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fortran语言的程序

     LLout  = Line length of termination transmission line
     LD     = Length to diameter ratio of antenna elements
     Navail = Number of available wires or tubes for the elements
     Davail = Diameters of available tubes for the elements
     SB     = Spacing of boom tubes or wires
     DB     = Diameter of boom tubes or wires
     Tau    = Geometric ratio (see Section 11.4.2)
     Sigma  = Spacing factor (see Section 11.4.2)

   DESIGN VARIABLES **
     L(n)   = Total length of element n
     D(n)   = Diameter of element n
     ZL(n)  = Location along the z axis of element n
     ZO     = Characteristic impedance of antenna transmission
              line
     ZinA   = ACTUAL input impedance, measured at the terminals
              of element 1 (the shortest element)
              
   *  Note that some of the input variables listed in the book
      are listed in Section 2.2., ANALYSIS PARAMETERS.
   ** Note that this list is somewhat abbreviated and that some
      variables, such as Tau and Sigma, can be considered as
      belonging to more than one category.
     
     Now that each design parameter is defined, how does one go
about choosing values?  For starters, some parameters are
available for more precise modeling of a particular application
or design.  For this reason, the source impedance (Rs), input
line length (LLin), and the output line length (LLout) all can
be set to zero.  Furthermore, setting the option to not quantize
the element diameters forces the program to ignore Navail and
Davail.

     Certain parameters must be known by the designer before the
design.  These include the characteristic impedance of the
source transmission line (ZCin), the frequency range (Fhigh and
Flow), and the desired gain (D0).  If the characteristic
impedance of the source transmission line (ZCin) is not known,
guess:  for most coaxial cable in the UHF band is 50 or 75 Ohms. 
Since we want to match the antenna to this cable, the desired
input impedance (Rin) should be equal to the source transmission
line characteristic impedance (ZCin).  Selecting the desired gain
sets Tau and Sigma for an optimum design.  Alternatively,
selecting Tau and Sigma allows independent control for special
applications.  All other parameters will be calculated by the
program.

     Since the program only estimates the transmission line
characteristic impedance (ZO) for the antenna to achieve the
desired input impedance (Rin), the actual input impedance (ZinA)
may not be correct.  For instance, assume that the actual input
impedance (ZinA) comes out to be 60 to 65 Ohms for a 50 Ohm
desired input impedance (Rin).  In this case, lower the desired
input impedance (Rin) so that the actual input impedance (ZinA)
comes out nearly correct (that is, approximately equal to ZCin).
More accurate estimates for ZO exist.[4][5]

     Now that the design is complete and satisfactory, quantize
the element diameters to the available wire or tube diameters. 
This quantization rounds each calculated element diameter to the
nearest available size.  The variable, Navail, tells how many
sizes are available.  Davail contains the available diameters. 
Next, perturb the design by adding a source impedance of about 
5 Ohms.  This should decrease the gain by about 1 dB for an
antenna with an input impedance (ZinA) 50 Ohms matched to a
50 Ohm source transmission line.

     Finally, add a matched load (Zout) to suppress reflections
from the open-circuit termination.  Notice the resulting
decrease in VSWR at many frequencies.


2.2.  ANALYSIS PARAMETERS

     In addition to the design parameters, the input screens
also ask for certain analysis parameters.  The user can select
single frequency E- and H-plane analyses, single frequency
custom plane analysis, and/or swept frequency analysis.  The
input parameters are as follows.

     AFSEH  = Frequency for single frequency analysis of E- and
              H- planes
     AFSC   = Frequency for single frequency analysis of custom
              plane
     AFhigh = Upper analysis frequency for swept frequency
              analysis
     AFlow  = Lower analysis frequency for swept frequency
              analysis
     Phi    = Angle of custom plane (90 degrees equals E-plane,
              0 degrees equals H-plane)
     AFpowr = Number of frequency steps per octave

     All parameters are self-explanatory except the last.  For
swept frequency analysis, the program starts at the lowest
analysis frequency, AFlow, and after each iteration increases
the analysis frequency by a certain amount until it exceeds the
upper analysis frequency.  The step size, AFstep, is defined by
the following relation.

     AFstep = FMHz * 10 ** (1/AFpowr)

where FMHz is the current analysis frequency.  This relation has
the advantage of providing equally spaced points when frequency
is plotted on a logarithmic scale.  Increasing AFpowr increases
the resolution.


3.  ALGORITHM DEVELOPMENT

     Some of the algorithms have already been explained, but for
the sake of clarity, all will be explained here.  There is
nothing fantastically difficult about any particular step of the
algorithm, but taken together there are so many topics that it
is easy to become confused.

     Since the design of the antenna is covered in the book, it
will be omitted here.  Let us begin the discussion knowing the
topology of the design, as if we had an antenna in hand, so that
we are ready to analyze it.

     There are several steps to the analysis of the antenna. 
First, we must calculate the self and mutual impedances of each
antenna element.  These calculations tell us how each excited
element interacts with each other element and how well each
antenna radiates.  Next, we need to calculate the
characteristics of the antenna transmission line.  This
calculation accounts for the termination impedance (Zout) as
well as the source impedance (Rs).  It tells us how energy
propagates down the transmission lines.  Third, we need to solve
for the currents on each antenna element as well as the input
current (Iin) and voltage (Vin) and the termination current
(Iout) and voltage (Vout).  Finally, we calculate the gain,
VSWR, and other important parameters.


3.1.  SELF AND MUTUAL IMPEDANCES

     The self and mutual impedances of radiating elements is a
subject of much research.  To understand the basic idea[8],
consider several radiating elements located in space.  Now
remove all elements except one, for instance element 1, and
excite it with a current.  The input impedance can be measured
as the ratio of the input voltage over the input current.  This
is the self impedance denoted Z11.  Now replace one of the other
elements, say element 2, and short its terminals together. 
Recalculate the input impedance of element 1.  This is the
mutual impedance denoted Z12 (impedance of element 1 due to
element 2).  Repeat the process for every pair of antennas. 
(The measurements can be roughly halved, because reciprocity
assures us that Z12 = Z21.  This means the resulting matrix is
symmetric.)

      To obtain very accurate results, finite difference methods
and projection methods, which include moment methods and
finite element methods often are used.  Finite difference
methods approximate the governing differential equations by
mathematically dividing the surface into very small segments, then
approximating a derivative by the equation

           f(x2) - f(x1)
     df = ---------------
              x2 - x1

  For projection methods, a set of basis functions which satisfy
the boundary conditions are weighted and summed to form an
approximate answer.  For moment methods, the basis functions are
valid for the entire antenna surface.  For finite element
methods, the basis functions are valid over a small part of the
antenna surface.

     An alternative approach, and the one used here, assumes
that the current distribution along each antenna varies
sinusoidally.  This assumption is valid for infinitesimally thin
dipoles sitting alone in space.  While this assumption is not
totally valid, the approximation is still a good one.

     With this assumption, the self and mutual impedances can be
written as integral equations.  These equations can be
recast in terms of the sine and cosine integrals[9][10].  With
these equations, the symmetric matrix, called ZA in the program,
can be found.


3.2.  TRANSMISSION LINE ADMITTANCE MATRIX

     Next, we must compute the characteristics of the antenna
transmission line.  Good documentation can be found in the
literature [6][7][8], although these references can
sometimes be hard to find.  Therefore, a summary will be
presented here.  We wish to create the same kind of data for the
transmission line as we did for the self and mutual impedances. 
That is, we will excite the transmission line with a unit
voltage everywhere an antenna element attaches, one place at a
time.  The remaining places will be shorted.  This procedure is
derived directly from N-port admittance matrix theory.  The task
is to find the resulting current at each port (place of antenna
attachment).

     FIGURE 5 illustrates the concept for an N element antenna
excited at port 4.  Only a few of the ports are shown.  The
distance between ports is given by the variable DZL.

            PORT:  2        3        4        5         
          ----------------------------------------------
                   |        |        +        |         
                   |        |                 |         
                   |        |                 |         
                   |        |                 |         
           o o o   |        |        V        |    o o o 
                   |        |                 |         
                   |        |                 |         
                   |        |                 |         
                   |        |        -        |         
          ----------------------------------------------
                   |<-DZL2->|<-DZL3->|<-DZL4->|         

          FIGURE 5.  Transmission Line Equivalent Circuit

     For the following discussion, please refer to any standard
electromagnetics text.  For example, see [2][3].  Also see
[4][7][8].

     It is obvious by inspection that given an excitation at
element 4, a current will flow only through the shorts at ports
3, 4, and 5.  Current will not flow at the other ports.  The
current at port 4 is the current through the source, V.  The
transmission line equation tells us that the impedance seen by
port 4 in the direction of port 3 is equal to

     Z43 = j ZO tan(Beta * DZL3)

where ZO is the characteristic impedance of the line, and Beta
is the wavenumber.  The admittance (Y) is one over the impedance
so,

     Y43 = -j YO cot(Beta * DZL3)

where YO = 1/ZO.  Similarly, the admittance seen by port 4 in
the direction of port 5 is 

     Y45 = -j YO cot(Beta * DZL4)

Therefore, the current flowing through port 4 (excited by a unit
voltage) is

     Y43 + Y45 = I4 / 1

     To find the current in port 3, the following general
transmission line equation is used.

     V(DZL3) = V3 * cos(Beta*ZL3) + j * I3'' * ZO * sin(Beta*ZL3)

where V3 and I3'' are the voltage and current at port 3,
respectively.  (Note:  the primes do not represent
differentiation.)  Since port 3 is shorted, V3 = 0. 
Furthermore, V(DZL3) is just the excitation voltage, 
V4 = 1 Volt.  Therefore,

     1 = j * I3'' * ZO * sin(Beta*ZL3)

or

     I3'' / 1 = -j YO * csc(Beta*L)

However, this definition of I3'' is reversed from that of the
standard N-port definitions;  it flows out of the port instead
of in to it.  Therefore, we remove one prime ('') and change the
sign.

     I3' / 1 = j YO * csc(Beta*L)

One step remains.  Since we arranged for a phase reversal by
crossing the wires in the transmission line [], we must account
for this by changing the sign again.  The final form for the
current is then