TLW (Transmission Line for Windows)
Version 3.00, March 14, 2006
Copyright ARRL, 2002-2006, by R. Dean Straw, N6BVFor those of you who may be familiar with my older transmission-line program TLA
distributed with the 18th Edition of The ARRL Antenna Book, the new TLW is a full-featured
upgrade that takes full advantage of the Windows programming environment. Many users during
the beta testing phase successfully navigated through all of TLW’s many features without thebenefit of an instruction manual. Consider the advantage you have, dear reader, since you are
now reading the instruction manual! Version 3.0 now includes additional graphing capabilities
described below.

Computer Requirements
The minimum requirements to run TLW (and its companion programs YW, Yagi for
Windows, and HFTA, HF Terrain Assessment) are a PC running Windows 95 or later, including
Windows 98, Windows XP and Windows 2000. The processor should be at least a Pentium

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90 MHz, with at least VGA 640 × 480 screen resolution (with “Small” font size, so you can see
the whole window), 24 MB of RAM (32 MB for Windows 2000) and a CD-ROM. Note that ascreen resolution of 800 × 600 or even better yet, 1024 × 768, will result in easier-to-readwindows. These higher resolutions are best viewed with “Large” font size.
To set the screen size from the Windows Desktop Taskbar, select Start, then Settings,
Control Panel, Display and then click on the Settings tab. Choose either 800 × 600 or
1024 × 768 in the Screen Area list box. Next, click on the Advanced button and select “Large
Fonts” in the Font Size list box. Then reboot your computer (if necessary), and exit by clicking
on the OK buttons until you can exit the Control Panel folder.
A Short History of the TLW Program
TLW, short for “Transmission Line for Windows” started out life as TL, short for just“Transmission Line.” TL was replaced by TLA, short for “Transmission Line Advanced.” Thecore algorithms in TLW have been under development, intermittently, for more than 10 years andthe program has developed into a sort of “Swiss Army Knife” for transmission lines and antenna
tuners.
TLW does assume that the user has some technical knowledge about transmission lines andantenna tuners. The user must be familiar with the so-called rectangular representation ofcomplex impedance, in the form Z = R ± j X. Later in this document there are two tables oftypical impedance data for two types of antennas. You can use this data with TLW to experimentwith realistic situations and to gain familiarity with the program.
Installing TLW
Normally, you would automatically install TLW when you use SETUP.exe to install the otherprograms from the CD-ROM included with the 20th Edition of The ARRL Antenna Book. Thissection describes how to re-install TLW, or install it for the first time if you opted not to install it
previously.
At the lower left-hand of your Desktop, click Start, then Run. Click on the Browse button
and then select the drive corresponding to your CD-ROM. We’ll assume here that it is drive D.
Select the Setup.exe program by clicking on it twice and then clicking OK. Follow the on-screen
instructions to “Modify” your installation. Check the TLW option and click on Next to proceed.
(Note that clicking on an option that has already been installed with uninstall it. Be careful here.)
Possible Problems During TLW Installation
You may possibly encounter warnings or problems during installation or re-installation of
TLW. The program uses DLLs (Dynamic Linked Libraries) and other files (such as OCX
ActiveX Controls) supplied from Microsoft for Visual Basic 6, the language in which TLW was
written. Microsoft will occasionally update its DLLs and OCXs.
If the installation program finds an older file that must be updated, it will ask yourpermission to do so. It is OK to allow this updating, since older programs that also use these
DLLs and OCXs should still work—in other words, they are backwards compatible. On rareoccasions, however, a newer DLL or OCX will not function with older programs. Should thisPage 2

occur, please contact the publisher of the other program, or contact ARRL for problems with
TLW, using the e-mail address at the end of this document.
We have found that some auxiliary “Uninstall” programs can interact with an installation or
re-installation of TLW because certain uninstall programs automatically makes DLLs and OCXs
“read-only.” Consult your operator’s manual for such uninstall programs if you see a warning
message about a “read-only” file during TLW installation. You will probably have to Cancel
your TLW installation and run the auxiliary uninstall program to update its file inventory. Then
you can run the TLW installation again.
TAKING TLW FOR A TEST DRIVE
From the Desktop Taskbar at the lower left-hand corner of the screen, select Start, thenPrograms, followed by scrolling down the list of programs and clicking on TLW. You will now
see the TLW icon to one side. You could start TLW immediately by left-clicking on the TLW icon
if you like. At this point, however, you could also create an shortcut icon on your Desktop by
right-clicking on the TLW icon and choosing Create Shortcut. This creates a shortcut, which
you may select by right-clicking on it, dragging it onto your Desktop and then selecting Move
Here. If you wish, you can use the same procedure to create a shortcut on your Desktop for theentire Program Group (by default called “Antenna Book Software”) containing all the icons for
the Antenna Book programs.
So, let’s assume you’ve started TLW. You will see the main screen, which contains a lot of
information. Note that there are only a small number of places on the main screen where you canchoose or enter numeric data. The primary areas are:
1.
2.
3.
4.

Choosing the type of cableSpecifying the length of the cableSpecifying the operating frequency
Specifying the load impedance (or input impedance)

There are default values for each of these data entries when you first boot up TLW. When you
exit the program, TLW stores whatever values you’ve entered in the TL.DEF file located in yourdefault subdirectory. This way you can resume operations from where you last stopped.
Type of Cable
First, move the mouse cursor and let it hover over the list box labeled Cable Type. A “tooltip” will show, explaining what is expected for that area. In this case the tool tip says “Choose
type of transmission line.” You can try this for the other data entry boxes or option buttons.
Now, click the arrow at the right side of the drop-down list box with the label Cable Type.
This is located under the Version number label at the top of the main TLW screen. See Fig 1.
You have a choice of the 34 different types of transmission lines in TLW. The first 30 choices are
coaxial cables, mainly with “RG” designations and (where available) Belden part numbers. At
the end of the list are two-wire balanced transmission lines, such as 300-Ω transmitting line,
450-Ω “window ladder line” or 600-Ω wire line.

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The last choice in the list is for a “User-Defined Transmission Line.” For this choice, the user
manually enters the matched-line attenuation (in dB/100 feet or dB/100 meters), the velocity
factor, the resistive part of the characteristic impedance, and the maximum RMS voltage forwhich its manufacturer rates the line. The program then allows you to compute the value of thereactive part of the characteristic impedance. (You may override the reactance-calculation
feature if you like, although it doesn’t make a lot of sense to do so, since the first transmissionline characteristics determine the reactive portion.)Fig 1—Selecting the type of transmission line.
If TLW requires an updated computation for a user-defined cable (for example, when you
change frequency), TLW will show a highlighted red warning on screen next to the arrow in the
Cable Type list box. The values for the user-defined cable are stored in the TL.DEF file, so thatonce you enter your own values for a particular type of transmission line, you needn’t manuallyenter them the next time you open the program.
All cables in TLW use the parameters listed in Chapter 24 of the 21th Edition of The ARRL
Antenna Book. The default value for the type of transmission line is RG-8A (Belden 8237),
nominally 50-Ω cable solid-dielectric cable. For our test drive, choose the 450-Ohm Window
Ladder Line.

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Setting the Cable Length
The default value for the length of the transmission line is 100 feet. Note that you can force
TLW to work in metric units by clicking the Meters option button in the frame next to theLength box. The fact that you are working in meters will also be stored in the TL.DEF file sothat TLW boots up in the metric mode the next time you start it.
Go ahead and specify a length of, say, 120 feet. The easiest way to do this is simply to
double-click on the 100 and then type in 120. Or you can edit the 100 manually, using theright/left arrow keys and the Delete key, plus the keyboard numeric keys.
One very convenient feature is that you may enter the transmission-line length inwavelengths. The program automatically converts the value to either feet or meters, taking into
account the velocity factor of the chosen line at the operating frequency. To enter a length inwavelengths, append a “w” immediately after the length. For example, to specify a quarter
wavelength, type:.25w or 0.25w
Once you press the “w” key, TLW will instantly compute the physical length of an electricalquarter-wave of line (in feet or meters). This will be used by the program for all subsequent
computations. The physical length will remain constant even if you change frequency. This
makes it easy to evaluate the effects of shorted quarter-wave stubs, for example, at twice thefundamental frequency. After you have finished exploring what length changes do, respecify alength of 100 feet to continue our example using the 450-Ω line.
Changing the Frequency
The default frequency is 3.5 MHz. You can enter any frequency as high as 5999 MHz(6 GHz), or as low as 0.02 MHz (20 kHz). As you enter each digit of the frequency you will seethat TLW automatically computes all other parameters. It’s fascinating to watch the Total Line
Loss change when you start out at 1 MHz and add zeroes one at a time to the end — first
10 MHz, then 100 MHz and finally 1000 MHz. Note how the reactive portion of the
Characteristic Z0 also changes subtly with changes in frequency. [Note: TLW uses a morerigorous algorithm to compute the R0 than the older DOS-based TLA program. There will be
subtle differences between TLW and TLA computations for this reason.]
For now, type in a frequency of 1.83 MHz. Note that at this frequency a 100-foot piece of
450-Ω line is 0.204 λ long electrically. (The symbol λ is the Greek letter “lambda,” anabbreviation for wavelength.)
Entering Load Impedance
The default method of specifying impedance is at the load end of a transmission line. To
continue our example using 100 feet of 450-Ω line at 1.83 MHz, assume that we simulate theload of a 100-foot long dipole, 50 feet above flat ground. The feed-point impedance of thiselectrically short antenna at 1.83 MHz is 4.5 – j 1673 Ω. This shows that this antenna isextremely short at this frequency! Enter 4.5 into the input box labeled Resistance and –1673 in
the input box labeled Reactance.
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Now look at what TLW computes for this severe load condition. Despite the fact that thetransmission line is a “low loss” line (with just 0.032 dB/100 feet of loss), under these conditions
where the SWR at the load is 792.97, the additional loss due to this high SWR is an astounding
8.899 dB! This brings the total loss in the line alone up to 8.931 dB. Because of this loss, theSWR at input end of the transmission line is “only” 202.22. The losses in the line have masked
the true level of SWR at the load.
The impedance looking into the input end of the cable under these conditions is quite low, at
1.95 – j 19.73 Ω. In polar coordinates this is 19.83 Ω at a phase angle of –84.35°. See Fig 2.
We’ll find out later that this very low impedance makes the job of the antenna tuner feeding thisline much more difficult.
Some extreme combinations of load resistance and reactance can result in a computed load
SWR that is negative—try a load of 1.5 + j 1900 in the example above. TLW warns you byhighlighting the output SWR in red text. A negative value for SWR happens only under
exceptional circumstances, with loads that you’d never actually connect to a real-worldtransmission line because of the severe losses involved. Rest assured, however, that the math iscorrect.

Fig 2—An extreme load at 1.83 MHz!

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Graphing the Voltage/Current Along the Line
Select the Volt./Current option button and then click on the Graph button. These arelocated towards the bottom right of the screen. TLW generates a graph showing how the current
and the voltage vary along this transmission line, for an input power of 1500 W at the input of
the 450-Ω line with the 100-foot long dipole at 1.83 MHz. The maximum RMS voltage, which
occurs at the load end of the line, is almost 11,000 V, while the maximum RMS current is almost
28 A, occurring at the input end of the line. Clearly this line is in danger of arcing over underthese extreme conditions, because its nominal voltage-handling capability is 10,000 V. See
Fig 3.
You can use the mouse cursor to see the exact values at points along the line. A “tool tipbox” will display the value of current or voltage as you move it along the curves. TLW computes
the current and voltage at 200 points along the line, so you will see this degree of granularity as
you move the mouse cursor.
If you want to see what happens at a different power level at the input of the line, you can goback to the main TLW screen and select Tuner. Try entering 100 W in the input box labeled
Transmitter Power, W in the Tuner Selection, TLW form that comes on-screen. Now click on
Back to return to the TLW main screen, and select Graph again to see the graph. The maximum
RMS voltage has decreased to 2837 V and the maximum RMS current goes down to 7.2 A. Theline probably won’t arc over at this power level.

Fig 3—The voltages and currents along a highly mismatched open-wire line feeding a 100foot high dipole at 1.83 MHz.
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Graphing Resistance/Reactance Along the Line
After you select Resistance/Reactance and click the Graph button you will see a graph of
how the resistance and reactance vary along the transmission line. For the example we’ve beenworking with, the resistance goes from a maximum of 4.5 Ω at the load end of the line, to aminimum of about 1 Ω at about 60 feet from the input end of the line. This puts a really severe
strain on any antenna tuner trying to match the line to 50 Ω. In fact, any length of line with sucha severe load will severely tax an antenna tuner! Click on the Cancel button to close the graphand get back to the main TLW window.
Zooming and Scrolling the Graph
You can zoom or scroll about the graphs in TLW by using the left or right mouse button
while dragging the mouse cursor. Holding down the left mouse button while dragging
downwards from left to right to zoom the area outlined in the resulting rectangular box when you
release the left-button. Reverse the procedure (dragging upwards from right to left) to unzoom.
By holding down the right mouse button and dragging you can scroll the graph around.

Fig 4—The impedance along the highly mismatched line in Fig 2.

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Specifying Impedance at the Line’s Input
If you measure the complex impedance at the input of a transmission line from the comfort ofthe operating shack, you can use TLW to compute the load impedance at the end of that line.
Simply click on the option Input (rather than Load) in the frame containing the entries forresistance and reactance.
For example, for the 100-foot of 450-ohm window ladder line at 1.83 MHz, enter for
Resistance 35 ohms, with a Reactance of –10 ohms, after clicking Input. TLW computes thatthe impedance at the load is 453.85 − j 1372.61 Ω. As opposed to the previous example using anelectrically short 100-foot dipole as a load for the same ladder line, the SWR now is much morereasonable with this load (at 12.01), and as a consequence, the total loss on the line is only
0.224 dB.
There are combinations of input resistance and reactance that result in a negative value forthe resistance at the load end of the line. This condition is flagged by TLW by highlighting thecomputed load impedance in red. While the mathematics are correct, this is a very special
circumstance and you should exercise caution interpreting such results. What TLW is in effecttelling you is that you would never actually measure such an impedance at the input end of a realtransmission line!
Using the Autek RF-1 to Compute the Impedance at the Input
You can use an Autek RF-1 antenna analyst to measure the magnitude of the impedance andthe SWR at the input of a transmission line. Then you can use TLW to compute the complex
input impedance and then the impedance at the load end of the line. These two scalar quantitiesof the magnitude of impedance and SWR give enough information to compute the resistive andreactive portions of the impedance at the line input, but you can’t determine from them directly
the sign of the reactance. You must choose the sign of the reactance based on your knowledge ofwhat the load actually is. Note that certain lengths of line will reverse the sign — this includes
any odd multiple of a quarter wavelength of line.
Let’s try another line: an RG-213 coax that is 128 feet long at 3.8 MHz. Assume that the loadat the end of this line is an 80-meter dipole, resonant at 3.7 MHz. In the frame labeled Source,
click on Autek. A new form will appear on-screen labeled Calculation of Impedance from
Autek. Let’s assume that the Autek RF-1 shows the magnitude of Z to be 34 ohms, with an SWRof 2.0. Enter these values and TLW computes that the complex impedance at the input of the line
is 29.3 ± j 17.3 Ω. You must determine the sign of the reactance.
In this example we are using 128 feet of RG-213 to feed an 80-meter dipole, which isresonant at 3.700 MHz. (The electrical length of the line is very close to ¾ λ = 0.75 × 984 / 3.8
MHz × 0.66, where the 0.66 is the velocity factor.) The feed-point impedance of a typical
80-meter dipole is somewhere about 60 Ω, with no reactance at resonance. At frequencies higher
than resonance can expect to see an inductive reactance at the dipole’s feed point. Since the coax
is a multiple of ¼ λ, the sign of the reactance will be reversed at the input compared to what it isat the load. This means that we should expect to see a capacitive (negative) reactance at the inputof this line, not the true inductive reactance. Yes, it sounds complicated, but you’ll get the hangof it.

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Now click the Negative option in the frame labeled Choose sign of reactance. Notice that
there is another piece of information showing on the form, labeled Minimum SWR for Z chosen.
This shows that you must enter an SWR value of at least 1.5 in order for TLW to make sense of
the magnitude of impedance you specified at 34 Ω. (For a 50-Ω line, the SWR would be 50/34 =1.47 minimum if there is no reactance.)
Now, click OK to return to the TLW main screen, where you can see that the Impedance atthe load (that is, the impedance at the dipole’s feed point) is 64.72 + j 41.67 Ω, just as you’d
expect. Note also that TLW has clicked the Input option automatically for you, with the Autek
option encircled by a dotted box.
You can see that it’s a good idea to check the sign of the reactance at the input of atransmission line by manually entering expected resistance and reactance values using the Load
option. Then you can see the effect that the transmission line has on transforming that load
impedance to another impedance at the input of the line.
Let’s continue with this example, but at 3.5 MHz, a frequency lower than the resonance of
the 80-meter dipole. At this frequency we can expect the dipole to exhibit a feed-point
impedance that is on the order of 40 Ω, with a capacitive reactance of around –100 Ω.
Assume that your Autek RF-1 shows Z = 10 and SWR = 5.1 at the shack end of the line. See
Fig 5. When you enter these values into TLW at 3.5 MHz, TLW computes the impedance at the
input of the line as 9.8 ± j 1.9 Ω. In this case, you would choose “+”, since again you mustreverse the sign of the reactance due to the impedance inversion of that length of line, which
TLW shows you is 0.690 λ long. Now, TLW computes that the load at the antenna is 38.15 –j 100.31 Ω up at the antenna, very close to what we would have expected.
You should see that the number of decimal points that TLW computes (two) are not justified
by the amount of decimal points (one) that the Autek RF-1 computes SWR or Z. Computers
programs are wonderful, but they are only as good as the data fed to them!

Fig 5—Sample Autek input box.
Using a Noise Bridge to Determine the Impedance at the Input
If you click on Noise Bridge, you will open a new form entitled Input from Parallel-Form
Noise Bridge. You will enter values for the shunt resistance and then the shunt capacity (in pF)
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that you read from the Noise Bridge. If the shunt capacity is negative (meaning that the unknown
impedance is inductive), enter the capacity value preceded with a minus sign, since “negative
picoFarads” indicates inductance on these types of bridges. A capacitive reactance need not be
preceded with a “+” (plus) sign, although you may enter one if you wish.
Not all Noise Bridges are calibrated in shunt values. For example, the units in late issues of
the ARRL Handbook are calibrated in series impedance at 10 MHz. However, I built the NoiseBridge function into TLW because my own homebrew unit uses shunt values.
The Noise Bridge routine in TLW also can compensate for the series resistor I must
sometimes use to bring the unknown impedance into the range of the noise bridge’s shunt
capacitor, particularly on the lower frequencies. I often must use a series 100-Ω adapter on 80 or
40 meters, where the range of capacitive reactance of the variable capacitor in the noise bridge issmall.
CAVEATSI must caution you at this point. TLW displays results out to two, or even three, decimal
places. Internally, computations are carried out to even more decimal places. 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 varyslightly for two pieces of cable cut from the same bulk roll! Along with the Velocity Factor, theexact value for the characteristic impedance Z0 also varies.
TLW 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: TLW is fundamentally an educational tool. It can also be used very effectively as adesign tool, provided that you know the exact parameters of your transmission lines and yourantennas. If TLW 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.
TLW can show a negative value for SWR when the load impedance is very highly reactive
and inductive: for example, a 1.5 + j 1800 ohm load on a 95-foot long, 450-ohm line at 1.9 MHz
yields a computed SWR of −258.35. This is certainly non-intuitive, but it is correct and it has no
physical significance. What is happening is that TLW computes that the reflection coefficient islarger than 1.0, yielding the negative value for SWR. TLW flags a negative SWR computation byhighlighting it in red, to warn the operator that something unusual is afoot.
EVALUATING ANTENNA TUNER CONFIGURATIONS
Return to a frequency of 1.83 MHz, with 100 feet of 450-Ω ladder line, terminated in a loadof 4.5 − j 1673 Ω. Now, select Tuner, and TLW will display the Tuner Selection, TLW form.
You should always remember that TLW’s antenna tuner is assumed to be located in the shack, atthe input end of the transmission line feeding the load. Presumably, the load at the end of thetransmission line is an antenna. (After all, putting the antenna tuner out at the antenna would
result in a trivial computation for TLW, since the tuner would match the Z0 of the transmission
line going to the shack, yielding a 1:1 SWR!)

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You may choose one of four different Tuner Network Types:••••

Low-Pass L-Network (shunt capacitance, series inductance)
High-Pass L-Network (shunt inductance, series capacitance)
Pi-Network (shunt capacitances, series inductance)
Tee-Network (series capacitances, shunt inductance)

Choose one of the antenna-tuner configurations. For either high-pass or low-pass Lnetworks, TLW will immediately compute all values, using default unloaded Qs of 200 for any
inductor and 1000 for any capacitor. (You may alter these values if you like.) The inductor isusually, but not always, the most lossy component in an antenna tuner. The default value of
Q = 200 is pretty typical for a practical inductor mounted in a metal case.
The model for a lossy inductor is an lossless inductive reactance in series with a loss
resistance. For example, if the unloaded Q is 200 and the inductive reactance at the chosenfrequency is +400 ohms, then the loss resistance is 2 ohms in series with the +400 ohms
reactance (Q unloaded = 200 = 400/2).
TLW assumes a default value of 1000 for the unloaded Q of any capacitor, although you canchange this too. Again, the model for a lossy capacitor in TLW is a lossless capacitive reactancein series with a small loss resistance. (This is the series equivalent of a parallel combination of aperfect capacitor and a high-resistance loss resistor. See The ARRL Handbook for details about
unloaded Q and series/parallel equivalent circuits.) The default value of unloaded Q = 1000 is
typical of transmitting air-variable capacitors with wiping contacts.
If you choose either the Pi-network or Tee-network, you will be prompted to enter the value(in pF) of the output capacitor in the network. For the Pi-network the default value is 500 pF, andfor the Tee-network configuration the default value is 100 pF. These values will not necessarily
yield the most efficient tuner!

Fig 6—Setting up an antenna tuner.

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For now, click on the High-Pass Tee Network using the default values, then click on the
Draw Tuner button. Click OK and TLW will compute all component values needed to transformthe impedance at the antenna tuner output to 50 Ω (or to any value of resistance you choose) andwill change to a schematic-diagram page. You may need to move the window with your mouseto see all parts of it, depending on your screen resolution. See Fig 6.
If the chosen network configuration cannot perform the desired transformation, an audible
alarm will sound, and TLW will either recommend another network or another output capacitor
value to try.
The Antenna Tuner Schematic Screens
Examine the antenna tuner schematic 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. The next line shows the impedance atthe load end of the line, in both rectangular and polar forms, as well as the SWR at the load endof the line. This SWR is usually computed for a default value of 50 Ω, although if you change
the input impedance at the tuner’s input, let’s say to 200 Ω, the SWR shown on this line willchange appropriately.

Fig 7—Antenna schematic screen for tuner configuration in Fig 6.

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Look carefully at the on-screen schematic of the Tee-network you chose. The impedance atthe output terminals of the tuner (that is, at the input end of the transmission line) is shown at theright side of the schematic drawing. (This is a departure from earlier versions of TLA or TL and I
changed it because I sometimes became confused using the old method.)
TLW shows something called the “Effective Q,” also known commonly as the “loaded Q” ofa network. This is the loaded Q in the network at the specified load impedance, and is anindication 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 toachieve the desired transformation.
Thanks to an algorithm developed by Frank Witt, AI1H, this line also shows the computed
1.5:1 and 2:1 SWR bandwidths for the tuning network itself, calibrated both in kHz and inpercentage of the tuned frequency. Here, the load is assumed to be constant and the frequency isshifted internally to compute the bandwidth numbers. If the computed bandwidth is greater than
30% of the center frequency, TLW will display “Large” rather than a value in kHz. Note that
real-world antennas are very often narrowband devices, and the antenna — not the tuner — sets
the limits for how far you can change your frequency without retuning the antenna tuner.
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 as:
Efficiency (%) = 100 × (1 − (QL/QU))
where QL is the loaded Q, and QU is the unloaded Q of the network components. See Chapter 13
in late editions of The ARRL Handbook for more details on this subject.
For a given network loaded Q (“effective network Q” in TLW), 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.
Changing the Tuner Defaults
Once you have changed any default values, they will remain in effect until you either reboot
TLW or respecify the values from within TLW. Just for your information, I’ve limited the
maximum amount of power from the transmitter to 5 Megawatts. I suspect that limit won’t affecttoo many of you.
The ability to specify the resistance seen at the tuner’s input terminal when it is tuned allows
you to experiment with other tuner configurations. You might, for example, use a wideband
impedance transformer, such as a 50:200-Ω balun at the input of a tuner. You access this featurein the Tuner Selection, TLW form using the Tuner’s input resistance input box.
You may find that the physical component values for various loads are more practical for adifferent impedance at the tuner’s input than for 50-Ω, the default value. Another use is given indetail below  evaluating a Pi-network tank circuit in a transmitter.
Tuner Losses, Details
Examine the line showing the estimated power loss in the tuner. The loss shown is computedfor the level of transmitter power you have specified. The loss is expressed in watts, in dB, andPage 14also as a percentage of the power at the input. For example, a particular tuner configuration
might lose 114 W out of 1,500 W put into it, yielding a loss of 0.34 dB, or 7.6% 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
7.6% of 100 W = 7.6 W.
The next line on-screen summarizes the system losses: the loss in the transmission line itself
and the total loss in the line and the antenna tuner, both expressed in dB. The final entry at theend of the line is how many watts actually make it to the load. This can be sobering to see!
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, andthe power lost. Each is computed for the value of transmitter power you specify. (Note that thereactances are displayed to three decimal points, so that the purists among you may take thesenumbers and manually verify that the program is working the way it should. I too used this data
to validate the program during development.)
Note that the voltage shown by TLW is the peak voltage across each component. Pardon thepun, 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 thevoltage across the component itself. In addition, the current shown is that flowing through eachcomponent, but here the current is the RMS value, because this is what heats up a component.
Exceeding the peak voltage rating across any component in a tuner will probably cause anarc. This may or may not be disastrous, depending on whether the arcing component develops apermanent “carbon track” or not. Exceeding the RMS 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.
Inductor damage occurs most frequently with low-resistive loads, with or without a highreactive component. For example, you can simulate a stressful situation by specifying a load
impedance for the tuner of 3 + j 0 Ω at 3.5 MHz (Hint: use a length of 0 feet for the transmissionline), for a high-pass Tee-network configuration having a 100 pF output capacitor. For the fullamateur legal power level of 1500 W, the insulation of the shunt inductor will not only have towithstand almost 10,000 V peak, but worse yet, it will have to dissipate almost 700 W of power
at more than 20 A of circulating current. This level of current will toast the coil, if it doesn’t arc
first.
Next on the screen is a line showing the voltages at the input and output of the tuning
network chosen. The RMS input voltage is determined by the power fed into the tuner at the
input resistance of the tuner (usually 50 Ω). The phase angle of the output voltage is assumed to
be zero degrees, although you can change it if you wish. The magnitude and phase of the RMS
output voltage are shown to the right. The magnitude and phase angle of the output voltage areparticularly interesting to people designing networks for phased antenna arrays.
TLW 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, evenones supposedly rated to handle a “full gallon” of RF. Now, for fun, increase the size of theoutput capacitor in the Tee-network and/or increase the unloaded Q of the inductor to help
Page 15

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 for a transmission-line
length of 0 feet, enter a value of 0.001 Ω for the resistive part of the load, with a reactance of
0 Ω. Then select the Tee-network, with an output capacitor of 100 pF. The tuner will absorb all
1500 W of input power  in other words it tunes up wholly into itself, given a short at theoutput!
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
configuration is often used because it can accommodate a wider range of impedances withpractical 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 forcapacitors.
TLW and Transmitter Output Pi-Networks
TLW also allows you to evaluate the capabilities and losses in a Pi-network used at theoutput of a vacuum-tube power amplifier. You can change the default input resistance seen at the
input of the network from the 50 Ω most commonly used for an antenna tuner to the desiredloadline resistance needed for a tube or transistor. For example, an 8877 power tube wants to see
a load of about 2200 Ω for a plate voltage of 3100 V. You would change the default from 50 to2200 Ω in TLW.
Now, following the recommendations in the ARRL Handbook, you want to achieve aneffective network Q between 12 to 15 in order to ensure adequate suppression of harmonics. At afrequency of, let’s say, 29.7 MHz, with a 50-Ω load at the output of the Pi-network tank, TLW
tells you that an output capacitor of 500 pF (the default value) yields an effective network Q of
33.1. This will result in good harmonic suppression, but it will also result in excessive losses,
burning up 290 W in the tank circuit at 1500 W into the tank circuit. It’s obvious that we need tolower the network Q somehow.
An output capacity of 200 pF at 29.7 MHz will lower the network Q to 15.2, but now therequired value of the capacity at the input of the Pi-network is only 32.6 pF. The plate capacityof the 8877 is about 15 pF, and there will inevitably be stray capacitance of at least 10 pF. Thismeans that the minimum value of the tuning capacitor must be less than 7.6 pF in order toachieve the desired overall capacity of 32.6 pF. This is a tough requirement, especially for an airvariable capacitor that is used on 80 or even 160 meters too. Further trials with TLW will resultin a compromise, although you may still find it necessary to use an expensive vacuum-variablecapacitor to achieve a low minimum value.
See Fig 8, which again uses a zero-length cable to simulate just the tuning network by itself.
The load at the output of the Pi-network is 50 Ω in this case.
Printing Out a Graph or Screen
If you wish to print out a particular graph or TLW screen, simply select the Print button
while that graph or screen window is on-screen. Note that if you try to print a full-screen graphic,
parts of it may be cut off towards the edges of the print. Resize the graphic to print it fully on

Page 16

your particular printer. You can also copy the entire screen to the Windows Clipboard using the<Print Screen> key on your keyboard or you can use the <Alt><Print Screen> combination tocopy only the active window to the Windows Clipboard. Once a graphic is on the Windows
Clipboard, you can bring it into other Windows programs.

Fig 8—A Pi-network for a tube-type transmitter.
FEEDBACK, PLEASE!
This is where TLW stands. In a very complex program like this, I’m sure people will findbugs. I’d really appreciate detailed feedback concerning any problems found. My e-mail address
at ARRL HQ is n6bv@arrl.org.
R. Dean Straw, N6BV
Senior Assistant Technical Editor, ARRL
225 Main Street
Newington, CT 06111
e-mail: n6bv@arrl.org
January 24, 2005

Page 17APPENDIX A — TRANSMISSION-LINE LOSSES
Several years ago I wrote sidebars to two QST “New Ham Companion” articles by Steve
Ford, WB8IMY. These dealt with the stresses on transmission lines used with multiband centerfed dipoles. The computed losses, for both RG-213 coax and for open-wire transmission lines,
raised some eyebrows  and some hackles. Some people were astonished at how high thetransmission-line losses could be when an extremely high SWR was involved  such as whenan 80-meter dipole was used on 160 meters, an octave lower than its resonant frequency.
After much debate and correspondence, I revised the loss algorithm in several versions of theolder program TL. In October, 1995, Frank Witt, AI1H, and Scott Townley, NX7U, kindly
provided me with more information on the true nature of the complex characteristic impedance.
This was incorporated into TL, TLA and now TLW. After all the changes, the losses for severe
SWR cases are close to what the original TL computed, but they are more exact nonetheless.
Now, the loss computations very closely match the calculated examples for truly severe
mismatches in the book Reference Data for Radio Engineers, published by Howard W. Sams and
Co. The examples, on page 22-11 of the Fifth Edition, were for RG-218 (old type RG-17),
terminated at 2.0 MHz with a 0.4 − j 2000 Ω load. This is about what an unloaded mobile whip
would look like in the absence of ground-related losses. A 124-foot long RG-17 line would havemore than 35 dB of loss with this load, and a 24-foot long piece would dissipate almost 20 dB.

Page 18

APPENDIX B — SOME DATA TO PLAY WITH
Below are listed some sample impedance data you may use to play with using TLW.
Feed-point impedances for 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.
MHz
1.83 MHz:
3.8 MHz:
7.1 MHz:10.1 MHz:14.1 MHz:18.1 MHz:21.1 MHz:
24.9 MHz:
28.4 MHz:

Feed-Point
Impedance
4.5 − j 1673 Ω
39 − j 362 Ω
481 + j 964 Ω
2584 − j 3292 Ω
85 − j 123 Ω
2097 + j 1552 Ω
345 − j 1073 Ω
202 + j 367 Ω
2493 − j 1375 Ω

Feed-point impedances for a 66-foot long, center-fed inverted-V dipole, apex at 50 feet high overground with dielectric constant of 13, conductivity of 5 mS/m.
Freq.
MHz
1.83 MHz:
3.8 MHz:
7.1 MHz:10.1 MHz:14.1 MHz:18.1 MHz:21.1 MHz:
24.9 MHz:
28.4 MHz:

Feed-Point
Impedance
1.6 − j 2257 Ω
10.3 − j 879 Ω
64.8 − j 40.6 Ω
21.6 + j 648 Ω
5287 − j 1310 Ω
198 − j 820 Ω
103 − j 181 Ω
269 + j 570 Ω
3089 + j 774 ΩPage 19