Sec. 73.150  Directional antenna systems.

    (a) For each station employing a directional antenna, all 
determinations of service provided and interference caused shall be 
based on the inverse distance fields of the standard radiation pattern 
for that station. (As applied to nighttime operation the term ``standard 
radiation pattern'' shall include the radiation pattern in the 
horizontal plane, and radiation patterns at angles above this plane.)
    (1) Parties submitting directional antenna patterns pursuant to this 
section and Sec. 73.152 (Modified standard pattern) must submit patterns 
which are tabulated and plotted in units of millivolts per meter at 1 
kilometer.

    Note: Applications for new stations and for changes (both minor and 
major) in existing stations must use a standard pattern.

    (b) The following data shall be submitted with an application for 
authority to install a directional antenna:
    (1) The standard radiation pattern for the proposed antenna in the 
horizontal plane, and where pertinent, tabulated values for the 
azimuthal radiation patterns for angles of elevation up to and including 
60 degrees, with a separate section for each increment of 5 degrees.
    (i) The standard radiation pattern shall be based on the theoretical 
radiation pattern. The theoretical radiation pattern shall be calculated 
in accordance with the following mathematical expression:

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[GRAPHIC] [TIFF OMITTED] TC13NO91.014

where:

E(,)th Represents the 
          theoretical inverse distance fields at one kilometer for the 
          given azimuth and elevation.
k  Represents the multiplying constant which determines the basic 
          pattern size. It shall be chosen so that the effective field 
          (RMS) of the theoretical pattern in the horizontal plane shall 
          be no greater than the value computed on the assumption that 
          nominal station power (see Sec. 73.14) is delivered to the 
          directional array, and that a lumped loss resistance of one 
          ohm exists at the current loop of each element of the array, 
          or at the base of each element of electrical height lower than 
          0.25 wavelength, and no less than the value required by 
          Sec. 73.189(b)(2) of this part for a station of the class and 
          nominal power for which the pattern is designed.
n  Represents the number of elements (towers) in the directional array.
i  Represents the ith element in the array.
Fi  Represents the field ratio of the ith element 
          in the array.
i (th antenna. This value 
          depends on the tower height, as well as whether the tower is 
          top-loaded or sectionalized. The various formulas for 
          computing fi (73.160.
Si  Represents the electrical spacing of the ith 
          tower from the reference point.
i  Represents the orientation (with respect to true 
          north) of the ith tower.
  Represents the azimuth (with respect to true north).
i  Represents the electrical phase angle of the 
          current in the ith tower.
    The standard radiation pattern shall be constructed in accordance 
with the following mathematical expression:
[GRAPHIC] [TIFF OMITTED] TC01MR91.063

    where:
    E(,)std represents the inverse 
distance fields at one kilometer which are produced by the directional 
antenna in the horizontal and vertical planes. 
E(,)th represents the theoretical inverse 
distance fields at one kilometer as computed in accordance with Eq. 1, 
above.
    Q is the greater of the following two quantities: 0.025g() 
Erss or 10.0g()  PkW
    where:
    g() is the vertical plane distribution factor, 
f(), for the shortest element in the array (see Eq. 2, above; 
also see Sec. 73.190, Figure 5). If the shortest element has an 
electrical height in excess of 0.5 wavelength, g() shall be 
computed as follows:
[GRAPHIC] [TIFF OMITTED] TC01MR91.064

    Erss is the root sum square of the amplitudes of the 
inverse fields of the elements of the array in the horizontal plane, as 
used in the expression for E(,)th (see 
Eq. 1, above), and is computed as follows:
[GRAPHIC] [TIFF OMITTED] TC01MR91.065

    PkW is the nominal station power expressed in kilowatts, 
see Sec. 73.14. If the nominal power is less than one kilowatt, 
PkW=1.

    (ii) Where the orthogonal addition of the factor Q to E(, 
)th results in a standard pattern whose minimum 
fields are lower than those found necessary or desirable, these fields 
may be increased by appropriate adjustment of the parameters of 
E(, )th.
    (2) All patterns shall be computed for integral multiples of five 
degrees, beginning with zero degrees representing true north, and, shall 
be plotted to the largest scale possible on unglazed letter-size paper 
(main engraving approximately 7'  x  10') using only scale divisions and 
subdivisions of 1,2,2.5, or 5 times 10nth. The horizontal 
plane pattern shall be plotted on polar coordinate paper, with the zero 
degree point corresponding to true north. Patterns for elevation angles 
above the horizontal plane may be plotted in polar or

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rectangular coordinates, with the pattern for each angle of elevation on 
a separate page. Rectangular plots shall begin and end at true north, 
with all azimuths labelled in increments of not less than 20 degrees. If 
a rectangular plot is used, the ordinate showing the scale for radiation 
may be logarithmic. Such patterns for elevation angles above the 
horizontal plane need be submitted only upon specific request by 
Commission staff. Minor lobe and null detail occurring between 
successive patterns for specific angles of elevation need not be 
submitted. Values of field strength on any pattern less than ten percent 
of the maximum field strength plotted on that pattern shall be shown on 
an enlarged scale. Rectangular plots with a logarithmic ordinate need 
not utilize an expanded scale unless necessary to show clearly the minor 
lobe and null detail.
    (3) The effective (RMS) field strength in the horizontal plane of 
E(,)std, 
E(,)th and the root-sum-square (RSS) 
value of the inverse distance fields of the array elements at 1 
kilometer, derived from the equation for 
E(,)th. These values shall be tabulated 
on the page on which the horizontal plane pattern is plotted, which 
shall be specifically labelled as the Standard Horizontal Plane Pattern.
    (4) Physical description of the array, showing:
    (i) Number of elements.
    (ii) Type of each element (i.e., guyed or self-supporting, uniform 
cross section or tapered (specifying base dimensions), grounded or 
insulated, etc.)
    (iii) Details of top loading, or sectionalizing, if any.
    (iv) Height of radiating portion of each element in feet (height 
above base insulator, or base, if grounded).
    (v) Overall height of each element above ground.
    (vi) Sketch of antenna site, indicating its dimensions, the location 
of the antenna elements, thereon, their spacing from each other, and 
their orientation with respect to each other and to true north, the 
number and length of the radials in the ground system about each 
element, the dimensions of ground screens, if any, and bonding between 
towers and between radial systems.
    (5) Electrical description of the array, showing:
    (i) Relative amplitudes of the fields of the array elements.
    (ii) Relative time phasing of the fields of the array elements in 
degrees leading [+] or lagging [-].
    (iii) Space phasing between elements in degrees.
    (iv) Where waiver of the content of this section is requested or 
upon request of the Commission staff, all assumptions made and the basis 
therefor, particularly with respect to the electrical height of the 
elements, current distribution along elements, efficiency of each 
element, and ground conductivity.
    (v) Where waiver of the content of this section is requested, or 
upon request of the Commission staff, those formulas used for computing 
E(,)th and 
E(,)std. Complete tabulation of final 
computed data used in plotting patterns, including data for the 
determination of the RMS value of the pattern, and the RSS field of the 
array.
    (6) The values used in specifying the parameters which describe the 
array must be specified to no greater precision than can be achieved 
with available monitoring equipment. Use of greater precision raises a 
rebuttable presumption of instability of the array. Following are 
acceptable values of precision; greater precision may be used only upon 
showing that the monitoring equipment to be installed gives accurate 
readings with the specified precision.
    (i) Field Ratio: 3 significant figures.
    (ii) Phasing: to the nearest 0.1 degree.
    (iii) Orientation (with respect to a common point in the array, or 
with respect to another tower): to the nearest 0.1 degree.
    (iv) Spacing (with respect to a common point in the array, or with 
respect to another tower): to the nearest 0.1 degree.
    (v) Electrical Height (for all parameters listed in Section 73.160): 
to the nearest 0.1 degree.
    (vi) Theoretical RMS (to determine pattern size): 4 significant 
figures.
    (vii) Additional requirements relating to modified standard patterns 
appear in Sec. 73.152(c)(3) and (c)(4).

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    (7) Any additional information required by the application form.
    (c) Sample calculations for the theoretical and standard radiation 
follow. Assume a five kilowatt (nominal power) station with a 
theoretical RMS of 685 mV/m at one kilometer. Assume that it is an in-
line array consisting of three towers. Assume the following parameters 
for the towers:

                                                                        
------------------------------------------------------------------------
                                 Field   Relative  Relative    Relative 
             Tower               ratio    phasing   spacing  orientation
------------------------------------------------------------------------
1.............................     1.0     -128.5       0.0        0.0  
2.............................     1.89       0.0     110.0      285.0  
3.............................     1.0      128.5     220.0      285.0  
------------------------------------------------------------------------

    Assume that tower 1 is a typical tower with an electrical height of 
120 degrees. Assume that tower 2 is top-loaded in accordance with the 
method described in Sec. 73.160(b)(2) where A is 120 electrical degrees 
and B is 20 electrical degrees. Assume that tower 3 is sectionalized in 
accordance with the method described in Sec. 73.160(b)(3) where A is 120 
electrical degrees, B is 20 electrical degrees, C is 220 electrical 
degrees, and D is 15 electrical degrees.
    The multiplying constant will be 323.6.
    Following is a tabulation of part of the theoretical pattern:

                                                                        
------------------------------------------------------------------------
                                                                Vertical
           Azimuth                0          30         60       angle  
------------------------------------------------------------------------
0...........................      15.98      62.49      68.20           
105.........................    1225.30     819.79     234.54           
235.........................       0.43      18.46      34.56           
247.........................      82.62      51.52      26.38           
------------------------------------------------------------------------

    If we further assume that the station has a standard pattern, we 
find that Q, for 36 FR 919 , Jan. 20, 1971, as amended at  37 FR 529 , Jan. 13, 1972;  41 FR 24134 , June 15, 1976;  46 FR 11991 , Feb. 12, 1981;  48 FR 24384 , June 1, 
1983;  51 FR 2707 , Jan. 21, 1986;  52 FR 36877 , Oct. 1, 1987;  56 FR 64861 , 
Dec. 12, 1991;  57 FR 43290 , Sept. 18, 1992]