§ 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:
   eCFR graphic ec13no91.014.gif

   View or download PDF

   where:

   E(φ,θ)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 ith element in the array.

   Fi   Represents the field ratio of the ith element in the array.

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

   fi(θ) represents the vertical plane radiation characteristic of the ith
   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(θ) are given in § 73.160.

   Si   Represents the electrical spacing of the ith tower from the reference
   point.

   φi   Represents the orientation (with respect to true north) of the ith
   tower.

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

   ψi   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:
   eCFR graphic ec01mr91.063.gif

   View or download PDF

   where:

   E(φ,θ)std represents the inverse distance fields at one kilometer which are
   produced by the directional antenna in the horizontal and vertical planes.
   E(φ,θ)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(θ) Erss or 10.0g(θ)
   √ PkW

   where:

   g(θ) is the vertical plane distribution factor, f(θ), 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(θ)
   shall be computed as follows:
   eCFR graphic ec01mr91.064.gif

   View or download PDF

   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(φ,θ)th (see Eq. 1, above), and is computed as follows:
   eCFR graphic ec01mr91.065.gif

   View or download PDF

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

   (ii) Where the orthogonal addition of the factor Q to E(φ,θ)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(φ,θ)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 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 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(φ,θ)std,
   E(φ,θ)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(φ,θ)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(φ,θ)th
   and E(φ,θ)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 θ = 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]

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