Assignment-III and Its Solution 1. For a 4.0 GHz downlink link, if satellite TWTA power output is 10 dbw, on axis antenna gain is 34 db and Feeder loss is 1 db then the satellite EIRP on earth at 3 db ontour edge of overage will be A. 55 dbw B. 50 dbw C. 45 dbw D. 40 dbw EIRP in deibel on the main axis of the antenna will be ombination of the TWTA power, antenna main axis gain and feeder loss. Hene, EIRP on the main axis of the antenna is alulated as 10+34 1 43 dbw. So, on the 3 db ontour edge of the antenna it will be 43 3 40 dbw. Hene, the orret one is D. 2. A DTH terminal is loated at Goa at 2 db ontour edge of satellite transmit antenna footprint. Assuming path loss differene is negligible, for same C/N how muh the DTH antenna gain is to be hanged if it is shifted to Port Blair at 9 db ontour edge of satellite transmit antenna foot print. A. The antenna gain has to inreased by 7 times B. The antenna gain has to redued by 7 times C. The antenna gain has to inreased by 5 times D. The antenna gain has to redued by 5 times The Loation Port Blair is loated at 9dB ontour edge of the transmitting antenna footprint, Therefore, the same station will reeive 7 db less power than that loated at Goa. Now the arrier to noise ratio in db an be mathematially written as C/N EIRP L p +G k T B. Hene, to maintain same arrier to noise ratio, the antenna gain has to be inreased by the 7 db, whih is equivalently five times of the original one. Thus, the orret one is C. 3. Find the EIRP of the downlink operating at 4 GHz. The antenna has effetive aperture area of 10 sq-meters and 10 Watts of power is given input to it. A. 43.5 dbw B. 43.5 dbm C. 53.5 dbm D. 53.5 dbw The operating frequeny of the down link is 4 GHz. So, gain of the antenna an be alulated as G 4π A λ 2 e 4πf2 A e 4π (4 109 ) 2 10) 22340.21 or equivalently 2 (3 10 8 ) 2 43.5 dbi. The input power is 10 watts whih is 10 dbw. So, the EIRP is in dbw is 10+43.5 53.5dBw. hene the appropriate option is D. 1
4. A reeiver at 290K is having noise figure of 4 db. The noise power density of the reeiver is A. -228.6 dbw/hz B. -170 dbm/hz C. -202.2 dbw/hz D. -100 dbw/hz The reeiver noise figure is 4 db. Therefore, the equivalent noise temperature an be alulated as, T 290[F 1] 290[10 4 10 1] 438.45K, equivalently 26.41dBK. Now the formula for noise power density is N 0 kt, where k is Boltzmann s onstant and has value of 228.6 dbw/k/hz. So, the noise power density in db is k + T 228.6+26.41 202.19 dbw/hz. So, the appropriate hoie is C. 5. The effetive input noise temperature of a earth station reeiver is 30K when the effet of noise ontributions from antenna and feeder were not taken into onsideration. If the reeiver is fed from an antenna having a noise temperature of 50K via a feeder with a loss of 2.5 db, determine the noise temperature of the reeiver onsidering the effet of antenna and the feeder noise ontribution. Assume T 0 290 K A. 28.1 K B. 126.9 K C. 185 K D. 155 K It is mentioned in the question that the loss fator, L of the feeder is 2.5 db, whih is 1.778 in linear sale. Now, the ontribution of the antenna noise temperature when referred to the input of the reeiver noise is T A L 50 28.1K. 1.778 The ontribution of the feeder noise when referred to the input of the reeiver is T 0 (L 1) L 126.9K. Therefore, the effetive input noise temperature of the reeiver, taking into aount the effet of noise ontributions from antenna and feeder is 28.1+126.9+30 185K. So, the appropriate hoie is C. 6. A ertain 6 GHz satellite uplink has the following data: Earth station EIRP 80 dbw; Earth station to satellite distane 35780 Km; attenuation due to atmosphere 2 db; satellite antenna s aperture area0.5 sq-meter; satellite reeiver s system noise temperature 290 K; satellite reeiver s bandwidth 20 MHz. Determine the link margin for satisfatory quality of servie if the threshold value of reeived arrier to noise ratio is 25 db. A. 18.9 db B. 16.8 db C. 14.2 db D. none of these 2
The uplink frequeny is higher than that of down link. Therefore, the uplink wave length is λ 3 108 0.05m. Now, the satellite antenna gain an be alulated as 6 10 9 G 4πAe 2513.27, whih is equivalently 34 db. λ 2 The reeiver s noise temperature and effetive bandwidth is mentioned in the question, and hene very easily we an determine the noise power of the satellite reeiver. So, N 10log(kTB) 130.96 db. The path loss an be alulated as 20log 4πR 20log 4π35780 103 199.08 db. Therefore, the arrier to noise ratio of the reeived signal is(80 2 199.08+34) ( 130.96) λ 0.05 43.88 db. Hene, the link margin is 43.88 25 18.88dB. So, the appropriate hoie is A. 7. A LNB with gain of 12 db, a bandwidth of 150 MHz and a noise figure of 4 db feeds a reeiver with equivalent noise temperature of 900 K. Determine the noise figure of the overall system. A. 4.71 B. 5.1 C. 3.2 D. 2.71 the entire system an be represented by the figure given below: From the noise temperature speifiation of the reeiver, we an alulate the noise Figure 1: Representation the asaded system of the Q7 figure of the reeiver. So, the noise figure of the reeiver in ratio nf 2 1 + Te 4.1. Now by using the formula of the noise figure of the asaded system, 1+ 900 290 Hene, the orret hoie id D. nf nf 1 + nf 2 1 G 1 10 0.4 + 4.1 1 10 1.2 2.71 T 0 8. AnRFamplifierhas20dBgainand1GHzbandwidth. Hotandoldloadtemperatures (T 1 and T 2 ) and orresponding amplifier output powers (N 1 and N 2 ) were measured as at T 1 290 K, N 1 is 62dBm and at T 2 77 K, N 2 is 64.7 dbm. If the amplifier is used with input soure temperature T s 450 K, Find the output noise power. 3
A. -100 dbw B. -60 dbw C. -100 dbm D. -60 dbm Assume T e is the equivalent noise temperature, G is gain and B is bandwidth of the amplifier N 1 GkT 1 B +GkT e B and N 2 GkT 2 B +GkT e B. So, Y fator in db is Y (N 1 N 2 ) ( 62.0) ( 64.7) 2.7 db, equivalent to Y 1.86 in linear sale. The equivalent noise temperature due to noise fator is T e T 1 YT 2 290 1.86 77 170 K Therefore, the overall system noise temperature for Y 1 0.86 soure Temperature T s 450+170 620 K and G 20dB and B 1 10 9 Hz The Noise power of the amplifier is ( 228.6+10log(6200)+10log(10 9 )+20) 90.67dBw or equivalently 60.67 dbm. Hene, the appropriate answer is D. 9. Inasatellite link, operating in11 GHz, thepower reeived by theearth stationis 126 dbw. The power amplifier of the satellite supplies 100 watts power to the antenna. Determine the diameter of the down link antenna of the satellite if the gain of the earth station is 1.7 dbi. Assume the downlink satellite antenna has effiieny of 60% and the path loss ourred is 205 db. A. 2.8 meter B. 8.2 meter C. 4.2 meter D. 2.6 meter The reeived power in deibel, in ideal ase an be mathematially modelled as P rx P tx +G tx +G rx L p The satellite power amplifier transmits a power of 100 W, whih is equivalently 42 dbw. The power reeived by the earth station is 126 dbw, and the free spae loss is speified as L p 205 dbw. So, by replaing the parameters with their orresponding values, we get the gain of the downlink antenna G tx 205 126 20 1.7 57.3 db Now, we know that, the gain of a paraboli refletor antenna is related to the diameter of the aperture an effiieny of the antenna. S, G η( πdf ) 2. Where the entity D 4
represents the diameter of the antenna. Hene, by using above formula, we get η( πdf πdf Thus, the appropriate option is B ) 2 10 5.7 10 5.7 η 10 5.7 D η 10 5.7 πf 0.6 3 108 π 11 10 9 496.072 8.681 8.21 m 5