                Documentation for TLA.EXE Program
                   Version 2.05, January 18, 1999
                     by R. Dean Straw, N6BV
             Senior Assistant Technical Editor, ARRL

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OVERVIEW

For those of you who may be familiar with the older TL program, 
TLA, Version 2.05 incorporates ten new functions:

(1) You may reverse the sense of load/input of the known impedance 
   -- that is, the impedance can be specified at either the load 
   or input end of the line.

(2) The Z and SWR may be entered from an Autek RF-1 RF Analyst or 
   a Noise Bridge may be used.

(3) You may now change the unloaded Qs for both the inductor and 
   capacitor(s) in an antenna tuner, and the transmitter power 
   level as well -- up to 5 megawatts! 

(4) You may change the resistance seen at the input of an antenna 
   tuner to other than 50 ohms. This allows you analyze, for 
   example, the currents, voltages and losses both for a tube-
   type amplifier pi-network or a solid-state pi or tee-network.

(5) You may now specify transmission-line length in meters or 
   feet -- or in wavelengths, which is then converted to feet or 
   meters. The unit of feet or meters is stored to a file called 
   TL.DEF so that you needn't keep entering it for subsequent 
   operations.

(6) TLA also stores in TL.DEF the values you enter using the #16 
   choice ("other" cable) from the main menu. The reactive part 
   of the cable's characteristic impedance is automatically 
   computed, although you may override the value manually.
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(7) The 1.5:1 and 2:1 SWR bandwidths for a tuner configuration 
   are shown, along with the Effective Q of the tuner. This gives 
   you an indication of how narrow a bandwidth the tuner design 
   itself implies.

(8) The stray output capacitance for a tuner network with a 
   series output reactance is taken into effect. The amount of 
   stray can be changed by the operator.

(9) The magnitude and phase shift of the voltage across the load 
   is shown, along with the magnitude of the voltage at the input 
   of a tuning network. This allows the operator to determine the 
   voltage and phase shift, for example, of a tuning network used 
   in a phased-array antenna system. A so-called "line stretcher" 
   pi network may be iteratively designed using this function in 
   TLA. 

(10) The reflection coefficient (rho) at the load end of the 
   transmission line is shown next to the SWR at the load. 

   Version 2.05 fixes an error in the matched-line attenuation 
for 450-ohm "windowed" ladder line that gave overly pessimistic 
values when extremely high SWR cases were evaluated. The velocity 
factors and matched-loss characteristics of open-wire lines have 
been calibrated to match the values shown in the Transmission 
Line chapter of the 1999 ARRL Handbook in Table 19.1 on page 19.2. 

THE TLA PROGRAM

   "TLA" is short for "Transmission Line, Advanced." The TLA 
program started out as "TL," short for just "Transmission Line." 
TLA has been under development, intermittently, for about 7 years 
and has developed into a sort of "Swiss Army Knife" for 
transmission lines and antenna tuners. 

   TLA will complete a computation in a fraction of a second on a 
powerful modern microcomputer, like the 100-MHz Pentium 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 (with no numeric 
coprocessor.) TLA employs a lot of heavy-duty math, so a numeric 
coprocessor is extremely desirable. 

   The program is entirely character-based for output display. 
Hence any IBM-PC compatible computer will work with TLA. Hitting 
[Shift] [Print Screen] will print out a TLA screen on any printer 
that recognizes the 8-bit IBM character set. (You may have to set 
your printer for this manually.) TLA is a DOS program, although 
it works properly under all versions of Windows.

   TLA displays everything in color. If for some reason you use 
<Ctrl>C or <Ctrl>Break to exit the program, you will be left in 
DOS, with a messy blue background. Either type CLS [Enter] or 
MODE=CO80 [Enter] to restore the screen to normal.

USING TLA

   TLA 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 Z = R +/- j X. Later in this file there 
are two tables of typical impedance data for several types of 
antennas. You can use this data with TLA to experiment with 
realistic situations and to gain familiarity with the program.

   You boot up TLA once you have entered the subdirectory 
containing TLA.EXE, the executable file. You do this using the CD 
[change directory] command in DOS. Once there, Type:

      TLA [Enter]

THE OPENING SCREEN

   The opening screen shows a menu of the various types of 
transmission lines TLA models. The first eight choices are 
flexible coaxial cables, with "RG" designations and where 
available Belden part numbers. Choices 9 through 12 are Hardline 
coaxial cables. Choices 13 and 15 are for two-wire balanced 
transmission lines, such as 300-ohm transmitting 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 
resistive part of the characteristic impedance, 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. The 
program automatically computes the value of the reactive part of 
the characteristic impedance, which you can override if you like, 
although it doesn't make a lot of sense to do so, since the first 
characteristics determine the reactive portion.
 
   The values for choice number 16 are stored in the TL.DEF file, 
so that once you enter your own values for a particular type of 
transmission line, you needn't manually enter them the next time 
you choose number 16.

   Choices 1 through 15 use the parameters listed in Chapter 24 
of the 18th edition 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 onward. Note also that the velocity factors for open-wire 
lines have been revised downwards to match Table 19.1 on page 
19.2 of the 1999 ARRL Handbook.)

   If you merely hit the [Enter] key, TLA will select the default 
value of "4," meaning RG-8A/RG-213, 50-ohm cable solid-dielectric 
cable. In most data entry points in TLA, there is a default 
value, indicated by square brackets and highlighted in red; e.g., 
[4] in the main menu. Merely hitting [Enter] will select the 
default value automatically.

   TLA 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. 

   Note: From the main menu you may select "S" for Special to 
change the default from feet to meters. TLA writes this 
information to disk in the TL.DEF file so that it boots up with 
your desired unit of measurement.

   Note also that you may now enter the transmission-line length 
in wavelengths. The program automatically converts the value to 
either feet or meters, taking into account the velocity factor of 
the chosen line. To enter a length in wavelengths, append a "w" 
immediately after the length. For example, to specify a quarter 
wavelength, type: 

   .25w

followed by [Enter]. The length of an electrical quarter-wave of 
line (in feet or meters) 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. 

   Next, you will be prompted for the operating frequency, in 
MHz. The default is 3.5 MHz, selected as usual 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 0.02 MHz (20 
kHz). After you hit [Enter], TLA will compute and display the 
matched-line loss for the chosen line. The matched-line loss is 
for a load equal to the resistive part of the characteristic 
impedance for the particular transmission line chosen and for the 
length of line and the frequency chosen. 

ENTERING THE IMPEDANCE

   Next, TLA 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, TLA 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.) 

   You may specify "R" to reverse the sense of input/load 
impedance entry, or you may specify "A" for computation of the 
complex impedance from data provided by an Autek RF-1 RF Analyst 
or "N" from a Noise Bridge. Note that the on-screen prompt will 
change when you key in "R", changing from:

     Resistive part of impedance at load: 
to 
     Resistive part of impedance at line input: 

   You may either enter the value of resistance and reactance 
measured at the shack-end of a transmission line and compute the 
impedance at the load, or vice versa, toggled by "R".

   After you hit [Enter] for the resistive part of the load 
impedance, you will then be prompted to enter the reactive part 
of the load (or input), again in ohms. Note that an capacitive 
reactance must be preceded with a "-" (minus) sign. Merely 
hitting [Enter] will enter a reactance of zero ohms, the default 
value.

USING THE AUTEK RF-1 TO DETERMINE THE IMPEDANCE

   At the prompt to enter the resistive part of the impedance, 
you may choose "A" to enter Autek RF-1 data. TLA will ask you 
first for the magnitude of the impedance Z, and then the SWR 
measured by the Autek RF-1. Since the magnitude of Z and SWR are 
both scalar quantities, TLA cannot determine the sign of the 
reactance, only its magnitude. TLA will prompt you to choose 
either plus (the default) or minus. 

   You will choose the sign of the reactance based on your 
knowledge of what 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. For example, assume you are 
using 128 feet of RG-213 to feed your 80-meter dipole, which is 
resonant at 3.800 MHz. (The electrical length of the line is 3/4 
wavelengths = .75 x 984 / 3.8 MHz x 0.66, where the 0.66 is the 
velocity factor.) The feedpoint impedance of a typical 80-meter 
dipole is somewhere about 50 ohms, with no reactance at 
resonance. Assume that you want to determine the feedpoint 
impedance at 3.750 MHz. 

   Since this frequency is lower than resonance, there will be 
some capacitive reactance at the feedpoint. Assume for now that 
the feedpoint impedance at 3.750 MHz is 48 - j 20. If you enter 
these values directly, TLA computes the impedance at the input of 
the line (that is, down in the shack) as 43.73 + j 14.78. Note 
that the sign of the reactance has been reversed by the fact that 
the electrical length of the line is close to 3/4 wavelengths. 
You will have to use your own judgement to choose the correct 
sign of the reactance when using an instrument such as the Autek 
RF-1 at the input side of the line. 

   Continuing with this example, assume that your Autek RF-1 
shows Z = 46 and SWR = 1.4 at the shack end of the line. When you 
enter these values into TLA at 3.75 MHz using the "A" Autek entry 
mode, TLA computes the impedance as 43.7 +/- j 14.5. In this 
case, you would choose "+", since you must reverse the sign of 
the reactance due to the impedance inversion of that length of 
line. Now, TLA computes 48.34 - j 19.80 up at the antenna, very 
close to the value of 48 - j 20 we chose in this example. 

   You should see that the number of decimal points that TLA 
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!

USING A NOISE BRIDGE TO DETERMINE THE IMPEDANCE

   If you have chosen "N" to use Noise Bridge data, TLA will 
prompt you for the shunt resistance and then the shunt capacity 
(in pF) 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 
Noise-Bridge function into TLA because my own unit uses shunt 
values. 

   The Noise Bridge routine in TLA also can compensate for the 
series resistor I sometimes must use to bring the unknown 
impedance into the range of my noise bridge's shunt capacitor, 
particularly on the lower frequencies. I often must use a series 
100-ohm adapter on 80 or 40 meters, where the range of capacitive 
reactance of the variable capacitor is small.

TLA DOES ITS THING

   After you finish specifying the impedance, TLA will go through 
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 significant, 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.     

   On the next line down, TLA 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). The resistance and reactance are shown to two decimal 
places, as noted above in the Autek discussion. 

   Continuing on down the screen, 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. TLA 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. 

CAVEATS

   I must again caution you at this point. TLA 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 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.

   TLA 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: 
TLA 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 
TLA 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. 

OTHER INTERESTING THINGS

   TLA 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 -670.03. This is certainly nonintuitive, but it 
is correct and it has no physical significance. What is happening 
is that TLA computes that the reflection coefficient is larger 
than 1.0, yielding the negative value for SWR. 

EVALUATING ANTENNA TUNER CONFIGURATIONS

   If you now select either "T" or [Enter], TLA will erase the 
screen and then display the Antenna Tuners menu. It is very 
important to realize that TLA's antenna tuner is assumed to be 
located in the shack, at the input end of the transmission line 
feeding the load. Presumably, the load is an antenna. (After all, 
putting the antenna tuner out at the antenna would result in a 
trivial computation for TLA, since the tuner would match the Z0 
of the transmission line going to the shack, yielding a 1:1 SWR!)

   You select one of four different configurations:

   1 = Low-Pass L-Network
   2 = High-Pass L-Network
   3 = Pi-Network
   4 = Tee-Network

   A shortcut: from the screen following the main menu (showing 
the SWRs and losses in the transmission line) and from each 
antenna tuner screen, you may bypass the Antenna Tuners 
configuration menu by choosing directly "1", "2", "3" or "4", 
corresponding to the number of the desired antenna tuner network, 
followed by [Enter]. This is particularly useful when you want to 
quickly compare the efficiency of different tuning network 
configurations, one after another. 

   Choose one of the antenna-tuner configurations. For either 
high-pass or low-pass L-networks, TLA 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 
from the Default (D) selection in the Antenna Tuners menu. See 
below.) The inductor is usually, 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 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 (Q unloaded = 200 = 400/2). 

   TLA assumes a default value of 1000 for the unloaded Q of any 
capacitor, although the operator can change this too. 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 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, and 
for the Tee-network configuration the default value is 100 pF. 

   Once you have entered the necessary information, TLA will 
compute all component values needed to transform the impedance at 
the antenna tuner output to 50 ohms (or to a value of resistance 
you choose). If the chosen network configuration cannot perform 
the desired transformation, an audible alarm will sound, and TLA 
will either recommend another network or another output capacitor 
value to try. If TLA cannot match a particular load with any 
value you enter for the output capacitor, you can still escape 
back to the Network menu by hitting "N."

THE ANTENNA TUNER SCHEMATIC SCREEN

   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. On 
the next line the impedance at the load end of the line is 
displayed, in both rectangular and polar forms, as well as the 
SWR at the load end of the line. This SWR is usually computed for 
50 ohms, although if you change the input impedance at the 
tuner's input, let's say to 200 ohms, the SWR shown on this line 
will change appropriately.

   Look carefully at the on-screen schematic of the network you 
chose. The impedance at the output terminals of the tuner (i.e., 
at the input end of the transmission line) is shown at the right 
side of the schematic drawing. (This is a departure from earlier 
versions of TLA or TL and was changed because I sometimes became 
confused in the old method!)

   TLA shows something called the "Effective Q," also known 
commonly as the "loaded Q" of a network. This is the loaded 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. 

   Thanks to Frank Witt, AI1H, this line shows the computed 1.5:1 
and 2:1 SWR bandwidths for the tuning network itself, calibrated 
in kHz and in percentage of the tuned frequency. Here, the load 
is assumed to be constant and the frequency is shifted internally 
to compute the bandwidth numbers. If the computed bandwidth is 
greater than 30% of the center frequency, TLA 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 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 TLA), 
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 DEFAULT VALUES

   In TLA you may change the antenna-tuner default values for 
five parameters: 

(1) the unloaded Q of the inductor(s)         [default = 200]
(2) the unloaded Q of the capacitor(s)        [default = 1000]
(3) the transmitter power                     [default = 1500 W]
(4) the resistance seen at the tuner's input  [default = 50 ohms]
(5) the stray shunt capacitance at the output [default = 10 pF]

   Note that the stray shunt capacitance in item (5) is only used 
when the tuner configuration has a series element (either 
inductor or capacitor) at the output terminals. 

   You may change the defaults after TLA has finished its first 
tuner computation or directly from the Antenna Tuners menu 
screen. You enter "D" from one of the tuner screens to change the 
Default values to what you like. 

   Follow the on-screen prompts. As usual, hit [Enter] to use the 
default value shown on-screen. Once you have changed any default 
values, they will remain in effect until you either reboot TLA or 
respecify the values from within TLA, using "D" as above. Just 
for your information, I've limited the maximum amount of power 
from the transmitter to 5 MegaWatts. I suspect that limit won't 
affect too many of you.

   Note that default item number 4) above allows you to 
experiment with tuner configurations. You might, for example, use 
a wideband impedance transformer, such as a 50:200 ohm 
balun at the input of a tuner. This way to may see if the 
physical component values for various loads are more practical 
than for a 50-ohm input, the default value. Another use is given 
in detail below -- evaluating a pi-network tank circuit in a 
transmitter.

   Note that a change to these tuner defaults is not saved to 
disk. However, the change remains in effect until you exit from 
TLA. 

TUNER LOSSES, DETAILS

   Examine the line showing the estimated power loss in the 
tuner. The loss shown is computed for the level of transmitter 
power you specify from the "D" prompt, as explained above. The 
loss is expressed in watts, in dB, and 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 amount of loss in the 
transmission line itself, plus the total loss in the line and the 
antenna tuner, both expressed in dB. Below this 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 ohms). 
The phase angle of the input voltage is assumed to be zero 
degrees. The magnitude and phase of the RMS output voltage is 
shown to the right. The magnitude and phase angle of the output 
voltage are particularly interesting to people designing networks 
for phased antenna arrays. 

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 the value of transmitter power 
you specify. (Note that the reactances are displayed to three 
decimal points, so that the purists among you may take these 
numbers and manually verify that the program is working the way 
it should. I too used this data to verify the program myself 
during development.)

   Note that the voltage shown by TLA 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, 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 an arc. This may or may not be 
disastrous, depending on whether the arcing component develops a 
permanent "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. 

   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. For the full amateur legal power level of 1,500 W, the 
insulation of the shunt inductor will not only have to withstand 
almost 10,000 V peak, but worse yet, it will have to dissipate 
almost 650 W of power at more than 18 A of circulating current. 
Toasted coil, if it doesn't arc first, which deserves the term 
"zapped," I suppose. 

   TLA 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 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 (this is the default value when [Enter] is hit by 
itself), with a reactance of zero ohms. 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 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 
configuration is often used because it can accommodate a wider 
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 capacitors. 

TLA AND TRANSMITTER OUTPUT PI-NETWORKS

   TLA has another useful feature built into it that allows you to 
evaluate the capabilities and losses in a pi-network used at the 
output of a vacuum-tube power amplifier. You can change the 
default input resistance seen at the input of the network from 
the 50 ohms most commonly used for an antenna tuner to the 
desired loadline resistance needed for a tube or transistor. For 
example, an 8877 power tube wants to see a load of about 2200 
ohms for a plate voltage of 3100 V. You would change the default 
from 50 to 2200 ohms in TLA, as explained above. 

   Now, following the recommendations in the ARRL Handbook, you 
want to achieve an effective network Q between 12 to 15 in order 
to ensure adequate suppression of harmonics. At a frequency of, 
let's say, 29.7 MHz, with a 50-ohm load at the output of the pi-
network tank, TLA 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 to lower the 
network Q. 

   An output capacity of 200 pF at 29.7 MHz will lower the 
network Q to 15.2, but now the required value of the capacity at 
the input of the pi-network is only 32.6 pF. The plate capacity 
of the 8877 is about 15 pF, and there will inevitably be stray 
capacity of at least 10 pF. This means that the minimum value of 
the tuning capacitor must be less than 7.6 pF in order to achieve 
the desired overall capacity of 32.6 pF. This is a tough 
requirement, especially for an air-variable capacitor that is 
used on 80 or even 160 meters too! Further trials with TLA will 
result in a compromise, although you may still find it necessary 
to use an expensive vacuum-variable capacitor to achieve a low 
minimum value. 

FEEDBACK, PLEASE      
 
   This is where TLA 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 n6bv@arrl.org.

R. Dean Straw, N6BV
Senior Assistant Technical Editor, ARRL


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 center-fed 
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 the 
transmission-line losses could be when an extremely high SWR was 
involved -- such as when an 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 the older 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 
and now TLA. 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 ohm 
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 have more than 35 dB of loss with this load, and a 24-
foot long piece would dissipate almost 20 dB. 


APPENDIX B

   Below are listed some sample impedance data you may use to 
play with using TLA. 

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
