FCC 73.150 Revised as of October 1, 2006
Goto Year:2005 |
2007
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:
[MATH: :MATH]
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 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 i ^th element in the array.
F[i] Represents the field ratio of the i ^th 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 Sec. 73.160.
Si Represents the electrical spacing of the i^th tower from the reference
point.
φ[i] Represents the orientation (with respect to true north) of the i^th
tower.
φ Represents the azimuth (with respect to true north).
ψi 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(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) E[rss] or
10.0g(Θ) √ P[kW]
where:
g(Θ) is the vertical plane distribution factor, f(Θ), 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(Θ)
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(φ,Θ)[th] (see Eq. 1, above), and is computed as follows:
[MATH: :MATH]
P[kW] is the nominal station power expressed in kilowatts, see Sec. 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(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 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(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 Sec. 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:
------------------------------------------------------------------------
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 Θ=0, is 22.36.
Following is a tabulation of part of the standard pattern:
------------------------------------------------------------------------
Vertical
Azimuth 0 30 60 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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:MATH] 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 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 i ^th element in the array. F[i] Represents the field ratio of the i ^th 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 Sec. 73.160. Si Represents the electrical spacing of the i^th tower from the reference point. φ[i] Represents the orientation (with respect to true north) of the i^th tower. φ Represents the azimuth (with respect to true north). ψi 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(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) E[rss] or 10.0g(Θ) √ P[kW] where: g(Θ) is the vertical plane distribution factor, f(Θ), 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(Θ) 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(φ,Θ)[th] (see Eq. 1, above), and is computed as follows: [MATH:
:MATH] P[kW] is the nominal station power expressed in kilowatts, see Sec. 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(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 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(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 Sec. 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: ------------------------------------------------------------------------ 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 Θ=0, is 22.36. Following is a tabulation of part of the standard pattern: ------------------------------------------------------------------------ Vertical Azimuth 0 30 60 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]