38:
3684:
95:
1697:
3392:
3375:
1325:
3679:{\displaystyle {\begin{aligned}G_{\frac {\lambda }{2}}&={\frac {60^{2}}{30R_{\frac {\lambda }{2}}}}={\frac {3600}{30R_{\frac {\lambda }{2}}}}={\frac {120}{R_{\frac {\lambda }{2}}}}={\frac {1}{{}^{\int _{0}^{\frac {\pi }{2}}{\frac {\cos \left({\frac {\pi }{2}}\cos \theta \right)^{2}}{\sin \theta }}d\theta }}}\ ,\\&\approx {\frac {120}{73.1296}}\approx 1.6409224\approx 2.15088\ {\mathsf {\ dBi}};\end{aligned}}}
688:
radiator is known to be 1.64 and it can be made nearly 100% efficient. Since the gain has been measured with respect to this reference antenna, the difference in the gain of the test antenna is often compared to that of the dipole. The gain relative to a dipole is thus often quoted and is denoted using dBd instead of dBi to avoid confusion. Therefore, in terms of the true gain (relative to an isotropic radiator)
3965:
2908:
1692:{\displaystyle {\begin{aligned}P_{\text{rad}}&=\int _{0}^{2\pi }\int _{0}^{\pi }U(\theta ,\phi )\sin(\theta )\,d\theta \,d\phi =2\pi B_{0}\int _{0}^{\pi }\sin ^{4}(\theta )\,d\theta =B_{0}\left({\frac {3}{4}}\pi ^{2}\right)\\D&=4\pi \left({\frac {U_{\text{max}}}{P_{\text{rad}}}}\right)=4\pi \left={\frac {16}{3\pi }}\approx 1.698\end{aligned}}}
1830:
827:
Both dBi and dBd are in common use. When an antenna's maximum gain is specified in decibels (for instance, by a manufacturer) one must be certain as to whether this means the gain relative to an isotropic radiator or with respect to a dipole. If it specifies dBi or dBd then there is no ambiguity, but
258:
headed in a specified direction. In a receiving antenna, the gain describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, gain is understood to refer to the peak value of the gain, the gain in the direction of the
687:
However a true isotropic radiator cannot be built, so in practice a different antenna is used. This will often be a half-wave dipole, a very well understood and repeatable antenna that can be easily built for any frequency. The directive gain of a half-wave dipole with respect to the isotropic
3370:{\displaystyle {\begin{aligned}R_{\frac {\lambda }{2}}&=60\operatorname {Cin} (2\pi )=60\left=120\int _{0}^{\frac {\pi }{2}}{\frac {\cos \left({\frac {\pi }{2}}\cos \theta \right)^{2}}{\sin \theta }}d\theta \ ,\\&=15\left\ ,\\&=73.12960\ldots {\mathsf {\;\Omega ;}}\end{aligned}}\ }
2257:
675:
When actual measurements of an antenna's gain are made by a laboratory, the field strength of the test antenna is measured when supplied with, say, 1 watt of transmitter power, at a certain distance. That field strength is compared to the field strength found using a so-called
2345:
671:
Therefore, an antenna with a peak power gain of 5 would be said to have a gain of 7 dBi. dBi is used rather than just dB to emphasize that this is the gain according to the basic definition, in which the antenna is compared to an isotropic radiator.
274:
Gain or 'absolute gain' is defined as "The ratio of the radiation intensity in a given direction to the radiation intensity that would be produced if the power accepted by the antenna were isotropically radiated". Usually this ratio is expressed in
2470:
2685:
1913:
3726:
differs from gain in that it is "reduced by its impedance mismatch factor." This mismatch induces losses above the dissipative losses described above; therefore, realized gain will always be less than gain. Gain may be expressed as
1708:
989:
760:
592:
is the power supplied to the antenna's terminals. Losses prior to the antenna terminals are accounted for by separate impedance mismatch factors which are therefore not included in the calculation of radiation efficiency.
1063:
226:. Since the directive antenna radiates the same total power within a small angle along the z axis, it can have a higher signal strength in that direction than the isotropic antenna, and so a gain greater than one.
2885:
822:
373:
2135:
3742:(TRP) is the sum of all RF power radiated by the antenna when the source power is included in the measurement. TRP is expressed in watts or the corresponding logarithmic expressions, often dBm or dBW.
666:
2568:
3969:
3397:
2913:
1713:
1330:
2270:
1268:
3906:
549:
2032:
1193:
224:
1314:
835:
imply a comparison of that antenna's gain in each direction to a dipole's gain in that direction. Rather, it is a comparison between the antenna's gain in each direction to the
2361:
1955:
190:
163:
3748:
The TRP can be used to determine body loss (BoL). The body loss is considered as the ratio of TRP measured in the presence of losses and TRP measured while in free space.
2511:
1094:
2580:
1841:
1121:
468:
898:
2125:
1984:
2092:
2064:
918:
590:
499:
428:
1141:
875:
136:
116:
1825:{\displaystyle {\begin{aligned}G&=\eta D\approx (1)(1.698)=1.698\\G_{\text{dBi}}&\approx 10\,\log _{10}(1.698)\approx 2.30\,{\text{dBi}}\end{aligned}}}
926:
698:
1146:
As a result of this definition, we can conclude that the total gain of an antenna is the sum of partial gains for any two orthogonal polarizations.
1000:
769:= 5 would have a gain with respect to a dipole of 5/1.64 ≈ 3.05, or in decibels one would call this 10 log(3.05) ≈ 4.84 dBd. In general:
828:
if only dB is specified then the fine print must be consulted. Either figure can be easily converted into the other using the above relationship.
501:
of an antenna is "The ratio of the total power radiated by an antenna to the net power accepted by the antenna from the connected transmitter."
3856:
3895:
2696:
775:
3745:
When testing mobile devices, TRP can be measured while in close proximity of power-absorbing losses such as the body and hand of the user.
294:
2252:{\displaystyle {P \over S}={c_{\circ }\varepsilon _{\circ } \over 2}{E_{\theta }}^{2}={1 \over 2}{{E_{\theta }}^{2} \over Z_{\circ }}\ }
680:
at the same distance receiving the same power in order to determine the gain of the antenna under test. That ratio would be equal to
4011:
611:
3974:
839:
gain of the dipole (1.64). In any direction, therefore, such numbers are 2.15 dB smaller than the gain expressed in dBi.
3832:
2516:
254:
has been deprecated by IEEE. In a transmitting antenna, the gain describes how well the antenna converts input power into
2340:{\displaystyle Z_{\circ }={\sqrt {{\mu _{\circ } \over \varepsilon _{\circ }}\ }}=376.730313461{\mathsf {\ \Omega \ }}}
3956:
3943:
3879:
3702:
Sometimes, the half-wave dipole is taken as a reference instead of the isotropic radiator. The gain is then given in
81:
59:
52:
1702:
Since the antenna is specified as being lossless the radiation efficiency is 1. The maximum gain is then equal to:
1214:
3980:
1924:
As an example, consider an antenna that radiates an electromagnetic wave whose electrical field has an amplitude
2127:
The radiated wave can be considered locally as a plane wave. The intensity of an electromagnetic plane wave is:
98:
Diagram illustrating how isotropic gain is defined. The axes represent power density in watts per square meter.
507:
392:
1992:
1152:
17:
1279:
195:
4016:
2570:
The intensity of an isotropic antenna is the power so fed divided by the surface of the sphere of radius
877:
corresponding to a given polarization, divided by the total radiation intensity of an isotropic antenna.
2465:{\displaystyle \left({P \over S}\right)_{\mathsf {ant}}={1 \over 2Z_{\circ }}{A^{2}I^{2} \over r^{2}}\ }
4006:
1927:
1273:
Let us find the gain of such an antenna. First we find the peak radiation intensity of this antenna:
291:. Since a lossless dipole antenna has a gain of 2.15 dBi, the relation between these units is
380:
168:
141:
2680:{\displaystyle \left({P \over S}\right)_{\mathsf {iso}}={{1 \over 2}R_{s}I^{2} \over 4\pi r^{2}}\ }
46:
2478:
1908:{\displaystyle G_{\text{dBd}}=10\,\log _{10}\left({\frac {1.698}{1.64}}\right)=0.15\,{\text{dBd}}}
283:(dBi). An alternative definition compares the received power to the power received by a lossless
2891:
1072:
3767:
1099:
63:
3772:
851:
444:
883:
3922:
Mobile
Broadband Multimedia Networks: Techniques, Models and Tools for 4G by Luís M. Correia
2101:
1960:
2071:
2043:
903:
568:
484:
479:
413:
407:
388:
247:
118:
is the radiation pattern of a directive antenna, which radiates a maximum power density of
165:
is the radiation pattern of an isotropic antenna which radiates the same total power, and
8:
855:
3850:
1126:
860:
605:(dB), a logarithmic scale. From the gain factor G, one finds the gain in decibels as:
280:
121:
101:
3757:
831:
When considering an antenna's directional pattern, gain with respect to a dipole does
3952:
3939:
3875:
3838:
3828:
3762:
1123:
represent the radiation intensity in a given direction contained in their respective
559:
555:
264:
3984:
2348:
231:
984:{\displaystyle G_{\theta }=4\pi \left({\frac {U_{\theta }}{P_{\text{in}}}}\right)}
263:. A plot of the gain as a function of direction is called the antenna pattern or
755:{\displaystyle G_{\text{dBd}}\approx 10\log _{10}\left({\frac {G}{1.64}}\right).}
395:, the gain of any antenna when receiving is equal to its gain when transmitting.
239:
94:
376:
284:
138:
watts per square meter at some given distance from the antenna. The green ball
1058:{\displaystyle G_{\phi }=4\pi \left({\frac {U_{\phi }}{P_{\text{in}}}}\right)}
4000:
3842:
3731:
if further clarification is required to differentiate it from realized gain.
1319:
The total radiated power can be found by integrating over all directions:
3990:
432:
243:
3896:"CTIA Test Plan for Wireless Device Over-the-Air Performance Rev. 3.4.2"
2894:, the particular formulation works out to the following, including its
255:
3807:
IEEE Std 145-2013, IEEE Standard for
Definitions of Terms for Antennas
2880:{\displaystyle G={\left \over {\left}}\approx {A^{2} \over 30R_{s}}\ }
817:{\displaystyle G_{\text{dBd}}\approx G_{\text{dBi}}-2.15\,{\text{dB}}}
368:{\displaystyle \mathrm {Gain(dBd)} \approx \mathrm {Gain(dBi)} -2.15}
260:
1835:
Expressed relative to the gain of a half-wave dipole we would find:
192:
is the power density it radiates. The gain of the first antenna is
3777:
2895:
602:
276:
601:
Published numbers for antenna gain are almost always expressed in
2475:
If the resistive part of the series impedance of the antenna is
3874:(Second ed.). Reading, MA: Addison-Wesley. p. 612.
1208:
Suppose a lossless antenna has a radiation pattern given by:
684:
if the reference antenna were an isotropic radiator (irad).
3951:(3rd edition), by John D. Kraus, Ronald J. Marhefka, 2002,
661:{\displaystyle G_{\text{dBi}}=10\log _{10}\left(G\right).}
267:. It is not to be confused with directivity, which does
2563:{\displaystyle \scriptstyle {1 \over 2}{R_{s}I^{2}}\ .}
2520:
2094:
is a characteristic constant (in Ohm) of each antenna.
198:
3395:
2911:
2699:
2583:
2519:
2481:
2364:
2273:
2138:
2104:
2074:
2046:
1995:
1963:
1930:
1844:
1711:
1328:
1282:
1217:
1155:
1129:
1102:
1075:
1003:
929:
906:
886:
863:
778:
701:
614:
571:
510:
487:
447:
416:
387:
of the antenna's gain for a particular frequency and
297:
271:
take an antenna's radiation efficiency into account.
171:
144:
124:
104:
554:A transmitting antenna is supplied with power by a
3678:
3369:
2879:
2679:
2562:
2505:
2464:
2339:
2251:
2119:
2086:
2058:
2026:
1978:
1949:
1907:
1824:
1691:
1308:
1262:
1187:
1135:
1115:
1088:
1057:
983:
912:
892:
869:
850:is calculated as power gain, but for a particular
816:
754:
660:
584:
543:
493:
462:
422:
367:
238:is a key performance parameter which combines the
218:
184:
157:
130:
110:
3827:(4th ed.). Hoboken, New Jersey. p. 63.
406:is a unitless measure that combines an antenna's
3998:
2066:is the current (in Amps) fed to the antenna and
2902:(decibels referenced to isotropic radiator):
1263:{\displaystyle U=B_{0}\,\sin ^{3}(\theta ).}
765:For instance, the above antenna with a gain
3938:(3rd edition), by C. Balanis, Wiley, 2005,
379:is proportional to the gain. An antenna's
3855:: CS1 maint: location missing publisher (
3351:
3818:
3816:
3655:
2332:
2326:
1899:
1861:
1812:
1783:
1486:
1423:
1416:
1234:
808:
544:{\displaystyle \eta ={P_{R} \over P_{O}}}
287:, in which case the units are written as
82:Learn how and when to remove this message
2027:{\displaystyle E_{\theta }={AI \over r}}
692:, this figure for the gain is given by:
375:. For a given frequency, the antenna's
93:
45:This article includes a list of general
3912:from the original on February 16, 2016.
3822:
3734:
1188:{\displaystyle G=G_{\theta }+G_{\phi }}
473:
14:
3999:
3813:
3801:
3799:
3797:
3795:
3793:
3664:
3661:
3658:
3355:
3352:
2611:
2608:
2605:
2392:
2389:
2386:
2329:
3869:
219:{\textstyle {S \over S_{\text{iso}}}}
27:Telecommunications performance metric
3916:
3863:
1309:{\displaystyle U_{\text{max}}=B_{0}}
854:. It is defined as the part of the
31:
3825:Antenna theory: analysis and design
3790:
596:
24:
352:
349:
346:
340:
337:
334:
331:
320:
317:
314:
308:
305:
302:
299:
51:it lacks sufficient corresponding
25:
4028:
1919:
3968: This article incorporates
3963:
3823:Balanis, Constantine A. (2016).
3718:
2513:the power fed to the antenna is
1203:
36:
3981:General Services Administration
3929:
3872:Field and Wave Electromagnetics
2347:is a universal constant called
1950:{\displaystyle \ E_{\theta }\ }
842:
4012:Telecommunications engineering
3888:
3313:
3304:
3287:
3277:
3259:
3249:
3012:
3003:
2985:
2976:
2956:
2947:
1803:
1797:
1750:
1744:
1741:
1735:
1483:
1477:
1413:
1407:
1398:
1386:
1254:
1248:
355:
343:
323:
311:
185:{\displaystyle S_{\text{iso}}}
158:{\displaystyle R_{\text{iso}}}
13:
1:
3783:
3696:are usually the cited values)
564:power accepted by the antenna
3949:Antenna for all applications
2506:{\displaystyle \ {R_{s}}\ ,}
1986:That amplitude is given by:
920:components are expressed as
558:connecting the antenna to a
7:
3751:
1198:
1089:{\displaystyle U_{\theta }}
10:
4033:
2898:equivalency, expressed as
2890:For the commonly utilized
1116:{\displaystyle U_{\phi }}
880:The partial gains in the
3903:Certification Test Plans
3870:Cheng, David K. (1992).
3706:(decibels over dipole):
463:{\displaystyle G=\eta D}
285:half-wave dipole antenna
2690:The directive gain is:
893:{\displaystyle \theta }
398:
383:is proportional to the
66:more precise citations.
3976:Federal Standard 1037C
3970:public domain material
3768:Antenna effective area
3680:
3371:
2881:
2681:
2564:
2507:
2466:
2341:
2253:
2121:
2120:{\displaystyle \ r\ .}
2088:
2060:
2028:
1980:
1979:{\displaystyle \ r\ .}
1951:
1909:
1826:
1693:
1310:
1264:
1189:
1137:
1117:
1090:
1059:
985:
914:
894:
871:
818:
756:
662:
586:
545:
495:
464:
424:
369:
227:
220:
186:
159:
132:
112:
3989: (in support of
3681:
3372:
2882:
2682:
2565:
2508:
2467:
2342:
2254:
2122:
2098:For a large distance
2089:
2087:{\displaystyle \ A\ }
2061:
2059:{\displaystyle \ I\ }
2029:
1981:
1952:
1910:
1827:
1694:
1311:
1265:
1190:
1138:
1118:
1091:
1060:
986:
915:
913:{\displaystyle \phi }
895:
872:
819:
757:
663:
587:
585:{\displaystyle P_{O}}
546:
496:
494:{\displaystyle \eta }
465:
425:
423:{\displaystyle \eta }
370:
221:
187:
160:
133:
113:
97:
3987:on January 22, 2022.
3740:Total radiated power
3735:Total radiated power
3393:
2909:
2697:
2581:
2517:
2479:
2362:
2271:
2136:
2102:
2072:
2044:
1993:
1961:
1928:
1842:
1709:
1326:
1280:
1215:
1153:
1127:
1100:
1073:
1001:
927:
904:
884:
861:
776:
699:
612:
569:
508:
485:
480:radiation efficiency
474:Radiation efficiency
445:
414:
408:radiation efficiency
389:radiation resistance
295:
248:radiation efficiency
196:
169:
142:
122:
102:
3773:Antenna measurement
3542:
3045:
1463:
1382:
1367:
856:radiation intensity
279:with respect to an
4017:Engineering ratios
3905:. CTIA. May 2015.
3676:
3674:
3523:
3367:
3362:
3026:
2877:
2677:
2560:
2559:
2503:
2462:
2337:
2249:
2117:
2084:
2056:
2024:
1976:
1947:
1905:
1822:
1820:
1689:
1687:
1449:
1368:
1350:
1306:
1260:
1185:
1133:
1113:
1086:
1055:
981:
910:
890:
867:
814:
752:
658:
582:
541:
491:
460:
420:
365:
281:isotropic radiator
228:
216:
182:
155:
128:
108:
3834:978-1-119-17898-9
3763:Antenna boresight
3657:
3652:
3636:
3614:
3610:
3600:
3566:
3540:
3509:
3506:
3484:
3480:
3454:
3450:
3412:
3366:
3329:
3320:
3228:
3205:
3182:
3159:
3113:
3103:
3069:
3043:
2928:
2876:
2872:
2840:
2833:
2792:
2769:
2733:
2676:
2672:
2631:
2597:
2555:
2529:
2499:
2484:
2461:
2457:
2421:
2378:
2334:
2328:
2316:
2315:
2311:
2248:
2244:
2211:
2179:
2147:
2113:
2107:
2083:
2077:
2055:
2049:
2022:
1972:
1966:
1946:
1933:
1903:
1887:
1852:
1816:
1770:
1677:
1655:
1637:
1582:
1579:
1569:
1519:
1340:
1290:
1143:field component.
1136:{\displaystyle E}
1049:
1046:
975:
972:
870:{\displaystyle U}
812:
799:
786:
743:
709:
678:reference antenna
622:
560:radio transmitter
556:transmission line
539:
265:radiation pattern
214:
211:
179:
152:
131:{\displaystyle S}
111:{\displaystyle R}
92:
91:
84:
16:(Redirected from
4024:
4007:Antennas (radio)
3994:
3988:
3983:. Archived from
3967:
3966:
3923:
3920:
3914:
3913:
3911:
3900:
3892:
3886:
3885:
3867:
3861:
3860:
3854:
3846:
3820:
3811:
3810:
3803:
3712:0 dBd = 2.15 dBi
3685:
3683:
3682:
3677:
3675:
3668:
3667:
3650:
3637:
3629:
3621:
3612:
3611:
3609:
3608:
3601:
3599:
3588:
3587:
3586:
3581:
3577:
3567:
3559:
3544:
3541:
3533:
3531:
3521:
3515:
3510:
3508:
3507:
3499:
3490:
3485:
3483:
3482:
3481:
3473:
3460:
3455:
3453:
3452:
3451:
3443:
3433:
3432:
3423:
3414:
3413:
3405:
3376:
3374:
3373:
3368:
3364:
3363:
3359:
3358:
3336:
3327:
3326:
3322:
3321:
3319:
3299:
3298:
3297:
3275:
3273:
3272:
3239:
3238:
3229:
3221:
3216:
3215:
3206:
3198:
3193:
3192:
3183:
3175:
3170:
3169:
3160:
3152:
3147:
3146:
3120:
3111:
3104:
3102:
3091:
3090:
3089:
3084:
3080:
3070:
3062:
3047:
3044:
3036:
3034:
3019:
3015:
2930:
2929:
2921:
2892:half-wave dipole
2886:
2884:
2883:
2878:
2874:
2873:
2871:
2870:
2869:
2856:
2855:
2846:
2841:
2839:
2838:
2834:
2832:
2831:
2830:
2814:
2813:
2812:
2803:
2802:
2793:
2785:
2782:
2775:
2771:
2770:
2768:
2767:
2758:
2757:
2756:
2747:
2746:
2736:
2734:
2732:
2731:
2730:
2714:
2707:
2686:
2684:
2683:
2678:
2674:
2673:
2671:
2670:
2669:
2653:
2652:
2651:
2642:
2641:
2632:
2624:
2621:
2616:
2615:
2614:
2602:
2598:
2590:
2573:
2569:
2567:
2566:
2561:
2553:
2552:
2551:
2550:
2541:
2540:
2530:
2522:
2512:
2510:
2509:
2504:
2497:
2496:
2495:
2494:
2482:
2471:
2469:
2468:
2463:
2459:
2458:
2456:
2455:
2446:
2445:
2444:
2435:
2434:
2424:
2422:
2420:
2419:
2418:
2402:
2397:
2396:
2395:
2383:
2379:
2371:
2349:vacuum impedance
2346:
2344:
2343:
2338:
2336:
2335:
2317:
2313:
2312:
2310:
2309:
2300:
2299:
2290:
2288:
2283:
2282:
2258:
2256:
2255:
2250:
2246:
2245:
2243:
2242:
2233:
2232:
2227:
2226:
2225:
2214:
2212:
2204:
2199:
2198:
2193:
2192:
2191:
2180:
2175:
2174:
2173:
2164:
2163:
2153:
2148:
2140:
2126:
2124:
2123:
2118:
2111:
2105:
2093:
2091:
2090:
2085:
2081:
2075:
2065:
2063:
2062:
2057:
2053:
2047:
2033:
2031:
2030:
2025:
2023:
2018:
2010:
2005:
2004:
1985:
1983:
1982:
1977:
1970:
1964:
1956:
1954:
1953:
1948:
1944:
1943:
1942:
1931:
1914:
1912:
1911:
1906:
1904:
1901:
1892:
1888:
1880:
1871:
1870:
1854:
1853:
1850:
1831:
1829:
1828:
1823:
1821:
1817:
1814:
1793:
1792:
1772:
1771:
1768:
1698:
1696:
1695:
1690:
1688:
1678:
1676:
1665:
1660:
1656:
1654:
1653:
1649:
1648:
1647:
1638:
1630:
1623:
1622:
1612:
1611:
1602:
1587:
1583:
1581:
1580:
1577:
1571:
1570:
1567:
1561:
1535:
1531:
1530:
1529:
1520:
1512:
1505:
1504:
1473:
1472:
1462:
1457:
1448:
1447:
1381:
1376:
1366:
1358:
1342:
1341:
1338:
1315:
1313:
1312:
1307:
1305:
1304:
1292:
1291:
1288:
1269:
1267:
1266:
1261:
1244:
1243:
1233:
1232:
1194:
1192:
1191:
1186:
1184:
1183:
1171:
1170:
1142:
1140:
1139:
1134:
1122:
1120:
1119:
1114:
1112:
1111:
1095:
1093:
1092:
1087:
1085:
1084:
1064:
1062:
1061:
1056:
1054:
1050:
1048:
1047:
1044:
1038:
1037:
1028:
1013:
1012:
990:
988:
987:
982:
980:
976:
974:
973:
970:
964:
963:
954:
939:
938:
919:
917:
916:
911:
899:
897:
896:
891:
876:
874:
873:
868:
823:
821:
820:
815:
813:
810:
801:
800:
797:
788:
787:
784:
761:
759:
758:
753:
748:
744:
736:
727:
726:
711:
710:
707:
667:
665:
664:
659:
654:
640:
639:
624:
623:
620:
597:Gain in decibels
591:
589:
588:
583:
581:
580:
550:
548:
547:
542:
540:
538:
537:
528:
527:
518:
500:
498:
497:
492:
469:
467:
466:
461:
429:
427:
426:
421:
381:effective length
374:
372:
371:
366:
358:
326:
232:electromagnetics
225:
223:
222:
217:
215:
213:
212:
209:
200:
191:
189:
188:
183:
181:
180:
177:
164:
162:
161:
156:
154:
153:
150:
137:
135:
134:
129:
117:
115:
114:
109:
87:
80:
76:
73:
67:
62:this article by
53:inline citations
40:
39:
32:
21:
4032:
4031:
4027:
4026:
4025:
4023:
4022:
4021:
3997:
3996:
3973:
3964:
3962:
3932:
3927:
3926:
3921:
3917:
3909:
3898:
3894:
3893:
3889:
3882:
3868:
3864:
3848:
3847:
3835:
3821:
3814:
3805:
3804:
3791:
3786:
3754:
3737:
3721:
3673:
3672:
3654:
3653:
3628:
3619:
3618:
3589:
3582:
3558:
3557:
3553:
3552:
3545:
3543:
3532:
3527:
3522:
3520:
3519:
3514:
3498:
3494:
3489:
3472:
3468:
3464:
3459:
3442:
3438:
3434:
3428:
3424:
3422:
3415:
3404:
3400:
3396:
3394:
3391:
3390:
3379:(In most cases
3361:
3360:
3350:
3349:
3334:
3333:
3300:
3290:
3286:
3276:
3274:
3262:
3258:
3234:
3230:
3220:
3211:
3207:
3197:
3188:
3184:
3174:
3165:
3161:
3151:
3142:
3138:
3134:
3130:
3118:
3117:
3092:
3085:
3061:
3060:
3056:
3055:
3048:
3046:
3035:
3030:
2969:
2965:
2931:
2920:
2916:
2912:
2910:
2907:
2906:
2865:
2861:
2857:
2851:
2847:
2845:
2826:
2822:
2815:
2808:
2804:
2798:
2794:
2784:
2783:
2781:
2777:
2776:
2763:
2759:
2752:
2748:
2742:
2738:
2737:
2735:
2726:
2722:
2718:
2713:
2712:
2708:
2706:
2698:
2695:
2694:
2665:
2661:
2654:
2647:
2643:
2637:
2633:
2623:
2622:
2620:
2604:
2603:
2589:
2585:
2584:
2582:
2579:
2578:
2571:
2546:
2542:
2536:
2532:
2531:
2521:
2518:
2515:
2514:
2490:
2486:
2485:
2480:
2477:
2476:
2451:
2447:
2440:
2436:
2430:
2426:
2425:
2423:
2414:
2410:
2406:
2401:
2385:
2384:
2370:
2366:
2365:
2363:
2360:
2359:
2325:
2324:
2305:
2301:
2295:
2291:
2289:
2287:
2278:
2274:
2272:
2269:
2268:
2238:
2234:
2228:
2221:
2217:
2216:
2215:
2213:
2203:
2194:
2187:
2183:
2182:
2181:
2169:
2165:
2159:
2155:
2154:
2152:
2139:
2137:
2134:
2133:
2103:
2100:
2099:
2073:
2070:
2069:
2045:
2042:
2041:
2011:
2009:
2000:
1996:
1994:
1991:
1990:
1962:
1959:
1958:
1938:
1934:
1929:
1926:
1925:
1922:
1900:
1879:
1875:
1866:
1862:
1849:
1845:
1843:
1840:
1839:
1819:
1818:
1813:
1788:
1784:
1773:
1767:
1763:
1760:
1759:
1719:
1712:
1710:
1707:
1706:
1686:
1685:
1669:
1664:
1643:
1639:
1629:
1628:
1624:
1618:
1614:
1613:
1607:
1603:
1601:
1597:
1576:
1572:
1566:
1562:
1560:
1556:
1543:
1537:
1536:
1525:
1521:
1511:
1510:
1506:
1500:
1496:
1468:
1464:
1458:
1453:
1443:
1439:
1377:
1372:
1359:
1354:
1343:
1337:
1333:
1329:
1327:
1324:
1323:
1300:
1296:
1287:
1283:
1281:
1278:
1277:
1239:
1235:
1228:
1224:
1216:
1213:
1212:
1206:
1201:
1179:
1175:
1166:
1162:
1154:
1151:
1150:
1128:
1125:
1124:
1107:
1103:
1101:
1098:
1097:
1080:
1076:
1074:
1071:
1070:
1043:
1039:
1033:
1029:
1027:
1023:
1008:
1004:
1002:
999:
998:
969:
965:
959:
955:
953:
949:
934:
930:
928:
925:
924:
905:
902:
901:
885:
882:
881:
862:
859:
858:
845:
809:
796:
792:
783:
779:
777:
774:
773:
735:
731:
722:
718:
706:
702:
700:
697:
696:
644:
635:
631:
619:
615:
613:
610:
609:
599:
576:
572:
570:
567:
566:
533:
529:
523:
519:
517:
509:
506:
505:
486:
483:
482:
476:
446:
443:
442:
415:
412:
411:
401:
330:
298:
296:
293:
292:
234:, an antenna's
208:
204:
199:
197:
194:
193:
176:
172:
170:
167:
166:
149:
145:
143:
140:
139:
123:
120:
119:
103:
100:
99:
88:
77:
71:
68:
58:Please help to
57:
41:
37:
28:
23:
22:
15:
12:
11:
5:
4030:
4020:
4019:
4014:
4009:
3960:
3959:
3946:
3936:Antenna Theory
3931:
3928:
3925:
3924:
3915:
3887:
3880:
3862:
3833:
3812:
3788:
3787:
3785:
3782:
3781:
3780:
3775:
3770:
3765:
3760:
3753:
3750:
3736:
3733:
3720:
3717:
3716:
3715:
3714:
3713:
3700:
3699:
3698:
3697:
3671:
3666:
3663:
3660:
3649:
3646:
3643:
3640:
3635:
3632:
3627:
3624:
3622:
3620:
3617:
3607:
3604:
3598:
3595:
3592:
3585:
3580:
3576:
3573:
3570:
3565:
3562:
3556:
3551:
3548:
3539:
3536:
3530:
3526:
3518:
3513:
3505:
3502:
3497:
3493:
3488:
3479:
3476:
3471:
3467:
3463:
3458:
3449:
3446:
3441:
3437:
3431:
3427:
3421:
3418:
3416:
3411:
3408:
3403:
3399:
3398:
3387:
3386:
3385:
3384:
3383:, is adequate)
3357:
3354:
3348:
3345:
3342:
3339:
3337:
3335:
3332:
3325:
3318:
3315:
3312:
3309:
3306:
3303:
3296:
3293:
3289:
3285:
3282:
3279:
3271:
3268:
3265:
3261:
3257:
3254:
3251:
3248:
3245:
3242:
3237:
3233:
3227:
3224:
3219:
3214:
3210:
3204:
3201:
3196:
3191:
3187:
3181:
3178:
3173:
3168:
3164:
3158:
3155:
3150:
3145:
3141:
3137:
3133:
3129:
3126:
3123:
3121:
3119:
3116:
3110:
3107:
3101:
3098:
3095:
3088:
3083:
3079:
3076:
3073:
3068:
3065:
3059:
3054:
3051:
3042:
3039:
3033:
3029:
3025:
3022:
3018:
3014:
3011:
3008:
3005:
3002:
2999:
2996:
2993:
2990:
2987:
2984:
2981:
2978:
2975:
2972:
2968:
2964:
2961:
2958:
2955:
2952:
2949:
2946:
2943:
2940:
2937:
2934:
2932:
2927:
2924:
2919:
2915:
2914:
2888:
2887:
2868:
2864:
2860:
2854:
2850:
2844:
2837:
2829:
2825:
2821:
2818:
2811:
2807:
2801:
2797:
2791:
2788:
2780:
2774:
2766:
2762:
2755:
2751:
2745:
2741:
2729:
2725:
2721:
2717:
2711:
2705:
2702:
2688:
2687:
2668:
2664:
2660:
2657:
2650:
2646:
2640:
2636:
2630:
2627:
2619:
2613:
2610:
2607:
2601:
2596:
2593:
2588:
2558:
2549:
2545:
2539:
2535:
2528:
2525:
2502:
2493:
2489:
2473:
2472:
2454:
2450:
2443:
2439:
2433:
2429:
2417:
2413:
2409:
2405:
2400:
2394:
2391:
2388:
2382:
2377:
2374:
2369:
2353:
2352:
2331:
2323:
2320:
2308:
2304:
2298:
2294:
2286:
2281:
2277:
2262:
2261:
2260:
2259:
2241:
2237:
2231:
2224:
2220:
2210:
2207:
2202:
2197:
2190:
2186:
2178:
2172:
2168:
2162:
2158:
2151:
2146:
2143:
2116:
2110:
2096:
2095:
2080:
2067:
2052:
2035:
2034:
2021:
2017:
2014:
2008:
2003:
1999:
1975:
1969:
1957:at a distance
1941:
1937:
1921:
1920:Second example
1918:
1917:
1916:
1898:
1895:
1891:
1886:
1883:
1878:
1874:
1869:
1865:
1860:
1857:
1848:
1833:
1832:
1811:
1808:
1805:
1802:
1799:
1796:
1791:
1787:
1782:
1779:
1776:
1774:
1766:
1762:
1761:
1758:
1755:
1752:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1725:
1722:
1720:
1718:
1715:
1714:
1700:
1699:
1684:
1681:
1675:
1672:
1668:
1663:
1659:
1652:
1646:
1642:
1636:
1633:
1627:
1621:
1617:
1610:
1606:
1600:
1596:
1593:
1590:
1586:
1575:
1565:
1559:
1555:
1552:
1549:
1546:
1544:
1542:
1539:
1538:
1534:
1528:
1524:
1518:
1515:
1509:
1503:
1499:
1495:
1492:
1489:
1485:
1482:
1479:
1476:
1471:
1467:
1461:
1456:
1452:
1446:
1442:
1438:
1435:
1432:
1429:
1426:
1422:
1419:
1415:
1412:
1409:
1406:
1403:
1400:
1397:
1394:
1391:
1388:
1385:
1380:
1375:
1371:
1365:
1362:
1357:
1353:
1349:
1346:
1344:
1336:
1332:
1331:
1317:
1316:
1303:
1299:
1295:
1286:
1271:
1270:
1259:
1256:
1253:
1250:
1247:
1242:
1238:
1231:
1227:
1223:
1220:
1205:
1202:
1200:
1197:
1196:
1195:
1182:
1178:
1174:
1169:
1165:
1161:
1158:
1132:
1110:
1106:
1083:
1079:
1067:
1066:
1053:
1042:
1036:
1032:
1026:
1022:
1019:
1016:
1011:
1007:
992:
991:
979:
968:
962:
958:
952:
948:
945:
942:
937:
933:
909:
889:
866:
844:
841:
825:
824:
807:
804:
795:
791:
782:
763:
762:
751:
747:
742:
739:
734:
730:
725:
721:
717:
714:
705:
669:
668:
657:
653:
650:
647:
643:
638:
634:
630:
627:
618:
598:
595:
579:
575:
552:
551:
536:
532:
526:
522:
516:
513:
490:
475:
472:
471:
470:
459:
456:
453:
450:
419:
400:
397:
377:effective area
364:
361:
357:
354:
351:
348:
345:
342:
339:
336:
333:
329:
325:
322:
319:
316:
313:
310:
307:
304:
301:
207:
203:
175:
148:
127:
107:
90:
89:
72:September 2009
44:
42:
35:
26:
9:
6:
4:
3:
2:
4029:
4018:
4015:
4013:
4010:
4008:
4005:
4004:
4002:
3995:
3992:
3986:
3982:
3978:
3977:
3971:
3958:
3957:0-07-232103-2
3954:
3950:
3947:
3945:
3944:0-471-66782-X
3941:
3937:
3934:
3933:
3919:
3908:
3904:
3897:
3891:
3883:
3881:0-201-12819-5
3877:
3873:
3866:
3858:
3852:
3844:
3840:
3836:
3830:
3826:
3819:
3817:
3808:
3802:
3800:
3798:
3796:
3794:
3789:
3779:
3776:
3774:
3771:
3769:
3766:
3764:
3761:
3759:
3756:
3755:
3749:
3746:
3743:
3741:
3732:
3730:
3729:absolute gain
3725:
3724:Realized gain
3719:Realized gain
3711:
3710:
3709:
3708:
3707:
3705:
3695:
3691:
3687:
3686:
3669:
3647:
3644:
3641:
3638:
3633:
3630:
3625:
3623:
3615:
3605:
3602:
3596:
3593:
3590:
3583:
3578:
3574:
3571:
3568:
3563:
3560:
3554:
3549:
3546:
3537:
3534:
3528:
3524:
3516:
3511:
3503:
3500:
3495:
3491:
3486:
3477:
3474:
3469:
3465:
3461:
3456:
3447:
3444:
3439:
3435:
3429:
3425:
3419:
3417:
3409:
3406:
3401:
3389:
3388:
3382:
3378:
3377:
3346:
3343:
3340:
3338:
3330:
3323:
3316:
3310:
3307:
3301:
3294:
3291:
3283:
3280:
3269:
3266:
3263:
3255:
3252:
3246:
3243:
3240:
3235:
3231:
3225:
3222:
3217:
3212:
3208:
3202:
3199:
3194:
3189:
3185:
3179:
3176:
3171:
3166:
3162:
3156:
3153:
3148:
3143:
3139:
3135:
3131:
3127:
3124:
3122:
3114:
3108:
3105:
3099:
3096:
3093:
3086:
3081:
3077:
3074:
3071:
3066:
3063:
3057:
3052:
3049:
3040:
3037:
3031:
3027:
3023:
3020:
3016:
3009:
3006:
3000:
2997:
2994:
2991:
2988:
2982:
2979:
2973:
2970:
2966:
2962:
2959:
2953:
2950:
2944:
2941:
2938:
2935:
2933:
2925:
2922:
2917:
2905:
2904:
2903:
2901:
2897:
2893:
2866:
2862:
2858:
2852:
2848:
2842:
2835:
2827:
2823:
2819:
2816:
2809:
2805:
2799:
2795:
2789:
2786:
2778:
2772:
2764:
2760:
2753:
2749:
2743:
2739:
2727:
2723:
2719:
2715:
2709:
2703:
2700:
2693:
2692:
2691:
2666:
2662:
2658:
2655:
2648:
2644:
2638:
2634:
2628:
2625:
2617:
2599:
2594:
2591:
2586:
2577:
2576:
2575:
2556:
2547:
2543:
2537:
2533:
2526:
2523:
2500:
2491:
2487:
2452:
2448:
2441:
2437:
2431:
2427:
2415:
2411:
2407:
2403:
2398:
2380:
2375:
2372:
2367:
2358:
2357:
2356:
2350:
2322:376.730313461
2321:
2318:
2306:
2302:
2296:
2292:
2284:
2279:
2275:
2267:
2266:
2265:
2239:
2235:
2229:
2222:
2218:
2208:
2205:
2200:
2195:
2188:
2184:
2176:
2170:
2166:
2160:
2156:
2149:
2144:
2141:
2132:
2131:
2130:
2129:
2128:
2114:
2108:
2078:
2068:
2050:
2040:
2039:
2038:
2019:
2015:
2012:
2006:
2001:
1997:
1989:
1988:
1987:
1973:
1967:
1939:
1935:
1896:
1893:
1889:
1884:
1881:
1876:
1872:
1867:
1863:
1858:
1855:
1846:
1838:
1837:
1836:
1809:
1806:
1800:
1794:
1789:
1785:
1780:
1777:
1775:
1764:
1756:
1753:
1747:
1738:
1732:
1729:
1726:
1723:
1721:
1716:
1705:
1704:
1703:
1682:
1679:
1673:
1670:
1666:
1661:
1657:
1650:
1644:
1640:
1634:
1631:
1625:
1619:
1615:
1608:
1604:
1598:
1594:
1591:
1588:
1584:
1573:
1563:
1557:
1553:
1550:
1547:
1545:
1540:
1532:
1526:
1522:
1516:
1513:
1507:
1501:
1497:
1493:
1490:
1487:
1480:
1474:
1469:
1465:
1459:
1454:
1450:
1444:
1440:
1436:
1433:
1430:
1427:
1424:
1420:
1417:
1410:
1404:
1401:
1395:
1392:
1389:
1383:
1378:
1373:
1369:
1363:
1360:
1355:
1351:
1347:
1345:
1334:
1322:
1321:
1320:
1301:
1297:
1293:
1284:
1276:
1275:
1274:
1257:
1251:
1245:
1240:
1236:
1229:
1225:
1221:
1218:
1211:
1210:
1209:
1204:First example
1180:
1176:
1172:
1167:
1163:
1159:
1156:
1149:
1148:
1147:
1144:
1130:
1108:
1104:
1081:
1077:
1051:
1040:
1034:
1030:
1024:
1020:
1017:
1014:
1009:
1005:
997:
996:
995:
977:
966:
960:
956:
950:
946:
943:
940:
935:
931:
923:
922:
921:
907:
887:
878:
864:
857:
853:
849:
840:
838:
834:
829:
805:
802:
793:
789:
780:
772:
771:
770:
768:
749:
745:
740:
737:
732:
728:
723:
719:
715:
712:
703:
695:
694:
693:
691:
685:
683:
679:
673:
655:
651:
648:
645:
641:
636:
632:
628:
625:
616:
608:
607:
606:
604:
594:
577:
573:
565:
561:
557:
534:
530:
524:
520:
514:
511:
504:
503:
502:
488:
481:
457:
454:
451:
448:
441:
440:
439:
437:
434:
430:
417:
409:
405:
396:
394:
390:
386:
382:
378:
362:
359:
327:
290:
286:
282:
278:
272:
270:
266:
262:
257:
253:
249:
245:
241:
237:
233:
205:
201:
173:
146:
125:
105:
96:
86:
83:
75:
65:
61:
55:
54:
48:
43:
34:
33:
30:
19:
3985:the original
3975:
3961:
3948:
3935:
3930:Bibliography
3918:
3902:
3890:
3871:
3865:
3824:
3806:
3747:
3744:
3739:
3738:
3728:
3723:
3722:
3703:
3701:
3693:
3689:
3380:
2899:
2889:
2689:
2474:
2354:
2263:
2097:
2036:
1923:
1834:
1701:
1318:
1272:
1207:
1145:
1068:
993:
879:
852:polarization
848:Partial gain
847:
846:
843:Partial gain
836:
832:
830:
826:
766:
764:
689:
686:
681:
677:
674:
670:
600:
563:
553:
477:
435:
410:
403:
402:
384:
288:
273:
268:
251:
250:. The term
235:
229:
78:
69:
50:
29:
18:Antenna gain
3991:MIL-STD-188
3688:(Likewise,
433:directivity
393:reciprocity
385:square root
256:radio waves
244:directivity
64:introducing
4001:Categories
3784:References
259:antenna's
252:power gain
47:references
3851:cite book
3843:933291646
3645:≈
3642:1.6409224
3639:≈
3626:≈
3606:θ
3597:θ
3594:
3575:θ
3572:
3561:π
3550:
3535:π
3525:∫
3501:λ
3475:λ
3445:λ
3407:λ
3353:Ω
3347:…
3284:π
3253:−
3244:…
3232:π
3209:π
3195:−
3186:π
3163:π
3149:−
3140:π
3109:θ
3100:θ
3097:
3078:θ
3075:
3064:π
3053:
3038:π
3028:∫
3010:π
3001:
2995:−
2992:γ
2983:π
2974:
2954:π
2945:
2923:λ
2843:≈
2820:π
2728:∘
2659:π
2416:∘
2330:Ω
2307:∘
2303:ε
2297:∘
2293:μ
2280:∘
2240:∘
2223:θ
2189:θ
2171:∘
2167:ε
2161:∘
2002:θ
1940:θ
1873:
1807:≈
1795:
1778:≈
1733:≈
1727:η
1680:≈
1674:π
1641:π
1595:π
1554:π
1523:π
1491:θ
1481:θ
1475:
1460:π
1451:∫
1437:π
1428:ϕ
1421:θ
1411:θ
1405:
1396:ϕ
1390:θ
1379:π
1370:∫
1364:π
1352:∫
1252:θ
1246:
1181:ϕ
1168:θ
1109:ϕ
1082:θ
1035:ϕ
1021:π
1010:ϕ
961:θ
947:π
936:θ
908:ϕ
888:θ
803:−
790:≈
729:
713:≈
642:
512:η
489:η
455:η
418:η
391:. Due to
360:−
328:≈
261:main lobe
3907:Archived
3778:Cardioid
3752:See also
3694:2.15 dBi
3344:73.12960
1199:Examples
603:decibels
562:. The
277:decibels
3809:. IEEE.
3758:Antenna
3648:2.15088
3634:73.1296
2896:decibel
2264:where
2037:where:
240:antenna
60:improve
3955:
3942:
3878:
3841:
3831:
3656:
3651:
3613:
3381:73.130
3365:
3328:
3112:
2875:
2675:
2554:
2498:
2483:
2460:
2333:
2327:
2314:
2247:
2112:
2106:
2082:
2076:
2054:
2048:
1971:
1965:
1945:
1932:
1069:where
49:, but
3972:from
3910:(PDF)
3899:(PDF)
3226:70875
1882:1.698
1801:1.698
1757:1.698
1748:1.698
1683:1.698
3953:ISBN
3940:ISBN
3876:ISBN
3857:link
3839:OCLC
3829:ISBN
3692:and
3690:1.64
3462:3600
2355:and
1897:0.15
1885:1.64
1810:2.30
1096:and
994:and
900:and
837:peak
806:2.15
741:1.64
478:The
431:and
404:Gain
399:Gain
363:2.15
246:and
236:gain
3704:dBd
3631:120
3591:sin
3569:cos
3547:cos
3492:120
3203:630
3180:135
3094:sin
3072:cos
3050:cos
3024:120
2942:Cin
2900:dBi
1902:dBd
1864:log
1851:dBd
1815:dBi
1786:log
1769:dBi
1578:rad
1568:max
1466:sin
1402:sin
1339:rad
1289:max
1237:sin
833:not
798:dBi
785:dBd
720:log
708:dBd
633:log
621:dBi
289:dBd
269:not
242:'s
230:In
210:iso
178:iso
151:iso
4003::
3993:).
3979:.
3901:.
3853:}}
3849:{{
3837:.
3815:^
3792:^
3466:30
3436:30
3426:60
3236:10
3128:15
2998:Ci
2971:ln
2963:60
2939:60
2859:30
2574::
1868:10
1859:10
1790:10
1781:10
1667:16
1045:in
971:in
811:dB
724:10
716:10
637:10
629:10
438::
3884:.
3859:)
3845:.
3670:;
3665:i
3662:B
3659:d
3616:,
3603:d
3584:2
3579:)
3564:2
3555:(
3538:2
3529:0
3517:1
3512:=
3504:2
3496:R
3487:=
3478:2
3470:R
3457:=
3448:2
3440:R
3430:2
3420:=
3410:2
3402:G
3356:;
3341:=
3331:,
3324:]
3317:!
3314:)
3311:n
3308:2
3305:(
3302:n
3295:n
3292:2
3288:)
3281:2
3278:(
3270:1
3267:+
3264:n
3260:)
3256:1
3250:(
3247:+
3241:+
3223:4
3218:+
3213:8
3200:1
3190:6
3177:4
3172:+
3167:4
3157:3
3154:1
3144:2
3136:2
3132:[
3125:=
3115:,
3106:d
3087:2
3082:)
3067:2
3058:(
3041:2
3032:0
3021:=
3017:]
3013:)
3007:2
3004:(
2989:+
2986:)
2980:2
2977:(
2967:[
2960:=
2957:)
2951:2
2948:(
2936:=
2926:2
2918:R
2867:s
2863:R
2853:2
2849:A
2836:]
2828:2
2824:r
2817:4
2810:2
2806:I
2800:s
2796:R
2790:2
2787:1
2779:[
2773:]
2765:2
2761:r
2754:2
2750:I
2744:2
2740:A
2724:Z
2720:2
2716:1
2710:[
2704:=
2701:G
2667:2
2663:r
2656:4
2649:2
2645:I
2639:s
2635:R
2629:2
2626:1
2618:=
2612:o
2609:s
2606:i
2600:)
2595:S
2592:P
2587:(
2572:r
2557:.
2548:2
2544:I
2538:s
2534:R
2527:2
2524:1
2501:,
2492:s
2488:R
2453:2
2449:r
2442:2
2438:I
2432:2
2428:A
2412:Z
2408:2
2404:1
2399:=
2393:t
2390:n
2387:a
2381:)
2376:S
2373:P
2368:(
2351:.
2319:=
2285:=
2276:Z
2236:Z
2230:2
2219:E
2209:2
2206:1
2201:=
2196:2
2185:E
2177:2
2157:c
2150:=
2145:S
2142:P
2115:.
2109:r
2079:A
2051:I
2020:r
2016:I
2013:A
2007:=
1998:E
1974:.
1968:r
1936:E
1915:.
1894:=
1890:)
1877:(
1856:=
1847:G
1804:)
1798:(
1765:G
1754:=
1751:)
1745:(
1742:)
1739:1
1736:(
1730:D
1724:=
1717:G
1671:3
1662:=
1658:]
1651:)
1645:2
1635:4
1632:3
1626:(
1620:0
1616:B
1609:0
1605:B
1599:[
1592:4
1589:=
1585:)
1574:P
1564:U
1558:(
1551:4
1548:=
1541:D
1533:)
1527:2
1517:4
1514:3
1508:(
1502:0
1498:B
1494:=
1488:d
1484:)
1478:(
1470:4
1455:0
1445:0
1441:B
1434:2
1431:=
1425:d
1418:d
1414:)
1408:(
1399:)
1393:,
1387:(
1384:U
1374:0
1361:2
1356:0
1348:=
1335:P
1302:0
1298:B
1294:=
1285:U
1258:.
1255:)
1249:(
1241:3
1230:0
1226:B
1222:=
1219:U
1177:G
1173:+
1164:G
1160:=
1157:G
1131:E
1105:U
1078:U
1065:,
1052:)
1041:P
1031:U
1025:(
1018:4
1015:=
1006:G
978:)
967:P
957:U
951:(
944:4
941:=
932:G
865:U
794:G
781:G
767:G
750:.
746:)
738:G
733:(
704:G
690:G
682:G
656:.
652:)
649:G
646:(
626:=
617:G
578:O
574:P
535:O
531:P
525:R
521:P
515:=
458:D
452:=
449:G
436:D
356:)
353:i
350:B
347:d
344:(
341:n
338:i
335:a
332:G
324:)
321:d
318:B
315:d
312:(
309:n
306:i
303:a
300:G
206:S
202:S
174:S
147:R
126:S
106:R
85:)
79:(
74:)
70:(
56:.
20:)
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