Appendix B - Communications

B Communications Nomenclature BER = bit error rate [bits/bit] R = receiving antenna efficiency [-]  = transmitting antenna efficiency [-] DR = receiving antenna diameter [m] DT = transmitting antenna diameter [m] d = distance of link [km] EIRP = effective isentropic radiated power [dBW] f = transmission frequency [GHz] GR = receiving antenna gain [dBi] GT = transmitting antenna gain [dBi] G/T = antenna Fig. of merit [dBi/K] k = Boltzmann’s constant [-228.6 dBW / K-Hz] Latm = atmospheric loss [dB] Lfs = free space loss [dB] M = link margin [dB] PT = transmission power [W] RD = data rate [bps] T = noise temperature [K] SNRavail = available signal-to-noise ratio [dB]  = half wavelength r = ratio of half wavelength to conductor diameter k = multiplying factor hantenna = height of antenna

B.1 Frequency Selection Appendix – Ben Toleman The selection of the frequencies used in the communications systems is based on analyzing the different characteristics of frequencies. These include the availability of the frequency, bandwidth that it can carry, power needed to transmit on that specific frequency, and Table B.1 Atmospheric Losses atmospheric losses. We Attenuation Loss determined the Rain Attenuation (heavy down pour) 20 db availability of a Gaseous Absorptions (H2O, O2) 1 db Cloud Attenuation (Average) 1 db frequency by how much Safety Factor* 3 db traffic is currently * Scintillation, Depolarization, Atmospheric Noise, Wet Antenna operating on that frequency and the purpose of allocation set by the National Telecommunications and Information Administration AAE 450 Senior Spacecraft Design Spring 2004 83 Appendix B - Communications

(NTIA)1. Bandwidth that a frequency can carry is based on the spectrum in which it is operating on. In general, the higher in the spectrum the frequency exists, the more bandwidth it can carry. The power needed to transmit on a frequency is based on the distance between two points, the sizes of the transmitting and receiving dishes, the atmospheric losses, and other variables, which Brian Ventre discusses in Appendix B. The last criterion is atmospheric loss. This property can only be measured by tests. The basic results that we found for the Ka-band are displayed in Table B.12. Using the criteria above, we searched through all of the bands that are currently available. The lack of availability and that they can carry only low bandwidth, made S, C, and Ku bands unsuitable for our purposes. This left three main choices: X, Ka, and W bands. We determined that W-band was not fitting, because the atmospheric losses associated with this band would cause too many problems when transmitting. We are left with X – band and Ka – band, the only difference of which is that Ka – band had higher atmospheric losses, compared to the X – band. This means that X-band can be used, except when we did calculations for the communication link between Earth and the Transport Module, the diameter of the antenna on the Transport Module would be 38 meters, with a power consumption of 10 kW (Refer to Appendix B by Brain Ventre ). This left only one selection, which is the Ka-band. This reasoning also became evident when calculating the communication link between the Rover and Transport Module, so Ka-band was chosen for this link also. The reason that Ultra High Frequency is used for the communication link between the Rover and the Lander comes from the fact that the antennas on these two vehicles are omni-directional and the distance that the signal needs to travel is very small.

B.2 Communication Failure Modes Appendix – Ben Toleman Each failure mode determined the probabilistic method used. The servo is just a basic electric motor that moves the communication antenna around so that the antenna is pointing toward its target. To determine the probability of it failing we looked at the historical data of how many hours one of these motors could run, which was 8,000 – 10,000 hrs. From this we made a conservative assumption that it runs non-stop for its entire lifespan of 10,000 hrs. The micrometeorite failure mode is determined by a series of steps. The first step is to decide on the size of micrometeorite that we wish to protect the critical components against. The second step is to determine the area of the vital components that would cause the communication

AAE 450 Senior Spacecraft Design Spring 2004 84 Appendix B - Communications system to completely fail. This area is based on the size of the critical parts that would cause total failure of communication system, which would be the servo and the transmitter. Once determined a code written by Robert Manning to calculate the probability of a micrometeorite hitting one of these critical areas (Refer to Appendix I for Robert Manning’s code) would be used. The hardware failure mode was done by first determining the failure rates of all of the components that would be used in the system; these components include the antenna, signal processor, switches, cables, controllers, and other equipment. With the failure rates we used Eq. B–1, which is the equation for reliability.

R(t)  e t B–1

Then we placed the components in a configuration, which showed the relations of the components to each other and where they were placed. The components placed in a series shows their dependency to each other and the components in parallel show the redundant subsystems. The configuration used for the communication hardware is displayed in

AAE 450 Senior Spacecraft Design Spring 2004 85 Appendix B - Communications

Fig. B.1 Communication Hardware Config. Adapted from http://www.ece.cmu.edu/~koopman/depend/ahsstudy/tr_97_44.pdf

g. B.1. Using the code written by Benjamin Toleman we determined the reliability of the communications system and in turn the failure probability. The probability of failure of the system over 2.5 years with a redundant system is shown in Fig. B.2. This Fig. shows the probability of failure as time progresses. This means that if nothing breaks in 1 year then there is a probability of about 18 % that something will break, but three facts need to be addressed. One, none of these failures are life threaten. Two, all of the components are fixable on the ship. Three, once something breaks the probability of failure will shift down, lowering the probability of the next failure. The same principle applies if something is fixed also, with the probability of failure shifting down.

Fig. B.2 Failure Probability vs. Time

B.3 Link Budget – Brian Ventre In order to design any communications link, we must produce a link budget. This budget accounts for all variables involved in a link and indicates if the variables chosen are capable of producing a viable communications path. It is based on a variety of factors, including distance, antenna sizes, frequency, temperature and power. The method to produce a link budget is valid for all wireless communications links, and each link requires a link budget. Below are detailed instructions on the implementation of a link budget, particularly as it applies to the design of our spacecraft, but also generally toward the calculation of any other link budget. The end goal of the method presented here is to solve for one of two variables: either the transmission power or the transmitting antenna diameter. These two were picked because of their central roles in our design. Aboard the spacecraft, power, volume, and mass available are finite and must be optimized in the design process. The size and power required for the communications system then become of paramount importance.

While other sources exist upon which to base the calculation of a link budget, the following was adapted from Comparetto.3 Many publications rely on the calculation of a positive link margin were all other values are chosen prior to beginning design, which results in a trial-and-error process. We optimize the equations here to generate one of the two parameters discussed above, and these equations then serve as the basis for the design of our mission. Finally, the entire implementation of the link budget is based around functions and encapsulation. We encourage the reader to understand the purpose of each calculation as it applies to the entire process and its integration within the link budget to gain a better understanding of the mechanics of communications. Each function was designed to both stand alone and form a portion of the whole; the Matlab scripts which we wrote for the calculations are shown in Section B.10.2.

B.3.1 Decibels Before we discuss the link budget, it is beneficial to investigate a unit which is very common in communications—the decibel. Decibels are an operation we can perform on units that converts variables into logarithmic forms. The use of logarithms allows for simple addition and subtraction operations instead of complicated multiplication and division. An example of this is shown with a generic variable x below, in Eq. B–2. The factor Y depends on the units of x, and is 20 for most cases, although this depends on the power to which x is raised and its physical interpretation. We avoid relying on decibels for most quantities in this document, instead showing the direct conversion from base units into decibels within the equations. Also, note that the addition or subtraction of values in decibels is equivalent to multiplication and division, so the cancellation of units—such as dB-K or dB-W—is dissimilar to standard arithmetic.

xdB = Ylog10 ( x) B–2

B.3.2 Determination of Initial Conditions A number of the variables involved in the link budget calculations must be determined prior to beginning the process. Many of these are products of engineering judgment and past history, which are presented below for familiarization.

B.3.2.1 Data Rate – RD The determination of the data rate for a link is dependent on the information traveling through that link. See section 3.9.3 for a discussion of the data rates chosen for our spacecraft. In the equations below, data rate is accounted for in bits per second (bps).

B.3.2.2 Bit Error Rate – BER The bit error rate indicates the probability of a bit—one binary piece of information— being received incorrectly. Measured in bits per bit, historical trends place the probability at 5 to 10 x 10-6 bits per bit. For all links in this design, we set an aggressive value of 5 x 10-6 bits per bit.

B.3.2.3 Antenna Efficiencies –  Antenna efficiency is a measure of the effectiveness of an antenna at either converting received power into a useful signal or at converting supplied power into an electromagnetic signal. Most parabolic dish antennas operate at roughly 0.55 efficiency, but those with high quality control and careful tuning—such as those used in the Deep Space Network—can achieve efficiencies of 0.72. In this design, the transmission efficiency of all antennas was set at 0.65, while reception efficiency was chosen at 0.72.

B.3.2.4 Noise Temperature – T The noise temperature indicates the amount of random thermodynamic motion of electrons which contributes to signal degradation. It is measured in absolute degrees Kelvin and is usually near 400 K for a well-cooled space-based antenna, and 100 to 200 K for ground-based antennas.

B.3.2.5 Distance – d The transmission distance of a signal has the greatest effect on the required power. For the Transport Vehicle to Earth link, a distance of 3.74 x 108 km was chosen as the maximum distance between the orbits of Mars and Earth.

B.3.2.6 Atmospheric Loss – Latm When an electromagnetic signal passes through an atmosphere, it undergoes scattering and damping. These effects weaken the signal and make it more difficult to establish a secure link. The amount of loss depends on the frequency of the link, and is found through historical

AAE 450 Senior Spacecraft Design Spring 2004 89 Appendix B - Communications data. For the Ka-band link of our spacecraft, passing only through the Earth’s atmosphere, the loss was calculated at 6 decibels.

B.3.2.7 Frequency – f The frequency of the link is a representation of the oscillation speed of the electromagnetic signal. See Section B.1 for a discussion of frequency and the choices made for this design.

B.3.2.8 Link Margin – M Link margin is included in the calculation of a link budget to allow for small perturbations in the conditions of any section of the link, while still retaining a positive lock on the signal. These include higher-than-expected atmospheric losses, insufficient antenna efficiencies, and power underflows. Values between 2 and 4 decibels are traditional, with the higher values offering a more robust design. In the design of our mission’s communications system, 2 dB was chosen to minimize antenna size and power.

B.3.2.9 Receiving Antenna Diameter – DR The diameter of the receiving antenna must be chosen large enough to adequately “listen” to the signal, but small enough to be manageable in its installed location. For a ground-based antenna, 40-meters is the advisable limit to dish antenna size. The Deep Space Network operates a number of antennas at this size, in addition to a large 72-meter diameter antenna that is not maneuverable and is built into the ground. However, for this design, the smaller size proves sufficient and more cost-efficient. Onboard a spacecraft, available volume and mass will dictate the antenna’s size. We advise calculation of the space-borne transmitting antenna’s diameter first, as this antenna may be reused for both reception and transmission. The primary communications antenna on the Transport Vehicle is approximately 9.5-meters in diameter, while the corresponding antenna on Earth is 40-meters in diameter. The antenna used for communication with the rover is 2-meters in diameter and the rover’s high gain antenna is 0.35 meters.

B.3.2.10 Transmission Parameter – PT or DT

Finally, either the transmission power (PT) or the transmission antenna diameter (DT) must be chosen. Choosing one of these, the other can be calculated. Transmission power is

AAE 450 Senior Spacecraft Design Spring 2004 90 Appendix B - Communications generally restricted by the available power aboard the spacecraft, while those antennas on the ground are not similarly affected. The diameter, as noted above, is dependent on space available and the feasibility of moving the antenna. In designing the primary communications system, 10 kW of power was allocated for ship-board transmission, while a transmitting/receiving antenna diameter of 40-meters was chosen for the ground antenna. When we perform the rover calculations, we choose the maximum antenna size to be 2-meters aboard the Transport Vehicle.

B.3.3 Calculation of the Link Budget

B.3.3.1 Available signal-to-noise ratio – SNRavail The first step in the calculation of the link budget is to compute the available signal-to- noise ratio (SNR). This value is an indicator of the power of the signal above the noise level that must remain at the end of the transmission path. It is found by converting the bit error rate into a signal-to-noise ratio and then adding the link margin (Eq. B–3). The particular function used to calculate a SNR from the BER is based on binary-phase-shift-keying, an encoding scheme where 0 and 1 are represented by 180o shifts in the electromagnetic signal. Using a different keying system may decrease the SNRavail required to establish a link. The lower the SNRavail, the less clear the signal can be against background noise and still be detected. The units of each of the quantities in all equations are indicated in the Nomenclature section, and should be referred to in order to ensure accurate calculations.

2 B–3 SNRavail =( erfcinv(2 BER)) + M

B.3.3.2 Receiving antenna gain – GR Our next step is to calculate the gain of the receiving antenna. The gain of an antenna refers to its ability to concentrate on one portion of the sphere surrounding it. An isentropic antenna is one that broadcasts and receives equally from all points surrounding it. The gain, given in decibels-isentropic (dBi), shows how focused an antenna is on a specific arc. A high gain antenna has the benefit of being able to detect weak signals or concentrate all of its power on a specific location, but requires accurate pointing mechanisms. Conversely, a low gain antenna wastes much of its power by broadcasting in directions other than its intended receiver, but does not require a precise alignment. Note that a half-dipole antenna, similar to a car antenna, does not require a gain calculation, but is known to have a 2.1 dBi gain.

The gain of the receiving antenna is a function of a constant, the receiving efficiency, the frequency of the link, and the diameter (Eq. B–4). The constant, 20.4, is dependent on the units of the other three variables and is specific to frequency in gigahertz and diameter in meters.

GR=20.4 + 10log10h R + 20log 10 f + 20log 10 D R B–4

B.3.3.3 Free space loss – Lfs The dispersion of the electromagnetic signal as it travels through space is known as the free space loss. It is a function of a constant, the frequency—in GHz—and distance—in km (Eq. B–5). The inclusion of the frequency term shows that higher frequencies suffer from greater free space loss and are thus less desirable. However, these losses may be offset by the benefits of lower atmospheric loss or higher possible data rates, as well as spectrum crowding. Again, the constant, 92.45, is dependent on the units of frequency (GHz) and distance (km).

Lfs =92.45 + 20log10 f + 20log 10 d B–5

B.3.3.4 Fig. of merit – G/T Next, we calculate the Fig. of merit for the receiving antenna. This term is a measure of the ability of an antenna to detect signals from another antenna, and is a function of the receiving antenna’s noise temperature and the receiving antenna’s gain (Eq. B–6).

G/ T= GR - 10log10 T B–6

B.3.3.5 Effective isentropic radiated power – EIRP The effective isentropic radiated power, EIRP, is a measure of the apparent power transmitted if the antenna were isentropic. It is a function of the available signal-to-noise ratio, the Fig. of merit, free space loss, atmospheric loss, Boltzmann’s constant, and data rate (Eq. B– 7). In a different form, Eq. B–8, the property of EIRP as the sum of the transmitting antenna gain and the transmission power may be observed.

EIRP= SNRavail - G/ T + L fs + L atm + k + 10log10 R D B–7

B.3.3.6 Transmitting antenna gain – GT The gain of the transmitting antenna that is required to achieve the link budget can now be calculated by subtracting the transmitted power from the EIRP (Eq. B–8).

GT= EIRP -10log10 P T B–8

B.3.3.7 Transmitting antenna diameter – DT Finally, the diameter of the transmitting antenna can be determined by rearranging Eq. B–4. This leads to Eq. B–9 and the conclusion of the link budget.

GT-20.4 - 10log10h T - 20log 10 f B–9 20 DT =10

B.3.3.8 Solving for transmission power – PT If the diameter of the transmitting antenna is known, and the transmission power is desired, the procedure is somewhat different. Eq. B–3 to B–7 remain the same, but a new approach is needed to complete the calculations. First, the gain of the transmitting antenna is calculated from Eq. B–10.

GT=20.4 + 10log10h T + 20log 10 f + 20log 10 D T B–10 The transmission power can now be found by rearranging Eq. B–8 into Eq. B–11.

EIRP- GT B–11 10 PT =10 By following the above procedures, we solve for each of the communications links in order to generate the necessary information for design of the mission.

B.3.4 Sample Link Budget Table B.2, below, contains the variables determined prior to calculating the Transport Vehicle-to-Earth link. Table B.3summarizes the intermediate and final results of the link budget for demonstration purposes.

Table B.2 – Transport Vehicle-to-Earth Link Budget Parameters Link property Symbol Value

Data rate RD 100 Mbps Bit error rate BER 5 x 10-6 bits/bit Receiving antenna efficiency R 0.72 Receiving antenna efficiency T 0.65 Noise temperature T 400 K Distance d 3.74 x 10-8 km

Atmospheric loss Latm 6 dB Frequency f 31.8 GHz Link margin M 2 dB Receiving antenna diameter DR 40 m Transmission power PT 10,000 W

Table B.3 – Transport Vehicle-to-Earth Link Budget Results Link property Symbol Value

Available signal-to-noise ratio SNRavail 11.8 dB Receiving antenna gain GR 81.1 dBi Free space loss Lfs 294.0 dB Fig. of merit G/T 55.0 dBi/K Effective isentropic radiated EIRP 108.1 dBW power Transmitting antenna gain GT 68.1 dBi Transmitting antenna diameter DT 9.5 m

B.4 Antenna Selection — David Goedtel To start the process of figuring out what our communication system is, we have to determine which type(s) of antennas we must use. Once the communication network was laid out, as seen in Fig. B.6, we were able to determine the ideal antennas for the mission. Fig. B.3 Blueprint of the design of the First, we researched the different types of communication network. antennas available currently in great detail, analyzing efficiency, frequency, scale distance, power consumption, size, weight, and signal cleanliness. Upon searching through Spacecraft Systems Engineering,4 we were able to reduce our options down to three major types of antennas, based on the aforementioned factors. We determined that these types, described below, would fit our communications needs.

The first and most important component of the communications system is the reflector antenna. This antenna has more benefits than drawbacks, and allows for communication over the large distances that our mission achieves. Fig. B.45 is a picture of a general reflector antenna, which is the most common antenna form. Its parabolic shape allows for the aiming of a strong communication beam in a desired direction with minimal space loss. Also, the shape of the parabolic antenna can be “appropriately formed” to create a desired beam in strength.1 Fig. B.4 General reflector Along with the large distance capabilities, this type of antenna. antenna does not have any limits concerning frequencies of the beam. This allows us to send any form of communication through the antenna we desire, and also allows us freedom in choosing data rate and bandwidth (discussed in Section X.X.X). However, this antenna type requires large support structure, meaning large size and heavy weight. Also, the power consumption to run this antenna type, especially for long distances, is very high. But, we decided that the benefits outweigh the drawbacks. So, we designed our communication system to use a reflector antenna in communication with the Earth (see Section 4.9.4 for further discussion about the Earth communication system, which is comprised of reflector antennas). Also, we employ a reflector antenna to communicate directly to the Rover (see Section B.7) and also for an additional antenna, which remains stowed as a Fig. B.5 backup. General omni- Another antenna type that our communication system makes use of is directional antenna. the omni-directional antenna (half-dipole). This antenna is similar to that of a car antenna. Fig. B.5 gives the general shape of an omni-directional antenna. This antenna type is extremely simple in structure and very lightweight. Also, the power consumption is very low, which is beneficial to the operation of our design. The signal from this antenna type radiates outward in all directions. The strength of this broadcast— low gain—diminishes quickly over distance. Also, this type of antenna collects static and noise

AAE 450 Senior Spacecraft Design Spring 2004 95 Appendix B - Communications from its surrounding environment, whether in atmosphere or space. Another note is that this antenna operates very efficiently, but is limited to low frequencies. Most notably, the omni- directional antenna is the best choice for Rover-Lander communications. The third type of antenna that our design considered was the horn antenna. Although we do not use this type of antenna in our design, this type did get the same amount of attention as the other two antennas. A general picture of a horn antenna is in Fig. B.6, where the horn antenna can be circular or rectangular. The shape of the horn antenna does not matter other than if it needs to be form-fitted into a mounting bracket, considering other components surrounding it. Similar to the reflector antenna, the horn antenna requires directional aiming of the beam. However, as opposed to the reflector antenna, this antenna uses a reasonable consumption Fig. B.6 General rectangular horn antenna. of power, has small structure, and is light in weight. The horn antenna can only handle high frequencies. The range of the horn antenna is larger than the omni-directional antenna, but much shorter than the reflector antenna. This antenna type was considered for communicating directly to the Rover from the Transport Module, until we realized that the link required a low frequency (see Section B.1).

B.5 UHF Antenna Sizing – Leigh Janes We designed the UHF antennas for the rover and lander to be dipole, half wavelength antennas. Knowing the frequency on which the antenna will be operating allows for the antennas to be sized using Eq. B–12 and Eq. B–13.

492   B–12 f (MHz)

( *12)  r B–13 0.5

Now that we know the ratio of half wavelength to conductor diameter, r, we find the multiplicity factor, k, from the graph in Fig. B.76. Using the graph in Fig. B.7, k of the rover antenna and the lander antenna are found to be approximately 0.95. The height of the antenna is calculated by applying the multiplicity factor to Eq. B–14.

(492* k) B–14   *0.3048  hantenna  f (MHz)  Fig. B.7 Mulitplicity Factor, K, Plot Schetgen, KU7G, Robert, The AARL Handbook for Radio We selected a UHF Amateurs 1993, ed. 70, 1993, p.17-3. frequency for communication between the Mars Rover and the Mars Lander because the distance over which the radio signals must travel is much less than when the Rover communicates with the Transport Module. Also, the link can operate on a lower data rate because real time video is not being transmitted. A shorter distance and lower data rate allows for the use of a lower frequency. We modified the link budget code in order to produce a link budget for the UHF antennas. The code no longer solves for an antenna diameter because the UHF antenna are omni directional

AAE 450 Senior Spacecraft Design Spring 2004 Fig. B.8 Data Rate vs. Transmitting Power97 for Rover to Lander Communication Appendix B - Communications antennas. The variable inputs for the Rover UHF antenna and the Lander UHF antenna are given in MATLAB script COMM_script_MR_to_L_plot.m and MATLAB script COMM_script_L_to_MR_plot.m, respectively. The most notable difference in the link budget codes is that the plots that the UHF link budget produces show Data Rate vs. Transmitter Power. The graph in Fig. B.8 shows this plot for the rover to lander communication. Data rate and transmitting power are taken from the plot in Fig. B.8. Since power is more of a driving factor in the design, a low power choice is selected and the data rate that corresponds to that transmitting power is the UHF antenna data rate.

B.6 UHF Antenna Sizing – Leigh Janes We designed the UHF antennas for the Rover and Lander to be dipole, half wavelength antennas. Knowing the frequency on which the antenna will be operating allows for the antennas to be sized using Eq. B–12 and Eq. B–13.

492   B–15 f (MHz)

( *12)  r B–16 0.5

Now that we know the ratio of half wavelength to conductor diameter, r, we find the multiplicity factor, k, from the graph in Fig. B.77. Using the graph in Fig. B.7, k of the rover antenna and the Lander antenna are found to be approximately 0.95. The height of the antenna is calculated by applying the multiplicity factor to Eq. B–14.

(492* k) B–17   *0.3048  hantenna  f (MHz)  Fig. B.9 Mulitplicity Factor, K, Plot Schetgen, KU7G, Robert, The AARL Handbook for Radio Amateurs 1993, ed. 70, 1993, p.17-3. AAE 450 Senior Spacecraft Design Spring 2004 98 Appendix B - Communications

We select a UHF frequency for communication between the Mars Rover and the Mars Lander because the distance over which the radio signals must travel is much less than when the Rover communicates with the Transport Vehicle. Also, the link can operate on a lower data rate because real time video is not being transmitted. A shorter distance and lower data rate allows for the use of a lower frequency. We modified the link budget code in order to produce a link budget for the UHF antennas. The code no longer solves for an antenna diameter because the UHF antenna are omni directional antennas. The variable inputs for the Rover UHF antenna and the Lander UHF antenna are given in MATLAB script COMM_script_MR_to_L_plot.m and MATLAB script COMM_script_L_to_MR_plot.m, respectively. The most notable difference in the two link budget codes is that the plots that the UHF link budget produces show Data Rate vs. Transmitter Power. The graph in Fig. B.8 shows this plot for the rover to Lander communication. Data rate and transmitting power are taken from the plot in Fig. B.8. Since power is more of a driving factor in the design, a low power choice is selected and the data rate that corresponds to that transmitting power is the UHF antenna data rate.

B.7 Antenn a Sizing for Rover

Fig. B.10 Data Rate vs. Transmitting Power for Rover to Lander Communication

Communication – Leigh Janes Communication between the Mars Rover and the Transport Vehicle occurs on a Ka-band frequency using a high gain antenna (HGA) on the Rover and a parabolic antenna on the Transport Vehicle. The uplink and downlink frequencies are selected from available frequencies

AAE 450 Senior Spacecraft Design Spring 2004 99 Appendix B - Communications in the Ka-band. We choose separate uplink and downlink frequencies so that the same antenna can be used for both transmitting and receiving data. We performed a study to decide whether Ka-band or X-band frequency should be used. Ka-band frequencies are being used for Rover to Transport Vehicle links because they require a lower transmitter power than X-band frequencies. The diameters of the two dishes are determined using the link budget code. MATLAB script COMM_script_MR_to_CV_vars.m, and script COMM_script_CV_to_MR_vars.m show the input files for the Rover high gain antenna as the receiving antenna and the Transport Vehicle antenna as the receiving antenna, respectively. The maximum link distance of both antennas is 229,700 km. This value is the apoapsis value of the Transport Vehicle in its orbit about Mars. We assume this to be the maximum distance the two antennas will need to communicate. The selection of the rover high gain antenna diameter is a trade off between the size of the antenna and the transmitting power required. Both quantities are restricted. The size is limited by the dimensions of the Rover and the transmitting power is limited by the power capabilities of the Rover. Plots of Antenna Transmitting Diameter vs. Transmitting Power are

Fig. B.11 Rover to Transport Vehicle Communication used to visualize and select antenna diameters. The trade for Mars Rover to Transport Vehicle communication is shown in Fig. B.11 and that of the Transport Vehicle to the Mars Rover is presented in Fig. B.12.

Fig. B.12 Transport Vehicle to Rover Communication The diameter of the high gain on the Rover is selected from Fig. B.11, which sets its power requirement. We size this antenna first because its power requirement is more stringent than that of the Transport Vehicle. The diameter of the Rover high gain antenna is 0.32 m, which has a transmitting power requirement of 10 W. Once the Rover high gain antenna is sized, Fig. B.12 is used in conjunction with Fig. B.11 to size the Transport Vehicle antenna. The diameter of the Transport Vehicle antenna is 2 m, with a transmitting power of 500 W. The receiving power of both antennas is minimal in comparison to the transmitting power required, so we size the antennas based on their transmitting power required instead of their receiving power required. The rover communication antenna on the Transport Vehicle is a parabolic antenna with a focal distance of 40% of the antenna diameter. It is made of Aluminum 6061-T6 which has a density of 2700 kg/m3. The aluminum thickness of the dish is 0.5 mm, which is a mass of the antenna of 8.473 kg without any thermal shielding.

B.8 A Brief Look at Laser Communication – Devin Fitting When the project was initiated, it was quickly determined that we would need an enormous amount of power to transmit the bandwidth we desired from Mars on a traditional communication band. Bearing this in mind, we initiated a brief look into alternative forms of communication. AAE 450 Senior Spacecraft Design Spring 2004 101 Appendix B - Communications

The most promising form found was that of laser communication.8 The ultimate goal of the laser communication project that we looked at was to transmit from a craft on Mars to a satellite in Earth orbit. This is done be using a laser with a beam focuser on the Martian end and a telescope on the Earth satellite. Two items ended our move towards using laser communication. First the data transmission rate is too unstable to provide a reliable link. Second the power budget allowed for the ship drastically increased. This allowed group members to move on to more important tasks. However, this would be a possible communication method to look at for future reference. If a significant power savings is required in a future design, more research is recommended in this field.

B.9 Calculating Moment of Inertia – Devin Fitting It became evident as the project progressed that it would be necessary to know the moments of inertia to calculate spin-up rate. Ultimately this is determined by the CAD model that was produced. However, it was necessary to create a Matlab script that generated a close approximation.

To create the script, all components of the spacecraft were assumed to be simple geometric shapes with known equations of moment of inertia. The parallel axis theorem was then used to shift the axis to the center of mass of the total spacecraft. Please see Appendix B.9.1 for the scripts themselves. The Fig.s above and below contain the equations used in the moment of inertia calculation.

Fig. B.13 – First page of moments of inertia. Picture is from Dynamics and Vibrations by J. M. Longuski

AAE 450 Senior Spacecraft Design Spring 2004 Fig. B.14 - Second page103 of moments of inertia. Picture is from Dynamics and Vibrations by J. M. Longuski Appendix B - Communications

Fig. B.15 – Third page of moments of inertia. Picture is from Dynamics and Vibrations by J. M. Longuski

B.10 Matlab Code

B.10.1 Inertia Code %%Spaceship.m

%AAE 450 - Spring 2004 %Author/s: Devin Fitting %Date Created: 3/15/04 %Last Modified: 3/25/04

%This script determines the moment of the spaceship. It does this by %breaking do the ship into simple components. Then uses parallel axis %theorem to transfer the axes to the COM. %In our case I am using the coordinate notation where y is along the long %axis. Z is defined as traveling straight through the com dish. X is %defined now using the right hand rule.

%Step 1 Defining the components of the ship

%Nose: this is the very front of the heat shield and every thing it %contains m_nose = 5000; %kg r_nose = 5.4; %m disty_nose = 21.24+3/8*r_nose; %m distz_nose = -.125; %m

%Aeroshell: this is the aeroshell - the nose m_aero = 15000; %kg r_aero = 5.4; %m h_aero = 30; %m disty_aero = 21.24-15;%m distz_aero = -.125; %m

%Hab: this is the habitation module it assumes all mass is on the outer %wall and it is a hollow cylinder m_hab = 80000; %kg r_hab = 5.2;% m h_hab = 10; %m disty_hab = 21.24-5;%m distz_hab = -.125; %m

%Fuel: this is the section that contains the fuel. It is estimated as a %solid cylender m_fuel = 100000; %kg r_fuel = 5; %m h_fuel = 14; %m disty_fuel = 21.24 - 17; %m distz_fuel = -.125; %m

%Engine: this is the section containing the engine and all power components m_engine = 80000; %kg r_engine = 5; %m h_engine = 10; %m AAE 450 Senior Spacecraft Design Spring 2004 105 Appendix B - Communications disty_engine = 21.24 - (24+5); %m distz_engine = -.125; %m

%CRV: this is the section containing the CRV. Assuming negligible mass for %structure this will be estimated as a cone which is the CRV m_crv = 6000; %kg r_crv = 2.5; %m h_crv = 4; %m disty_crv = 21.24-12; %m distz_crv = -.125-2; %m

%Step 2 - Calculate all the individual moments of inertia

I_nose = hemisphere_inertia(r_nose,m_nose); I_aero = thin_cyl_inertia(r_aero,h_aero,m_aero); I_hab = thin_cyl_inertia(r_hab,h_hab,m_hab); I_fuel = right_cyl_inertia(r_fuel,h_fuel,m_fuel); I_engine = right_cyl_inertia(r_engine,h_engine,m_engine); I_crv= cone_inertia(r_crv,h_crv,m_crv);

%Step 3 - calculate the shifts of moments of inertia to achieve actual %moments of inertia

I = [0 0 0]; Ixx = paraxis(I_nose(1), disty_nose, m_nose) +paraxis(I_aero(1),disty_aero,m_aero)+... paraxis(I_hab(1), disty_hab, m_hab)+paraxis(I_fuel(1),disty_fuel,m_fuel)+... paraxis(I_engine(1), disty_engine, m_engine) +paraxis(I_crv(1),disty_crv,m_crv);

Iyy = paraxis(I_nose(2), distz_nose, m_nose) +paraxis(I_aero(2),distz_aero,m_aero)+... paraxis(I_hab(2), distz_hab, m_hab)+paraxis(I_fuel(2),distz_fuel,m_fuel)+... paraxis(I_engine(2), distz_engine, m_engine) +paraxis(I_crv(2),distz_crv,m_crv);

Izz = paraxis(I_nose(3), disty_nose, m_nose) +paraxis(I_aero(3),disty_aero,m_aero)+... paraxis(I_hab(3), disty_hab, m_hab)+paraxis(I_fuel(3),disty_fuel,m_fuel)+... paraxis(I_engine(3), disty_engine, m_engine) +paraxis(I_crv(3),disty_crv,m_crv);

I = [Ixx Iyy Izz] %kg-m^2 %%Spaceship_Ext.m

%AAE 450 - Spring 2004 %Author/s: Devin Fitting %Date Created: 3/15/04 %Last Modified: 3/25/04

%This script determines the moment of the spaceship when it is fully extended. %It does this by breaking do the ship into simple components. %Then uses parallel axis theorem to transfer the axes to the COM. %In our case I am using the coordinate notation where y is along the long %axis. Z is defined as traveling straight through the com dish. X is %defined now using the right hand rule.

%Step 1 Defining the components of the ship

%Nose: this is the very front of the heat shield and every thing it %contains m_nose = 5000; %kg r_nose = 5.4; %m disty_nose = 77.349+3/8*r_nose; %m distz_nose = -.125; %m

%Aeroshell: this is the aeroshell - the nose m_aero = 15000; %kg r_aero = 5.4; %m h_aero = 30; %m disty_aero = 77.349-15;%m distz_aero = -.125; %m

%Hab: this is the habitation module it assumes all mass is on the outer %wall and it is a hollow cylinder m_hab = 80000; %kg r_hab = 5.2;% m h_hab = 10; %m disty_hab = 77.349-5;%m distz_hab = -.125; %m

%Fuel: this is the section that contains the fuel. It is estimated as a %solid cylender m_fuel = 100000; %kg r_fuel = 5; %m h_fuel = 14; %m disty_fuel = 77.349 - 17; %m distz_fuel = -.125; %m

%Engine: this is the section containing the engine and all power components m_engine = 80000; %kg r_engine = 5; %m h_engine = 10; %m disty_engine = 77.349 - (24+5); %m distz_engine = -.125; %m

%CRV: this is the section containing the CRV. Assuming negligible mass for %structure this will be estimated as a cone which is the CRV m_crv = 6000; %kg r_crv = 2.5; %m h_crv = 4; %m disty_crv = 77.349-12; %m distz_crv = -.125-2; %m

%Step 2 - Calculate all the individual moments of inertia

I_nose = hemisphere_inertia(r_nose,m_nose); I_aero = thin_cyl_inertia(r_aero,h_aero,m_aero); I_hab = thin_cyl_inertia(r_hab,h_hab,m_hab); I_fuel = right_cyl_inertia(r_fuel,h_fuel,m_fuel); I_engine = right_cyl_inertia(r_engine,h_engine,m_engine); I_crv= cone_inertia(r_crv,h_crv,m_crv);

%Step 3 - calculate the shifts of moments of inertia to achieve actual AAE 450 Senior Spacecraft Design Spring 2004 107 Appendix B - Communications

%moments of inertia

I = [0 0 0]; Ixx = paraxis(I_nose(1), disty_nose, m_nose) +paraxis(I_aero(1),disty_aero,m_aero)+... paraxis(I_hab(1), disty_hab, m_hab)+paraxis(I_fuel(1),disty_fuel,m_fuel)+... paraxis(I_engine(1), disty_engine, m_engine) +paraxis(I_crv(1),disty_crv,m_crv);

Iyy = paraxis(I_nose(2), distz_nose, m_nose) +paraxis(I_aero(2),distz_aero,m_aero)+... paraxis(I_hab(2), distz_hab, m_hab)+paraxis(I_fuel(2),distz_fuel,m_fuel)+... paraxis(I_engine(2), distz_engine, m_engine) +paraxis(I_crv(2),distz_crv,m_crv);

Izz = paraxis(I_nose(3), disty_nose, m_nose) +paraxis(I_aero(3),disty_aero,m_aero)+... paraxis(I_hab(3), disty_hab, m_hab)+paraxis(I_fuel(3),disty_fuel,m_fuel)+... paraxis(I_engine(3), disty_engine, m_engine) +paraxis(I_crv(3),disty_crv,m_crv);

I = [Ixx Iyy Izz] %kg-m^2

%%paraxix()

%AAE 450 - Spring 2004 %Author/s: Devin Fitting %Date Created: 3/12/03 %Last Modified: 3/15/04 function Icom = paraxis(I, x, m) %This function uses the parallel axis theorem to convert Inertias calculated %at a place other then the com. %I is the inertia to transfer %x is distance from axis to transfer %m = mass of component

Icom = I + m.*x.^2; function I = cone_inertia(r,h,m)

% this finds the principal moments of inertia assuming mass is evenly % distributed along the wall. This also assumes your coordinates are % oriented to that y is the vertical axis. %r = radius at the broadest point

%m = the mass of the cylinder

Ixx = 3*m/80*(4*r^2+h^2); Izz = Ixx; Iyy =3/10*m*r^2;

I = [Ixx Iyy Izz];

%%hemisphere_inertia()

%AAE 450 - Spring 2004 AAE 450 Senior Spacecraft Design Spring 2004 108 Appendix B - Communications

%Author/s: Devin Fitting %Date Created: 3/15/04 %Last Modified: 3/15/04 function I = hemisphere_inertia(r,m)

% this finds the principal moments of inertia assuming mass is evenly % distributed along the wall. This also assumes your coordinates are % oriented to that y is the vertical axis. %r = radius at the broadest point

%m = the mass of the cylinder

Ixx = 83/320*m*r^2; Izz = Ixx; Iyy =2/5*m*r^2;

I = [Ixx Iyy Izz];

%%right_cyl_inertia()

%AAE 450 - Spring 2004 %Author/s: Devin Fitting %Date Created: 3/15/04 %Last Modified: 3/15/04 function I = right_cyl_inertia(r,h,m)

% this finds the principal moments of inertia assuming mass is evenly % distributed along the wall. This also assumes your coordinates are % oriented to that y is the vertical axis. %r = radius to the center of the wall %m = the mass of the cylinder

Ixx = m/12*(3*r^2+h^2); Izz = Ixx; Iyy =1/2*m*r^2;

I = [Ixx Iyy Izz];

%%thin_cyl_inertia

%AAE 450 - Spring 2004 %Author/s: Devin Fitting %Date Created: 3/15/04 %Last Modified: 3/15/04 function I = thin_cyl_inertia(r,h,m)

% this finds the principal moments of inertia assuming mass is evenly % distributed along the wall. This also assumes your coordinates are % oriented to that y is the vertical axis. %r = radius to the center of the wall %h = the height of the cylinder %m = the mass of the cylinder

Ixx = m/12*(6*r^2+h^2); Izz = Ixx; Iyy = m*r^2;

I = [Ixx Iyy Izz];

B.10.2 Link Budget Code % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/31/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function ant_diam = COM_func_ant_diam(ant_eff, trans_freq, ant_gain) % % DESCRIPTION % This function determines the diameter of an antenna given its % efficiency, the transmission frequency, and the gain. % % INPUTS % ant_eff : Efficiency of the antenna % trans_freq : Transmission frequency, in GHz % ant_gain : Gain of the antenna, in dB % % OUTPUTS % ant_diam : Diameter of the antenna, in m % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES % ant_diam_dB : antenna diameter, in decibel-meters % %**************************************************************************** ****** function ant_diam = COM_func_ant_diam(ant_eff, trans_freq, ant_gain)

% Calculate diameter in dB-m. ant_diam_dB = ant_gain - 20.4 - 10*log10(ant_eff) - 20*log10(trans_freq);

% Convert to meters. ant_diam = 10^(ant_diam_dB/20);

% EOF COM_func_ant_diam.m % AAE 450 - Spring 2004 % Author: Devin Fitting % E-mail: [email protected] % Created: 1/22/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** %

% function recv_ant_gain = COM_func_ant_gain(ant_eff, trans_freq, ant_diam) % % DESCRIPTION % This function determines the gain of an antenna given its % efficiency, the transmission frequency, and the diameter. % % INPUTS % ant_eff : Efficiency of the antenna % trans_freq : Transmission frequency, in GHz % ant_diam : Diameter of the antenna, in m % % OUTPUTS % ant_gain : Gain of the antenna, in dBi % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES % None % %**************************************************************************** ****** function ant_gain = COM_func_ant_gain(ant_eff, trans_freq, ant_diam) ant_gain = 20.4 + 10*log10(ant_eff) + 20*log10(trans_freq) ... + 20*log10(ant_diam);

% EOF COM_func_ant_gain.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/31/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % function ant_gain = COM_func_ant_gain_EIRP(trans_power, EIRP) % % DESCRIPTION % % This function determines the gain of an antenna given its % transmission power and EIRP % % INPUTS % trans_power : Transmitting power, in W % EIRP : Effective isentropic radiating power, in dBW % % OUTPUTS % ant_gain : Gain of the antenna, in dBi % % METHODS OF CALCULATION % See Communications Appendix - Link Budget

% % CALLED FUNCTIONS % None % % VARIABLES % None % %**************************************************************************** ****** function ant_gain = COM_func_ant_gain_EIRP(trans_power, EIRP) ant_gain = EIRP - 10*log10(trans_power);

% EOF COM_func_ant_gain_EIRP.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function trans_power = COM_func_dipole_link_budget(trans_freq, distance, ... % BER, noise_temp, atm_loss, link_margin, data_rate) % % DESCRIPTION % This function calculates the transmission power required when both % antennas are half-wavelength dipole antennas (2.1 dBi). % % INPUTS % trans_freq : Transmission frequency, in GHz % distance : Distance between antennas, in km % BER : Bit error rate % noise_temp : Noise temperature, in K % atm_loss : Atmospheric loss (all non-freespace losses), in dB % link_margin : Link margin, in dB % data_rate : Data rate, in bps % % OUTPUTS % trans_power : Transmission power, in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_SNR_avail % COM_func_free_space_loss % COM_func_GT % COM_func_EIRP_data_rate % COM_func_trans_power % % VARIABLES % SNR_avail : Available signal to noise ratio, in dB % recv_ant_gain : Gain of the receiving antenna, in dBi

% free_space_loss : Free space loss, Lfs, in dB % GT : Receiving antenna Fig. of merit % EIRP : Effective isentropic radiated power, in dBW % trans_ant_gain : Gain of the transmitting antenna, in dBi % %**************************************************************************** ****** function trans_power = COM_func_dipole_link_budget(trans_freq, distance, ... BER, noise_temp, atm_loss, link_margin, data_rate)

% Calculate the available signal-to-noise ratio. SNR_avail = COM_func_SNR_avail(BER, link_margin);

% Calculate the gain of the receiving antenna - dipole antenna. recv_ant_gain = 2.1; % dBi

% Calculate free space loss. free_space_loss = COM_func_free_space_loss(trans_freq, distance);

% Calculate the Fig. of merit for the receiving antenna. GT = COM_func_GT(recv_ant_gain, noise_temp);

% Calculate the effective isentropic radiating power. EIRP = COM_func_EIRP_data_rate(SNR_avail, GT, free_space_loss, atm_loss, data_rate);

% Calculate the transmitting antenna gain. trans_ant_gain = 2.1; % dBi

% Calculate the transmission power. trans_power = COM_func_trans_power(EIRP, trans_ant_gain);

% EOF COM_func_dipole_link_budget.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/24/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function EIRP = COM_func_EIRP_data_rate(SNR_avail, GT, free_space_loss, ... % atm_loss, data_rate) % % DESCRIPTION % This function determines the effective isentropic radiating power given % the available signal to noise ratio, the Fig. of merit for the receiving % antenna, free space loss, atmospheric loss, and data rate. % % INPUTS % SNR_avail : Available signal-to-noise ratio, in dB % GT : Fig. of merit for receiving antenna, in dBi/K % free_space_loss : Free space loss, in dB % atm_loss : Atmospheric loss, in dB

% data_rate : Data rate of link, in bps % % OUTPUTS % EIRP : Effective isentropic radiating power, in dBW % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES % k : Boltzmann's constant, -228.6 dB-W / K-Hz % data_rate_dB : Data rate in dB-bps % %**************************************************************************** ****** function EIRP = COM_func_EIRP_data_rate(SNR_avail, GT, free_space_loss, ... atm_loss, data_rate)

% Define Boltzmann's constant k = -228.6; % dB-W / K-Hz

% Convert data rate to dB-bps. data_rate_dB = 10*log10(data_rate);

% Calculate the effective isentropic radiated power. EIRP = SNR_avail - GT + free_space_loss + atm_loss + k + data_rate_dB;

% EOF COM_func_EIRP_data_rate.m % AAE 450 - Spring 2004 % Author: Devin Fitting % E-mail: [email protected] % Created: 1/22/04 % Last updated: 1/24/04 BDV % %**************************************************************************** ****** % % function free_space_loss = COM_func_free_space_loss(trans_freq, distance) % % DESCRIPTION % This function determines the amount of freespace loss given transmission % frequency and distance. % % INPUTS % trans_freq : Transmission frequency, in GHz % distance : Current distance from transmission target, in km % % OUTPUTS % free_space_loss : Free space loss, in dB % % METHODS OF CALCULATION % See Communications Appendix - Link Budget %

% CALLED FUNCTIONS % None % % VARIABLES % None % %**************************************************************************** ****** function free_space_loss = COM_func_free_space_loss(trans_freq, distance) free_space_loss = 92.45 + 20*log10(trans_freq) + 20*log10(distance);

% EOF COM_func_free_space_loss.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/31/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function GT = COM_func_GT(ant_gain, noise_temp) % % DESCRIPTION % This function determines the Fig. of merit for an antenna based on its % gain and the system noise temperature. % % INPUTS % ant_gain : Gain of the antenna, in dBi % noise_temp_dB : Noise temperature in K % % OUTPUTS % GT : Fig. of Merit, in dBi/K % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES % noise_temp_dB : Receiver noise temperature, in dB-K % %**************************************************************************** ****** function GT = COM_func_GT(ant_gain, noise_temp)

% Convert K to dbK. noise_temp_dB = 10*log10(noise_temp);

% Calculate Fig. of merit. GT = ant_gain - noise_temp_dB;

% EOF COM_func_GT.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function COM_func_power_vs_atm_loss_plot(COM_script_link, atm_loss_array) % % DESCRIPTION % This function calculates the power required for a variety of atmospheric % losses for a given link. % % INPUTS % COM_script_link : String containing name of file that holds variables for % the link that is of interest. % atm_loss_array : Array of atmospheric losses, in dB % % OUTPUTS % Plot of power required for a link given different values of atmospheric % loss % % METHODS OF CALCULATION % After loading the current link variables, this function iterates through % each of the given atmospheric losses to produce a plot of the required % transmission power at each atmospheric loss. % % CALLED FUNCTIONS % COM_script_link - runs the file specified in this string % COM_func_space_link_budget_power % % VARIABLES % trans_power_array : Array of different transmission powers required, in W % trans_power : Transmission power required for current run % ii : Current index % %**************************************************************************** ****** function COM_func_power_vs_atm_loss_plot(COM_script_link, atm_loss_array)

% Run script to get variables for current link. if exist(COM_script_link) == 2 run(COM_script_link); else fprintf('Error: File %s could not be found, exiting COM_func_power_vs_atm_loss_plot\n', ... COM_script_link); return end

% Activate a new Fig. window and turn on the hold. Fig.

AAE 450 Senior Spacecraft Design Spring 2004 116 Appendix B - Communications hold on

% Presize the transmission power. trans_power_array = atm_loss_array*0;

% Iterate over each bitrate. for ii = 1:length(atm_loss_array) % Pick out the bitrate. atm_loss = atm_loss_array(ii);

% Find the power required. trans_power = COM_func_space_link_budget_power(trans_ant_eff, recv_ant_eff, ... trans_freq, link_distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... data_rate, trans_ant_diam);

% Store the value of the transmitting antenna diameter trans_power_array(ii) = trans_power; end

% Plot the transmitting power against the diameter. plot(atm_loss_array, trans_power_array/1000)

% Add labels to the plot ylabel('Transmitting power, P_t, kW') xlabel('Atmospheric loss, L_a_t_m, dB') grid on title([link_name,' - Power vs. atmospheric loss'])

% EOF COM_func_power_vs_atm_loss_plot.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function COM_func_power_vs_bitrate_plot(COM_script_link, data_rate_array) % % DESCRIPTION % This function calculates the power required for a variety of bitrates for % a given link. % % INPUTS % COM_script_link : String containing name of file that holds variables for % the link that is of interest. % data_rate_array : Array of bitrates, in bps % % OUTPUTS % Plot of power required for a link given different values of data rate % % METHODS OF CALCULATION % After loading the current link variables, this function iterates through

% each of the given data rates to produce a plot of the required % transmission power at each bit rate. % % CALLED FUNCTIONS % COM_script_link - runs the file specified in this string % COM_func_space_link_budget_power % % VARIABLES % trans_power_array : Array of different transmission powers required, in W % trans_power : Transmission power required for current run % ii : Current index % %**************************************************************************** ****** function COM_func_power_vs_bitrate_plot(COM_script_link, data_rate_array)

% Run script to get variables for current link. if exist(COM_script_link) == 2 run(COM_script_link); else fprintf('Error: File %s could not be found, exiting COM_func_power_vs_bitrate_plot\n', ... COM_script_link); return end

% Activate a new Fig. window and turn on the hold. Fig. hold on

% Presize the transmission power. trans_power_array = data_rate_array*0;

% Iterate over each bitrate. for ii = 1:length(data_rate_array) % Pick out the bitrate. data_rate = data_rate_array(ii);

% Plot the transmitting power against the diameter. plot(data_rate_array/(1e6), trans_power_array/1000)

% Add labels to the plot ylabel('Transmitting power, P_t, kW') xlabel('Bitrate, R_D, Mbps') grid on AAE 450 Senior Spacecraft Design Spring 2004 118 Appendix B - Communications title([link_name,' - Power vs. bitrate'])

% EOF COM_func_power_vs_bitrate_plot.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function COM_func_power_vs_distance_plot(COM_script_link, distance_array) % % DESCRIPTION % This function calculates the power required for a set of distances and % then plots that information. % % INPUTS % COM_script_link : String containing name of file that holds variables for % the link that is of interest. % distance_array : Array of transmission distances, in km % % OUTPUTS % Plot of power required for a link given different values of distance % % METHODS OF CALCULATION % After loading the current link variables, this function iterates through % each of the given distances to produce a plot of the required transmission % power at each distance. % % CALLED FUNCTIONS % COM_script_link - runs the file specified in this string % COM_func_space_link_budget_power % % VARIABLES % trans_power_array : Array of different transmission powers required, in W % trans_power : Transmission power required for current run % ii : Current index % %**************************************************************************** ****** function COM_func_power_vs_distance_plot(COM_script_link, distance_array)

% Run script to get variables for current link. if exist(COM_script_link) == 2 run(COM_script_link); else fprintf('Error: File %s could not be found, exiting COM_func_power_vs_distance_plot\n', ... COM_script_link); return end

% Activate a new Fig. window and turn on the hold.

Fig. hold on

% Presize the transmission power. trans_power_array = distance_array*0;

% Iterate over each bitrate. for ii = 1:length(distance_array) % Pick out the bitrate. link_distance = distance_array(ii);

% Plot the transmitting power against the diameter. plot(distance_array, trans_power_array/1000)

% Add labels to the plot ylabel('Transmitting power, P_t, kW') xlabel('Distance, d, km') grid on title([link_name,' - Power vs. distance'])

% EOF COM_func_power_vs_distance_plot.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/31/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function COM_func_power_vs_trans_recv_diam_plot(COM_script_link, ... % recv_ant_diam_array, trans_power_array) % % DESCRIPTION % This function displays a plot of the transmitting antenna diameter against % the transmission power, parameterized by receiving antenna diameter. % % INPUTS % COM_script_link : String containing name of file that holds variables for % the link that is of interest. % recv_ant_diam_array : Array of 4 receiving antenna diameters, in m (must % be 4 values) % trans_power_array : Array of transmission powers, in W % % OUTPUTS

% Plot of power required for a link given different values of atmospheric % loss % % METHODS OF CALCULATION % After loading the current link variables, this function iterates through % each of the 4 given receiving antenna diameters and the transmission % power array to determine the size of the transmitting antenna. This is % then shown in a plot. % % CALLED FUNCTIONS % COM_script_link - runs the file specified in this string % COM_func_space_link_budget_power % % VARIABLES % params : Array of plot color/linestyle options % trans_power : Transmission power required for current run % trans_ant_diam : Transmission diameter for current run % ii : Current index % %**************************************************************************** ****** function COM_func_power_vs_trans_recv_diam_plot(COM_script_link, ... recv_ant_diam_array, trans_power_array)

% Run script to get variables for current link. if exist(COM_script_link) == 2 run(COM_script_link); else fprintf('Error: File %s could not be found, exiting COM_func_power_vs_trans_recv_diam_plot\n', ... COM_script_link); return end

% Check size of receiving antenna diameter array. if length(recv_ant_diam_array) ~= 4 fprintf('Error: Receiver diameter array incorrect size, exiting COM_func_power_vs_trans_recv_diam_plot\n'); return end

% Curve display parameters. params = ['k- '; 'g- '; 'b- '; 'r- '];

% Activate a new Fig. window and turn on the hold. Fig. hold on

% Iterate through each receiving antenna diameter. for jj = 1:4 % Pick out the next receiving antenna diameter. recv_ant_diam = recv_ant_diam_array(jj);

% Reset/presize the transmission antenna size. trans_ant_diam_array = trans_power_array*0;

% Iterate over each transmitting power. for ii = 1:length(trans_power_array) % Pick out the next transmitting power. trans_power = trans_power_array(ii);

% Find the diameter of the transmitting antenna. trans_ant_diam = COM_func_space_link_budget(trans_ant_eff, recv_ant_eff, trans_freq, ... link_distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, data_rate, trans_power);

% Store the value of the transmitting antenna diameter trans_ant_diam_array(ii) = trans_ant_diam; end

% Plot the transmitting power against the diameter. plot(trans_power_array/1000,trans_ant_diam_array,params(jj,:)) end

% Add labels to the plot xlabel('Transmitting power, P_t, kW') ylabel('Transmitting diameter, D_t, m') grid on legend(['D_r = ',num2str(recv_ant_diam_array(1))],['D_r = ',num2str(recv_ant_diam_array(2))],... ['D_r = ',num2str(recv_ant_diam_array(3))],['D_r = ',num2str(recv_ant_diam_array(4))]) title([link_name,' - Power and antenna diameters'])

% EOF COM_func_power_vs_trans_recv_diam_plot.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/24/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function SNR_avail = COM_func_SNR_avail(BER, link_margin) % % DESCRIPTION % This function determines the available signal to noise ratio given the % bit error rate and the link margin. % % INPUTS % BER : Bit error rate, in bits/bit % link_margin : Link margin, in dB % % OUTPUTS % SNR_avail : Available signal to noise ratio, in dB % % METHODS OF CALCULATION

% See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES % SNR : Signal-to-noise ratio for a binary-phase-shift-keying system % %**************************************************************************** ****** function SNR_avail = COM_func_SNR_avail(BER, link_margin)

% Calculate signal to noise ratio based on a binary-phase-shift-keying % system. This line is different if an encoding system other than BPSK is % used. SNR = ( erfcinv(2*BER) ) ^ 2;

% Caculate available signal-to-noise ratio by adding link margin. SNR_avail = SNR + link_margin;

% EOF COM_func_SNR_avail.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/31/04 % Last updated: 1/31/04 BDV % %**************************************************************************** ****** % % function trans_ant_diam = COM_func_space_link_budget(trans_ant_eff, recv_ant_eff, ... % trans_freq, distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... % data_rate, trans_power) % % DESCRIPTION % This function determines the diameter of the transmitting antenna given % all link budget information. % % INPUTS % trans_ant_eff : Efficiency of the transmitting antenna % recv_ant_eff : Efficiency of the receiving antenna % trans_freq : Transmission frequency, in GHz % distance : Distance between antennas, in km % BER : Bit error rate % noise_temp : Noise temperature, in K % atm_loss : Atmospheric loss (all non-freespace losses), in dB % link_margin : Link margin, in dB % recv_ant_diam : Diameter of the receiving antenna, m % data_rate : Data rate, in bps % trans_power : Transmission power, in W % % OUTPUTS % trans_ant_diam : Diameter of the transmitting antenna, in m

% % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_SNR_avail % COM_func_ant_gain % COM_func_free_space_loss % COM_func_GT % COM_func_EIRP_data_rate % COM_func_ant_gain_EIRP % COM_func_ant_diam % % VARIABLES % SNR_avail : Available signal to noise ratio, in dB % recv_ant_gain : Gain of the receiving antenna, in dBi % free_space_loss : Free space loss, Lfs, in dB % GT : Receiving antenna Fig. of merit % EIRP : Effective isentropic radiated power, in dBW % trans_ant_gain : Gain of the transmitting antenna, in dBi % %**************************************************************************** ****** function trans_ant_diam = COM_func_space_link_budget(trans_ant_eff, recv_ant_eff, ... trans_freq, distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... data_rate, trans_power)

% Calculate the gain of the receiving antenna. recv_ant_gain = COM_func_ant_gain(recv_ant_eff, trans_freq, recv_ant_diam);

% Calculate the transmitting antenna gain. trans_ant_gain = COM_func_ant_gain_EIRP(trans_power, EIRP);

% Calculate the transmitting antenna diameter. trans_ant_diam = COM_func_ant_diam(trans_ant_eff, trans_freq, trans_ant_gain);

% EOF COM_func_space_link_budget.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected]

% Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function trans_power = COM_func_space_link_budget_power(trans_ant_eff, recv_ant_eff, ... % trans_freq, distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... % data_rate, trans_ant_diam) % % DESCRIPTION % This function determines the power required given all other link % parameters. % % INPUTS % trans_ant_eff : Efficiency of the transmitting antenna % recv_ant_eff : Efficiency of the receiving antenna % trans_freq : Transmission frequency, in GHz % distance : Distance between antennas, in km % BER : Bit error rate % noise_temp : Noise temperature, in K % atm_loss : Atmospheric loss (all non-freespace losses), in dB % link_margin : Link margin, in dB % recv_ant_diam : Diameter of the receiving antenna, m % data_rate : Data rate, in bps % trans_ant_diam : Diameter of the transmitting antenna, in m % % OUTPUTS % trans_power : Transmission power, in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_SNR_avail % COM_func_ant_gain % COM_func_free_space_loss % COM_func_GT % COM_func_EIRP_data_rate % COM_func_trans_power % % VARIABLES % SNR_avail : Available signal to noise ratio, in dB % recv_ant_gain : Gain of the receiving antenna, in dBi % free_space_loss : Free space loss, Lfs, in dB % GT : Receiving antenna Fig. of merit % EIRP : Effective isentropic radiated power, in dBW % trans_ant_gain : Gain of the transmitting antenna, in dBi % %**************************************************************************** ****** function trans_power = COM_func_space_link_budget_power(trans_ant_eff, recv_ant_eff, ...

trans_freq, distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... data_rate, trans_ant_diam)

% Calculate the gain of the receiving antenna. recv_ant_gain = COM_func_ant_gain(recv_ant_eff, trans_freq, recv_ant_diam);

% Calculate the transmitting antenna gain. trans_ant_gain = COM_func_ant_gain(trans_ant_eff, trans_freq, trans_ant_diam);

% Calculate the transmitting power. trans_power = COM_func_trans_power(EIRP, trans_ant_gain);

% EOF COM_func_space_link_budget_power.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 1/24/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % function trans_power = COM_func_trans_power(EIRP, trans_ant_gain) % % DESCRIPTION % This function determines the transmission power given the effective % isentropic radiating power and the gain of the transmitting antenna. % % INPUTS % EIRP : Effective isentropic radiating power, in dB % recv_ant_gain : Gain of the transmitting antenna, in dBi % % OUTPUTS % trans_power : Transmission power, in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % None % % VARIABLES

% None % %**************************************************************************** ****** function trans_power = COM_func_trans_power(EIRP, trans_ant_gain) trans_power = 10^((EIRP - trans_ant_gain)/10);

% EOF COM_func_trans_power.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_E_to_TM_vars.m % % DESCRIPTION % This script parses the COM_script_TM_E_link_vars.m file to obtain the % correct variables for the Earth to Transport Module link (TM receiving). % % INPUTS % See COM_script_TM_E_link_vars.m (runs this script) % % OUTPUTS % Places the following values in the workspace of the calling entity % (function or script): % BER : Bit error rate, in bits/bit % link_margin : Link margin, in dB % atm_loss : Atmospheric loss, in dB % link_distance : Link distance, in km % link_name : Name of the link in a string for display purposes % trans_ant_eff : Efficiency of the transmitting antenna (E) % recv_ant_eff : Efficiency of the receiving antenna (TM) % recv_ant_diam : Diameter of the receiving antenna (TM), in m % trans_ant_diam : Diameter of the transmitting antenna (E), in m % trans_freq : Transmission frequency, in GHz % noise_temp : Receiver noise temperature (TM), in K % data_rate : Data rate of the link, in bps % trans_power : Transmission power (E), in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_script_TM_E_link_vars % % VARIABLES % See output list % %**************************************************************************** ******

COM_script_TM_E_link_vars;

% Earth to Transport Module (TM receiving) link_name = 'Earth to Transport Module';

% Antenna efficiencies trans_ant_eff = E_ant_eff; recv_ant_eff = TM_ant_eff;

% Receiving antenna diameter, m recv_ant_diam = TM_ant_diam; % m

% Transmitting antenna diameter, m trans_ant_diam = E_ant_diam; % m

% Frequency of link, GHz trans_freq = E_to_TM_trans_freq; % GHz

% System noise temperature, K noise_temp = E_to_TM_noise_temp; % K

% Data rate, bps data_rate = E_to_TM_data_rate; % bps

% Transmitting power, W trans_power = E_trans_power; % W

% EOF COM_script_E_to_TM_vars.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_power_vs_atm_loss.m % % DESCRIPTION % This script generates a plot of the power required aboard the Transport % module for various atmospheric losses. % % INPUTS % None % % OUTPUTS % Plot of power required % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_power_vs_atm_loss_plot %

% VARIABLES % None % %**************************************************************************** ****** close all clear all clc

% Transport module to Earth (Earth receiving) COM_func_power_vs_atm_loss_plot('COM_script_TM_to_E_vars',linspace(0,20,300))

% EOF COM_script_power_vs_atm_loss.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_power_vs_bitrate.m % % DESCRIPTION % This script generates a plot of the power required for various bitrates. % % INPUTS % None % % OUTPUTS % Plot of power required % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_power_vs_bitrate_plot % COM_script_TM_to_E_vars % COM_func_space_link_budget_power % % VARIABLES % None % %**************************************************************************** ****** close all clear all clc

% Transport Module to Earth (Earth receiving) COM_func_power_vs_bitrate_plot('COM_script_TM_to_E_vars',linspace(1e6,150e6,3 00))

% Run script to grab variables for link. COM_script_TM_to_E_vars;

% Add markers for three bitrates - full, and two emergency states. data_rate_array = [100,20,10]*1e6; params = ['rx';'gx';'kx']; for ii = 1:length(data_rate_array) % Get transmission power. trans_power = COM_func_space_link_budget_power(trans_ant_eff, recv_ant_eff, ... trans_freq, link_distance, BER, noise_temp, atm_loss, link_margin, recv_ant_diam, ... data_rate_array(ii), trans_ant_diam);

% Place marker on plot. plot(data_rate_array(ii)/ (1e6),trans_power/1000,params(ii,:),'LineWidth',2,'MarkerSize',10); end legend('Power required','Full rate','Emergency 1','Emergency 2',4)

% EOF COM_script_power_vs_bitrate.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_power_vs_distance.m % % DESCRIPTION % This script generates a plot of the power required for various distances % (Earth orbit to Martian orbit). % % INPUTS % None % % OUTPUTS % Plot of power required % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_power_vs_distance_plot % % VARIABLES % None % %**************************************************************************** ******

AAE 450 Senior Spacecraft Design Spring 2004 130 Appendix B - Communications close all clear all clc

% Transport Module to Earth (Earth receiving) COM_func_power_vs_distance_plot('COM_script_TM_to_E_vars',linspace(500,3.74e8 ,500))

% EOF COM_script_power_vs_distance.m % AAE 450 - Spring 2004 % Authors: Brian Ventre and Leigh Janes % E-mail: [email protected] / [email protected] % Created: 1/31/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_power_vs_trans_recv_diam.m % % DESCRIPTION % This script plots the transmitting antenna diameter against the transmitted % power for the Earth to Transport Module link (both directions). % % INPUTS % None % % OUTPUTS % Plot of power required % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_power_vs_distance_plot % % VARIABLES % None % %**************************************************************************** ****** close all clear all clc

% Transport Module to Earth (Earth receiving) COM_func_power_vs_trans_recv_diam_plot('COM_script_TM_to_E_vars',[30, 35, 40, 45],linspace(5e3,20e3,100))

% Earth to Transport Module (TM receiving) COM_func_power_vs_trans_recv_diam_plot('COM_script_E_to_TM_vars',[7, 8, 9, 10],linspace(1e3,10e3,100))

% EOF COM_script_power_vs_trans_recv_diam.m % AAE 450 - Spring 2004

% Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_TM_E_link_vars.m % % DESCRIPTION % This script contains the link variables for both the Earth to the Transport Module % link and the TM to Earth link. Other files use this to generate their own link % specific information. All number changes should occur inside here! % % INPUTS % None % % OUTPUTS % Places the following values in the workspace of the calling entity % (function or script): % TM_ant_eff : Efficiency of the TM antenna % E_ant_eff : Efficiency of the Earth antenna % TM_to_E_trans_freq : Frequency of the link from the TM to Earth, in GHz % E_to_TM_trans_freq : Frequency of the link from Earth to the TM, in GHz % BER : Bit error rate, in bits/bit % link_margin : Link margin, in dB % TM_to_E_noise_temp : Noise temperature on TM to Earth link, in K % E_to_TM_noise_temp : Noise temperature on Earth to TM link, in K % atm_loss : Atmospheric loss, in dB % link_distance : Link distance, in km % TM_to_E_data_rate : Data rate from the TM to Earth, in bps % E_to_TM_data_rate : Data rate from Earth to the TM, in bps % TM_trans_power : Transmission power aboard the TM, chosen, in W % E_ant_diam : Antenna diameter on Earth, chosen, in m % TM_ant_diam : Antenna diameter on Earth, calculated, in m % E_trans_power : Transmission power on Earth, calculated, in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_func_space_link_budget % COM_func_space_link_budget_power % % VARIABLES % See output list % %**************************************************************************** ******

% Antenna efficiencies TM_ant_eff = 0.65; E_ant_eff = 0.72;

% Frequency of links, GHz TM_to_E_trans_freq = 31.8; % GHz E_to_TM_trans_freq = 31.3; % GHz

% Bit error rate BER = 5e-6;

% Link margin, dB link_margin = 2; % dB

% System noise temperatures, K TM_to_E_noise_temp = 400; % K E_to_TM_noise_temp = 404.38; % K

% Atmospheric loss, dB atm_loss = 6; % dB

% Distance between antennas, km link_distance = 3.74e8; % km

% Data rates, bps TM_to_E_data_rate = 100e6; % bps E_to_TM_data_rate = 30e6; % bps

% Crew vehicle transmitting power, W TM_trans_power = 10e3; % W

% Antenna diameters, m E_ant_diam = 40; % m TM_ant_diam = COM_func_space_link_budget(TM_ant_eff, E_ant_eff, ... TM_to_E_trans_freq, link_distance, BER, TM_to_E_noise_temp, atm_loss, link_margin, E_ant_diam, ... TM_to_E_data_rate, TM_trans_power); % m

% Earth transmitting power, W E_trans_power = COM_func_space_link_budget_power(E_ant_eff, TM_ant_eff, ... E_to_TM_trans_freq, link_distance, BER, E_to_TM_noise_temp, atm_loss, link_margin, TM_ant_diam, ... E_to_TM_data_rate, E_ant_diam); % W

% EOF COM_script_TM_E_link_vars.m % AAE 450 - Spring 2004 % Author: Brian Ventre % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/15/04 BDV % %**************************************************************************** ****** % % COM_script_TM_to_E_vars.m % % DESCRIPTION % This script parses the COM_script_TM_E_link_vars.m file to obtain the % correct variables for the Transport Module to Earth link (Earth receiving). %

% INPUTS % See COM_script_TM_E_link_vars.m (runs this script) % % OUTPUTS % Places the following values in the workspace of the calling entity % (function or script): % BER : Bit error rate, in bits/bit % link_margin : Link margin, in dB % atm_loss : Atmospheric loss, in dB % link_distance : Link distance, in km % link_name : Name of the link in a string for display purposes % trans_ant_eff : Efficiency of the transmitting antenna (TM) % recv_ant_eff : Efficiency of the receiving antenna (E) % recv_ant_diam : Diameter of the receiving antenna (E), in m % trans_ant_diam : Diameter of the transmitting antenna (TM), in m % trans_freq : Transmission frequency, in GHz % noise_temp : Receiver noise temperature (E), in K % data_rate : Data rate of the link, in bps % trans_power : Transmission power (TM), in W % % METHODS OF CALCULATION % See Communications Appendix - Link Budget % % CALLED FUNCTIONS % COM_script_TM_E_link_vars % % VARIABLES % See output list % %**************************************************************************** ******

COM_script_TM_E_link_vars;

% Transport Module to Earth (Earth receiving) link_name = 'Transport Module to Earth';

% Antenna efficiencies trans_ant_eff = TM_ant_eff; recv_ant_eff = E_ant_eff;

% Receiving antenna diameter, m recv_ant_diam = E_ant_diam; % m

% Transmitting antenna diameter, m trans_ant_diam = TM_ant_diam; % m

% Frequency of link, GHz trans_freq = TM_to_E_trans_freq; % GHz

% System noise temperature, K noise_temp = TM_to_E_noise_temp; % K

% Data rate, bps data_rate = TM_to_E_data_rate; % bps

% Transmitting power, W AAE 450 Senior Spacecraft Design Spring 2004 134 Appendix B - Communications trans_power = TM_trans_power; % W

% EOF COM_script_TM_to_E_vars.m

B.10.3 Rover Code %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COM_script_MR_to_L_plot.m % % Authors: Leigh Janes % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/16/04 LRJ % % This script plots the data rate vs. the transmitting power between two % dipole half wavelength antennas for the communication from mars rover to % mars lander. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all clear all clc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUT VARIABLES % Antenna efficiencies trans_ant_eff = .65; recv_ant_eff = .65;

% Frequency of link, GHz trans_freq = 0.41; % GHz

% System noise temperature, K noise_temp = 300; % K

% Distance between antennas, km distance = 1; % km

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% initialzing i = 1; d_r = [1000 5000 1e4 1e5];

% calculate transmitting power for i = 1:1:4

if i == 1 data_rate = d_r(1); elseif i == 2 data_rate = d_r(2); elseif i == 3 data_rate = d_r(3); else i == 4 data_rate = d_r(4); end

trans_power = COM_func_dipole_link_budget(trans_freq, distance, ... BER, noise_temp, atm_loss, link_margin, data_rate); trans_pwr(i) = trans_power; i = i+1; end

% plot Fig.(1) plot(trans_pwr*1000, d_r) title('Rover to Lander Communication - Transmitting Power vs. Data Rate'); xlabel('Power (W)'); ylabel('Data Rate (bps)'); grid minor; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COM_script_L_to_MR_plot.m % % Authors: Leigh Janes % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/16/04 LRJ % % This script plots the data rate vs. the transmitting power between two % dipole half wavelength antennas for the communication from mars lander to % mars rover. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

close all clear all clc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUT VARIABLES % Antenna efficiencies trans_ant_eff = .65; recv_ant_eff = .65;

% Distance between antennas, km distance = 1; % km

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % initialzing i = 1; d_r = [1000 5000 1e4 1e5];

% calculate transmitting power for i = 1:1:4 if i == 1 data_rate = d_r(1); elseif i == 2 data_rate = d_r(2); elseif i == 3 data_rate = d_r(3); else i == 4 data_rate = d_r(4); end

% plot Fig.(1) plot(trans_pwr*1000, d_r) title('Lander to Rover Communication - Transmitting Power vs. Data Rate'); xlabel('Power (W)'); ylabel('Data Rate (bps)'); grid minor; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COM_script_L_to_MR_plot.m % % Authors: Leigh Janes % E-mail: [email protected] % Created: 2/15/04 % Last updated: 2/16/04 LRJ % % This script plots the data rate vs. the transmitting power between two % dipole half wavelength antennas for the communication from mars lander to % mars rover. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% close all clear all clc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUT VARIABLES % Antenna efficiencies trans_ant_eff = .65;

recv_ant_eff = .65;

distance = 229700; %km % % Distance between antennas, km % distance = 1; % km %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % initialzing i = 1; d_r = [1 1000 1e4 1e5]; % d_r = [1000 5000 1e4 1e5];

% calculate transmitting power for i = 1:1:4 if i == 1 data_rate = d_r(1); elseif i == 2 data_rate = d_r(2); elseif i == 3 data_rate = d_r(3); else i == 4 data_rate = d_r(4); end

% plot Fig.(1) plot(trans_pwr/1000, d_r) title('Lander to Spacecraft Communication - Transmitting Power vs. Data Rate'); xlabel('Power (kW)'); ylabel('Data Rate (bps)'); grid; grid minor; axis([0 15 0 2e4]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COM_script_MR_to_CV_vars.m % % Authors: Brian Ventre and Leigh Janes % E-mail: [email protected] / [email protected]

% Created: 1/31/04 % Last updated: 2/25/04 BDV/LRJ % %This script defines the variables to completet the link budget from the %Rover to the Crew Vehicle. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Mars rover to Crew Vehicle (CV receiving) link_name = 'Mars rover to Crew vehicle';

% Antenna efficiencies trans_ant_eff = .65; recv_ant_eff = .65;

% Receiving antenna diameter, m recv_ant_diam = 2; % m

% Distance between antennas, km link_distance = 229700; % km

% Data rate, bps data_rate = 1e6; % bps

% Transmitting power, W trans_power = 10; % W %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% COM_script_CV_to_MR_vars.m % % Authors: Brian Ventre and Leigh Janes % E-mail: [email protected] / [email protected] % Created: 1/31/04 % Last updated: 2/25/04 BDV/LRJ % %This script defines the variables to completet the link budget from Crew %Vehicle to the Rover. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Crew Vehicle to Mars rover (Rover receiving) link_name = 'Crew Vehicle to Mars rover';

% Antenna efficiencies trans_ant_eff = .65; recv_ant_eff = .65;

% Receiving antenna diameter, m recv_ant_diam = 0.32; % m

% Distance between antennas, km link_distance = 229700; % km

% Data rate, bps data_rate = 1e6; % bps

% Transmitting power, W trans_power = 500; % W

B.10.4 Reliability Code ******************************************************************************

%Ben Toleman %AAE 450 %Reliability code

clc clear all close all

lam_motor = 80*10^-6; %failure rate of an electric motor lam_ant1 = 1.82*10^-6; %failure rate of an antenna for radio lam_MIMIC = 2.13*10^-6; %failure rate of a MIMIC Chip lam_sig = 3.4*10^-6; %failure rate of a Signal Processor lam_ant2 = 1.82*10^-6; %failure rate of an antenna for RF tag lam_RFswitch = 19*10^-6; %failure rate of a RF Switch lam_CMOS = .66*10^-6; %failure rate of a CMOS Driver & Logic lam_mem = .45*10^-6; %failure rate of Memory lam_clock = .94*10^-6; %failure rate of a Clock Generator lam_inter = .02*10^-6; %failure rate of a Intercom cable lam_Con = 25*10^-6; %failure rate of Control Electronics

lam_ele = 19*10^-6; %failure rate of Electrical Cabling %All values of lamda are from http://www.ece.cmu.edu/~koopman/depend/ahsstudy/tr_97_44.pdf

t = 1:10:21900; %hrs in 2.5 yrs rel_motor = calcul_reliability(lam_motor,t); lam_radio = [lam_ant1 lam_MIMIC lam_sig]; lam_RFtag = [lam_ant2 lam_RFswitch lam_CMOS lam_mem lam_clock]; lam_inter_sys = [lam_inter lam_Con lam_ele lam_radio];

rel_lam_radio = calcul_reliability(lam_radio,t); rel_radio = parallel_series(rel_lam_radio,t,0); rel_lam_RFtag = calcul_reliability(lam_RFtag,t); rel_RFtag = parallel_series(rel_lam_RFtag,t,0); rel_lam_inter_sys = calcul_reliability(lam_inter_sys,t); rel_inter_sys1 = parallel_series(rel_lam_inter_sys,t,0); rel_inter_sys = parallel_series([rel_inter_sys1 rel_inter_sys1],t,1); rel_sys = parallel_series([rel_inter_sys rel_RFtag],t,0); rel_sys1 = parallel_series([rel_inter_sys1 rel_RFtag],t,0);

Fig. semilogy(t/24/365,(1-rel_sys1)) grid title('Failure probability vs. Time') xlabel('Time (years)') ylabel('Probability of Failure')

Fig. semilogy(t/24/365,(1-rel_sys)) grid title('Failure probability vs. Time back-system') xlabel('Time (years)') ylabel('Probability of Failure')

*********************************************************************** *******

%Ben Toleman %AAE 450 %Function to calculate the Reliability of each component

function rel = calcul_reliability(lam,t) for ii = 1:length(t) for j=1:length(lam) rel(ii,j) = exp(-lam(j)*t(ii)); end end

*********************************************************************** *******

%Ben Toleman %AAE 450 %Function to calculate the reliability of a paralell/series system %If series calculation is needed put choice = 0. If parallel calculation is %needed put choice = 1. AAE 450 Senior Spacecraft Design Spring 2004 141 Appendix B - Communications

function rel = parallel_series(reliability,t,choice) if choice == 0 for ii = 1:length(t) inter = 1; for j = 1:size(reliability,2) inter =inter*reliability(ii,j); end rel(ii,1) = inter; end elseif choice ==1 inter = 1; for ii = 1:length(t) for j = 1:size(reliability,2) inter =inter*(1-reliability(ii,j)); end rel(ii,1) = 1 - inter; end else fprintf('Choice must be equal to 0 or 1.'); end return

AAE 450 Senior Spacecraft Design Spring 2004 142 1 http://www.ntia.doc.gov/osmhome/allochrt.pdf 2 http://cuhwww.upr.clu.edu/~advance/documents/GONZALEZ,%20ROSANA.pdf 3 Comparetto, G. M., “Command, Control, and Communications Architecture,” Human Spaceflight: Mission Analysis and Design, edited by W. J. Larson and L. K. Pranke, Space Technology Series, McGraw-Hill, New York, p. 896-902 4 Smith, Howard. Spacecraft Systems Engineering. P. 396-415. 5 Q-par Angus Limited. http://www.q-par.com/pages/Reflector_Antennas.htm 6 Schetgen, KU7G, Robert, The ARRL Handbook for Radio Amateurs 1993, ed. 70, pp. 17-3

7 Schetgen, KU7G, Robert, The ARRL Handbook for Radio Amateurs 1993, ed. 70, pp. 17-3

8 Biswas, A. and S. Piazzolla, Deep-Space Optical Communications Downlink Budget from Mars: System Parameters, August 15,2003, IPN Progress Report 42-154