§  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 § 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:
   [MATH:  :MATH]

   where:

   E (f,TH)[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 § 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
   § 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 i ^th element in the array.

   F [i]  Represents the field ratio of the i ^th element in the array.

   TH  Represents the vertical elevation angle measured from the
   horizontal plane.

   fi(TH) represents the vertical plane radiation characteristic of the i
   thantenna. This value depends on the tower height, as well as whether
   the tower is top-loaded or sectionalized. The various formulas for
   computing fi(TH) are given in § 73.160.

   S i  Represents the electrical spacing of the i ^th tower from the
   reference point.

   f[i]  Represents the orientation (with respect to true north) of the i
   ^th tower.

   f  Represents the azimuth (with respect to true north).

   qi  Represents the electrical phase angle of the current in the i ^th
   tower.

   The standard radiation pattern shall be constructed in accordance with
   the following mathematical expression:
   [MATH:  :MATH]

   where:

   E (f,TH)[std]represents the inverse distance fields at one kilometer
   which are produced by the directional antenna in the horizontal and
   vertical planes. E (f,TH)[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(TH) E[rss]or
   10.0g(TH) SQRT P[kW]

   where:

   g(TH) is the vertical plane distribution factor, f(TH), for the
   shortest element in the array (see Eq. 2, above; also see § 73.190,
   Figure 5). If the shortest element has an electrical height in excess
   of 0.5 wavelength, g(TH) shall be computed as follows:
   [MATH:  :MATH]

   E[rss]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 (f,TH)[th](see Eq. 1, above), and is computed as
   follows:
   [MATH:  :MATH]

   P[kW]is the nominal station power expressed in kilowatts, see § 73.14.
   If the nominal power is less than one kilowatt, P[kW]=1.

   (ii) Where the orthogonal addition of the factor Q to
   E(f,TH)[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 (f,TH)[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' * 10') using only scale
   divisions and subdivisions of 1,2,2.5, or 5 times 10^nth . 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
   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
   (f,TH)[std], E (f,TH)[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 (f,TH)[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
   (f,TH)[th]and E (f,TH)[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 § 73.152(c)(3) and (c)(4).

   (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:
   Tower Field ratio Relative phasing Relative spacing Relative
   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 § 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 § 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:
   Azimuth    0      30     60   Vertical 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 TH=0, is 22.36.

   Following is a tabulation of part of the standard pattern:
   Azimuth    0      30     60   Vertical angle
   0         28.86  68.05  72.06
   105     1286.78 860.97 246.41
   235       23.48  26.50  37.18
   247       89.87  57.03  28.87

   The RMS of the standard pattern in the horizontal plane is 719.63 mV/m
   at one kilometer.

   [ 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]