RF Column 37 - November 1994 Copyright (c) 1994,1995 H. Douglas Lung ALL RIGHTS RESERVED TOPICS: Introduction to RF Path Analysis - What is K Factor? Internet news groups FCC Rules on CD-ROM FCC demands use of new emission designators How to contact me ------------------------------------------------------------------------ The last few months my columns have focused on the work I've been doing with digital video compression and other practical matters. This month I'll get back to a more technical subject - the K-factor used in predicting line of sight propagation. I know it sounds boring, but it is one way to explain long distance UHF-TV reception and microwave fades. In this column I'll show you how you can use almost any computer spreadsheet program to plot signal paths, including K-factor adjustment and obstructions. I'll also update you on some new resources of interest to RF engineers on the Internet. You might wonder why I chose K-factor as a topic this month. A discussion with Luis Duarte, Chief Engineer at our Miami station, WSCV channel 51 prompted it. We were discussing how WSCV manages to consistently put a signal into Cuba, well beyond "line of sight" UHF propagation. I used "K-factor" as part of the explanation and it seemed like a good topic for this month's column. What is "K-factor"? Usually, a "K" factor is a constant added to an equation to fudge it to match the real world. For RF propagation, K-factor is a fraction representing the curvature of a RF signal through the atmosphere. The most commonly used K-factor is 4/3 or 1.333. K-factor is the ratio between the effective diameter of the earth (as it appears to the RF signal) and the actual diameter of the earth. For example, a K-factor of 4/3 means that the RF wave will behave as if the earth were 4/3 (or 1.333 if you prefer decimals) times larger in diameter.With K = 4/3 an RF wave won't travel in a straight line through the atmosphere (into space), but instead will curve towards the earth. This happens because the refractive index normally decreases with height (it is normally cooler at higher altitudes). The result is to increase the "line of sight" range between two locations because the extra refraction will make the earth appear flatter (larger diameter). You may be wondering if the ratio can ever get large enough to make the earth appear flat. The answer is yes, it can! At an infinite K-factor, the RF signal will be refracted (bent) enough in the atmosphere that it follows the curvature of the earth. Large amounts of refraction can cause some unusual events, not only to RF waves but visible light as well. You've seen it in the "mirage" on the road in hot weather. A layer of hot air near the road refracts light from the sky, making it appear like a pool of water. The more esoteric modes of propagation that can result from unusual atmospheric conditions require covering quite a bit of meteorological science, so I'll leave that for future columns. This month I'll show you how to use the K-factor when calculating path clearance. As K-factor varies, it will have the effect of flattening or bulging the earth. An RF path shooting over fog may see the earth bulging, due to the temperature inversion usually associated with fog (cooler air near the ground, warmer air above). If the opposite condition exists such that there is a sharp decrease in refractive index with height the earth will flatten. Graphs of refractivity vs. height may be difficult to locate, but they can be constructed from standard meteorological charts showing temperature and water vapor pressure at specific pressure levels. I may get into this in a future column, but if you want to read about it now I found a good description in the "VHF-UHF Manual", Third Edition, published by the Radio Society of Great Britain. The discussion in this book doesn't include K-factor but instead uses the refractive index, from which you can calculate the K-factor. I found some details on K-factor variations for various locations around the world in Peter Saveskie 's excellent "Radio Propagation Handbook", published by Tab Books, Inc. He obtained the graphs from a U.S. NTIA (National Telecommunication and Information Agency) publication. If you don't have time to research all this data for every microwave path, search out other engineers who have experience building microwave systems over similar paths to get an idea of what to expect. For most paths, plotting a microwave path at K-factors of 4/3, 1, 3/4 and 1/2 will cover most conditions. This is easier than you think. I used to sit down and plot paths using 4/3 K-factor paper. If multiple paths were involved, studying UHF "line of site" coverage for example, this could take a lot of paper. I've now come up with a much easier way to plot paths using a standard computer spreadsheet program. We're going to have to get into some math here, but it isn't difficult. You might think that because the earth is round, plotting a path taking into account earth curvature and the K-factor correction would require using spherical geometry and complicated math. There is a much simpler way. Using a K-factor to change the effective radius of the earth permits path calculation using simple geometry -- the Pythagorean theorem. The sides of the right angle triangle are the path, the line from one end of the path to the center of the earth and the line from the other end of the path to the center of the earth. Work it out on paper if you like. After reducing the equation down to its simplest terms, we end up with: h = (2 x D1 x D2) / (3 x K) where h = the height of the earth's "bulge" in feet, D1 = the distance to the bulge in miles from the start of the path D2 = the distance from the bulge in miles to the end of the path and K = K-factor, described above. For h in meters and D1 and D2 in kilometers the formula becomes: h = (D1 x D2) / (12.75 x K) If you were plotting the path on graph paper you would define the X and Y axis of the graph with the appropriate scale, choose a K-factor, then use the formula above to calculate the bulge of the earth at certain intervals along the path. Connect the points with a curve and you have the effective curvature of the earth. Add topographical features like hills and mountain peaks to the base heights calculated here and you have a chart you can use to check path clearance. If this sounds like a lot of receptive calculations, you're right. We can use a computer spreadsheet to do the calculations. Some will even plot a graph. Here's an example. Lets consider a path that is twenty five miles long. The transmitting antenna is 200' above AMSL and the receive antenna is 300' above AMSL. The only obstructions on the path are buildings and trees which are spread all along the path but do not exceed 30' AMSL in height at any location. Will we have line of sight during normal refractive conditions with a K-factor of 4/3? Refer to Figures 1 and 2 to see how I set up the spreadsheet using Quattro Pro. Figure 1 shows a print out of the full spreadsheet, while Figure 2 shows the layout with the row and column numbers and a list of formulas for the first few columns. You can ignore the "A:" in front of each cell number since that refers to the "notebook" reference that some of the newer spreadsheets support. This spreadsheet doesn't require more than one "notebook", so it will work even on older spreadsheets. You may have to change the formula layout if you are using one of the Microsoft spreadsheet programs, which don't follow the "Lotus" formula style I used. Notice that the formulas in rows 12 through 14 start in column B and repeat all the way to the last column (AA in this case). I didn't show all the formulas, since using the normal spreadsheet cell copy commands will automatically increment the references for each succeeding column. When you are all done, if your spreadsheet has graphing capability you should be able to print out a chart looking like Figure 3. It's a lot easier than plotting on graph paper! If what I said above and Figures 1 and 2 make perfect sense to you, you can skip this section. If not, here is an explanation of what is going on. I first stored all the constants in their own cells at the top of the spreadsheet. These include path length, transmit antenna height, receive antenna height, the height of the maximum obstruction and the K-factor used. If you store these values in a separate table instead of in the formulas it is a lot easier to change them if you want to see what happens with lower antenna heights, higher obstructions or different K-factors. In my spreadsheet, these values are in cells F3 through F7. In row 9, starting with cell B9, I filled in the path length at one mile intervals up to the total path length (stored in F3). Most spreadsheets offer a "Fill" command that allows filling a block of cells with values that increment at a fixed interval. You could use smaller increments if you have a complicated path and need to deal with specific obstructions . Row 10 is the most complicated one. Starting with cell B10, it contains the formula for calculating the earth bulge. I could have used range names to make the formula easier to read, but not all spreadsheets support that feature. Here's the formula for cell B10 as shown in Figure 2: (2*B9*($F$3-B9))/(3*$F$7) Here is it re-written using more descriptive variables: 2 x Distance x (Path_Length - Distance) --------------------------------------- 3 x K-factor Distance is the distance we are calculating the bulge at, measured from the path start. It is stored along row 9, as described above. Path_Length is the total length of the path and is fixed. It stored in the table of values at the top of the spreadsheet, in cell F3. The "$" symbols keep it from incrementing when copied to the next column. K-factor is the K-factor we are using for the path plot. It too is fixed and stored in the table of values, in cell F7. Like Path_Length, "$" symbols are used to make the reference absolute (fixed). When the formula is copied into cell C10, everything stays the same except for the Distance, which is now taken from cell C9. These numbers track all the way to the end of the path. Cell B11 and the rest of row 11 contain the obstruction height at the start of the path. To keep this example simple, I used the same height throughout the path. If you have access to a computer program that can output terrain data along a path actual numbers could be inserted here. If you did that the graph would show the actual terrain. The old fashioned way would be to plot the path on a topographical map and enter the maximum terrain height in each one mile segment of the path. Cell B12 and other cells in row 12 contain a formula which adds the height of the earth bulge plus the height of the obstruction from the cells above it. Cell B13 and the rest of the cells in row 13 plot the path height above flat earth. It is simple arithmetic. Since we've already accounted for refraction when calculating the earth bulge, this path will yield a straight line, going up or down in height depending on whether or not the receive antenna is higher or lower than the transmit antenna. Since the path heights at each end of the path are fixed, the points in between are extrapolated used by adding the difference between the receive and transmit antenna height multiplied by ratio of the distance from the start of the path to the maximum path length to the transmit tower height. Note that the difference will be a negative number if the receive antenna is lower than the transmit antenna. The formula is: +$F$4+($F$5-$F$4)*B9/$F$3 or, using descriptive variables: Tx_Height + ((Rx_Height - Tx_Height) x (Distance / Path_Length)) With all these numbers, its easy to calculate path clearance. Subtract the Path Height from the Total Height of the obstructions to obtain the clearance. While these drawings make the path look like a guaranteed success, running the same path using a K-factor of 0.5 reduces the clearance at one point in the path to only 9 feet above obstructions. That certainly doesn't provide fresnel zone clearance and the signal would be attenuated. That's all there is to it. If you'd like a copy of the spreadsheet send me an e-mail message and I'll send it to you UUENCODED in a reply message. I can supply the file in Lotus WKS or WK1 formats, Quattro Pro WQ1 format or Excel XLS format. Let me know which you want. Since I published my Internet address here I've been amazed at the huge response I've gotten from it. The number of people and resources on the Internet keep growing. This month I have a couple changes to announce. The rec.video.satellite group I referred to a few months ago has been reorganized and split into three separate groups. The group rec.video.satellite.misc is for commercial satellite users, including uplink operators, VSAT users, etc. The group rec.video.satellite.tvro contains the core of the old rec.video.satellite, now focused on home dish satellite reception excluding small dishes like DBS. Direct to home satellite reception using services like DirecTV, USSB and PrimeStar now has its own group -- rec.video.satellite.dbs. While European satellite users have their group, don't be surprised if more of those discussions move into these new groups. If you have access to a "World-Wide Web" server such as Lynx, Cello, or Mosaic, check out the new FCC home page at "http://fcc.gov:70/0h/AAA_HOMEPAGE.hmtl". The capitalization is critical and the 0's in 70 and 0h are zeroes. This page has an FCC logo and links to the FCC Web Server as well as some international radio / TV related resources. You can get direct to the FCC Web Server without graphics but without the links to other global resources by pointing your URL at "http://www.fcc.gov/AAA_homepage.html". David Cronshaw, a photographer and editor at KCAL sent me some news on his new World Wide Web TV server. He's offering it as a spot where TV stations can make photos of talent, technical info and such available to the Internet community. Currently available on the server is a list of TV stations in the U.S. By the time you read this much more should be available. You'll find David's service at "http://tvnet.com/TVnet.html". That page includes graphics. The non-graphic page, according to David's e-mail message, is "http://tvnet.com/". Don't include the "'s when typing in the URL's. I've been looking for other sources for the F.C.C. Rules in electronic form. I had a subscription to Pike & Fisher's "Rules on Disk", but gave up on that when my subscription ran out. (I won't get into the details here.) While browsing around on the Internet I found a new company offering not only FCC Rules electronically, but the entire Code of Federal Regulations and the Federal Register. This service isn't free but I've found it worth the $450 I paid to get access to all of Code of Federal Regulations Part 47 - Telecommunications. Unlike the disk based offerings, this Internet source provides text of all of Part 47. As technologies merge, it is handy to have not only broadcast regulations, but regulations on cable, telco and private operational fixed services available as well. There is no usage charge beyond the yearly fee, so if you want to do a quick check on Part 97 it won't cost the company any extra. The CFR's are currently updated monthly but they plan to have daily updates available in the future. The regulations are accessible via Gopher with each section and subsection having its own Gopher directory. This makes it difficult to download big sections of the rules, but since most Gopher programs permit capturing to disk it's possible to save a portion of the rules for quoting or reference away from an Internet connection. Counterpoint Publishing also offers the CFR's on CD-ROM and a tracking service that will e-mail you when rules are changed. For more information contact Hal Kingsley at Counterpoint Publishing, 800-998-4515 or email hal@counterpoint.com. If you are filing new applications for TV Auxiliary services administered out of Gettysburg, you might want to take a look at your FCC Rules (electronic or otherwise) to check out the proper emission designators. Over a year ago the F.C.C. said all licenses would have to use the same standard emission designators, but some services, like TV Auxiliary, were allowed to continue using the old designators. The FCC announced that they will no longer accept applications with the old designators. Information on the approved emission designators is in 47CFR 2.201. I also covered this some time ago in TV Technology. If you need a copy of the excerpt on emission designators, send me an e-mail. That's it for this month. Next month I hope to have some news from the SBE/SMPTE/RTNDA jumbo conference in Los Angeles. As I numbered this column I see I'm now into my fourth year writing this column. I didn't expect it to last this long! Your comments, suggestions, news and tips help keep it going. Thank you! If you operate a high power TV transmitter, don't forget to send me the tube life statistics I requested last month. The easiest, fastest way to reach me is via e-mail, either to dlung@gate.net or to 70255,460 if you are on CompuServe. Please do not e-mail messages to me from Internet using my CompuServe address. CompuServe charges me for each one I accept (they come in showing "POSTAGE DUE") and also for the reply, if I do it through CompuServe. On the other hand, if you are on CompuServe, feel free to use that address. You can also call me at 305-884-9664, but be warned I have a busy schedule from about 10AM to 6PM eastern time. You can fax me at 305-884-9661. Don't expect a fast reply, but if you must use mail send it to 2265 Westwood Blvd., Suite 553, Los Angeles, CA 90064. All the best to you and yours during the upcoming holidays! Copyright (c) 1994 H. Douglas Lung ALL RIGHTS RESERVED