noise temperature in dBs
relative to 1 degree Kelvin. The system noise temperature depends where the antenna is pointing
(see above) and also the quality (and temperature) of the receiver electronics. For example, a
ground station’s G/T may be from 20 to 40 dB/K; mobile terminals will be much lower (e.g., –25
dB/K). The G/T of a satellite receiver is usually between -25 dB/K and 5 dB/K due to a smaller
antenna and simpler input amplifiers (therefore higher noise temperature).
Losses
The total loss in the budget is made up of many terms, eg :
[LOSSES] = [FSL] + [AA] + [TFL] + …
Including:
FSL = free-space spreading loss, dB (by far the biggest!)
AA = atmospheric absorption loss, dB
TFL/ RFL = transmitter/receiver feeder loss, dB
AML = antenna misalignment (depointing) loss, dB
PL = polarisation mismatch loss, dB
IL = modem Implementation Loss due to imperfections
The free space loss (FSL) depends on the distance and the frequency. For example, a
geostationary satellite has an altitude of R = 35786 km above earth.
FSL = (4 π R / λ)2
Frequency (GHz)
FSL(R0) (dB)
1
183
5
197
10
203
20
209
Note from this equation that the FSL is proportional to the square of the frequency and to the
square of the link distance.
Link Budget Equation
We will now try to combine all these terms. The numerical relation between the quantities
mentioned above is vitally important to the design of satellite communications systems. This
equation is called the “link budget” and applies to all communications links. Conceptually the key
relationship is quite simple:
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Transmit Power x Antenna Gains
Received Signal Power =
Link Losses
Or Received Power (dB) = Transmit Power (dB) + Antenna Gains (dB) – Link Losses (dB)
with L representing all the link losses, we therefore have
Prx (dBW) = Ptx(dBW) + Gtx(dBi) + Grx(dBi) – L (dB)
By taking the ratio of the received (signal) power to the noise power density (ie the noise power
per Hertz of bandwidth), the equation above can then be used to determine the link performance
(e.g., the BER for a given data rate with a certain type of modulation and coding). This happens
as follows:
In a digital system with information bit rate of rb bit/s, the received energy per info bit is equal to the
received energy per second divided by the number of bits per second, or Eb = Prx / rb
Now since N0 ( noise power per Hz) = kTs, where k is Boltzmann’s constant 1.38 x 10-23 and Ts is
the system noise temperature in Kelvin, then by combining all our partial results,
or
Eb / N0 = Ptx (dBW) + Gtx (dBi) + Grx (dBi) – L (dB) – 10 log rb – 10 log k – 10 log Ts
Eb / N0 = EIRP (dBW) + G/T (dB/deg K) – L (dB) – 10 log rb – 10 log k
For each particular type of modulation and coding a given value of Eb / N0 results in a known bit
error rate (BER). The Eb / N0 may therefore be considered like a “signal to noise” ratio for a
digital communications system.
Margin
This equation above allows a relatively simple evaluation of the actual value of Eb / N0, typically by
a spreadsheet. The actual value may be compared to the required value of Eb / N0 to achieve a
certain BER. The difference between these two quantities is called the link margin.
For example, in Binary Phase Shift Keyed (BPSK) systems without coding, if Eb / N0 is 10 dB then
the BER is 4e-6 (ie 4 bits in error per million bits). Suppose the (worst case) target BER for our link
is 4e-6. Then the (minimum) required Eb / N0 is 10dB. If the actual Eb / N0 is more than 10dB our
BER will be less that the specified limit. In this case the “link margin” is positive and the customer
will be satisfied.
On the other hand, if say the right hand side of the equation about evaluates to only 7dB, then we
have a link margin of -3 dB. The BER will be too high (~8e-4 in this case) and the customer will
require the performance to be improved. This might be achieved by adjusting one of the link
parameters, say increasing the transmit power by 3dB (eg from 10W to 20W)
Once the basic link budget parameters are understood the system designer may readily evaluate
overall performance and trade off different parameters to ensure the link will operate as required.
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