University of Colorado Boulder



TLEN 5830 Homework #1The purpose of this assignment is to review the essential concepts of radio as per the lectures and lecture notes. Be careful on your attempts to research answers on the Internet as the field of radio has many specific applications, lots of jargon, and perhaps most confusing of all there are many hobby sites with somewhat specialized (and sometimes dubious) information. The lectures and slides should give you all you need to answer the following questions. Try to use these problems to gain some insights. That is, don’t consider these just as mathematical tasks. Look at the results and try to reflect on their implications to gain engineering insights and intuition.Review Question 1:Briefly explain the difference between an analog and a digital electromagnetic signalWhat are three important characteristics of a periodic signal?How many radians are there in a complete circle of 360 degrees?What is the relationship between the wavelength and frequency of a sine wave?What is attenuation?Differentiate between guided media and unguided media?List some significant differences between broadcast radio and microwave.Review Question 2:What two functions are performed by an antenna?What is an isotropic antenna?What is the advantage of a parabolic reflective antenna?What factors determine antenna gain?Why is polarization important? What is a primary method to mitigate polarization efficiency loss?Problem 1. Without resorting to the use of calculators, calculate the following dB conversions. Show your work using the table method demonstrated in class. Convert from a power ratio to dB: a. 50 b. 0.005 c. 800 d. 1/2,000,000 e. 64 Convert from dB to a power ratio: a. -60 dB b. 57 dB c. 53 dB d. 9 dB e. 16 dB Problem 2. Some "absolute dB" problems:?a. Express 2 milliwatts in dBm. b. How many watts is -19 dBm. c, d, and e. 2dBm = C dBw = D dBμ = E dBn. What are the values of C, D, and E? [Note that dBn reference to nanowatts.] Problem 3. Do the dB calculations of Problem #1 USING A CALCULATOR. Make a table showing the estimated results from your answers, and the "actual" calculated values. While we learned that you usually don’t need a calculator to estimate dB values, let’s get a little practice using our calculators in this regard.Problem 4. Assuming the velocity factor in antenna elements is approximately 1 (that is, v = c), what is would be the length of 1/4 wavelength “whip” antennas for the following:a) Common Carrier (telecommunications company) microwave at 7.5 GHz.b) IEEE 802.11a wireless LAN at 5.5 GHz.c) IEEE 802.11g wireless LAN at 2.4 GHz.d) Broadcast TV Channel #54 at 711.2 MHz.e) Broadcast TV Channel #2 at 55.2 MHz.f) FM Radio Station KVOD at 90.1 MHz.g) Citizens Radio Emergency Channel #9 at 27.065 MHz.h) BBC World Services beamed to South America at short wave frequency 6195 KHz.i) AM Broadcast station KHOW at 630 KHz.j) Marconi’s original transatlantic frequency of 272 KHz.k) WWVB’s time signal from Ft. Collins, Colorado at 60 KHz.Problem 5. There’s a picture of a technician climbing a radio tower on the last slide of Lecture Slides-04.Answer these questions based on the picture:a) What kind of antenna do you think is immediately above his head?b) What gain would you estimate this antenna provides?c) Estimate (very generally) what frequency this antenna is used for. (You can assume that the antenna is about half this Royal Army man’s height.)Problem 6. Based on the lecture and slides only and using the formula below, perform the following analysis. Be sure to show your work to get credit:Prec = PinGtGr/(4πR/λ)2We try to get some insight into wireless LAN performance by attempting to calculate the maximum distance an IEEE 802.11g (2.4 GHz) wireless LAN might be usable. We will assume the Access Point (the connection to the LAN) is using a 4 dBi antenna, and our laptop’s built-in LAN card has a built-in “patch” antenna with a gain of -1 dBi. Furthermore, the AP is connected to its antenna through 10 meters of miniature RG-114 coaxial cable with a loss of 3 dB for its short length. The power output of both the laptop wireless LAN card and of the AP is 17 dBm (50 milliwatts), and the antenna is part of the laptop wireless card which has an input impedance of 50 ohms.Problem 6(a). To get a signal (which might not be usable), we need at least 10 microvolts at each receiver. What is the maximum distance we can be from the AP? The procedure for this calculation is complicated but not difficult. Give yourselves enough time for this calculation. Here’s one way you can proceed:? Realize that the 4 dBi gain antenna at the AP and the -1 dBi antenna at the laptopwill result in a total gain factor of 3 dB or two times (GtGr = 2).? Pin is given and is the same for both directions, and the calculation issymmetrical. That is, you need only do the math one way to get your answer.? You will need to calculate Prec to meet the criteria of this design. The receivermust be presented with the given voltage. This is calculated by the familiarformula for power (P = V2/R) with the resistance given as 50 ohms. Remember that half the power is lost in the feedline from the antenna before this voltage can becalculated. Therefore, Pr in the formula is double the power at the actual receiver.? You will want to solve for R/λ first and then multiple by the wavelength to getyour answer.Hint: Remember that his problem is really a simple calculation. Do it step by step as above and you shouldn’t have much problems. You should always check your answers against your knowledge and experience and see if your answer make sense regarding what you have seen with using laptops on wireless LANs. Here we are making a calculation without taking receiver noise into account. This will yield a maximum distance you might expect under the most ideal circumstances. See the next part for a more realistic answer.Problem 6(b). To get a connection at the maximum rate of 54 Mbps, we will need a signal to noise ratio at least 20 dB better than the minimum assumed above. What will be the realistic distance to achieve the maximum speed? (You can “correct” you answer to part a) above by realizing that the receive power will need to be increased by a factor of 100 and therefore the distance will be reduced by the square root of 10 as given by the “inverse square law”.)Problem 6(c). Somebody tells us that IEEE 802.11a at 5.5 GHz is better because there’s less interference. Even though we don’t believe there’s no other nearby users of 2.4 GHz equipment, we are worried about leakage from our microwave oven (which also operates at 2.4 GHz). So weare interested in trying out IEEE 802.11a since we are told that our next door neighbor has aIEEE 801.11a/b/g AP. So we replace our laptop device with an IEEE 802.11a compatiblecard. We want to calculate the maximum distance we can go now, but we don’t want to dothe calculation from scratch. We remember from the lecture that the “effective area” of theantennas, which is directly related to the antenna gain, goes as the square of thewavelengths. This would say that—with other losses and antenna gains being the same—that the effective distance would be approximately halved. Why is this true?Problem 6(d). What do you think would be done to improve the range (or at least make it as good at 2.4 MHz) of IEEE 802.11a 5 GHz LANs?Problem 7. As discussed in class, we know that “line of sight” radio transmissions are limited by the curvature of the Earth. That’s why antennas for long distance VHF or higher frequencies are put on high towers. The formula for estimating the distance to the horizon, H, in kilometers for any given height, H, in meters is:D = 4.124 HProblem 7(a). How far is the horizon for FM station KGUD in Longmont (90.7 MHz) for their antenna at 30 meters above the ground?Problem 7(b). I can’t receive this station at my home. Assuming that I am at the same elevation as the base of KGUD’s antenna tower, how much further would the range of KGUD be if I put an antenna on my roof, 4 meters above the ground? (To do this very simple minded calculation,just add the two distances obtained.)Problem 7(c). What is the maximum distance that United 807 flying at 42,000 feet over the Pacific can communicate with a radar controller antenna located in San Francisco? Assume the base station antenna is at a negligible height above the ground?Problem 7(d). What is the “path loss” for this distance for Oakland Radar Center’s frequency of 133.95 MHz? ................
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