A.2.2.2 Link Budget Analysis
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A.2.2.2 Link Budget Analysis
In order for our vehicle to effectively communicate with a tracking station, a communications
“link” is established. This link is made between two radio systems: a transmitter on the launch
vehicle and a receiver on the tracking system. It should be noted that the tracking system can be
in the form of a ground station, an aircraft in flight, or a satellite in orbit – the link will be similar
across all of these systems. Within the link, a number of factors are analyzed in a linear format,
each contributing a signal strength component. Each component is calculated in decibels (dB), a
dimensionless unit related to the strength of the signal. By converting signal strengths to
decibels, these components can be added together to form the link budget for the vehicle. The
final result from the link budget is the link margin. The link margin describes the final signal
strength once the signal has completed its full path from the transmitter to the receiver. If this
signal strength falls below 3 dB, the signal is considered to be below half strength, making signal
reception and analysis unreliable. Our design has a final margin of 39.22 dB, well above the
3 dB limit. The process below outlines the methodology for constructing and evaluating a link
budget analysis for one of our launch vehicles.
The first step in establishing a link budget is to select a signal frequency. The frequency plays an
important role throughout the link budget. It is a major part in determining the physical system
design and evaluating items such as space and propagation signal loss. For our vehicles, a base
frequency of 401 MHz was selected, as described in section A.2.2.1 of this report.
Once the signal frequency has been selected, the transmitter power, in Watts, is put into the link
budget. The transmitter power helps establish the initial signal strength and is largely dictated by
the vehicle’s size and power limits. More power will allow for a more powerful signal, but that
power will require a larger battery to support it. This causes an undesirable increase in the mass
of the vehicle.
Author: Justin Rhodes
A.2.2.2 Link Budget Analysis
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The vehicle itself is made up of physical systems that must be manufactured and assembled
together in the final design configuration. These physical systems will always have certain
imperfections inherent in the materials and construction.
In order to account for the
imperfections in the radio system, a line loss factor is added into the link budget for both the
transmitter and receiver. This is an estimated value based on historical data from other radio
communication systems. For our link budgets, an estimate of 1 dB was chosen to represent the
line loss on both the transmitter and receiver.1
The next step in the link budget process is to select the transmitter antenna’s beamwidth. Radio
antennas are essentially pieces of metal that radiate radio waves. The most basic antenna will
emit radio waves of equal strength in every direction. This is inefficient, as a lot of power is
wasted sending waves in directions that are not needed. A more efficient solution is to alter the
construction of the antenna such that the radiation pattern is no longer spherical but is instead a
series of lobes. Most of the signal strength will be focused in the main lobe, and the design will
attempt to minimize the size and strength of the subsequent side lobes. The antenna beamwidth
is a property of the main lobe. This allows for a stronger signal to be sent across a smaller area,
but it uses less power than its omnidirectional equivalent. By knowing the beamwidth, an
approximation of the maximum antenna pointing offset angle is also factored into the link
budget. This approximation allows the analysis to account for errors due to the antenna pointing
in a slightly different direction than intended. Based on other communications systems, we
chose a maximum offset of 27 degrees for our transmitting antenna.1
Knowing the antenna’s beamwidth and the signal frequency, the peak antenna gain for the
transmitter is calculated. The gain value represents the change in the signal radiation pattern
caused by selecting the desired beamwidth. The gain is recorded in decibels for addition in the
link budget and is calculated using Eq. A.2.2.2.1, below.
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A.2.2.2 Link Budget Analysis
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𝐺 = 44.3 − 20log⁡(𝜃)
(A.2.2.2.1)
where G is the peak antenna gain in decibels and 𝜃 is the antenna beamwidth in degrees.
At this point, a feasibility check can be made by calculating the transmitter’s required antenna
diameter. The diameter is directly related to the signal frequency and the antenna beamwidth,
and is calculated from Eq. A.2.2.2.2, below.
𝐷 =⁡𝑓
21
𝐺𝐻𝑧 𝜃
(A.2.2.2.2)
where D is the required diameter in meters, f is the signal frequency in GHz, and 𝜃 is the antenna
beamwidth in degrees. The launch vehicle design constrained the antenna diameter to be within
the diameter of the second stage of the vehicle, but it is assumed that the antenna diameter
calculated is that of a dipole antenna. A dipole antenna is essentially two poles of metal arranged
in a line. We assumed that a more advanced antenna design, one that would have a capacity
equivalent to that of our dipole calculations, could be used instead, but the design of such a
system is beyond the scope of this report.
If the antenna sizing is acceptable, the antenna pointing loss is then calculated. This calculation
represents the loss in signal strength due to the antenna pointing error and the chosen beamwidth,
as shown in Eq. A.2.2.2.3.
𝑒 2
𝐿𝜃 = ⁡ −12 ( )
𝜃
(A.2.2.2.3)
where 𝐿𝜃 is the antenna pointing loss in decibels, e is the antenna pointing offset in degrees, and
𝜃 is the antenna beamwidth in degrees. The net gain of the antenna is then found by adding the
negative pointing loss to the peak antenna gain.
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A.2.2.2 Link Budget Analysis
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The transmitter system and its antenna are now complete. As another feasibility check, the
equivalent isentropic radiated power (EIRP) of the antenna can be found by adding the
transmitter power, the transmitter line loss, and the net antenna gain together. Calculating the
EIRP compares the antenna to the “ideal” antenna which radiates at equal power in every
direction. This also allows for comparison against other communications systems.
In order to reach the desired tracking station, the signal that the transmitter emits must now fly
through space to reach its intended receiver. Space is an unfriendly place for signals, filled with
pesky items such as radiation and an atmosphere filled with water molecules that do their best to
degrade our poor little signals. In order to account for this in our link budget, a space loss value
is calculated using the empirical formula shown in Eq. A.2.2.2.4, below.
𝐿𝑆 = ⁡147.55 − 20 log(𝑆) − ⁡20log⁡(𝑓)
(A.2.2.2.4)
where 𝐿𝑆 is the signal loss due to space, S is the maximum signal path length in meters, and f is
the signal frequency in Hz. A more detailed path length analysis is needed to directly account
for signal refraction and bending through the atmosphere. For the purposes of this analysis, a
maximum path length of 5,000 kilometers was assumed.
In addition to the signal loss due to the signal’s trip through space, there is an additional loss due
to signal propagation and polarization as it travels toward its destination. In our analysis, we
estimated this to be -0.3 dB based off of other communications systems. We feel that this
assumption is reasonable, as the loss is typically low for low frequency signals such as the one
we selected.
As the signal frequency gets above the 20 GHz range, the propagation and
polarization losses can become much more significant.1
If we are following the signal as it progresses through the communications link, it will now
arrive at the tracking station, entering the receiver as it is picked up through the receiving
antenna. The evaluation of the receiving antenna is very similar to that of the transmitting
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A.2.2.2 Link Budget Analysis
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antenna above, but now we are allowed the freedom of choosing the antenna size. This allows us
to balance weaknesses in the transmitter by making a more robust receiver. A large antenna
using more power can make up for a weaker signal strength coming from the vehicle.
By choosing the receiving antenna diameter, its peak gain can be calculated using the empirical
formula given in Eq. A.2.2.2.5, below.
𝐺𝑅 = ⁡ −159.59 + 20 log(𝐷𝑟 ) + 20 log(𝑓) + ⁡10log⁡(𝜂)
(A.2.2.2.5)
where 𝐺𝑅 is the peak receiving antenna gain in decibels, 𝐷𝑅 is the receiving antenna diameter in
meters, f is the signal frequency in Hz, and 𝜂 is the antenna gain towards the satellite. In this
case, 𝜂 is assumed to be 0.55, based on other communications systems.
The receiving antenna beamwidth can be found by solving Eq. A.2.2.2.2 for 𝜃 using the desired
receiving antenna diameter. Likewise, the receiving antenna pointing loss can be calculated
from Eq. A.2.2.2.3, assuming e to be the same as the transmitting antenna. The net gain for the
receiving antenna comes from the peak gain calculated in Eq. A.2.2.2.5 added to the negative
pointing loss, giving us a complete evaluation for the tracking station.
The signal has now travelled from its origin to its destination, but there are still several factors to
be considered before the final margin can be calculated. The system noise temperature is a
property of the atmosphere in which the antennas exist at a certain point in time. The exact
calculation of this property is beyond the scope of this report, and as such an estimate of
135 Kelvin was taken based off of other communications systems.1
One of the key properties of a communications system is how much data it can send across the
link in a set amount of time. Assuming a digital system, this data rate is measured in bits per
second. Our vehicles are designed to be as simple as possible, which allows us to severely limit
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A.2.2.2 Link Budget Analysis
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the required data rate for the communications link. Sources suggest that telemetry and tracking
data can easily be communicated on the order of one thousand bits per second.2 Allowing for
small amounts of additional data and the possibility of multiple streams of telemetry data being
sent, we selected a data rate of 9,600 bps.
𝐸
Having the data rate, the energy per bit to noise power ratio (𝑁𝑏 ) can be calculated. This is a
0
normalized signal to noise ratio that will form the first main component of the final link margin.
The calculation of the ratio is given by Eq. A.2.2.2.6, below.
𝐸
⁡𝑁𝑏 = 𝑃 + 𝐿𝑓 + 𝐺𝑡 + 𝐿𝑝𝑟 + 𝐿𝑠 + 𝐿𝑎 + 𝐺𝑟 + 228.6 − 10 log(𝑇) − 10 log(𝑅)
0
where
𝐸𝑏
𝑁0
(A.2.2.2.6)
is the energy per bit to noise power ratio, P is the transmitter power, Lf is the
transmitter line loss, Gt is the net transmitter gain, Lpr is the receiving antenna pointing loss, Ls is
the loss due to space, La is the propagation and polarization loss, Gr is the net receiver gain, T is
the system noise temperature in degrees Kelvin, and R is the data rate in bps. With the exception
of the system noise temperature and data rate, all values are in units of decibels. From this, the
carrier to noise density ratio can also be calculated for use in further analysis. This ratio comes
from Eq. A.2.2.2.7.
𝐶
𝐸
⁡𝑁 = 𝑁𝑏 + ⁡10 log(𝑅)
0
where
𝐸𝑏
𝑁0
(A.2.2.2.7)
0
𝐸𝑏
is the carrier to noise signal ratio, in decibel-Hertz,
𝑁0
is the energy per bit to noise
power ratio in decibels, and R is the data rate in bits per second.
Using data from other communications systems, the required
𝐸𝑏
𝑁0
value is equal to 9.6 decibels.
𝐸
This is subtracted from the 𝑁𝑏 found above in the final margin. The last piece of the margin to be
0
considered is an additional implementation loss due to imperfections in the system as a whole.
Based on other systems, we allow a loss of 2 dB due to implementation issues. The final margin
𝐸
𝐸
of the system can now be concluded as the 𝑁𝑏 value from Eq. A.2.2.2.6 minus the required 𝑁𝑏 and
0
Author: Justin Rhodes
0
A.2.2.2 Link Budget Analysis
the implementation loss.
7
The link budget listed in Table A.2.2.2.1, below, follows this
procedure.
Table A.2.2.2.1 Vehicle Link Budget Analysis
Item
frequency
transmitter power
transmitter line loss
antenna gain towards vehicle
transmit antenna beamwidth
peak transmit antenna gain
transmit antenna diameter
transmit antenna pointing offset
transmit antenna pointing loss
transmit antenna gain (net)
equiv isotropic radiated power
propagation path length
space loss
propagation & polarization loss
receive antenna diameter
peak receive antenna gain (net)
receive antenna beamwidth
receive antenna pointing error
receive antenna pointing loss
receive antenna gain
system noise temp
data rate
Eb/No
carrier to noise density ratio
bit error rate
required Eb/No
implementation loss
final margin
Symbol
f
P
Lf
η
θt
Gpt
Dt
et
Lpt
Gt
EIRP
S
Ls
La
Dr
Grp
θr
er
Lpr
Gr
Ts
R
Eb/No
C/No
eb
(Eb/No)required
Value
401
5
-1
0.55
60
8.74
0.87
27
-2.43
6.31
12.30
5,000
-158.49
-0.30
10
29.88
5.24
0.20
-0.02
29.86
135
9,600
50.82
90.64
1x10-5
9.60
-2
39.22
Units
MHz
Watts
dB-W
dB
degrees
dB-i
m
degrees
dB
dB-i
dB-W
km
dB
dB
m
dB-i
deg
deg
dB
dB-i
K
bps
dB
dB-Hz
bps
dB
dB
dB
The link budget analysis above represents the final link budget for our launch vehicles. Each
vehicle will be carrying the same avionics package onboard, thus only one link budget is
required. The final margin of 39.22 dB is well above the absolute minimum of 3 dB required.
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A.2.2.2 Link Budget Analysis
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We feel this will allow the vehicle to survive a large margin of error potentially caused by using
cheaper components and less professional design methods.
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A.2.2.2 Link Budget Analysis
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References
1. Filmer, David. “Link Budget Analysis,” AAE 450 Lecture, Department of Aeronautical and
Astronautical Engineering, Purdue University. 23 January, 2008.
2. Wertz, James R., and Wiley J. Larson, eds. Space Mission Analysis and Design, 3rd ed.,
Torrance, Kluwer Academic and Microcosm Press, 1999.
Author: Justin Rhodes