A.2.2.3 Link Budget Analysis

A.2.2.3 Link Budget Analysis 1

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.2.2.2 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.2.2.3 Link Budget Analysis 2

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.2.2.3.1, below.

(A.2.2.3.1) where G is the peak antenna gain in decibels and 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.2.2.3.2, below.

(A.2.2.3.2) where D is the required diameter in meters, f is the signal frequency in GHz, and 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.2.2.3.3.

(A.2.2.3.3) where is the antenna pointing loss in decibels, e is the antenna pointing offset in degrees, and

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.

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.2.2.3.4, below.

(A.2.2.3.4) where 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

Author: Justin Rhodes A.2.2.3 Link Budget Analysis 5 antenna. The evaluation of the receiving antenna is very similar to that of the transmitting 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.2.2.3.5, below.

(A.2.2.3.5) where is the peak receiving antenna gain in decibels, is the receiving antenna diameter in meters, f is the signal frequency in Hz, and is the antenna gain towards the satellite. In this case, is assumed to be 0.55, based on other communications systems.

The receiving antenna beamwidth can be found by solving Eq. A.2.2.3.2 for using the desired receiving antenna diameter. Likewise, the receiving antenna pointing loss can be calculated from Eq. A.2.2.3.3, 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.2.2.3.5 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

Author: Justin Rhodes A.2.2.3 Link Budget Analysis 6 second. Our vehicles are designed to be as simple as possible, which allows us to severely limit 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.

Having the data rate, the energy per bit to noise power ratio ( ) can be calculated. This is a 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.2.2.3.6, below.

(A.2.2.3.6)

where is the energy per bit to noise power ratio, P is the transmitter power, L f 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.2.2.3.7.

(A.2.2.3.7) where is the carrier to noise signal ratio, in decibel-Hertz, 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 value is equal to 9.6 decibels.

This is subtracted from the found above in the final margin. The last piece of the margin to be 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

Author: Justin Rhodes A.2.2.3 Link Budget Analysis 7 of the system can now be concluded as the value from Eq. A.2.2.3.6 minus the required and the implementation loss. The link budget listed in Table A.2.2.3.1, below, follows this procedure.

Table A.2.2.3.1 Vehicle Link Budget Analysis

Item Symbol Value Units frequency f 401 MHz transmitter power P 5 Watts

transmitter line loss Lf -1 dB-W antenna gain towards vehicle η 0.55 dB

transmit antenna beamwidth θt 60 degrees

peak transmit antenna gain Gpt 8.74 dB-i

transmit antenna diameter Dt 0.87 m

transmit antenna pointing offset et 27 degrees

transmit antenna pointing loss Lpt -2.43 dB

transmit antenna gain (net) Gt 6.31 dB-i equiv isotropic radiated power EIRP 12.30 dB-W propagation path length S 5,000 km

space loss Ls -158.49 dB

propagation & polarization loss La -0.30 dB

receive antenna diameter Dr 10 m

peak receive antenna gain (net) Grp 29.88 dB-i

receive antenna beamwidth θr 5.24 deg

receive antenna pointing error er 0.20 deg

receive antenna pointing loss Lpr -0.02 dB

receive antenna gain Gr 29.86 dB-i

system noise temp Ts 135 K data rate R 9,600 bps

Eb/No Eb/No 50.82 dB

carrier to noise density ratio C/No 90.64 dB-Hz -5 bit error rate eb 1x10 bps

required Eb/No (Eb/No)required 9.60 dB implementation loss -2 dB final margin 39.22 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.

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.

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