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Find the N-S and E-W dimensions from a map of the US, and use geometry to calculate the required 3 dB beamwidths of the satellite antenna. Calculate the approximate gain of the antenna. Answer: Dimensions of the rectangle from a map are approximately km in the N-S direction and km in the E-W direction. Similar dimensions based on the latitudes and longitudes are given in part a above. In this case, the dimensions of the antenna must create an elliptical footprint that fits inside the rectangle.
A more accurate result can be obtained by recalculating the distance from the satellite to the upper and lower edges of the rectangle and then using the rule of sines to find the angle at the satellite. The approximation of a flat earth is reasonable for the E-W direction.
The state of Pennsylvania is approximately one degree wide E-W by one half degree high N-S when viewed from geostationary orbit at a longitude of 75 degrees west. Calculate: a. The dimensions of a downlink Ku-band antenna on a geostationary satellite with 3 dB beamwidths equal to the width and height of Pennsylvania. Use a frequency of Identify the dimensions as E-W and N-S.
Answer: The wavelength for The dimensions of an uplink Ka-band antenna on a geostationary satellite with 3 dB beamwidths equal to the width and height of Pennsylvania. Suppose that the maximum dimension of the satellite at launch is 3 m wide, determined by the shroud of the ELV. Describe in a paragraph how you would launch the satellites in a and b above carrying: a the Ku band antenna, and b the Ka band antenna.
Answer: The dimensions of the antenna for 30 GHz in part b are below the diameter of the ELV shroud, so the antenna will fit inside the shroud. The antenna might need to be folded down against the satellite body for launch. In a , the 11 GHz antenna dimension exceeds the shroud diameter, so the reflector of the antenna would have to be folded. This is difficult to do mechanically and is avoided whenever possible. Various methods have been used to make reflectors that can be folded or collapsed for launch read Chapter 3 for the details.
A constellation of low earth orbit satellites has an altitude of km. Each satellite has two multiple beam antennas that generate 16 beams. One antenna is used to transmit at 2. Using simple geometry, find the coverage angle of the satellite antenna when the lowest elevation angle for an earth station is 10 o.
Hint: draw a diagram of the earth and the satellite and use the law of sines to solve the angles in a triangle. S o G O Geometry to find angle at satellite.
Coverage zone with 16 beams O is the center of the earth, G is the earth station, and S is the satellite. Answer: The tiangle SGO in the above figure is used to solve for the angle , which is one half of the coverage angle of the satellite. The coverage angle is Estimate the coverage area over the surface of the earth, in km. Assuming that all 16 beams from the satellite antennas have equal beamwidths, determine the beamwidth of one beam.
Hint: draw a circle representing the coverage area and fit 16 circles representing the 3 dB beamwidths of the beams inside the first circle. Answer: Between four and five of the multiple beams must fit across the coverage circle. Hence the multiple beams have a beamwidth in the range Find the gain and the dimensions of each antenna on the satellite. Answer: At the uplink frequency of 1.
At the downlink frequency of 2. At both frequencies the gain is the same because the beamwidths are the same. A geostationary satellite carries a C-band transponder which transmits 15 watts into an antenna with an on-axis gain of 32 dB. An earth station is in the center of the antenna beam from the satellite, at a distance of 38, km. For a frequency of 4. Calculate the received power level in watts and in dBW at the antenna output port.
Calculate the on-axis gain of the antenna in decibels. Answer: At 4. Calculate the free space path loss between the satellite and the earth station. Make your calculation in dB units and give your answer in dBW. Calculate the total power radiated by the sun in watts and in dBW. Hint: The sun is 93 million miles about million kilometers from the earth.
At that distance, the sun produces a flux density of 1. This power density is present over all of a sphere with a radius of million km. Answer: The entire light output of the sun passes through the surface of an imaginary sphere with a radius of x 10 6 km. At that distance, the flux density crossing the sphere is 1.
Hence the output of the sun is 1. If calculations show any transmitter power to approach dBW, the calculations are wrong. A C-band earth station has an antenna with a transmit gain of 54 dB. The transmitter output power is set to W at a frequency of 6. The signal is received by a satellite at a distance of 37, km by an antenna with a gain of 26 dB.
The signal is then routed to a transponder with a noise temperature of K, a bandwidth of 36 MHz, and a gain of dB. Calculate the path loss at 6.
Wavelength is 0. Calculate the power at the output port sometimes called the output waveguide flange of the satellite antenna, in dBW. Calculate the noise power at the transponder input, in dBW, in a bandwidth of 36 MHz. Calculate the carrier power, in dBW and in watts, at the transponder output. Answer: The gain of the transponder is dB.
The satellite in Question 1 above serves the 48 contiguous states of the US. The antenna on the satellite transmits at a frequency of MHz to an earth station at a distance of 39, km. The antenna has a 6 o E-W beamwidth and a 3 o N-S beamwidth. The receiving earth station has an antenna with a gain of 53 dB and a system noise temperature of K and is located at the edge of the coverage zone of the satellite antenna. Assume antenna gain is 3 dB lower than in the center of the beam Ignore your result for transponder output power in Question 1 above.
Assume the transponder carrier power is 10 W at the input port of the transmit antenna on the satellite. Calculate the gain of the satellite antenna in the direction of the receiving earth station. Hence satellite antenna gain towards earth station is Calculate the carrier power received by the earth station, in dBW. Answer: Calculate the path loss at 3. Calculate the noise power of the earth station in 36 MHz bandwidth.
The satellite transmit antenna gain at 11 GHz is 30 dB towards a particular earth station. Path loss to this station is dB , including clear air atmospheric loss. Each coded BPSK signal has a symbol rate of 50 kbps and requires a receiver with a noise bandwidth of 50 kHz per channel. Calculate the power transmitted by the satellite in one voice channel.
Answer: Each channel receiver has a noise bandwidth of 50 kHz or 47 dBHz. Path loss at 11GHz is Geostationary satellites use L, C, Ku and Ka bands. The path length from an earth station to the GEO satellite is 38, km. For this range, calculate the path loss in decibels for the following frequencies: Note: Round all results to nearest 0. Using the result for 1. Low earth orbit satellites use mainly L band, with ranges varying from km to 2, km.
Calculate the maximum and minimum path loss from earth to a satellite, in dB, for the uplink frequency of 1. Answer: Wavelengths are: 1. A geostationary satellite carries a transponder with a 20 watt transmitter at 4 GHz. The transmitter is operated at an output power of 10 watts and drives an antenna with a gain of 30 dB. An earth station is at the center of the coverage zone of the satellite, at a range of 38, km. Using decibels for all calculations, find: a.
The power received by an antenna with a gain of 39 dB, in dBW. Answer: Received power can be calculated from the effective area of the antenna aperture and the incident flux density, but since the antenna gain is given in dB, it is better to use path loss and the link budget.
A LEO satellite has a multi-beam antenna with a gain of 18 dB in each beam. A transponder with transmitter output power of 0. An earth station is located at the edge of the coverage zone of this beam, where the received power is 3 dB below that at the center of the beam, and at a range of 2, km from the satellite.
The noise power of the earth station receiver for a noise temperature of K and an RF channel bandwidth of 20 kHz. A satellite in GEO orbit is a distance of 39, km from an earth station.
The required flux density at the satellite to saturate one transponder at a frequency of The earth station has a transmitting antenna with a gain of 52 dB at Find: a. The output power of the earth station transmitter. A 12 GHz earth station receiving system has an antenna with a noise temperature of 50K, a LNA with a noise temperature of K and a gain of 40 dB, and a mixer with a noise temperature of K.
Find the system noise temperature. A geostationary satellite carries a C-band transponder which transmits 20 watts into an antenna with an on-axis gain of 30 dB.
Calculate the on-axis gain of the antenna in dB. Answer: At a frequency of 4. Repeat parts a through d of Question 10 for a Ka band transponder transmitting at a frequency of Answer: Flux density is independent of frequency, so the result is the same as in Problem 10 above.
Answer: Given a flux density at the earths surface, an antenna of area A eff m 2 collects the same power at any frequency. Hence the result is the same as in question 10 above.
Note to instructor: Questions 12, 13 and 14 are based on problems from Take Home exams. A significant length of time is needed to complete the solutions. The uplink station is located on the 2 dB contour of the satellite footprint. Allow 0. Calculate the transmitting earth station antenna gain and path loss at 6.
Under conditions of heavy rain, the C-band path from the transmitting station suffers an attenuation of 2dB. Check: When the uplink is attenuated by 3. Under conditions of heavy rain, the C-band path to the receive station suffers an attenuation of 1. Hint: You need to find the sky noise temperature that results from a total excess path attenuation of 1. Answer: Under clear air conditions, the gaseous attenuation of 0.
When rain affects the downlink and rain attenuation is 1. The sky noise temperature increases because the downlink attenuation has increased. For a path attenuation of 1. The system noise temperature in clear air conditions was 75 K. The carrier power has fallen by 1. This is because sky noise temperature is low under clear air conditions and the LNA has a low noise temperature. The increase of The combined effect is disastrous to the link, which goes into outage. A larger receiving antenna, with 1.
Fortunately, rain attenuation of 1. Question Allow 1. Calculate the transmitting earth station antenna gain and path loss at You may assume a high gain LNA and ignore the noise generated in other parts of the receiver. Determine the diameter of the receiving antenna. The receiving terminal is located on the 3 dB contour of the satellite footprint, and clear air attenuation on the path and other losses total 0. Answer: Set the receiving earth station antenna gain as G r dB.
Path loss at the downlink frequency of Downlink power budget P t Under conditions of heavy rain, the Ku-band path to the satellite station suffers an attenuation of 6 dB. Using the same analysis as in Problem Under conditions of heavy rain, the Ku-band path to the receive station suffers an attenuation of 5 dB.
Answer: The analysis must follow the method used in Problem The sky noise temperature is then 1 0. In clear air, the downlink C. N ratio was The downlink margin is again negative, at - 0. However, with a FEC coding gain of 5. It carries 16 transponders, each with a saturated output power of W and a bandwidth of 25 MHz. The antenna on the satellite has a gain on axis of 34 dB. The noise bandwidth of the digital TV receiver is 20 MHz. Use a distance to the GEO satellite of 38, km in your calculations.
Calculate the free space path loss and the receiving terminal antenna gain at Draw up a link budget for the downlink from the satellite to an earth station on the 3 dB contour of the satellite antenna beam. Assume that the satellite transmits at a power level of W.
Include a clear air atmospheric loss of 0. The receiving terminal has a system noise temperature of K in clear air. Draw up a noise power budget for the receiver using the receivers noise bandwidth. Answer: Earth station receiver input noise power budget k Boltzmanns constant What is the clear air link margin? For 0. Answer: The increase in system noise temperature is from K to K.
Calculate the clear air link margin and 0. Answer: The previous results were for a receiving earth station located on the 3 dB contour of the satellite antenna footprint. Customers on the 2 dB contour have a signal that is 1 dB greater. Each transponder operates at a different carrier frequency in the 17 GHz band, and the RF channel noise bandwidth is 20 MHz. The noise temperature of the satellite receiver is K the satellite always looks toward the "hot" earth.
Use these values in the remaining parts of this question. Calculate the uplink path loss and the uplink antenna gain at The gain of the receiving antenna on the satellite in the direction of Utah is 31 dB.
Draw up a clear air uplink budget for the link from the earth station to a single transponder on the satellite using a transmit power of P t watts, and atmospheric and other losses of 1. Calculate the noise power at the input to the satellite receiver in a noise bandwidth of 20 MHz. Answer: Transponder input noise power budget k Boltzmanns constant Hence the earth station transmitter power is given by P t where P t The gain of the satellite transponder must be set to amplify the received signal at the transponder input to an output level of watts.
Calculate the gain of the transponder in decibels. Ignore the change in frequency in the transponder. When designing RF equipment, a common rule to avoid oscillation is to make the amplification at any given frequency no higher than 60 dB. How would you design a bent-pipe DBS-TV transponder to provide the end to end gain that you calculated? Answer: The power at the input to the transponder is P t In this transponder we need a gain of This should be distributed through the amplifer,.
Typically, transponders are built with excess gain and include an RF or IF attenuater. Calculate the clear air link margin for the uplink. This gives a margin over Question 14 This is a multipart question. All the questions are about the satellite communications system described below.
Description of System A satellite communication system consists of 50 LEO satellites in km orbits, several hubs stations operating in Ka-band, and many handheld transceivers operating in L-band. The handheld units transmit to transponders at MHz and receive from transponders at MHz.
The system uses digital speech compressed into a transmission channel RF bandwidth of 16 kHz. Channels are spaced 20 kHz apart to allow a guard band between channels. The Parameters of the system are given below: You may not need all of these. Calculate the path loss, in dB, for a km path at 1.
For a worst case analysis, we must take the longest path length of km. Calculate the noise power, in dBW, for the receiver in the transponder and for the receivers at the hub station and the handheld unit, in a single voice channel bandwidth of 10 kHz. Note: use the bandwidth of one speech channel, 10 kHz for all the calculations, not 2 MHz. The satellite has broad coverage antennas at L-band and Ka-band with half-power beamwidths of degrees. Estimate the gain, in dB, of the antennas at each frequency.
Take care to use the correct path loss and receiver noise power values for each frequency. Give your answers in decibels. Answer: This calculation is to establish a reference case for a single 10 kbps channel uplink. This calculation is to establish a reference case for a single 10 kbps channel downlink. Downlink power budget: EIRP The handheld phone has an antenna gain of 0 dB. The hub station and transponder transmitter power can be shared among a group of voice channels.
Using the higher of the two values, find the 3 dB beamwidth of one of the multiple beams. Estimate the number of beams that will be needed to serve the coverage zone of a single o beamwidth antenna. We cannot increase the gain of the satellite telephone because it needs an omni-directional antenna, which has a gain of 0 dB y definition.
We must now try to fit a number of these beams inside the coverage zone of o at the satellite. We can fit approximately three beams of The example at the right shows a 9 beam arrangement. The center beam could be expanded to provide a more even coverage.
When a terminal is in the central part of the coverage area the path length to the satellite is much shorter allowing the use of a broader center beam with a lower gain. For example, three beams could be used in the central area instead of one giving a total of eleven beams.
If the channel spacing is 20 kHz, can all of these channels fit into a 2 MHz bandwidth transponder? Since the available transponder bandwidth is 2. The 1. Any number of these channels can be added to the transponder until the bandwidth is fully occupied, since each uplink channel operates in SCPC mode. In the 2. The multiple beam antenna provides an additional Determine whether the transponders are power limited or bandwidth limited. Give reasons for your answer.
Answer: As can be seen from the answers above in part b , three of the links are bandwidth limited and could carry channels each. The fourth link, from the satellite to the handheld satellite phone, is power limited. Additional antenna gain of 8. The antenna gain must be increased to The illustration shows and example with 35 beams. The communication system described needs two transponders to permit two way voice communication between the hub station and the many transceivers. Based on your answers in Question 3, find the gain of each transponder from input port to output port.
Note: the transponder gain does not include antenna gain. Lets assume that the satellite is redesigned with a different multiple beam antenna such that each transponder carries channels. The transponder output of 20 W is divided between channels, giving 0.
Power per downlink channel is again 7. The situation in which the inbound link can carry channels and the outbound link carries only 13 channels is impractical, because a pair of channels, one inbound and one outbound, is needed to make a telephone link.
This question looks at the cost of the system over its lifetime and calculates a minimum cost per voice circuit. Each LEO satellite carries 20 transponders. What is the total number of speech channels that the satellite can support when fully loaded? How many telephone circuits it takes two channels to make a telephone circuit?
Answer: We will assume that each transponder can carry telephone channels, so the capacity of one satellite is one way channels, or two way telephone conversations, when fully loaded.
The expected lifetime of the satellites is 10 years, and the system requires a total of 10 spare satellites to be launched over the 10 year period. Calculate the cost of operating the system for a ten year period. There are , minutes in a year, so we can sell 50 10 , circuit minutes in the 10 year period.
Write two paragraphs discussing the cost of the system and the cost of a voice circuit. What price per minute would you set for a satellite voice circuit? Would you expect customers to be willing to pay this amount for a satellite telephone connection?
How does the cost compare to terrestrial cellular telephone charges? However, there are a number of difficulties with the LEO satellite system that are not obvious in the above analysis. If the satellites are in polar orbits, most of them are over the poles or the oceans and cannot be used. For example, if this system used polar orbits, only two satellites would be visible from the United States at any time, giving the entire population of the US a capacity of only telephone circuits.
Put this way, it is clear that a large number of overseas customers must be recruited to make the system pay. One further factor that makes satellite telephones less attractive than cellular phones is that the weak signals will not penetrate buildings.
You have to go outside to make and receive calls, - not pleasant in the middle of winter. The difficulty for the satellite system owner is that the above calculation is misleading.
Customers cannot be signed up until the system is operational, and then the customer base will grow only slowly. This has crippled several of the LEO satellite telephone systems built in the late s. The baseband bandwidth of the TV signal is 4. Calculate the peak frequency deviation of the FM carrier using Carsons rule. Answer: Carsons rule gives the bandwidth of an FM signal in terms of the peak frequency deviation, f pk, and the maximum baseband frequency, f max.
Calculate the unweighted FM improvement factor for the video signal. The signal to noise ratio improvement is reduced when two TV signals are transmitted rather than one because the frequency deviation must be reduced. The bandwidth of each signal is 16 MHz. Calculate the peak frequency deviation of the FM signal using Carsons rule. The de-emphasis and subjective weighting factors for the video signal total 17 dB.
How would you rate the quality of the video signal? There would be some perceptible noise in the TV picture. Each FM carrier occupies a bandwidth of 16 MHz. A digital T1 carrier with a bandwidth of 2. You will need to solve problem 2 before attempting this problem.
The power at the output of the transponder must be shared between the three RF signals in proportion to bandwidth occupied by each signal. For convenience, assume that the transponder radiates a total power of 20 watts. Calculate the power allocated to each signal when only two FM-TV signals are transmitted, and when all three signals are transmitted.
Hence each carrier gets 10 W. When an additional T1 signal is added, power must be shared in proportion to bandwidth occupied by each signal to keep PSD across the transponder constant. Each TV signal gets 0. Answer: The TV signals were transmitted at a power of 10 W with two signals in the transponder. When the third signal is added, transmitted power drops by 10 log 9. The T1 carrier gets less power, but also is received against a lower noise background because of its narrower bandwidth.
A satellite telemetry link operating in S-band uses frequency modulation to transmit the value of an analog voltage on the satellite to a receiving earth station. The voltage has a range from 1. The FM modulator on the satellite has a constant of 10, Hz per volt. What is the Carsons rule bandwidth for the FM signal? Answer: We must first calculate the peak frequency deviation for this signal.
A satellite link has an RF channel with a bandwidth 2. What is correct symbol rate pulse rate for this link? A Ku band satellite uplink has a carrier frequency of What is bandwidth occupied by RF signal, and what is the frequency range of the transmitted RF signal? Note: There is a typo in the text in the first printing that gives the frequency as A T1 data transmission system transmits data at 1. Find the BER at the receiver output and the average time between errors.
What is the bit error rate now? A satellite data transmission system transmits data from two T1 carriers as a single 3. The symbol rate on the link is 1. What is the bandwidth occupied by this signal, and the noise bandwidth of the receiver for this signal? Answer: From equation 5. FEC would be needed to maintain a more reasonable error rate on this link. A 36 MHz bandwidth transponder is used to carry digital signals. What is the bit rate of the QPSK signal? How often does a bit error occur. Give your answer in days, hours, minutes, or seconds, as appropriate.
Put another way, we have one error every seconds. What Bit Error Rate would you expect in the recovered bit stream? How often does a bit error occur? A satellite communication system is built as a star network with one large hub station and many remote small earth stations. The system operates at Ka band using the K9 geostationary satellite, and carries digital signals which may be voice, data, or compressed video.
The K9 satellite has transponders with a bandwidth of 60 MHz that can be operated in either of two modes: as a bent pipe or with a 40 Msps QPSK baseband processor.
The outbound link from the hub to the remote stations has an uplink from the hub station to the satellite that is the input of transponder 1. In the initial system design the remote earth stations use receivers capable of receiving 40 Msps QPSK signals. The 5- 10 transponder is operated in bent pipe mode with sufficient back-off to make it linear.
The receiver has a QPSK demodulator with an implementation margin of 1. For the purposes of this question you may assume that all transmitters and receivers in the network and on the K9 satellite have ideal RRC filters. What is the correct noise bandwidth for the earth station receiver that receives the QPSK signal, and what is the bit rate of the link? There are no errors on this link in clear air conditions.
An uplink fade occurs which causes an attenuation of 10 dB between the hub station and the satellite. The transponder is operated in bent pipe mode. There are now thousands of errors every second and the link is in an outage. Transponder 1 is switched to operate with the 40 Msps baseband processor. Answer: With a baseband processor on the satellite, the uplink and downlink are independent, and the bit error rates on the uplink and downlink add.
Rainfall statistics for the location of the hub station show that attenuation at the uplink frequency will exceed 20 dB for 0. If the hub station uses uplink power control to mitigate the effects of uplink rain attenuation, determine the maximum uplink transmitter power in watts that must be transmitted to ensure that the link BER does not exceed 10 -6 at the remote earth station receiver output for Answer: The requirement here is that the bit error rate at the earth station receiver output not exceed 10 -6 for more than 0.
This is a substantial increase in transmitter power a factor of Check: The limiting condition is when there is 5. A baseband processor on the satellite makes the uplink and downlink independent. Thus rain attenuation of Discuss the value of UPC at the hub station transmitter in this application. Would you recommend a linear transponder or a baseband processing transponder be used on the K9 satellite?
Answer: Uplink power control is effective at preventing the downlink from going into outage because of rain attenuation on the uplink, when a linear transponder is used. Without UPC, a typical Ku band link is likely to fail because of uplink rain attenuation. If there is nt any link of you are lookin for then please feel free to request.
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