tarea de propagaciÓn

TAREA DE PROPAGACIÓN

OMAR GUZHÑAY

ALEX CHALEN

BENJAMIN ZAMBRANO

CAPÍTULO 1 EJERCICIO 1

• Find the electric field vector (direction and intensity) for the following; • (a) At a distance of 1m from a 5-C point charge, if the medium is polystyrene.

• E =Q

4π𝑟2εrε0=

5C

4π 1𝑚 2(2,7)(8,854 𝑥 10−12)= 1,66 x1010

• (b) At a distance of 0.5 m from an infinite line charge of 2 C, if the medium is

distilled water.

• E =Q

2πr εrε0=

2C

2π(0.5𝑚) (81)(8,854 𝑥 10−12)= 887,68 x106

• (c) At a distance of 2m from an infinite plane charge of 1 C in air.

• E =

• (d) At a distance of 20 m from an infinite plane charge of 1 C in air

• E =


• Determine the angle of refraction of an electric field that that is incident on a body of calm water at an angle of 30 degrees relative to the horizon. The electric field originates in air, and the water may be considered pure and treated as distilled water.

• ᶓ1= 8,86 x 10 −12

• ᶓ2= (81) 8,86 x 10 −12

• Ф2= arctan(ᶓ2/ ᶓ1 tan(Ф1))= 88,77°


• Find the magnetic field vector at a distance of 1m from a conductor carrying a 1-A current. The conductor is oriented vertically in free space, with the current flowing in the positive z direction.

• 𝐵 =𝝁0𝐼

2π𝑑

• B= 𝝁0(1𝐴𝑚𝑝)

2π(1 𝑚) = 2𝑥10−7

𝑊𝑏

𝑚2


• What is the approximate gain of a circular dish antenna with 30-cm diameter at 40 GHz? Assume a total efficiency of 65% and give your answer in dB.

• Tenemos que: 𝐺 =4𝜋𝐴𝑐

𝜆2

• 𝐴𝑐 = 𝜋 ∗𝑑

2

2∗ 0.65

• 𝐴𝑐 = 𝜋 ∗0.3

2

2∗ 0.65 = 0.045𝑚

• 𝜆 =𝑐

𝑓=

3∗108

40∗109= 7.5 ∗ 10−3𝑚

• 𝐺 =4𝜋(0.045)

(7.5∗10−3)2= 10053.1 = 40 𝑑𝐵


• What is the approximate gain of a rectangular antenna dish with dimensions 100 cm by 20 cm at 10 GHz? Assume a total efficiency of 60%.

• Tenemos que: 𝐺 =4𝜋𝐴𝑐

𝜆2

• 𝐴𝑐 = 1 ∗ 0.2 ∗ 0.6

• 𝐴𝑐 = (0.2) ∗ 0.6 = 0.12𝑚

• 𝜆 =𝑐

𝑓=

3∗108

10∗109= 0.03𝑚

• 𝐺 =4𝜋(0.12)

(0.03)2= 1675.51 = 32.24 𝑑𝐵


• If a system can tolerate 0.5 dB of antenna mismatch loss, what are the minimum and maximum acceptable antenna driving point impedances? Assume that the system’s characteristic impedance is 50 ohms.

• 𝐿𝑝 = 1 − 𝜌2

• 𝜌 =𝑍1−𝑍0

𝑍1+𝑍0

• 𝐿𝑝 = 1 − (𝑧1−𝑧0

𝑧1+𝑧0)2

• (𝑧1−𝑧0

𝑧1+𝑧0)2= 1− Lp

•𝑧1−𝑧0

𝑧1+𝑧0= 1 − 𝐿𝑝 = 1 − 1.12 = −0.12 = ±0.35𝑗

• 𝑍1 − 50 = ±0.35𝑗 𝑍1 + 50

• 𝑍1 − 50 = ±0.35𝑗 𝑍1 + ±0.35𝑗 50

• 𝑍1 ± 0.35𝑗 𝑍1 = 50 ± 17.5𝑗

• 𝑍1 1 ± 0.35𝑗 = 50 ± 17.5𝑗

• 𝑍1 =50±17.5𝑗

1±0.35𝑗⇒ 𝑍1 𝑚𝑎𝑥 = 50 𝑂ℎ𝑚𝑠; 𝑍1 𝑚𝑖𝑛 = 39.086− 31.18𝑗


• Generate a plot of antenna mismatch loss versus VSWR.

• 𝑉𝑆𝑊𝑅 =1+ 𝜌

1− 𝜌

• 𝐿𝑝 = 1 − 𝜌2

• 𝐿𝑝 = 1 − (𝑉𝑆𝑊𝑅−1

𝑉𝑆𝑊𝑅+1)2


• What is the minimum and maximum possible polarization loss factor for a point-to-point communication system if each of the antennas used has an axial ratio of 2dB.You may neglect environmental effects.

• Según la gráfica:

• El máximo valor posible es aproximadamente 0,65 y el mínimo es 0,05


• What are the effective height and effective area of a 0.1 wavelength dipole antenna if the antenna is resonant at 80MHz?

• 𝜆 = 𝑐

𝑓

• 𝜆 = 3∗108

80∗106= 3.75𝑚 = 𝑙

• 𝐼 𝑥 = 𝐼𝑂𝑠𝑒𝑛 𝜋𝑥

• ℎ𝑒 = 1

𝐼0 𝐼 𝑥 𝑑𝑥𝑙

0

• ℎ𝑒 = 𝑠𝑒𝑛 𝜋𝑥 𝑑𝑥𝑙

0

• ℎ𝑒 = 𝑠𝑒𝑛(𝜋𝑙)

𝜋𝑙=0.017m (Effecttive Height)

• 𝐴𝑒 = ℎ𝑒

2𝑍0

4𝑅𝑟=

(0.017)(0.017)(377)

4(73)= 0.00037𝑚2(Effective Area)


• If an aperture antenna has -17-dB sidelobes and the EIRP is 100dBW, what is the worst-case power density that will be received at a distance of 2m from the antenna if the receiver is outside of the transmit antenna’s mainlobe?

• La fórmula de Densidad de potencia:

• 𝐷 =𝐸𝐼𝑅𝑃

4𝜋𝑑2

• 𝐷 = 10100

4∗𝜋∗22

• 𝐷 = 1.9894 ∗ 1098


• Consider a receiver with a 4-dB noise figure and a 2-MHz bandwidth. If a carrier-to-noise ratio of 15dB is requiered for acceptable BER (bit error rate) performance, what carrier (signal) strenght is requiered at the receiver? At what point would this signal be measured or referenced?


• In the preceding problem, if the transmitter at the other end of the comunications link is 2km away, both the transmitter and receiver use a 4-dB antenna, and the frequency is 800MHz, what is the minimun required transmit power?


• Given a receiver with a 100-KHz bandwidth and an effective noise temperature of 600K, what is the noise power level at the input to the receiver? Give the units with your answer.


• Given a symmetrical line-of-sight communication link with a minimun detectable signal of -90dBw, a transmit power of +10dBw, antenna gain of 28dB, and frequency of 10GHz , mounted on a 100-ft tower, what is the maximum communication distance (neglecting all sources of interference or fading)?


• Consider a point-to-point communication link operating at 38GHz, using 35dB dish antennas at each end. The radome loss is 2dB at each end, and a 10 dB fade margin is required to allow for rain fades. If the transmit power is -10dBm, the receiver noise figure is 7dB, the bandwidth is 50MHz, and the link distance is 1.2km, what is the signal-to-noise ratio at the receiver in dB? Assume that free-space loss applies

CAPÍTULO 4 EJERCICIO 5 (continuación…)


• Consider a communication link operating at 28GHz, using 30dB dish antennas at each end. A 10dB fade margin is required to allow for rain fades. If the transmit power is 0dBm, the receiver noise figure ir 7dB, the bandwidth is 50 MHz, and the required carrier-t-noise ratio for reliable operation is 12dB, find the following:

• The required received signal level

• The allowable path loss

• The maximum allowable range.


• A base station antenna with a 9 dBd gain is supplied with 10Wof input power. What is the effective isotropic radiated power?


• Demonstrate that free space loss increases by 6 dB each time the distance between transmitter and receiver is doubled.


• The speech quality for a particular mobile communication system is just acceptable when the received power at the terminals of the mobile receiver is 104 dBm. Find the maximum acceptable propagation loss for the system, given that the transmit power at the base station is 30W, base station feeder losses are 15 dB, the base station antenna gain is 6 dBi, the mobile antenna gain is 0 dBi and the mobile feeder losses are 2 dB. Express the field strength at the receiver antenna in dBmVm_1.


• Tomamos una frecuencia de 900 MHz.


• See Problem 4.12 (Chapter 4): Calculate the received power (in dBm) at antenna B if antenna A is transmitting at 60W.


• Calculate the maximum range of the system described in 5.3 using (a) the free space loss and (b) the plane earth loss, assuming a frequency of 2 GHz and antenna heights of 15 m and 1.5 m.

(a)

(b)


• A 1 V RMS sinusoidal source is applied across the terminals of a half-wave dipole, with source and load impedances perfectly matched. An identical dipole is placed 10 m from the first. What is the maximum power available at the terminals of the receive antenna and under what conditions is this power produced? State any assumptions made in the calculation.

Con una frecuencia de 900 MHz


• A satellite is operated at C-band (6 GHz in the uplink and 4 GHz in the downlink) for video broadcasting. Calculate the free-space loss experienced at this frequency, if the satellite is in geostationary orbit (GEO), located at 36 000 km above ground Basic Propagation Models 103 level. What is the minimum EIRP needed to provide adequate reception, assuming a receiver sensitivity of _120 dBm and effective antenna gain of 20 dBi?


• A one-way microwave link operating at 10 GHz has these parameters:

• Transmitter power 13 Dbw

• Transmitter feeder loss 5 dB

• Transmitter antenna gain 18 dBd

• Receiver antenna gain 10dBi

• Receiver feeder loss 3 dB

• Receiver noise bandwidth 500 kHz

• Receiver noise figure 3 dB

• The receiver operates satisfactorily when the signal-to-noise ratio at its input is at least 10 dB. Calculate the maximum acceptable path loss.


• A transmit antenna produces an EIRP of 1Wand is received by an antenna with an effective aperture of 1 m2 at a distance of 1 km. The frequency is 100 MHz calculate the received power and the path loss. Assuming this is the maximum acceptable path loss for the system, how does the maximum system range change at 1 GHz and 10 GHz, assuming all other parameters remain constant?


• El rango es [10m – 100m]

tarea de propagaciÓn

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