World of Ham Radio 1997

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Text File | 1997-02-01 | 24KB | 529 lines

Documentation for TL.EXE Program Ver. 3.09, Jan 24, 1996 by R. Dean Straw, N6BV Senior Assistant Technical Editor, ARRL OVERVIEW [Note: Version 3.09 fixed a silly little bug computing the voltage maximum point along a mismatched transmission line. Version 3.08 added the ability to change the unloaded Qc of the capacitors in the tuning networks. Beyond Version 3.06, the voltage ratings for some cables were revised per Belden's latest catalog.] "TL" is short for "Transmission Line." The TL program has been under development, intermittently, for about 7 years. It started out as a small, personal utility to analyze my own antenna and feed-line system. Over the years, friends and associates asked for new features; I also added a number of capabilities on my own. Gradually, TL grew larger and larger, so that now there are more than 2400 lines of code in the program. TL also got complicated enough that I decided I had better add a documentation file to go along it! TL has a lot of capabilities. The original purpose was simply to determine the impedance at the shack-end of a transmission line terminated with a complex load impedance. Modern Method-of- Moment programs like NEC can accurately compute the feed-point impedance of an antenna over actual ground. Essentially, TL allowed me to continue the antenna analysis down into the shack. TL uses the hyperbolic Transmission Line Equation to compute the line input impedance. To do that, it needs the type of line (coax RG type or open-wire type), the physical length of the line, and the frequency of operation. TL also determines the losses on the line, separated into two components: the inherent matched-line loss, and the additional loss due to SWR when the load is not equal to Z0 of the line. About four years ago, I added the ability to picture various antenna tuner configurations that could be used to transform the impedance at the input end of a transmission line to 50 ohms. This was for "perfect" components without any losses. About two years after that addition, I worked extensively with Don Patterson, KK6JI. I thus became curious about the sort of stresses the line is subject to under various load conditions. So I added a search for the maximum RMS voltage along the line, in 1 degree increments. (For your information, the highest voltage will usually be near the load end of a line terminated in a highly reactive load impedance.) TL stabilized for awhile in this configuration, until Frank Witt, AI1H, started investigating the losses in various antenna tuner configurations. Frank had developed an elegant approach to 1 measuring real tuners using simple instrumentation. While Frank had used TL to rapidly evaluate numerous test cases, he wanted more information. He persuaded me to expand the program (to about double its original size) to add iterative search algorithms. TL could thus determine explicitly the losses in the various components making up real antenna tuners. CAVEATS I must caution you at this point. TL displays results out to two, or even three, decimal places. Internally, computations are carried out to even more decimal places, of course. In the real world, the one factor that varies the most in actual transmission lines is the Velocity Factor. This may easily vary plus or minus 10% for typical lines -- in fact, the velocity factor may even vary slightly for two pieces of cable cut from the same bulk roll! Along with the Velocity Factor, the exact value for the characteristic impedance Z0 also varies. TL will give you a good indication of what you can expect in the real world, but only plus or minus the velocity factor and the actual impedance at the antenna feed point! Please remember: TL is fundamentally an educational tool. It can also be used very effectively as a design tool, provided that you know the exact parameters of your transmission lines and your antennas. If TL helps open your eyes about transmission lines and antenna tuners, particularly the losses associated with each, then I will have achieved my goal in writing it. TL will complete a computation in a fraction of a second on a powerful modern microcomputer, like the 80486DX/33MHz machine I am using now to write this documentation file. It takes about five seconds to work on an ancient 8088-based 4.77 MHz PC, with an 8087 numeric coprocessor installed. Roughly the same amount of time is needed for a 33 MHz 80486SX computer (without numeric coprocessor.) TL employs a lot of heavy-duty math, so a numeric coprocessor is very desirable. The program is entirely character-based for output display. Hence any IBM-PC compatible computer will work with TL. Hitting [Shift] [Print Screen] will print out a TL screen on any printer that recognizes the 8-bit IBM character set. USING TL TL is menu-driven and is reasonably "friendly." However, I must assume that the user has some technical knowledge about transmission lines and antenna tuners. The user must be familiar with the so-called rectangular representation of complex impedance, in the form Za = Ra +/- j Xa. Later in this file there is a table of typical impedance data for several types of antennas. You can use this data with TL to model realistic situations. You boot up TL once you have gotten into the subdirectory 2 containing TL.EXE, the executable file, using the CD [change directory] command in DOS. Once there, Type: TL [Enter] The opening screen shows a menu of the various types of transmission lines TL models. The first eight choices are flexible coaxial cables, with "RG" designations. Choices 9 through 12 are Hardline coaxial cables. Choices 13 and 15 are for two-wire balanced transmission lines, such as 300-ohm transmit- ting line, 450-ohm "window ladder line" or 600-ohm wire line. Choice number 16 is for "other" transmission lines not found on the main menu. For this choice, the user manually enters the characteristic impedance (both resistive and reactive parts), the matched-line loss (in dB/100 feet), the velocity factor and the maximum rms voltage for which the line is rated by its manufacturer. Choices 1 through 15 use the parameters listed in Chapter 24 of The ARRL Antenna Book, including the values for matched-line attenuation versus frequency, found in Fig 22, on page 24-16. (Note that the matched-line loss for 450-ohm "window" ladder line has been revised to have the same slope as #12 open-wire line, from the second printing of the 17th Edition. TL reflects that change.) If you merely hit the [Enter] key, TL will select the default value of "4," meaning RG-8A/RG-213, 50-ohm cable solid-dielectric cable. In most data entry points in TL, there is a default value, indicated by square brackets; e.g., [4] in the main menu. TL will then prompt you for the length of the transmission line, in feet. The default value is zero feet -- this is useful when evaluating antenna tuners by themselves, without an intervening transmission line between the tuner and the load. Just hit [Enter]. Next, you will be prompted for the operating frequency, in MHz. The default is 3.5 MHz, simply by hitting the [Enter] key without entering anything else. You can enter any frequency as high as 5000 MHz (5 GHz), or as low as 0.002 MHz (20 kHz). After you hit [Enter], TL will compute and display the matched-line loss for the chosen line. The matched-line loss is for a load equal to the characteristic impedance of the particular transmission line chosen, for the length of line and the frequency chosen. Next, TL will prompt you to enter the resistive part of the load impedance, in ohms. If you don't enter a number, but simply hit the [Enter] key, TL will automatically enter a resistive value of 0.00001 ohms. It doesn't enter zero ohms, because that would result in embarrassing "divide by zero" problems later on. After you hit [Enter] for the resistive part of the load 3 impedance, you will then be prompted to enter the reactive part of the load, again in ohms. Note that a capacitive reactance must be preceded with a "-" (minus) sign. An inductive reactance need not be preceded with a "+" (plus) sign, although you may enter one if you wish. Merely hitting [Enter] will enter a reactance of zero ohms. After you finish specifying the impedance, TL will do its computations. It will present you with a screen showing the information you entered, plus the SWR at the load, followed by the SWR at the input of the transmission line. In general, the two SWRs will be different. If the line is very lossy or the SWR at the load is very high, the difference between the two SWR values may be great, with the lower value at the input of the line. Measuring the SWR at the input of a lossy line with a high SWR at the load will mask the magnitude of the SWR at the end of that line, and may possibly lull you into complacency as you measure the SWR in the shack. The next line on-screen shows the additional loss in the line due to the SWR at the load, followed by a line showing the sum of the matched-line loss and the additional loss due to SWR. This is the total loss in the transmission line. The power computations are based on a power of 1500 W at the input of the transmission line. (I tacitly assume at this point that there is a lossless antenna tuner to match the line's input impedance to the 50 ohms needed by a typical transmitter.) TL also displays the transformed impedance at the input of the transmission line, both in rectangular (R +/- jX ohms) and polar coordinates (magnitude in ohms, phase angle in degrees). For 1,500 W of rf into the input of the line, the maximum RMS voltage along the line is displayed, along with the distance from the load where the peak voltage occurs. Note that transmission lines are rated by their manufacturers in terms of RMS voltage. TL displays the rms voltage rating for the particular transmission line chosen, for comparison. At the bottom of the screen is a prompt to choose the next action -- the default is [T], for antenna Tuner. EVALUATING ANTENNA TUNER CONFIGURATIONS If you select either "T" or [Enter], TL will erase the screen and then display the Antenna Tuners menu. You can select one of four different configurations: 1 = Low-Pass L-Network 2 = High-Pass L-Network 3 = Pi-Network 4 = Tee-Network You can also exit from this menu back to either the main menu or back to DOS if you like, by selecting "M" or "X" respectively. Choose one of the antenna-tuner configurations. If you choose either the pi-network or tee-network antenna tuners, you will be 4 prompted to enter the value, in pF, of the output capacitor in the network. For the pi-network the default value is 500 pF, and for the tee-network the default value is 100 pF. Once you have entered the necessary information, TL will compute the values needed to transform the impedance at the antenna tuner output to 50 ohms. If the chosen network configuration cannot perform the desired transformation, an audible alarm will sound, and TL will recommend another network or another output capacitor value to try. The inductor is usually, but not always, the most lossy component in an antenna tuner. TL assumes a default value for unloaded Q of 200 for an inductor, a typical value for a practical inductor mounted in a metal case. The model for a lossy inductor is an inductive reactance in series with a loss resistance. For example, if the unloaded Q is 200 and the inductive reactance at the chosen frequency is +400 ohms, then the loss resistance is 2 ohms in series with the +400 ohms reactance. TL assumes that the unloaded Q for any capacitor in the antenna tuner is 1000. Again, the model for a lossy capacitor is the capacitive reactance in series with a small loss resistance. The default value of unloaded Q = 1000 for a capacitor is typical of transmitting variable capacitors. The operator can modify the unloaded Q value for both the inductors and capacitors in a tuner, using the "Q" prompt from one of the screens showing a schematic antenna-tuner representation. The unloaded Q values chosen will remain for subsequent network computations. THE ANTENNA TUNER SCREEN Examine the antenna tuner screen carefully -- a lot of information is displayed there! At the top of the display, there is a summary of the transmission line parameters chosen: the frequency, the type of line, and the length of the line. On the next line the impedance at the input of the line is displayed, in rectangular and polar forms. This is the impedance presented to the antenna tuner to be transformed to 50 ohms. Then TL shows something called the "Highest effective network Q," also known commonly as the "loaded Q" of a network. This is the highest Q in the network, at the specified load impedance, and is an indication of how "touchy" the tuning will be. The higher the effective network Q, the more carefully you must tune the variable capacitor(s) and/or variable inductor in the tuner in order to achieve the desired transformation to 50 ohms. The loss in an antenna tuner is also closely related to the effective network Q -- the higher the effective network Q, the higher will be the loss. Efficiency in an L-C network is defined 5 as: Efficiency (%) = 100 x (1 - (QL/QU)) where QL is the loaded Q, and QU is the unloaded Q of the network components. See page 13.7 of the 1995 ARRL Handbook for more details on this subject. For a given network loaded Q ("effective network Q" in TL), components with higher unloaded Qs will result in lower tuner losses. This makes intuitive sense, especially if you recall that "Q" stands for "Quality Factor," and higher unloaded Qs mean higher quality, less lossy components. TUNER LOSSES, DETAILS Examine the line showing the estimated power loss in the tuner. The loss shown is for an rf input to the tuner of 1,500 W, the full Amateur legal limit. The loss is expressed in watts, in dB, and also as a percentage of the 1,500 W at the input. For example, a particular tuner configuration might lose 114 W out of the 1,500 W put into it, yielding a loss of 0.34 dB, or 7.44% of the input power. If the input to the tuner is 100 W, rather than 1,500 W, the loss would still be 0.34 dB, or 7.44% of 100 W = 7.44 W. The next line on-screen summarizes the amount of loss in the transmission line itself, plus the total loss in the line and the antenna tuner, both expressed in dB. STRESSING THE TUNER Now examine carefully the table for the individual components in the antenna tuner. The reactances for each element are shown first, followed by the peak voltage, the RMS current, and the power lost. Each is computed for 1,500 W of power. For lower power levels, multiply the voltages and currents by the square root of the ratio of power in use divided by 1500. For example, if the power into the tuner is 100 W: Multiplying factor = Square Root (100/1500) = 0.2582 Note that the voltage shown by TL is the peak voltage across each component. Pardon the pun, but this is potentially a little confusing, especially where a series element is concerned. What is shown is not the voltage from the element to "ground" (the common terminal); it is the voltage across the component itself. In addition, the current shown is that flowing through each component. Look carefully at the on-screen schematic. Note that the impedance actually seen at the output terminals of the tuner is listed towards the top of the screen, not on the schematic itself, due to lack of space. The load impedance at the end of the transmission line is shown schematically, preceded by 6 squiggly lines that symbolize the intervening transmission line. Exceeding the peak voltage rating across any component in a tuner will probably cause an arc. Exceeding the current-carrying ability for a component will often result in smoke, due to the excessive amount of power dissipated in that element! The inductor in a tuner will sometimes melt because of excess power dissipation. This occurs most frequently with low-resistive loads, with or without a high reactive component. For example, you can simulate a stressful situation by specifying a load impedance of 3 + j0 at 3.5 MHz, for a tee-network configuration having a 100 pF output capacitor. The shunt inductor will not only have to withstand more than 6000 V peak, but worse yet, it will have to dissipate almost 700 W of power at more than 20 A of circulating current! Toasted coil, if it doesn't arc first. TL allows you to play around with various impedances, unloaded Qs and different network configurations, without having to endure the smoke and arcing that occurs in many tuners, even ones supposedly rated to handle a "full gallon" of rf. Now, for fun, increase the size of the output capacitor in the tee-network and/or increase the unloaded Q of the inductor or the capacitors to help unstress the beleaguered antenna tuner in the example above -- or change to a lower-loss configuration than the tee- network. Now, let's try something really dramatic. At a frequency of 3.5 MHZ, enter a value of 0.00001 ohms for the resistive part of the load, with a reactance of zero ohms. Then select the Tee network, with an output series capacitor of 100 pF. The tuner will absorb all 1500 W of input power -- in other words it tunes up into itself with a short at the output! In general, L-networks will exhibit the least loss among the various network configurations, but they often require awkward values for inductance and capacitance. The tee-network configura- tion is often used because it can accommodate a wide range of impedances with practical values of variable capacitors and inductors, albeit with sometimes disastrous internal losses. The pi-network configuration is flexible, but it too will often require very large values for the shunt capacitors. Another hint: from the screen showing the SWRs and losses in the transmission line, you may bypass the antenna tuner configuration menu by choosing directly "1", "2", "3" or "4", corresponding to the number of the desired antenna tuner network, followed by [Enter]. TL will then prompt you for the next piece of information needed. 7 SAMPLE TEST DATA 100-foot long, center-fed dipole, 50 feet over ground with dielectric constant (relative permittivity) of 13, conductivity of 5 mS/m. Computed by NEC2 for flat-top configuration. Freq. Feedpoint MHz Impedance ---------------------------------- 1.83 MHz 4.5 - j 1673 ohms 3.8 MHz 39 - j 362 ohms 7.1 MHz 481 + j 964 ohms 10.1 MHz 2584 - j 3292 ohms 14.1 MHz 85 - j 123 ohms 18.1 MHz 2097 + j 1552 ohms 21.1 MHz 345 - j 1073 ohms 24.9 MHz 202 + j 367 ohms 28.4 MHz 2493 - j 1375 ohms 66-foot long, center-fed inverted-V dipole, apex at 50 feet high over ground with dielectric constant of 13, conductivity of 5 mS/m. Freq. Feedpoint MHz Impedance ----------------------------------- 1.83 MHz 1.6 - j 2257 ohms 3.8 MHz 10.3 - j 879 ohms 7.1 MHz 64.8 - j 40.6 ohms 10.1 MHz 21.6 + j 648 ohms 14.1 MHz 5287 - j 1310 ohms 18.1 MHz 198 - j 820 ohms 21.1 MHz 103 - j 181 ohms 24.9 MHz 269 + j 570 ohms 28.4 MHz 3089 + j 774 ohms FEEDBACK, PLEASE This is where TL stands. In a very complex program like this, I'm sure people will find bugs. I'd really appreciate detailed feedback concerning any problems found. My e-mail address at ARRL HQ is rdstraw@arrl.org or by CompuServe: 73063,773. 8