FCC 73.150
Revised as of October 1, 2014
Goto Year:2013 | 2015
```§ 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
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
calculated in accordance with the following mathematical expression:
eCFR graphic ec13no91.014.gif

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 ith element in the array.

Fi   Represents the field ratio of the ith 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
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(th) are given in § 73.160.

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

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

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

qi   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

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) Erss or
10.0g(th) SQRT PkW

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:
eCFR graphic ec01mr91.064.gif

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

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(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 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(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.)

(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

(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

(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]