Ham Radio 2000/Ham Radio 2000.iso/ham2000/antenna/yagiopt/yo.doc

Text File | 1988-12-16 | 62KB | 1,137 lines

                  The Yagi Optimizer



    YO.EXE is a Yagi-Uda antenna analysis and optimization program for
IBM-PC and compatible computers.  YO will analyze a Yagi hundreds of times
faster than general-purpose antenna modeling programs, such as MININEC or MN.
A fast Yagi model is implemented with high accuracy for forward gain and
overall pattern, and good accuracy for F/B and input impedance.  The Yagi model
used in YO is significantly more complex than the well-known W2PV Yagi model.
YO includes an algorithm for automatically optimizing the forward gain,
radiation pattern, and input impedance of a Yagi.  This algorithm
simultaneously adjusts all element lengths and spacings to iteratively converge
an antenna design to an optimal set of dimensions, using performance criteria
and objectives which you specify.

    The Yagi analysis algorithm used in YO employs a method-of-moments
solution for element currents.  It includes correction factors to prevent
convergence to supergain geometries, and to more closely match the YO-computed
gain and pattern to those obtained with MN.  Compared with MN, the accurate
arbitrary-geometry antenna modeling program based on MININEC, YO is typically
within 0.1 dB for forward gain, within a few dB for F/B, and within a couple of
ohms for input impedance.  Patterns produced by YO and MN for the same Yagi
usually appear nearly identical.  Occasionally, F/B differences of 10 dB or
more will occur for unusual Yagis which YO computes as having all backlobes
more than 30 dB down.

    The speed of the YO Yagi analysis algorithm permits several Yagi
iterations per second to be performed for small Yagis (8 MHz XT with 8087).
Using YO, a small beam can be completely optimized for gain, pattern, and SWR
over a frequency band in just a few minutes.  For antennas having many
elements, such as long-boom VHF Yagis, the optimizer may be run unattended with
constraints to automatically find the best antenna -- while you sleep, if
necessary.  Yagis having up to 50 elements can be modeled.

    YO will analyze a Yagi at a spot-frequency or at the low, middle, and
high frequencies of a band of interest.  It will update plots on your screen of
the far-field radiation patterns at each frequency while it iterates the Yagi
dimensions, and will continuously display the forward gain, F/B, input
impedance, and SWR.  This running graphics/alphanumeric display lets you
interactively direct the optimization.  You may interrupt the optimization at
any time to save the current design or to change optimization strategy.


                 System Requirements


    YO.EXE requires an IBM-PC or compatible computer with 384K bytes of
memory.  You'll need 512K bytes if you invoke the high-resolution PLOT.EXE
plotting program directly from YO.  A Color Graphics Adapter, Enhanced Graphics
Adapter, or Hercules Graphics Card is necessary.  YO will run much faster if a
math coprocessor chip is installed, but one is not required.  A hard disk is
not necessary.  An editor or wordprocessor program is needed to create or
modify Yagi files.  DOS 3.00 or later is recommended in order to avoid certain
bugs in earlier DOS versions which may impact YO.


                 Input Files


    YO reads the geometry of a Yagi from an input text file.  The file may
be in one of three formats.

    The YO file format uses an easy-to-read table for Yagi dimensions,
specifies one or three analysis frequencies, and allows a separate tapering
schedule to be used for each element.  YO files always have the extension .YAG.

    YO will also read files in MN format.  These files always have the
extension .ANT.  You may analyze and optimize a Yagi which you have previously
examined using MN.  MN-format files specify only one frequency.  The elements
must not be tapered to be read correctly by YO, and they must be listed in
order, starting with the reflector.  The Yagi must be aimed in the +X MN
direction, but it may have any polarization.

    The last file format supported is that used by the N6BV Yagi analysis
programs.  Two frequencies, the low and high band limits, are specified in the
file, and independent tapering is allowed for each element.  Many antenna
designs, including commercial antennas and high performance contest arrays, are
available in N6BV format.

    Yagi files are always ordinary DOS text files composed of ASCII
characters.  You may create your own Yagi files by using any text editor or
wordprocessor.  Refer to the YO file format description given later.  If you
use a wordprocessor to create Yagi files, be sure to have it generate a
standard DOS text file instead of a file in wordprocessing format.  Files in
wordprocessing format contain embedded control codes which will confuse YO.


                Output Files


    When you exit YO, the current design will be output using one of the
three file formats.  The output file format can be selected with the Other
Parameters command.  The name of the output file is always OUT.YAG, OUT.ANT, or
OUT.BV, depending on the format selected.  You may also save an intermediate
design without quitting YO by using the Save This Design option.  The name of
the first file saved is OUT1.* and the digit is incremented each time another
design is saved during a YO run.  Don't forget to rename the output files
before your next YO run if you want to save them, or they may be overwritten.

    When making an MN-format file YO will specify 24 analysis segments per
element if possible.  The self-impedance computed by MN for dipole elements is
most accurate when 24 segments are used.  If the Yagi has six or more elements,
so that the MN limit of 126 pulses per antenna would be exceeded, YO will
partition the available segments evenly among the elements.  Then it will
allocate any leftover segments beginning with the reflector and proceeding
forward along the boom.  If you want to reduce the MN analysis time you may
lower the number of segments in the MN-format file by editing the file.  For
MN-format files the center of the Yagi boom is put at X=0.  This facilitates
studies of stacked dissimilar Yagis using MN.


                 Before Running YO ...


    Before running YO do the following, according to your display type:

 HGC:    The HERCULES.COM graphics driver must be loaded.  To do
     this, simply enter HERCULES at a DOS prompt.  This
     needs to be done only once per boot, so HERCULES may be
     put in your AUTOEXEC.BAT file for convenience.

 CGA:    Load GRAFTABL and GRAPHICS once per boot (you may put
     them in your AUTOEXEC.BAT file).  These are standard DOS
     programs.  They will improve the CGA graphics characters
     and allow you to transfer the CGA plots to your printer.

 EGA:    The EGA requires no preliminaries.

    When executed, YO automatically determines which type of graphics
display is present, and then configures itself accordingly.  The graphics
features of YO vary according to the display type.  For example, screen writing
is visible on the CGA during plot updates because the CGA has only one graphics
buffer.  For the EGA and HGC, YO composes a new screen in one graphics buffer,
while the current screen is being displayed from another, and then switches the
screens instantly.  This gives the illusion of motion.  The patterns appear to
be objects which change shape, rather than sequences of static drawings.  Color
is not used on the YO screens, but the high-resolution PLOT program will
produce color plots on the EGA.


                    Starting Up YO


    You may specify a Yagi filename on the command line when you invoke YO,
for example, YO 204SSB.  If you know the filename you want this is the quickest
way to get going.  Otherwise, YO will list the *.YAG files available, and then
prompt you for a filename.  If you enter <Esc> YO will terminate and return you
to DOS.

    The following special command line sequence will not be interpreted as
a Yagi filename specification:

             YO PRINT Filename

    For this special sequence only, YO will format and print the text file
specified and then terminate.  You may use upper or lower case for the PRINT
keyword.  The documentation files supplied with YO are formatted for direct
viewing on your screen, allowing a quick paperless reference.  YO PRINT will
add margins and pages while printing these files.

    Normally you do not need to specify a file extension or a directory for
Yagi files.  If neither is specified YO will first look for the file in the
current directory in YO format using the extension .YAG.  If the file is not
found it then looks for the file in MN format using the extension .ANT.  If
still not found it looks for the file in N6BV format using no extension.  If
the file cannot be located in the current directory the whole process is
repeated using the Yagi library directory (see below).

    If you specify a file extension YO looks for that exact file, in both
the current and library directories.  If you specify a drive or path, YO looks
for the file only in the directory specified.  You may specify an extension if
necessary to resolve ambiguities, or when analyzing an N6BV file where the
extension usually denotes the Yagi boom length in feet.

    After making a menu selection, <Esc> is used to return to the main
menu.  It is used both for normal returns and to abort an operation.  If you
have not entered anything, pressing <Esc> during a data entry operation will
cancel the operation and return you to the main menu.  If the data has been
typed but not entered, pressing <Esc> will enter the data, terminate the
operation normally, and return you to the main menu.

    <Esc> is also used to get rid of the main menu in order to reveal the
whole screen.  The menu can be brought back by pressing any key other than
<Esc>, and if this key corresponds to a valid command, the command will be
executed.

    For menu selections involving numerical input you may use an arrow key
to enter the number and simultaneously advance to a new item.  <Enter> is used
to enter a number and remain at the item selected.  This is useful for changing
the value of one item repeatedly to experiment with its effect.

    When YO asks a question you may press "y" for "yes" and any other key
for "no", except the <Esc> key.  <Esc> will cancel the operation and return you
to the main menu.

    The numbers listed inside each of the Yagi patterns are not labeled in
order to reduce screen clutter.  The numbers have the following meanings:

                Frequency
                   Forward Gain
              F/B or F/Worst Backlobe
                 Input Impedance
                   SWR

    The Yagi count in the lower left corner is incremented each time a new
Yagi evaluation is performed.  The evaluations which do not result in a pattern
update are either part of the gradient computation described later, or are
iteration trials which do not result in improved antenna performance.  The
complete filename, including path and extension, appears in the lower right
corner.


                Frequencies


    YO handles either spot-frequency Yagi designs or designs intended to
operate over a frequency band.  A single frequency is specified for
spot-frequency designs, while low, middle, and high frequencies are specified
for designs covering a band.  The middle frequency should be between the low
and high frequencies, but otherwise there are no restrictions.

    In YO-format files you may specify one or three frequencies.  In N6BV
files only the low and high frequencies are specified, and YO uses the
geometric mean of the two as the middle frequency.  This is the way the N6BV
Yagi programs treat the two frequencies.  MN-format files have only one
frequency, and this is used to specify a spot-frequency by YO.

    You may add, change, or delete frequencies with the Frequency command.
This command changes only the analysis frequencies; it does not rescale the
beam dimensions.  You must use one or three frequencies, two are not allowed.
To convert to a spot-frequency analysis enter 0 for either the low or the high
frequency; YO will then set both frequencies to 0.  It takes longer for YO to
iterate a design over a frequency band than at a spot-frequency.  You should
always use just one frequency for spot-frequency designs to get the fastest
iteration cycles.

    A Yagi may be modeled at any frequency with YO.  Frequencies of 1 GHz
or more will cause frequency digits to be displayed with a leading % character,
indicating screen field overflow, but otherwise YO will operate normally.
Frequency fields in output files will not overflow until 10 GHz.


             Pattern Optimization Criteria


    YO can use the standard front-to-back power ratio (F/B) as a quality
measure for Yagi patterns during automatic optimization.  A second pattern
quality criterion is also available.  This is the ratio of the forward power to
the total power in the rear half-plane (F/R).  Designs maximizing F/B often
have large backlobes -- they are just not at 180 degrees.  When used as a
pattern quality measure during automatic optimization, the F/R criterion yields
antennas with better overall patterns.  This criterion prevents large lobes
from appearing anywhere to the rear of the antenna, including at 180 degrees.

    YO measures the rear power by computing the radiated power every 5
degrees and then summing the terms from 95 to 180 degrees.  You may select
either the F/B or F/R pattern optimization criterion with the Other Parameters
command.  You may choose to have either F/B or the ratio of the forward power
to that of the worst backlobe displayed numerically for each frequency.  The
latter display seems more appropriate when using the F/R design criterion, and
it can be related directly to the patterns you see on the screen.  Try
optimizing the patterns of several antennas using both the F/B and F/R methods
to get a feel for the differences involved.


                Simple Optimization


    You can direct YO to maximize forward gain, optimize the radiation
pattern, or increase the input impedance.  The latter also reduces the SWR
across a frequency band, so this operation is referred to as "minimizing the
SWR" when three frequencies are specified.  For each of these objectives YO
will employ the Method of Steepest Descent, an iterative optimization technique
described later.  You may select one of these performance objectives, run for a
while, and then select another and iterate with it.  This simple optimization
mode is useful for exploring the characteristics and performance tradeoffs of a
particular Yagi configuration, and in finding limiting values.  However, in
general, optimizing an antenna solely using one of these criteria will not
result in a satisfactory design for the following reasons:

    In general, maximum-gain antennas are characterized by very low input
impedance, small SWR bandwidth, a narrow front lobe, and a high-amplitude rear
lobe.  Some maximum-gain designs that YO will find will have an input impedance
of only an ohm or two.  These are wholly impractical antennas, but they do
serve as useful reference points when determining the amount of gain you must
give up to get a realizable design.  Other maximum-gain designs having input
impedances in the 5-10 ohm region, while still high-Q antennas, are quite
practical for narrowband applications, such as use on the 12 meter HF band or
for weak-signal work at 144.200 MHz.

    Antennas optimized for best pattern are generally good all-around
antennas for general-purpose work.  They are often selected for receiving
applications.  (However, in situations involving omnidirectional or random
direction noise or QRM, an antenna designed for maximum gain will deliver a
higher average receive S/N than any other antenna design).  Most commercial
Yagis are optimized for best F/B.  Antennas designed for best pattern tend to
have 1-2 dB less gain than maximum-gain designs, reasonable input impedances,
broad front lobes, and low-amplitude rear lobes.  However, it is frequently the
case that a small sacrifice in pattern shape will result in a worthwhile
increase in forward gain, or a welcome broadening of the SWR bandwidth.  As
with maximum-gain designs, you pay some price in the other performance
parameters when you optimize strictly for best pattern.

    Yagis are not optimized with impedance itself as an objective.  Rather,
the impedance value, or the SWR bandwidth in the case of antennas operated over
a frequency band, acts as a constraining characteristic.  Some combination of
gain and pattern is optimized, as long as the impedance is high enough or the
SWR bandwidth is great enough.


               Constrained Optimization


    Because of the shortcomings of Yagis designed using simple
optimization, YO includes an optimization mode where you may pick your own
gain/pattern/SWR tradeoff and then optimize an antenna within the chosen
constraints.  For example, you might maximize the antenna forward gain subject
to the constraints that the F/B not drop below 25 dB and that the SWR across
the band not rise higher than 2.  Or, you might optimize the pattern subject to
the condition that the gain not fall below 6 dBd and the SWR remain less than 2
across the band.  Automatic constrained optimization is a very powerful tool
for arriving at a final design.  Even when using antenna modeling programs,
optimizing an antenna by trial-and-error experimentation while trying to
satisfy constraints can consume a great deal of time and effort.

    To get the most out of a particular Yagi you need to explore the
antenna first using the unconstrained optimization mode.  This will enable you
to get a feel for the potential of the antenna configuration and for the way
that the various performance parameters trade off among themselves.  You may
even discover a region of antenna geometry where the desired objectives tend to
maximize simultaneously.  After exploring the Yagi design in this way you will
be able to choose the best set of starting dimensions for constrained
optimization, and a set of realistic constraint values.

    If two constraints are in effect YO will attempt to satisfy both.  If
that is not possible then it will satisfy one or the other.  If that is not
possible then you should set more realistic constraint values.

    When F/B is used for the pattern quality measure the pattern constraint
is a minimum value of F/B.  When F/R is used the constraint is a minimum value
of the ratio of the forward power to the power of the largest lobe in the rear
half-plane.  The latter constraint is indicated by "Min F/L" on the constraint
menu.

    The default values for the constraining variables are such that no
constraints are in effect.  Use the Constraints command to change the
constraint values.  Note that if you are maximizing gain the constraining value
for gain is inoperative.  Similarly, while optimizing the pattern the pattern
constraint has no meaning and is not in effect.


                  Manual Optimization


    YO provides a way for you to change the element lengths and positions
individually by hand.  This is a great way to get a feel for how each element
affects the overall antenna performance.  It is also useful for touching up the
results of the automatic optimization, especially the pattern at the low and
high frequencies.  In order to run quickly, the YO optimizer only operates at
the middle frequency.  As a result the patterns at the outer frequencies are
never as good as that at midband when you optimize for best pattern.  If you
want an antenna with a more uniform pattern across the band you can modify the
elements by hand to achieve the desired response.  In general, to broaden the
response lengthen the reflector and shorten one or more directors.  For long
Yagis you may manually modify the first 19 elements.


                 Optimization Method


    The automatic optimization procedure used by YO employs a modified
Method of Steepest Descent technique.  This technique is also known as Newton's
Method.  (Yagis had not yet been invented in Newton's time, so he had to make
do with dipoles).

    First, each element length (and position, if enabled) is changed
individually by a very small amount, with all other antenna dimensions
unchanged, to calculate the sensitivity of the desired objective (gain,
pattern, or impedance) to each variable.  The collection of these sensitivities
is called a gradient.  The gradient amounts to an n-dimensional vector, where n
is the number of elements plus element spacings, which points in the direction
of maximizing the objective.  After the gradient is calculated, an iteration
step is taken wherein all of the element lengths and positions are updated
simultaneously along the gradient vector, each in proportion to its respective
sensitivity, and all in proportion to a step size.  If the step size is not too
large, after the update the new antenna will have incrementally higher
performance, according to the objective selected.

    Because it takes a long time to calculate the gradient, the modified
algorithm will keep iterating the lengths and positions along the same gradient
vector until no further improvement is found.  A new gradient is then
calculated and the process repeated.  The size of the iteration steps is
controlled automatically by various internal criteria with the objective of
finding the maximum value of the objective function in the smallest number of
iterations.  (The step size is too small when a larger step would have improved
performance more, but too large when unstable convergence occurs or the
performance maximum is overshot.)  The whole process is terminated either by
operator interruption or when the step size is automatically reduced many times
in a row, that is, when essentially no further improvement in the objective is
possible with small perturbations of the antenna dimensions.

    This optimization technique is quite efficient, locating optimal
dimensions for an antenna without wild goose chases.  However, the method does
not guarantee that the global optimum is found (nor does any other optimization
technique, except for exhaustive search).  The global optimum is the very best
set of antenna dimensions out of all possible dimensions, according to your
chosen criteria of "best".  The reason that the global optimum may be missed is
that the optimization algorithm may converge to a local optimum, and then
terminate because immediate movement in any direction only produces worse
results.

    Optimization using perturbation techniques is inherently nearsighted.
If the algorithm is trying to maximize forward gain, for example, and there is
a small bump in the gain curve for a certain set of element lengths and
positions, it is possible that it may wind up on top of the bump rather than at
the highest overall point of the whole curve.  If you imagine trying to climb
to the very top of a mountain range having multiple peaks, in dense fog, you
will be able to visualize the problem.

    If you believe that YO is converging to a local optimum you may vary
the starting dimensions to begin the search in a different region of the
performance space.  In general, converging to a local optimum is not much of a
problem with Yagi antennas when using simple optimization.  However, when
optimizing with constraints you are more likely to encounter this situation.
The constrained optimizer tends to stop at the first set of Yagi dimensions it
encounters which are just within the constraint limits.  If you have explored
the Yagi design first using simple optimization you will have some idea whether
a better region of the performance space exists, and therefore whether to try
another set of initial dimensions.

    Automatic optimization is done at the middle frequency only.  If the
optimizer were run at the low and high frequencies as well, the program would
execute quite a bit more slowly.  Once you get the hang of working with YO it
is pretty easy to control the response over the whole band while optimizing
only at the middle frequency.  For example, you may equalize the response at
the low and high frequencies by changing the location of the middle frequency,
as it need not be at the center of the band.  In addition, manual changes may
be made to the individual element dimensions to touch up the response at the
outer frequencies.  Future versions of YO may offer the option of automatic
optimization over a band.  (By its nature, the SWR constraint takes the SWR at
the low and high frequencies into account.)

    To avoid terminating the optimization prematurely, YO will continue to
iterate even when only very small performance improvements are being made.
Occasionally this will slowly inch the design into a new region of the
performance space where significant improvements become possible.  However,
this situation seldom occurs, so when you are satisfied that no further
improvements are possible you may press any key to interrupt the optimization
and pop up the main menu.  The optimization may be restarted if you change your
mind.  YO will terminate optimization itself eventually, but only after the
step size has been automatically reduced many times in succession, indicating a
performance maximum has been found.

    If the key used to interrupt optimization is a valid YO command key,
the command will be executed immediately.  For example, you may press <Esc> to
stop the optimization and also get rid of the main menu, in order to view the
whole screen.

    During optimization, checks are made on the reasonableness of the Yagi
dimensions.  Elements are not allowed to become shorter than 0.4 wavelengths,
nor longer than 0.55 wavelengths.  No pair of elements are allowed to migrate
closer than .05 wavelengths.


                    SWR


    During optimization, YO computes the SWR at the low, middle, and high
frequencies using a simple broadband matching network (see below).  The
matching network is adjusted each iteration cycle for unity SWR at a fourth
frequency, called the matching frequency.  In general this frequency is not the
same as the middle frequency, although it is usually somewhere near the middle
of the band.  The matching frequency itself is adjusted each iteration to make
the SWR at the low and high frequencies approximately equal.  This condition
minimizes the maximum SWR across the band.  The matching frequency can also be
updated in a separate iterative loop by using the B command to balance the SWR
at the low and high frequencies.  When you eventually construct the Yagi it
should be matched for unity SWR at the matching frequency, not at the center of
the band or at the middle analysis frequency, in order to achieve the maximum
possible SWR bandwidth.  Note that the SWR displayed for the middle frequency
will not be 1.00 unless the matching frequency is very close to the middle
frequency.

    For spot-frequency designs SWR is not an important design parameter
because you can always, in principle, match the antenna perfectly to any
feedline.  In this case, instead of minimizing SWR, you can tell YO to raise
the antenna input impedance.  This is useful for getting out of the low ohmic
range where conductivity losses in the elements may significantly lower the
realizable gain, or where small construction errors in a high-Q design may
result in performance degradation.  YO tries to raise the input impedance in 1
ohm steps.  This permits you to watch the operation proceed and then terminate
it when your desired impedance is reached.  The impedance-raising loop differs
from the gain and pattern maximization loops in that a new gradient is
calculated every iteration cycle.  While slower, this strategy causes the
design to take the straightest path to a desired impedance condition, thereby
sacrificing the least gain or pattern when starting from an optimized design.


                  Matching Networks


    YO contains models for three fundamental matching networks, plus some
variations.

1.  Broadband Network

    The simple broadband matching network consists of a broadband
transformer and a series reactance.  The transformer matches the resistive part
of the Yagi input impedance to the feedline impedance, and the series reactance
tunes out any residual Yagi reactance.  While you might actually construct such
a network, it is mainly useful for finding the inherent bandwidth properties of
the Yagi, independent of any particular reactive network which might modify the
SWR bandwidth.  The transformer is modeled as being perfectly broadband in
response, and the small series reactance has an insignificant effect on SWR
bandwidth.  This simple matching network is used during all optimization
iterations, even after another matching network has been designed, because it
allows well-behaved SWR convergence during constrained optimization.

2.  Gamma Match

    YO also contains a model for gamma matches.  A gamma matching network
uses a small-diameter rod parallel to one side of the driven element.  The rod
extends from the center of the element and is strapped to the element some
distance down the rod.  The coax center conductor is attached to the gamma rod
and the shield is connected to the center of the driven element.  A capacitor
is placed in series with the gamma rod, usually at the feedpoint, to compensate
for the inductance introduced by the rod.  The driven element is not broken at
the center and may be attached electrically to the boom.

    The YO gamma match model uses the W7ITB equations.  You specify the
gamma rod diameter and center-to-center spacing from the driven element.  YO
will then calculate the required rod length and series capacitance, and will
adjust the matching frequency to balance the SWR at the band edges.  The
element diameter used in the gamma match equations is that of the first taper
section which is longer than 1/20th of the element half-length.  This prevents
a short inner taper section representing a mounting plate from being
erroneously employed in the gamma match.  No correction is made if the gamma
rod extends into the next taper section, and no check is made for rods which
extend beyond the end of the driven element.

    Although it is not well-known by amateurs, the gamma match is capable
of compensating for the input impedance variation of a Yagi across a frequency
band.  You may take a narrowband high-performance Yagi design and flatten out
the SWR over a wide band by using a carefully designed gamma match.  Because
the operational bandwidth of Yagis is typically limited by their SWR bandwidth,
rather than by their gain or pattern bandwidth, this is a very useful property
of the gamma match, not shared by other matching networks in common use.  The
drawback of a compensating gamma match is that it usually requires a long rod.
This makes it more sensitive to geometry changes caused by mechanical flexing
of the element and matching assembly.

3.  T Match

    A T match is a balanced double-sided gamma match which is fed by
connecting a balanced transmission line (or coax through a balun) between the
two gamma rods ends near the boom.  Two series capacitors are used to tune out
the rod reactance.  You can design a T match with YO by using the gamma match
model and specifying half the actual feedline impedance.  The rod length and
capacitance calculated should be applied each side of the driven element.

4.  Hairpin Match

    YO also contains a model for hairpin matches.  The hairpin match uses a
shunt inductance across the split driven element feedpoint to raise the
resistive part of the Yagi input impedance to that of the feedline.  The driven
element is then shortened from its resonant length to compensate for the added
inductive reactance, and the system is fed with coax through a balun.  The
inductance can be provided by a coil, by a loop composed of stiff wire or rod,
or by a shorted transmission line consisting of two parallel rods.  YO will
compute the inductance required, and for the transmission line inductor, will
calculate the distance to the shorting bar.  You specify the hairpin rod
diameter and spacing between rods.  YO then iteratively modifies the driven
element length and the matching frequency to obtain unity SWR at the matching
frequency and equal SWR at the low and high frequencies.

    Hairpin matches on commercial Yagis use wide spacing between the
hairpin rods.  For the small values of inductance normally required the
distance to the shorting bar is on the order of the rod spacing.  This
geometry, which amounts to a rectangular loop, is not well-modeled by a shorted
transmission line.  For this kind of hairpin you should expect to require a
longer distance to the shorting bar than indicated by the transmission line
model.  However, the values calculated by YO for inductance and driven element
length are accurate for all inductor geometries.  The inductance value is
displayed for cases where it is more convenient to use a lumped inductor
directly across the feedpoint rather than a loop or transmission line.  Future
versions of YO may contain a separate model for stubby hairpins.

    The hairpin match will not compensate for Yagi input impedance
variations as will the gamma match, but it will not significantly narrow the
inherent bandwidth of the Yagi either.  Hairpin matches are favored by those
troubled by the unbalanced nature of a gamma match, and by the extra mechanical
components involved in a balanced T match.  However, unlike these systems, the
hairpin match requires a split driven element which must be insulated from the
boom.

5.  Beta Match

    The beta match is Hy-Gain's version of the hairpin match.  It uses two
rods which straddle the boom, and a shorting bar across the rods which also
electrically connects the rods to the boom.  The presence of the boom has a
negligible effect on the inductance of the hairpin, so the beta match is
electrically identical to a conventional hairpin match.

    Keep in mind that the broadband matching network is used during all
optimization iterations.  When doing optimization with an SWR constraint, you
should set the SWR constraint value according to the matching network you
eventually intend to use.  For example, if you intend to use an
SWR-compensating gamma match, you might choose an SWR constraint of 4, knowing
that it is easy to design a noncritical gamma match which will reduce this SWR
to well below 2.  Conversely, the hairpin match will not compensate for SWR
variations, so you should set the constraint to your ultimate SWR limit.

    The matching network menu operates like a spreadsheet.  You may reenter
a network parameter and YO will immediately recalculate the network dimensions
and the SWR at all frequencies.  You may use this feature to interactively
design a matching network, or to explore the impedance-compensating properties
of gamma matches.  You should try various driven element lengths when designing
gamma matches.  The different Yagi input reactances which result will enable
additional gamma match geometries to become realizable designs.

    Occasionally a Yagi may exhibit an unusual input impedance variation
with frequency which inhibits convergence of the SWR balancing operation during
gamma and hairpin match design.  If this occurs simply press any key to
terminate the balancing operation.


                Driven Element Length


    The gain and pattern of a Yagi are not significantly affected by the
length of the driven element, so this length is not changed by the YO
optimization algorithm.  YO modifies the driven element length only during
adjustment of the hairpin match.  You may change the driven element length
manually when designing a gamma match to vary the input impedance seen by the
matching network, permitting different gamma dimensions to be used.  You may
also change the driven element length to accomodate a matching network not
modeled by YO.

    One interesting matching scheme involves lengthening the driven element
until the real part of the Yagi input impedance is 50 ohms.  Then a series
capacitor is added to tune out the inductive reactance caused by the long
driven element.  In addition to simplicity, this matching scheme has the
advantage that the higher input impedance results in a somewhat broader SWR
bandwidth, without resorting to an impedance-compensating gamma match.


                 Element Tapering


    Yagi modeling algorithms internally work with cylindrical elements
having a uniform diameter.  A tapering algorithm is necessary to convert from
real antennas using tapered telescoping tubing to the cylindrical (monotaper)
equivalent.  Generally the monotaper length is chosen such that the monotaper
dipole exhibits the same reactance as that of the tapered element at the
central design frequency.  Tapering can greatly affect the reactance of a Yagi
element, and therefore can have a substantial effect on antenna performance.
Tapered elements must be physically longer than their monotaper equivalents to
exhibit the same reactance (for some tapers, much longer).  Tapering must be
accurately modeled to realistically characterize HF Yagis.

    YO contains two tapering algorithms.  One is the W2PV tapering
algorithm, from the ARRL Yagi Antenna Design book and the most recent edition
of the ARRL Antenna Book.  This algorithm has been widely used for Yagis and
generally gives good results.  However, a careful study using MN of many
different tapered dipoles and their W2PV-derived monotaper equivalents showed
that often the computed reactance values of the dipoles really were not very
close.  In addition, the reactance values diverged rapidly with frequency
excursion from the central design frequency.

    YO contains a second tapering algorithm designed to correct these
shortcomings.  This algorithm is a modified version of the W2PV.  The modified
algorithm yields monotaper equivalent dipoles whose computed reactances are
much closer to those computed for the original tapered elements.  For some
taper schedules the resulting difference in predicted Yagi performance is
dramatic.

    In addition, the new tapering algorithm computes the diameter of the
monotaper equivalent in such a way that its reactance and that of the original
tapered element match over a wide frequency band, not just at a single
frequency.  Effectively, the Q of the monotaper equivalent dipole is made equal
to that of the original tapered element.  Using the original W2PV algorithm,
the monotaper equivalent diameter ("standard diameter") is chosen variously as
7/8", as the middle taper diameter, or in some implementations as the average
diameter of the taper sections.  Such equivalent diameters are approximately
correct for many taper schedules in common use.  In addition, for
spot-frequency designs the equivalent diameter can be chosen arbitrarily
without introducing error.  However, to accurately model Yagi performance over
a frequency band, either the equivalent diameters must be accurately
represented, or else the taper conversion must be completely redone at each
frequency analyzed.  Reactance errors in the element models away from the
central design frequency can give a misleading indication of antenna
performance at the band edges.

    The new tapering algorithm is the default for YO.  To experiment with
the original W2PV tapering algorithm use the Other Parameters command.  The
standard diameter used with the YO implementation of the original W2PV tapering
algorithm is the average diameter of the taper sections, where the diameter
contribution of each section is weighted by the length of the section.  This
method avoids problems introduced by very short taper sections which represent
element mounting plates.  The maximum number of taper sections is seven.

    YO will output the current design using the current taper schedule, for
YO and N6BV output file formats.  For output files in MN format the equivalent
monotaper lengths are always output directly, without tapering.  When the
output file is written, the length of the outermost taper section (the element
tip) is adjusted to reflect the current antenna design, while the inner
sections remain as specified in the taper schedule.  It is possible for an
element to acquire a negative tip length if it gets shortened enough during
optimization.  To allow you to exit YO quickly, this condition is not brought
to your attention as the output file is written.  An error will be generated
later if YO tries to read such a file.  The error will also be caught if you
try to construct the antenna.  Not many hardware stores stock tubing in
negative lengths these days.


              Element Mounting Brackets


    A conductive element-to-boom mounting bracket lowers the inductance of
an element in the vicinity of the bracket, raising the element resonant
frequency.  This effect may be modeled by increasing the diameter of the
element where it passes over the bracket.  The amount of the increase depends
in a complicated way on the geometry of the bracket and its proximity to the
element.  The Mushiake-Uda equations are used to model this effect for one
common type of mounting bracket, the flat rectangular mounting plate.

    The mounting bracket model is selected with the [ or ] keys.  After you
specify the plate geometry, YO will calculate the length and diameter of a new
inner taper section which will be added to the taper schedule.  The new section
has a diameter which is equivalent electrically to the combination of the
original element and the mounting plate.  The length of the section is the same
as the half-length of the mounting plate.

    When you return to the main menu all elements of the current Yagi
design will be updated with the new taper section, and it will appear in the YO
output files.  The original input file is not modified.  To permanently recover
the mounting plate correction simply copy the output file onto your original
input file.  If your Yagi uses more than one size of mounting plate you should
use YO to calculate the dimensions of the equivalent taper sections and then
add them by hand to your Yagi file.  Don't forget to shorten the original inner
taper section by the length of the new section added, as the mounting plate
does not alter the total length of tubing in the Yagi.

    If YO finds that the existing inner taper section is very short (less
than 1/20th of the element half-length), it assumes that this section already
represents a mounting plate correction.  Additional mounting plate computations
will modify this section, and not cause a new section to be added.  If you are
using a very short inner taper section of tubing for mechanical reinforcement
of the element, rather than to represent a mounting plate correction, you
should use YO to calculate any mounting plate corrections and then add them by
hand to the Yagi file.  Otherwise, YO will substitute mounting plate
corrections for your reinforcement section.

    If you enter zero for the plate width, length, or thickness, so that YO
lists "None" for the equivalent taper, when you return to the main menu any
existing very short inner taper section will be removed from the taper
schedule.

    The width of the mounting plate is its dimension along the boom, and
the length is its dimension along the element.  Enter the dimensions of the
whole plate, even though YO uses half-lengths for element dimensions.  The
element-plate distance is the closest distance between the element and mounting
plate.  If U-bolt saddles are not used then this distance is 0.

    The element dimensions used during on-screen mounting plate
calculations are those of the driven element.  However, when YO adds the new
taper section to the current design, the correction is recalculated for each
individual element to ensure that the correct element diameter is used.

    The element mounting method should always be taken into account when
modeling Yagis.  Large mounting plates can significantly affect the frequency
response of a Yagi, moving the desired response completely out of a band in
extreme cases.   Small mounting plates can upset a carefully optimized F/B at a
spot frequency.  However, some mounting methods which use very small mounting
hardware require no correction factor.  One such method is that used by
Cushcraft for their smaller HF beams.  This method employs a single U-bolt and
a small saddle which fits between the boom and element; no mounting plate is
used.  This mounting method should have a negligible effect on element
resonance.  Other element mounting arrangements are not well-modeled by a
simple flat plate.  These include the Hy-Gain clamping mount which surrounds
the element and effectively passes it through the boom, and the Wilson
right-angle bracket mount.  More information on element mounting correction can
be found in the ARRL Yagi Antenna Design book.


              Frequency and Taper Scaling


    YO contains a scaling routine permitting any Yagi design to be
translated to a new frequency while maintaining essentially the same
performance characteristics.  This provides an easy way to replicate a favorite
Yagi design on a new band without having to design an entirely new antenna.
The taper schedule may be completely different at the new frequency.  YO will
take everything into account, generating a set of dimensions for a Yagi having
electrical performance nearly identical to that of the original antenna.

    Taper modifications may also be made in the absence of any frequency
scaling.  This is useful when experimenting with different tubing diameters to
determine the effect on bandwidth characteristics.  It is also useful in
generating an equivalent electrical design for new mechanical parameters.  For
example, you might use the taper scaling feature if you come across a bargain
hamfest beam having good aluminum but unusual tapering and unknown electrical
design.  You could replicate your favorite Yagi design onto this beam by taper
scaling, as long as the boom is long enough and the element positions are
adjustable (if they aren't you can always reoptimize).

    Although the YO scaling feature can virtually duplicate the performance
of an existing Yagi at a new spot-frequency, the duplication will not be exact
across a new frequency band unless the diameters of the monotaper equivalent
elements happen to scale in exact proportion with frequency.  This is seldom
the case because practical mechanical considerations or tubing material on hand
normally dictate element diameters.  In addition, the two bands may not have
the same percentage bandwidth.  Therefore, after frequency scaling you should
check the performance of the Yagi over the new band of interest.  Usually the
unmodified performance of scaled antennas is entirely satisfactory.  If not,
the new design can be used as the starting point for a quick reoptimization.

    The frequency and taper scaling algorithm used by YO does not rely on a
simple polynomial approximation for element reactance as does the W2PV scaling
technique.  Instead, the method-of-moments algorithm used to compute
self-impedance during normal YO Yagi analysis is invoked iteratively for each
element while the tip lengths are adjusted.  The adjustment loop is terminated
when the reactance of the new element matches that of the original element to
within 0.1 ohm.

    The YO and N6BV file formats permit each element to have a completely
different taper schedule.  This is very handy when building a Yagi using
elements obtained from a variety of old antennas.  However, to keep things
simple, during taper scaling YO will apply only one new taper schedule to scale
all elements.

    The new taper schedule is entered by selecting Tapering/Scaling from
the main menu.  Simply enter the new taper diameters, separated by spaces, on
the Diameters line.  Then enter the new taper lengths on the Lengths line.  The
length of the last taper section, which varies among the elements and is
indicated by [var] for the current schedule, need not be entered.  YO will
compute this length for each element according to the new schedule.  The set of
dimensions listed for reference as the current taper schedule are those of the
driven element.  If you wish to use the listed diameters or lengths for the new
schedule (for all elements) just press <Enter> on the Diameters or Lengths
line.  This is handy when frequency-scaling a Yagi within a band.

    If you press <Esc> when prompted for the new diameters you will exit
Tapering/Scaling.  Use this to examine the current taper schedule without
making any changes.  Once you have specified the diameters you are committed to
a taper scaling operation, and entering <Esc> on the Lengths line will complete
the calculations rather than aborting.  If YO finds that the taper lengths
specified result in an element tip having a negative length, you are prompted
to reenter the lengths.

    The tapering algorithm selected (W2PV or modified W2PV) will affect the
results during taper or frequency scaling.  Select the algorithm you prefer
before beginning any scaling operations.


                  Two-Element Yagis


    YO expects every Yagi to have a reflector element.  Two-element Yagis
having a driven element and a director pose a special problem.  These antennas
can be modeled by placing a dummy reflector a great distance away from the two
active elements.  This arrangement will satisfy YO while leaving the response
of the two-element array unaffected.


                Pattern Plots


    The plots displayed on the screen by YO during optimization use the
standard ARRL log dB antenna polar plotting scale.  Half-scale represents about
12 dB down and quarter-scale is about 24 dB down.  Yagis plotted with this
scale produce familiar beam shapes which may be compared with those in ARRL
antenna publications and QST articles.  Scale markings are not shown in order
to reduce screen clutter.  Yagi response is computed every 5 degrees and these
points are connected with straight lines in the plots.  The slight asymmetry in
the patterns near the polar centers is due to inherent inaccuracies in the
Microsoft plotting routines.

    You may also plot the mid-frequency pattern in high resolution with the
H command.  This invokes PLOT.EXE, a general-purpose antenna pattern plotting
program.  PLOT produces annotated polar and rectangular plots with a variety of
display options.  The patterns are generated every 1 degree for Yagis having 15
elements or more, and every 2 degrees for smaller antennas.  You may do a
switched-overlay comparison of two Yagis using the instant plot comparison
feature in PLOT (unless you have a CGA screen).  This feature can reveal subtle
differences between Yagis which would otherwise go unnoticed.

    When PLOT is invoked from YO, a plot file is generated with the same
root name as that of the Yagi file, but with the extension .PLT.  Later, after
quitting YO, you may execute PLOT by itself to view and compare the plot files
you have generated.  PLOT uses its own highly accurate drawing routines to
avoid the plotting errors inherent in the Microsoft routines.  The PLOT drawing
routines are not used by YO because they are slower.  See PLOT.DOC for more
information on PLOT.


                Other Parameters


    The Other Parameters menu selection allows you to control some
additional aspects of YO.

    If you change the tapering algorithm, and if the Yagi is not a
monotaper design, when you exit Other Parameters you will asked whether the
Yagi file should be reread using the new tapering algorithm.  The current
design will be overwritten if the file is reread.  To save the current design
first, press <Esc> to cancel the question, and then select Save This Design.

    When you select fixed element positions only the element lengths are
varied during automatic optimization.  This is useful for optimizing antennas
whose element positions cannot be changed due to mechanical constraints, such
as through-the-boom mounting.  It is also useful when you know that the element
positions are approximately correct, and you want the optimization to run
faster.  The gradient computations execute twice as fast when the element
positions are fixed.

    If you choose not to allow a longer boom, YO will monitor the position
of the last director during optimization.  It will allow this element to
migrate closer to the reflector than the initial design distance, but not
farther away.  The position of the reflector is not varied during optimization,
as it is the reference point for the whole array.  The boom length limit is
updated if you lengthen the boom manually by moving the reflector or the last
director.

    The numerical display selection controls the number displayed on the
third line inside each plot.  This number represents pattern quality.

    If you select vertical polarization the H-plane pattern is used instead
of the E-plane pattern.  A dot is placed at the plot origin for reference.  The
angular range for the F/R calculation remains 95 to 180 degrees for vertically
polarized antennas, even though you do not get a free null at 90 degrees in the
H-plane as you do in the E-plane.

    If you select Save These Settings a file named YO.PAR is written to the
current directory when you return to the main menu.  Codes for the Other
Parameters settings are placed in YO.PAR.  When YO begins execution, it checks
for YO.PAR, and if it exists, the codes are read and the Other Parameters are
set accordingly.  You can use this feature to customize the default setting for
each of the Other Parameters.


            Making a Hardcopy of the Screen


    You may print the screen if you have a dot matrix printer with
Epson-compatible graphics.  On 84-key keyboards press <Shift><PrtSc>.  For
other keyboards press <Shift><F10> instead.  For the EGA and HGC, if you start
a screen printout at the top of the page, a second printout may be put on the
same page without any manual realignment of the printhead.  YO does not respond
to <PrtSc> or <F10> for the CGA, or perform any printing function.  Instead,
DOS will intercept <Shift><PrtSc> and print your plot if the DOS program
GRAPHICS is loaded before starting YO.  Polar plots will come out somewhat
elliptical on paper, especially for the EGA.  The EGA ellipticity will be
reduced in future versions of YO (and PLOT), and support for 24-pin printers
will be added as well.


                DOS Environment Space


    DOS provides a convenient way for you to specify configuration
information to YO and to PLOT.  The DOS SET command places information into the
DOS Environment Space in memory, where it can be retrieved later by a program.
SET commands can be put into your AUTOEXEC.BAT file and they will be
automatically executed every time you boot the computer.

    You may see what is currently in the DOS Environment Space by typing
SET.  You may eliminate an individual parameter by typing SET [parameter]=.

    There are several SET parameters used by YO and PLOT:

1. Library Directories

    When you accumulate many Yagi and plot files it is nice to have
separate directories for them, so that the current directory doesn't get so
cluttered.  You might use the current directory for Yagi experiments, saving
optimized Yagi files and their plots elsewhere.  You can tell YO and PLOT to
automatically reference other directories with SET commands.  One directory can
be set up for Yagi files and another for plot files.  These libraries are used
only for loading files; when YO creates a plot file or an output file it always
writes it to the current directory.

    If your Yagi library is in the subdirectory YAGIS and your plot library
is in PLOTS then do the following:

                SET YAGLIB=YAGIS
                SET PLTLIB=PLOTS

    You may specify a drive and path for the directories if necessary.
When this library facility is used YO and PLOT will list available files both
in the current directory and in the appropriate library directory.  To specify
a file from the library directory you only need to enter the filename.

    YO and PLOT always search the current directory first.  If you need to
force the program to use the library (when the same filename appears in the
current directory) just specify the complete path and filename.

    If you are using a dual floppy disk system you can put your Yagi
library and plot library on a second disk drive.  This will give you plenty of
working space on your main drive and still allow access to the library files.

2. Reference dB

    To cause YO and PLOT to display gain figures in dBi rather than dBd do
the following:

                SET DB=dBi

    You may use any combination of upper or lower case for the three dBi
letters.  Gains in dBd are referenced to the peak gain of a half-wave dipole in
free space.  This is common for amateur antennas and is the YO default.  Gains
in dBi are referenced to an isotropic antenna in free space, which is an
antenna that radiates equally in all directions.  A dipole has 2.15 dB gain
over an isotropic antenna, so YO converts from one gain reference to the other
by adding or subtracting 2.15 dB.

3.  Location of COMMAND.COM

    YO needs to have access to the DOS command interpreter COMMAND.COM in
order to list Yagi files and to call PLOT.  PLOT needs COMMAND.COM to list plot
files.  Normally the DOS Environment Space will contain the location of
COMMAND.COM.  If it doesn't then you should do the following:

            SET COMSPEC=Drive:\COMMAND.COM

where Drive indicates the disk drive whose root directory contains COMMAND.COM
while YO is executing.  If you are using a single floppy disk system you must
copy COMMAND.COM from your DOS system disk onto the YO disk, or use a RAMDISK.


                YO File Format


    Here is an example of a beam using the YO file format.  You may include
descriptive text at the end of any Yagi file, after all of the essential
information.  The elements are always specified from the rear of the beam first
(R, DE, D1, D2, etc.), and element half-lengths must be used, i.e., from the
center of the boom to the element tip, not tip to tip.


 K7HYR's Max Gain Yagi
 24.890  24.940  24.990  MHz
 4 elements, inches
             1.617     1.250     1.125     0.875
   0.000     2.938    15.062    66.000    33.305
 124.000     2.938    15.062    66.000    28.248
 248.000     2.938    15.062    66.000    26.815
 372.000     2.938    15.062    66.000    28.313


    The first line is a title for the antenna which will be displayed at
the bottom of the YO screen.  The title may be up to 80 characters long, but
very long titles will be truncated when displayed.

    The second line consists of 1 or 3 analysis frequencies.  You may also
use Hz, KHz, or GHz.  If no frequency units are specified then MHz is assumed.

    The third line gives the number of elements and the dimension units.
You may use feet, meters, centimeters, or millimeters as well as inches.  The
spelling of these keywords must be exact.

    The next line lists the taper diameters, starting with those closest to
the boom.  If you use tabs to separate the numbers, including an initial tab as
illustrated, the taper diameters will line up with the taper lengths which
follow.  The maximum number of taper sections is seven.  The first taper
section of this antenna represents the mounting plates.

    The remaining lines list the element position followed by the taper
lengths, beginning with the taper closest to the boom.  The elements positions
do not need to begin at 0, but positions, not spacings, must be used.

    You may use any combination of spaces, commas, and tabs as separators,
and any combination of upper and lower case letters for the keywords.

    The example above uses the same taper schedule for all elements.  Here
is a Yagi which uses a monotaper (single diameter) for the driven element.
Three taper diameter lines are used, the last specified remaining in effect
until a new one is encountered:


 N2FB 6 el 20m, NCJ Jan. 86
 14.000   14.174   14.350
 6 Elements, Inches
          1.250     1.125     1.000
 0.000      18.000    54.000   138.970
          1.000
 86.380    196.578
          1.250     1.125     1.000
 164.090    18.000    54.000   126.640
 321.590    18.000    54.000   121.950
 464.450    18.000    54.000   121.900
 643.990    18.000    54.000   113.520


    You may include taper lengths of zero for convenience.  The following
file is equivalent to the file above, but is easier to read:


 N2FB 6 el 20m, NCJ Jan. 68
 14.000   14.174   14.350
 6 Elements, Inches
             1.250     1.125     1.000
   0.000    18.000    54.000   138.970
  86.380     0         0       196.578
 164.090    18.000    54.000   126.640
 321.590    18.000    54.000   121.950
 464.450    18.000    54.000   121.900
 643.990    18.000    54.000   113.520


    If the last taper section has zero length for an element (because the
tubing size is used only with other elements) you may omit the trailing zero
altogether.  The following Yagi has a 0.5 inch diameter tip for the reflector
only:


 Cushcraft 12-4CD
 24.94 MHz
 4 elements, inches
     .875    .75    .625    .5
 0    25    45    45    6
 67.625    25    45    45
 115    25    45    42.5
 210    25    29    44


    Any of the dimensions may have one of the following symbols appended to
it to use a different length unit than that specified on the number-of-elements
line.  Don't leave a space between the number and the unit abbreviation.  This
feature allows you to use feet for the taper lengths and inches for the taper
diameters, for example.  Here are the abbreviations:

    ft   '   in   "   m   cm   mm