This is a 13-part question (long, i know), but all of the questions are interrel

Question

This is a 13-part question (long, i know), but all of the questions are interrelated so I cannot ask them seperately; however, it shouldnt take too long.

Part 1. What is the 10- bit binary representation of a decimal number 517?

Part 2. You have a digital signal that you want to broadcast, which is 111100001111. Now you have a PRN, which is 101100110110. If you apply the XOR operation for each bit as we did in class, what will be the coded version of the signal? Now apply the XOR operation with the PRN again to your coded signal, and find what you get.

Part 3. Using the Newton’s second law and the law of gravity, (1) find the radius of the orbit for a GPS satellite revolving around the earth with a period of 12 hrs. (2) What is its speed in a unit of “m/s”?

Part 4. In a one dimensional space, a signal tower A is located at a coordinate of -100m and the other signal tower B is located at a coordinate of 100m. Each tower has an accurate atomic clock and sent a signal at 00:00:00 (HH:MM:SS). On the other hand, your receiver does not have such an accurate clock and so you have to correct it based on the signals you receive from the two towers. Following the method as discussed in class, if you receive the signal A at 00:00:10 and the signal B at 00:00:06 based on your uncorrected clock, what is your coordinate and what should the corrected time of your clock be if it would show 00:00:11 if it were not corrected? Assume that you are at rest and the speed of signal is 10 m/sec.

Part 5. Considering that water’s index of refraction is 4/3, how long will it take for light to travel through water over a distance of 1 km. Note that the speed of light in vacuum is 3 x 108 m/s.

Part 6. Considering that Rayleigh scattering is the main loss mechanism for visible light in an optical fiber, if you shoot equal intensity red and blue lasers together into one end of an optical fiber and after a long distance, you direct the other end of the fiber to a white paper, will the laser color hitting the white paper look more reddish or more bluish? Why?

Part 7. You have three gemstones in front of you. One is fully clear and transparent without any color. The second is transparent but it has a color due to small amount of metal impurities. The third one is white and opaque. If you want to use one of these gemstones as a laser medium for a visible light, which one would you choose and why?

Part 8. You are planning to buy a photodiode as a receiver for fiber-optic communication working on an infrared light of 1550 nm in wavelength. Noting that the band-gap of silicon is 1.1 eV, can a silicon photodiode work for this purpose? Explain.

Part 9. You are making an optical fiber using two glass materials, named ‘A’ and ‘B’. ‘A’ has the index of refraction of 1.440 and ‘B’ has the index of refraction of 1.455. Among these two, which will you use for the core and for the cladding, respectively?   What will be the critical angle of incidence for total internal reflection?

Part 10. The C-band in the fiber optic communication is 1530 to 1565 nm. Considering that a single analog TV channel requires 6 MHz of bandwidth, how many analog TV channels can be fit into the C-band of a single fiber if no data compression is used?

Part 11. Modern optical fiber has 0.2 dB/km loss at the signal wavelength of 1550 nm. You are sending 1mW of light signal on one end of the fiber, and you want to install an optical amplifier wherever the signal drops below 1 ?W. At what length of the fiber do you have to install your first optical amplifier?

Part 12. For comparison, even the best copper coaxial cable has ~3 dB of signal loss for every 100 m at a typical microwave carrier frequency. If you use the same criterion, at what length of the coaxial cable do you have to install your first amplifier?

Part 13. You need ferromagnetic materials for both hard disk and transformer core. If you are given two types of ferromagnets, one with a large magnetic hysteresis loop and the other with a negligible hysteresis loop, which one would you use for the hard disk and for the transformer, respectively? Explain why

Explanation / Answer

Part 1: The binary number system is base 2 and has 2 digits..0 and 1.

So, 517 = 1000000101

Part 2: Broadcast signal 1 1 1 1 0 0 0 0 1 1 1 1

PRN Signal 1 0 1 1 0 0 1 1 0 1 1 0

-----------------------------------------------------

XOR Operation is 0 1 0 0 0 0 1 1 1 0 0 1

Part 3: Here,

Time period , T = 12 hours

let the radius of the orbit

T^2/r^3 = 4pi^2/(G * M)

(12 * 3600)^2/r^3 = 4pi^2/(6.673 *10^-11 * 5.98 *10^24)

solving for r

r = 2.66 *10^7 m

the radius of orbit is 2.66 *10^7 m

Part 5: given data

index of refraction is 4/3,

t=?

distance of 1 km

speed of light in vacuum is 3 x 10^8 m/s.

index of refraction n = c/v

4/3 = 3*10^8/v

v=2.25*10^8 m/s

t=distance/velocity =1000m /( 2.25*10^8)

t=4.44*10^-6 sec

PLEASE RATE, ASK YOUR QUERY, THANK YOU :)

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