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SMITTY.DOC -- Page 1
SMITTY Documentation -- Transmission-Line Calculations
By Jerry Hall, K1TD Rev. 3.01, February 1988
SMITTY is a unique program for doing transmission line
calculations, as you would do them on a Smith Chart. But no knowledge
of a Smith Chart is required to use the program. SMITTY lets you
calculate input or terminating impedances, as most other Smith Chart
programs do. In addition, SMITTY lets you calculate line Zo,
electrical length, attenuation and velocity factor from measurements
with open- and short-circuit terminations. SMITTY also allows you to
design stub matches and series section matches, make admittance-
impedance conversions, series-parallel conversions, and SWR
calculations.
SMITTY.COM is written in Turbo Pascal and compiled for the IBM PC
and compatibles. It uses no graphics, nor is a math coprocessor
required. Three files make up the complete program, SMITTY.COM (the
program file), SMITTY.DOC (this file), and SMITTY.DEF. SMITTY.DEF
contains values defining the number of decimal digits SMITTY.COM
displays during calculations. More about this file later.
SMITTY.COM and the accompanying files are offered as copyrighted
software, but permission is hereby granted to copy the program and pass
it along to others at no personal gain. Be sure to include all three
files.
REGISTRATION
No registration fee for SMITTY is requested or expected. I wrote
this program to satisfy my own needs, but I am pleased to share it with
any other user who finds it to be of value.
If you find the program useful, I do request that you register
your copy. Just send me your name and mailing address, and mention
what version of SMITTY you are using. Registered users will be advised
of any later program releases.
GENERAL INFORMATION
There are no restrictions in SMITTY for data that is practical.
For example, you may use 0 + j0 for an impedance value (a short
circuit) or 1/4-wavelength for a line length, etc. (HINT: Should you
wish to specify an open-circuit termination, use 1E+09 + j0.) However,
impractical data such as zero for a frequency or for a line impedance
may create divide by zero errors, causing the program to abort.
SMITTY is menu driven. All menu options are selected merely by
pressing a letter key; upper or lower case is accepted. The letter-key
selections are itemized in the menu, as well as being highlighted in
the menu description of the function. From the main menu, the screen
will clear and the opening screen for the selection you've made will be
SMITTY.DOC -- Page 2
displayed. Some menu items cover two procedures, such as converting an
impedance to an admittance, or vice versa. At the opening screen of
these procedures you'll be prompted for which calculation you wish to
perform. Again, and throughout the program, responses to all prompts
other than for data entry are made by pressing a single key.
During program execution you'll be queried with prompts for
various program options. One example is taking line attenuation into
account, with a Y or N response expected. Default options are shown
for each of these prompts, an N in this case. The default may be
selected by pressing the ENTER key (as well as by pressing the letter
key for the default). Pressing any other keys (in this case, anything
but Y, N, or ENTER) does nothing.
In some procedures you will be asked to enter reactance or
susceptance values at the keyboard. Be sure to enter negative values
for capacitive reactance and for inductive susceptance.
You may exit the program gracefully from the main menu by pressing
Q (quit). You may also abort the program at any time by pressing Ctrl-
C.
SMITTY FEATURES
Probably the most common use of the Smith Chart is to determine
the load impedance on a transmission line based on a known input
impedance, and vice versa. SMITTY does indeed support such
calculations. These may be made with actual R + jX values or with
normalized values. A similar calculation is to determine the load
admittance, G + jB, based on a known input admittance, or vice versa.
SMITTY supports these calculations as well. The choice to work with
impedance or admittance data is made after you select "toward load" or
"toward generator" at the main menu. Once you've made that choice, say
for impedance, you will continue to work with impedance values until
you return to the main menu.
Frequency Correction
During the execution of some procedures, Smitty requires reactance
data in ohms. The data to be entered at the keyboard may be the result
of impedance bridge measurements. Many bridges, such as a General
Radio 1606-A, give a reactance dial reading that must be divided by the
measurement frequency in megahertz to get the ohmic reactance value. In
these procedures you may enter the dial values from such a bridge, and
allow the program to make the frequency correction. A message similar
to the beginning lines of this paragraph will first be displayed, and
after the data is entered you'll be prompted about correcting
reactances for frequency. Unless you enter bridge dial readings,
you'll want to choose the default response, N(o).
SMITTY.DOC -- Page 3
Line Length and Attenuation
In SMITTY there are several options for entering line lengths.
You may enter electrical lengths directly as either degrees, radians,
or wavelengths. Or you may enter a physical line length in feet and
SMITTY will calculate and display the electrical length. In this case,
additional data SMITTY requires for the calculation are the velocity
factor of the line and the frequency. Velocity factors are always
entered as a decimal fraction, and frequencies in megahertz. (These
are clearly indicated at the data prompts.)
Various options also exist for taking line attenuation into
account during calculations. You may indicate a lossless line (no
attenuation), or you may enter attenuation either in decibels or
nepers.
Other Capabilities of SMITTY
SMITTY lets you calculate line Zo, electrical length, attenuation
and velocity factor from measurements with open- and short-circuit
terminations. The basis for this procedure is contained in Chapter 28
of The ARRL Antenna Book, 15th Edition, 1988. If you are not familiar
with this technique and want to try the program feature, use these data
values. These values are the results of actual measurements on a
length of foam-dielectric cable.
Open-circuit readings: 85 + j1280/freq
Short-circuit readings: 4.8 - j80/freq
Frequency: 7.14 MHz
Line length: 100 feet
SMITTY allows you to design stub matches. You may specify a line
impedance for the stub that is different from the main transmission
line. Note that for some loads, such as 40 +/- j20 with a 50-ohm line,
one of the two possible solutions occurs with the stub placed 0.0
wavelength from the load. This is not a program error, but is a valid
solution meaning to shunt the load itself with a matching stub. Such a
situation exists any time the normalized conductance of the load is 1.0
siemen. Determining stub positions is an iterative procedure, and
calculations for some loads take more time than for others . . .
typically one second or less for most loads. Calculations taking the
longest, up to a few seconds, are for cases when the unmatched load
creates a high SWR on the main line.
You may also design series section matches with SMITTY. Details
for this match are contained in the chapter on matching the line to the
load in any recent edition of The ARRL Antenna Book. This form of
matching is not widely used, but is more efficient than a stub match.
A 1/4-wavelength transformer is a special case of the series section
match. Just as the 1/4-wavelength section of line having an
intermediate impedance can match two unlike impedances, a series
section of the proper length and almost any impedance, at the proper
SMITTY.DOC -- Page 4
position in the main line, can match two unlike impedances. The
advantage of the series section is that it may be a standard type of
line, and the load may contain reactance as well as resistance.
As presently written, no provisions are made in SMITTY for taking
line losses into account for stub matching or for series section
matching. I have investigated this and find it does make a slight
difference in the outcome of calculations when line attenuation is
considered. A later version of the program may include this
capability.
With SMITTY, admittances may be calculated from impedances, and
vice versa. Similarly, series equivalent impedances may be converted
to parallel equivalents, and vice versa. These are direct conversion
processes, with no data required for line length, attenuation, etc. If
the data you enter is normalized, the results will be normalized, and
if the data you enter is unnormalized, the results will be
unnormalized. (Never mind that these procedures may ask if the data is
normalized; your response is used only to determine how many decimal
places to display.)
SMITTY also lets you calculate standing wave ratios or SWR values.
This is a simple procedure that can be done on a 4-function calculator.
But I find that doing it quickly in the computer often beats digging
out the equation (which I can never seem to remember), and then doing a
couple of dozen keystrokes on a calculator.
SMITTY.DEF
SMITTY.DEF is an ASCII text file containing values that define how
many decimal places SMITTY displays during program calculations. You
can change these values to meet your requirements (any value in the
range from 0 to 9) with EDLIN.COM or your favorite word processor. The
results are rounded (not truncated) to the number of digits displayed.
Just be sure to treat SMITTY.DEF as an ASCII text file, and do not
change the order in which the values appear. The values included in
SMITTY.DEF as originally distributed are as follows.
Resistance and reactance -- 3
Resistance and reactance, normalized -- 5
Conductance and susceptance -- 6
Degrees -- 3
Wavelengths -- 5
Decibels (attenuation) -- 2
Standing wave ratio (SWR) -- 3
Feet (line lengths) -- 2
Velocity factor -- 2
Voltage reflection coefficient -- 4
SMITTY.DOC -- Page 5
PROGRAM ERRORS
Although I think the program is completely debugged, it is
possible that undetected errors exist. Please let me know if you
experience a problem. But do not confuse program errors with data
input errors. As mentioned earlier, impractical data will create
divide by zero errors. The program will abort and a message such as
this one will be displayed:
Run-time error 02, PC=50E7
The 02 run-time error code signifies a divide by zero error.
If you run into an actual program error causing it to abort,
please immediately jot down from the screen display the exact entries
you made for data and the complete error code line. (Or better yet,
immediately do a print-screen operation to a printer.) Do this before
you clear the screen or start SMITTY again. Send me this information,
and I'll get back to you.
During initial development of the program I carefully checked the
results of all procedures against those from manual Smith Chart
calculations, or against manual calculations if the Smith Chart was not
required. I believe you will not encounter calculation errors.
I hope you find SMITTY to be a useful tool for solving your
transmission-line problems. I'd appreciate comments and suggestions
for program improvements. With many thanks,
Jerry Hall, K1TD, 181 Brimfield Rd., Wethersfield, CT 06109
February 14, 1988