Problemas. ESNA1
Problemas ESNA 1
Problemas. ESNA1
Problema 1 Se diseña una Radar pulsado para iluminar la Luna. El radar tiene un diámetro de antena de 60 ft con una eficiencia de iluminación de un 60%. La frecuencia de operación es de 430 MHz y la potencia mínima en el radar para poder detectar es de 1,5 10
16
W.
La distancia del radar a la luna es de 3,844 10 mts. 8
La sección recta de la luna es 6,64 10 mts. 11
Se pide: a) El tiempo de ida y vuelta de un pulso radar. b) La PRF para no tener ambiguedades en la detección de la distancia c) La potencia de pico del radar requerida.
Problema 2 a) Cual debería ser el PRF de un radar para tener una distancia máxima no ambigua de 60 MN? b) Cuanto tarda la señal en ir y venir cuando el blanco está a la distancia máxima no ambigua? c) Si el radar tiene un pulso de ancho 1,5 s, cuál es la anchura en metros de la energía del pulso en el espacio? d) Cuánto tienen que estar separados dos blancos, en metros, para que sean discriminados, con una ancho de pulso de 1,5 s.? e) Si el radar tiene una potencia de pico de 800KW, cuál es la potencia media? f) Cual es el ciclo de trabajo del Radar?
Problema 3 Un radar PSR Banda L opera a 1300MHz. Su máxima distancia es 200 MN para la detección 2
de blancos con =1 m . Su antena es de 12 mts de ancho por 4 mts de alto y su eficiencia de área es del 65%. La potencia mínima detectable es de 10
13
W.
Determinar: a) b) c) d) e)
El área efectiva de la antena y su Ganancia La potencia de pico transmitida La PRF para tener una distancia máxima no ambigua de 200 MN El ciclo de trabajo, si el ancho del pulso es =2s El ancho de haz en acimut a –3dB
Nota: Se puede aproximar 3dB
72 D
(grados), siendo D el ancho de la antena en
mts.
Problema 4 a) Un radar PSR que radia con una potencia media de 200 w, un 0 =1s y un PRF=1KHz, ¿que potencia de pico tiene?
Problemas. ESNA1
2
b) Hallar la distancia en MN de este radar si tiene que detectar un blanco con = 2 m , si opera a una frecuencias de 2,9 GHz (Banda S) con una antena rectangular de dimensiones: D=5m, L=2,7m; a 0,6 , Smin= 10-12 w. c) ¿Cuál es la RmaxNA? Hallar el número de respuestas por blanco sabiendo que N=15rpm y
3dB 72 D
(grados).
Problema 5 Un radar a f =1,35GHz tiene unas dimensión horizontal de antena de D=33ft, y vertical de 9 ft, con una a 0,6 . Se diseñó para que no haya ambigüedad en distancia hasta 220MN. El tiempo de scan es de 10 seg. La eficiencia de radiación r =1. Nota:
3dB 72 (grados). D
a) Cual es el ancho de haz vertical
3dB en grados.
b) Cuantas respuestas se obtendrán de un blanco. c) Cual será la resolución angular horizontal (azimut) a la distancia máxima no ambigua. d) Si el pulso es de 0 =1s, ¿cual será el volumen de incertidumbre a una distancia R= RmaxNA/2?
Problema 6 Un radar montado en un coche se usa para determinar la distancia a un coche delante de él. El radar opera en una frecuencia de 9375MHz (Banda X), con un pulso 0 =10 ns, su Rmax= 500ft. (Nota: 3ft=1m) a) b) c) d)
¿Cual es el PRF para un R=500ft? ¿Cuál es la resolución en distancia (m)? Si el ancho de haz es de 6 0, ¿Cuál es la resolución angular a R=500ft? Si la antena tiene dimensiones de 1ft x 1ft, a 0,6 , ¿cuál es la ganancia de la antena en dB? 2
e) Encuentra la Pmed para detectar un blanco de = 10 m a R=500ft , sabiendo que Pr min= S -13 w. min= 5.10
Problema 7 Una antena Radar de Ganancia G1 ilumina un avión, a una distancia R, que tiene una antena con ganancia en la dirección del radar de G2 . Un receptor se conecta a la antena del avión y la mitad de la potencia recibida por el la antena del avión es absorbida por el receptor, mientras que la otra mitad se reenvía al radar. a) Hallar la expresión
Potencia. Re ceptor . Avión Potencia. Re cibida.Radar
b) Cual es el valor de la expresión anterior en dB si G1
G2 100
y
R
104
Problemas. ESNA1
Problema 8 En el diseño del diagrama de elevación ( ) de un antena radar PSR 2D, se necesita que la potencia recibida en la antena del radar de los ecos de blancos ( σ=cte) que estén a la misma altura h, sea la misma. a) Demostrar que, considerando D ( )
G ( ) y la potencia transmitida fija, el diagrama en
elevación que cumple este requisito se puede expresar como
G ( ) Go cos ec 2 ( ) . Qué valores intervienen en G0 ? b) Dibujar el diagrama de elevación desde un valor 45 hasta 2 o
o
c) Cómo tendría que ser el diagrama en elevación desde 2 hasta el horizonte para ser o
eficiente en la cobertura radar? Y desde los 45º hasta el cénit? Dibujar la posible forma del diagrama de elevación desde el cénit al horizonte. Razonar la respuesta.
Avión
R h
Radar
Problema 9 Un radar PSR con ganancia de antena G1 , potencia de pico Pt y longitud de onda , radía de forma perpendicular sobre una reflector metálico formado por una placa rectangular metálica de área física Am a una distancia R . El reflector metálico tiene una sección recta que se puede calcular como m
Am Dm ,
siendo la eficiencia para placas metálicas 1 y Dm su directividad. La placa no tiene pérdidas de radiación y su eficiencia de área es igual a 1.
Problemas. ESNA1
a) A partir de la ecuación radar simple y despreciando los efectos de pérdidas externas en la propagación, encontrar la expresión de la potencia recibida por el radar Pr b) Para el caso de Am
1m 2 ,
f 0
1GHz ,
G1
35dB ,
Pt
40dBW y
R
f ( Am , Pt , G1 , R)
5MN , encontrar
el valor de la sección recta del reflector y de la potencia recibida por el radar. c) Comparar el valor de la potencia recibida con la que se obtendría de un avión tipo B747 con
tipica
100m 2 que estuviera en fase de aproximación a 5 MN del radar.
Datos:
G
4 2 Aef
Problema 10 El pulso proveniente de un radar impacta frontalmente en un avión. Si el pulso tiene una duración de 1s y la longitud del avión es de 30 m. Calcule: a) La duración temporal del eco recibido b) ¿Cuál debería ser la duración del pulso para que el radar pudiera resolver (diferenciar) el morro de la cola del avión? c) ¿Qué ancho de banda debería manejar el receptor del radar en el supuesto anterior b?
Problema 11 Un radar de tráfico (fo=10.525 GHz) dispone de una antena de 20 dB de ganancia y 20 dB de relación lóbulo principal a secundario, está diseñado para detectar automóviles con una sección recta a distancias inferiores a R maxUN=50m. Si un coche está equipado con un detector de señales radar, el área efectiva de su antena es K (K=0.001) y su receptor tiene la misma sensibilidad que el receptor del radar, calcule: a) ¿A qué distancia detectará el coche al radar si recibe la señal por el lóbulo principal? b) ¿A qué distancia lo detectará por lóbulo secundario?
Problema 12 Calcular la sección recta radar de una disposición como la de la figura.
l
40
0
Problemas. ESNA1
Problema 13 Determine (a) the peak power (watts) and (b) the antenna physical area (m 2) which make the cost of the following Radar a minimum: Frequency: 1230 MHz (L Band) Antenna aperture efficiency: 0.6 Receiver minimum detectable signal: 3 e-13 W Unit cost of transmitter: $ 2.20 per watt of peak power Unit cost of antenna: $ 1400 per square meter of physical area Cost of receiver and other items: $ 1000000 The Radar must detect a target of 2 m 2 cross section at a range of 200MN (You will have to use one of the simple forms of the Radar range equation) c) What is the cost of the antenna and the cost of the transmitter? d) In a new radar design, how would you try, as a first attempt, to allocate the costs between the antenna and the transmitter (based only on the answer to the above problem)?
Problema 14 If the weight of a transmitter is proportional to the transmitter power (i.e., W T=kTPt) and if the weight of an antenna is proportional to its volume (so that we can say its weight is proportional to the 3/2 power of the antenna aperture area A, or W A=kAA3/2), what is the relationship between the weight of the antenna and the weight of the transmitter that makes the total weight W=WT+WA a minimum, assuming a fixed range? (You will need the simple form of the radar equation to obtain a relationship between Pt and A).
Problema 15 A Radar measures an apparent range of 7 nmi when the pulse repetition frequency is 4000 Hz, but it measures an apparent range of about 18.6 nmi when the prf is 3500 Hz. What is the true range (nmi)?
Problema 16 If the noise figure of a receiver is 2.5 dB, what reduction (measured in dB) occurs in the signalto-noise ratio at the output compared to the signal-to-noise ratio at the input?
Problema 17 A transmission line with loss L is connected to the input of a receiver whose noise figure is Fr. What is the overall noise figure of the combination?
Problemas. ESNA1
PROBLEMA 18 If the noise figure of a receiver is 2.5 dB, what reduction (measured in dB) occurs in the signalto-noise ratio at the output compared to the signal-to-noise ratio at the input?
PROBLEMA 19 The average time between false alarms is specified as 30 min and the receiver bandwith is 0.4 MHz. a) What is the probability of false alarm? b) What is the threshold-to-noise power ratio (VT2/0)? c) Repeat a) and b) for an average false alarm time of one year (8760h) d) Assume the threshold-to-noise power ratio is to be set to achieve a 30-min false-alarm time [value as in part (b)]; but, for some reason, the threshold is actually set lower by 0.3 dB than the value found in part (b). What is the resulting average time between false alarms with the lower threshold? e) What would be the average time between false alarms if the threshold were to increase by 0.3 dB? f) Examine the two values of threshold-to-noise ratio you have calculated in d) and e) and comment on the practicability of precisely achieving a specified value of false alarm time.
PROBLEMA 20 A radar has a bandwidth B=50 kHz and an average time between false alarms of 10 min. a) What is the probability of false alarm? b) If the pulse repetition frequency were 1000 Hz and if the first 15 nmi of range were gated out (receiver is turned off) because of the use of a long pulse, what would be the new probability of false alarm? (Assume the false-alarm time has to remain constant) c) Is the difference between a) and b) significant? d) What is the pulse width that results in a minimum range of 15 nmi?
PROBLEMA 21 A transmission line with loss L is connected to the input of a receiver whose noise figure is Fr. What is the overall noise figure of the combination?
PROBLEMA 22 A radar at frequency of 1.35 GHz has an antenna of width D= 32 ft, a maximum unambiguous range of 220 nmi, and an antenna scan time (time to make one rotation of the antenna) of 10 s. a) What is the number of echo pulses per scan received by the radar from a point target? [use the relationship that the antenna half-power beamwidth in radians is B=1.2 /D]. b) What is the integration loss and the integration-improvement factor when the probability of detection is 0.9 and the probability of false alarm is 10 -4?
PROBLEMA 23 A radar noncoherently integrates 18 pulses, each of uniform amplitude (the nonfluctuating case). The IF bandwidth is 100 kHz. If the average time between false alarm is 20 min, what must be the signal-to-noise ration per pulse (S/N)n in order to achieve a probability of detection of 0.8? What is the corresponding value of (S/N) 1? What would (S/N)1 be if the tarbet cross section fluctuated according to a Swerling Case 1 model?
Problemas. ESNA1
PROBLEMA 24 a) What SNR is required for a radar that makes a detection on the basis of a single pulse, when the probability of detection is 0.5 and the probability of false alarm is 10 -6? Assume a nonfluctuating target echo. b) Repeat for 0.99 probability of detection and the same probability of false alarm. c) Repeat parts a) and b), but for a Swerling Case 1 fluctuating target. d) Compare your results in a table. What conclusions can you obtain from this?
PROBLEMA 25 A radar measures an apparent range of 7 nmi when the pulse repetition frequency is 4000 Hz, but it measures an apparent range of about 18.6 nmi when the prf is 3500 Hz. What is the true range (nmi)?
PROBLEMA 26 Show that the echo signal power Pr received from an aircraft flying at a constant height h over a perfectly conducting flat earth is independent of the range R, when the antenna elevation gain varies as the consecant-squared of the elevation angle (that is; G=G0 csc2). In addition to having a received signal that is independent of the range (requiring less dynamic range in the receiver), what is another reason for employing an antenna with a csc 2 elevation pattern for an air-surveillance radar when compared to a conventional unshaped fan-beam elevation pattern? What are the limitations in applying the simple result of a) to a radar in the real world?
PROBLEMA 27 A radar receives five pulses within its half-power (3 dB) beamwidth as the antenna beam scans past a point target. The middle of the five pulses is transmitted when the maximum of the antenna pattern points in the direction of the target. The first and the fifth pulses are transmitted when the leading and trailing half-power points are, respectively, directed at the target. What is the two-way beam-shape loss (dB) in this case?
PROBLEMA 28 A civil marine radar is employed on boats and ships for observing navigation buoys, detecting land-sea boundaries, piloting, and avoiding collisions. Consider the following civil marine radar: Frequency: 9400 MHz Antenna: horizontal beamwidth = 0.8º Vertical beamwidth = 15 º Gain = 33 dB Azimuth rotation rate = 20 rpm Peak power: 25 kW Pulse width: 0.15 s Pulse repetition rate: 4000 Hz Receiver noise figure: 5 dB Receiver bandwidth: 15 MHz System losses: 12 dB Average time between false alarms: 4 hours a) Plot the single-scan probability of detection as function of range (nmi), assuming a constant cross-section target of 10 m 2 (a navigation buoy) and free-space propagation. [You will find it easier to select the probability of detection and find the corresponding
Problemas. ESNA1
signal-to-noise ratio, rather than the reverse. You need only consider probabilities of detection from 0.3 to 0.99. You may, for purposes of this problem, select a single (average) value of integration improvement factor rather than try to find it as a function of P d (since the curve in the text does not permit otherwise).] b) Repeat (a) for Swerling Case 1 target fluctuation model with average cross section of 10 m2. Plot on the same diagram as (a). c) Comment on whether the average power of this radar is too low, just right, or too high for the job it has to perform here.
PROBLEMA 29 Consider the following air-surveillance radar: Frequency: 2.8 GHz Peak power: 1.4 MW Pulse width: 0.6 s Pulse repetition frequency: 1040 Hz Receiver noise figure: 4 dB Antenna rotation rate: 12.8 rpm Antenna gain: 33 dB Antenna azimuth beamwidth: 1.35 º System losses: 12 dB Average false-alarm time: 20 min Target cross section: 2 m2 Plot each of the following on the same coordinates (with range as the abscissa): a) The free-space single-scan probability of detection as a function of range (in nautical miles) for a constant cross-section target. [You will find it easier to select the probability of detection and find the corresponding SNR, rather than the reverse]. You need only consider probabilities of detection from 0.3 to 0.99. You may, for purposes of this problem, select a single (average) value of the integration improvement factor rather than try to find it as a function of Pd. b) The probability of detection as a function of range for the same situation as part a) but with the detection criterion that the target must be found on at least 2 out of 3 scans of the rotating antenna. [You may assume that the range and the received signal power do not change appreciably over the three scans. For convenience of this calculation, you may assume that the single-scan false-alarm probability is the same as used in part a)]. c) Repeat a) for a Swerling Case 1 with average target cross section of 2 m2 d) Repeat b) for a Swerling Case 1 with average target cross section of 2 m2 e) Is the prf adequate for avoiding range ambiguities? (The radar in this problem is similar to the airport surveillance radar known as the ASR)
PROBLEMA 30 a) What is the probability of detecting a target on at least 2 out of 4 scans when the singlescan probability of detection is 0.8 ? b) What is the corresponding probability of false alarm in this case when the single-scan false alarm probability is 10 -8? c) What should be the single-scan false-alarm probability if the overall false-alarm probability with a detection criterion of 2 out of 4 scans is 10 -8? d) When the higher single-scan probability of false alarm of part c) is employed rather than a 10-8 single-scan probability of false alarm, what reduction in the SNR can be obtained?
Problemas. ESNA1
PROBLEMA 31 (correspon a l’examen de MQ 06/07) Un Radar dissenyat per determinar l’origen dels atacs de projectils té les següents característiques:
Freqüència de treball: 8 GHz Antena: o Amplada de feix en azimut: 1º Amplada de feix en vertical: 20º o o Guany: 35 dB Velocitat de rotació en azimut: 15 rpm o Potència de Pic: 25 kW Resolució en distància: 2.25 Km Freqüència de repetició del pols: 4000 Hz Factor de Soroll del receptor: 4 dB (k=1.38 10 -23 J/K, T0=290 K) Una relació senyal soroll mínima: 15 dB Temps mig entre falses alarmes: 3 hores 20 min Amb una secció recta Radar del blanc de 2 m 2 (vist de davant), i 1.4 m 2 (vist des de darrera)
(Indiqueu les unitats quan calgui). Cal entregar també els fulls amb els càlculs: 1.- Calculeu la màxima distància sense ambigüitat del Radar. 2.- Calculeu el volum d’incertesa a la meitat de la distància màxima sense ambigüitat 3.- Distància màxima a la que pot detectar un projectil allunyant-se del Radar. [Assumiu un receptor B=1/durada del pols transmès]. 4.- Quina és la probabilitat de Falsa Alarma i el nivell de decisió necessari per complir-la (VT2/0). 5.- Quin seria el temps entre falses alarmes si augmentem el nivell de decisió fins a 1 dB. 6.- Quina es la probabilitat de detecció quan rebem un únic pols. 7.- Calculeu el temps d’observació i el nombre d’ecos rebuts de un blanc 8.- Quines pèrdues d’integració en un detector no-coherent podem tolerar, per mantenir les mateixes prestacions en distància, probabilitat de detecció i probabilitat de falsa alarma inicials. 9.- Si el nostre radar té unes pèrdues de sistema de 12 dB, com es redueix el rang si volem mantenir la probabilitat de detecció i falsa alarma. 10.- Com afecta al nostre sistema si el target és fluctuant modelat per un model Swerling CASE 2.
PROBLEMA 32 (correspon a l’examen de MQ 06/07) Trobeu l’expressió analítica i dibuixeu la secció recta radar de la següent agrupació d’esferes en funció de l’angle d’observació ( ).
0
0 3 / 4
160
3 / 4
0
0 / 4 / 4
Problemas. ESNA1
FÓRMULES EMPÍRIQUES 10 log10 B 0.12 * B·C 1.7C 4.54 log10 B 0.12 * B·C 1.7C SNRn ( dB ) 5 log10 n 6.2 n 0.44 B ln(0.62 / Pfa ) C ln( Pd /(1 Pd )) SNR1 ( dB )
2
P fa
e
V T
2 0
Problemas. ESNA1
PROBLEMES MTI PROBLEMES 33 A satellite orbiting the earth in a circular orbit at an altitude of 5000 nmi has a speed of 2.7 nmi/s. a) What is the Doppler frequency shift if the satellite is observed by a ground based UHF radar (450 MHz) lying in the plane of orbit, just as the satellite appears over the horizon? (the radius of the earth is 3440 nmi. You may ignore the effects of refraction by the earth’s atmosphere and reflection from the earth’s surface.) b) what is the Doppler frequency shift when the satellite is observed at the zenith?
PROBLEMES 34 A VHF radar at 200 MHz has a maximum unambiguous range of 180 nmi. A) What is its first blind speed (in knots)? B) Repeat, but for and L-band radar at 1250 MHz. c) Repeat, but for an X-band radar at 9375 MHz. d) What would be the unambiguous range (nmi) of the X-band radar of part c) in order to give the same blind speed you found in part a) for the VHF radar? e) if you needed to have a radar with the first blind speed of the VHF radar of part a), would you rather have the VHF radar of part a) or the X-band radar of part d)? please explain your answer (There might not be a unique answer.)
PROBLEMES 35 An L-band Radar (1250 MHz) has a prf of 340 Hz. It detects a rainstorm moving at a radial velocity of 12 kt. Assume that the width of the thunderstorm’s Doppler spectrum is very small (a narrow spectral line; which is not, of course, reality but it makes the problem easier). The radar employs a single delay-line canceller. A) How much does the single delay-line canceller attenuate (in dB) the storm echo compared to the response if the storm were moving with a radial velocity corresponding to the velocity which gives the maximum filter response? b) what would be the attenuation of the storm compared to the maximum response, if a double delayline canceller were used?
PROBLEMES 36 a) Show that the product of the maximum unambiguous range Run and the first blind speed v1 is equal to c/4, where c= velocity of propagation and = radar wavelength. b) What guidance, if any, does this relation give for avoiding ambiguities?
PROBLEMES 37 What is the highest frequency that a radar can operate if it is required to have a maximum unambiguous range of 200 nmi and no blind speed less than 600 kt.
PROBLEMES 38 Show that a triple delay-line canceller is equivalent to a four-pulse delay-line canceller with weights equal to the coefficients of the binomial expansion with alternating sign.
PROBLEMES 39 An S-Band (3.1GHz) air-surveillance radar utilizes a staggered waveform with four different prfs, which are 1222, 1031, 1138, and 1000 Hz. a) what is the first blind speed (knots) if a constant prf is used which has a pulse repetition period equal to the average of the four periods of the staggered waveform?
Problemas. ESNA1
b) What is the first blind speed (knots) of the staggered prf waveform? Note that the ni for these four frequencies are 27, 32, 29, 33, respectively. c) What is the maximum unambiguous range of the staggered prf waveform?
