Old Test - Bilingual Problems
1. Un horno microondas emite radiación para cocinar un papa. Usa una frecuencia de 2.45GHz que resuena con las moléculas de agua y las hace vibrar, aumentando así su temperatura. (Las propiedades eléctricas de la papa son e= 40(1-j0.3) eo de donde se puede hallar que la constante de propagación es g= 48+j328 dentro de la papa.)
a) ¿Cuánto penetra la onda?
b) ¿Cuánto es la constante de fase de la onda dentro de la papa?
Solucion: (a) skin depth = 2 cm (b) 328 rad/m2. Un radar montado en un avión se usa para estudiar el capas de hielo glacial transmite una onda plana con campo eléctrico
Presumiendo que el hielo está en el plano z=0 y no tiene pérdidas y que tiene una permitividad de er= 9. (no es un material magnético.)
(a) Halle ki y qi:
(b) Halle el coeficiente de reflección.
Solucion: (a) Ki = π x + 1.2 πz and qi= 39.81 deg. (b) -0.585, qt= 12.3 deg3. Una antena de submarino operando a 1kHz debajo del agua transmite una onda circularmente polarizada (Right Hand => x-jy) con una intensidad de 100 V/m. (En el mar
s= 4 S/m,er= 80, mr=1). La incidencia es normal al plano xy. La altitud es eje z.
(a) Halle una expresión para el E instantáneo.
Solucion:
(b) ¿Cuánto será el Ei que incide en la interface entre agua/aire la cual está 2 metros más arriba?
Solucion: (a) E= 100(x-jy)e-.126zcos(2000pt-.126z) V/m
(b) E(2m) = 77.7 (x-jy) cos(2000pt -.25) V/m4. A lossless quarter-wave transmission line with intrinsic impedance of 50ohms is connected to a 100 W
load. The voltage at the load is 4 with phase of 10o V. Find the voltage at the input of the line (quarter wave from the load).
Answer: V = 2 angle 100o V5. The voltage reflection coefficient at the input of a lossless air transmission line is -1. What is the load impedance if the line is 2m long and operationg at a frequency of 150 MHz?
Answer: Zload = 0 W! (Hint: The line is half-wave long, and the reflection of -1 corresponds to a short).6. Measurements on a lossless transmission line of characteristic resistance of 75 W, show a standing
wave ratio of 2.4 and the first two voltage minima nearest to the load at 0.335m and 1.235m. Use the Smith Chart to determine the load impedance ZL. (The load is at z=0).
Answer: ZL = 105- j 75 ohms.7. Impedance Matching with Single Stub: For a lossless transmission line of last problem (s=2.4, Zo = 75W), but with ZL = 104+j74 W, find the 2nd location nearest to the load and the length of a short circuited stub required to match the line.
Answer: Stub location = .409 l, stub length = 0.368 l .
8. An air-filled cavity resonator operates in the TE110 mode. The cavity dimensions are 50 x 50 x 35mm (a=c>b), and is made of copper (s= 1.5 x 10-6 m)
a. Find the resonant frequency
b. The quality factor
Answer: fr 110= 523 GHz, θ = 2 volume/ (d surface area)= 9,7229. A microstrip line operating at 10 GHz has sc = 5.8 x 10 7 mho/m, w = 2 mm, and Zo = 50 W.
Assume that the dielectric losses are negligible.
a. the conduction attenuation in Np/m
b. the conduction attenuation in dB/m
c. If the line is fed with 10W, find the average power 1 meter from the input in dBW.
Answer: (a) 0.261 Np/m , (b) 2.26 dB/m, (c) 7.734 dBW (= 5.94 W).10. Ionospheric studies at the Arecibo Radar Observatory use a rectangular waveguide to connect the transmitter/receiver to the antenna. Can the dimensions of the waveguide be 30 cm by 70 cm (air filled) if the operating frequency is 450 MHz and the bandwidth is at least 200MHz?
a. find the cutoff frequency for the dominant mode of propagation
b. find the next 3 propagating modes cutoff frequencies
c. Justify your answer , ___Yes or ____No.
Answer: (a) 214 MHz, (b) 429, 500, 543 MHz (c) Nope, can't have more than one mode in bandpass.11. Design a rectangular air waveguide to operate in S band (2.6 - 3.95 GHz). The band should be 20% over the cutoff of the dominant mode, and 95% down from any higher order modes.
Answer: f10 = c/2a = 2.6/1.20 => a= 6.92cm. (for 20% over)
f20 = c/a = 4.3 GHz,
f01 = c/2b = 3.95/.95 (for 95% under) = 4.15 GHz => b = 3.6 cm.12. . Un radar que opera a 10GHz y transmite 2kW de potencia se usa para detectar camiones ( s= 12 m2). Debido al ruido inherente en los componentes del receptor del radar, la potencia mínima que éste puede detectar es de 10-9 W. ¿Cuál será la distancia máxima a la cual se pueden detectar camiones con este radar? (Gr=Gt = 300) Answer: 995 m (~1km).
13. Dos antenas dipolares de media onda (D= 1.6) son 90% eficientes y están separadas por 5 km operando a 300 MHz en aire. Determine la potencia recibida por la antena tomando en cuenta las pérdidas de las antenas, si la potencia transmitida es 40dBW.
Answer: Pr = -52.8dBW.14. For an antenna with a radiation intensity of
U=12.5 sin3φ for -90 to 90 in azimuth and all elevation angles.
Find the directivity, directive gain, and plot the radiation pattern. Answer: HPBW = -104 degrees**In addition, review the theory; basics of antenna parameters, basics of electromagnetism.
!Suerte!
