89:
215:
1523:
4515:, it is used as a measure of the radiation pattern from a source indicating how much of the total energy from the source is radiating in a particular direction. In electro-acoustics, these patterns commonly include omnidirectional, cardioid and hyper-cardioid microphone polar patterns. A loudspeaker with a high degree of directivity (narrow dispersion pattern) can be said to have a high
22:
1300:
2941:
4464:. For any pair of orthogonal polarizations (such as left-hand-circular and right-hand-circular), the individual power densities simply add to give the total power density. Thus, if expressed as dimensionless ratios rather than in dB, the total directive gain is equal to the sum of the two partial directive gains.
2333:
3968:
1655:
For a planar array, the computation of directivity is more complicated and requires consideration of the positions of each array element with respect to all the others and with respect to wavelength. For a planar rectangular or hexagonally spaced array with non-isotropic elements, the maximum
2580:
2177:
dB. If the array were tapered, this value would go down. The directivity, assuming isotropic elements, is 25.9dBi. Now assume elements with 9.0dBi directivity. The directivity is not 33.1dBi, but rather is only 29.2dBi. The reason for this is that the effective aperture of the individual
2070:
There is a physically intuitive reason for this relationship; essentially there are a limited number of photons per unit area to be captured by the individual antennas. Placing two high gain antennas very close to each other (less than a wavelength) does not buy twice the gain, for example.
3266:
45:
which measures the degree to which the radiation emitted is concentrated in a single direction. It is the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. Therefore, the directivity of a hypothetical
1518:{\displaystyle {\begin{aligned}D&=\max \left({\frac {U}{P_{\text{tot}}/\left(4\pi \right)}}\right)\\&={\frac {\left.U(\theta ,\phi )\right|_{\text{max}}}{{\frac {1}{4\pi }}\int _{0}^{2\pi }\int _{0}^{\pi }U(\theta ,\phi )\sin \theta \,d\theta \,d\phi }}.\end{aligned}}}
2732:
1134:
4508:, directivity is a measure of the difference in dB of the power output at a coupled port, when power is transmitted in the desired direction, to the power output at the same coupled port when the same amount of power is transmitted in the opposite direction.
733:, of an antenna is defined for all incident angles of an antenna. The term "directive gain" is deprecated by IEEE. If an angle relative to the antenna is not specified, then directivity is presumed to refer to the axis of maximum radiation intensity.
3735:
2181:
169:
Since the directional antenna radiates most of its power into a small solid angle around the z-axis its maximum signal strength is much larger than the isotropic antenna which spreads the same power in all directions. Thus the directivity
832:
1798:
3507:
1647:
3846:
4916:
Institute of
Electrical and Electronics Engineers, “The IEEE standard dictionary of electrical and electronics terms”; 6th ed. New York, N.Y., Institute of Electrical and Electronics Engineers, c1997. IEEE Std 100-1996.
2437:
3776:, is defined as the solid angle which all power would flow through if the antenna radiation intensity were constant at its maximal value. If the beam solid angle is known, then maximum directivity can be calculated as
3113:
4098:
3635:
2071:
Conversely, if the antenna are more than a wavelength apart, there are photons that fall between the elements and are not collected at all. This is why the physical aperture size must be taken into account.
2024:, and the directivity of an element (assuming all of the elements are identical) only in the limit as element spacing becomes much larger than lambda. In the case of a sparse array, where element spacing
4475:
is calculated in the same manner as the partial directive gain, but without consideration of antenna efficiency (i.e. assuming a lossless antenna). It is similarly additive for orthogonal polarizations.
2936:{\displaystyle D={\frac {\left(\sum \limits _{n=1}^{N}I_{n}\right)^{2}}{\sum \limits _{m=1}^{N}\sum \limits _{n=1}^{N}I_{m}I_{n}e^{j(\beta _{m}-\beta _{n})}\operatorname {sinc} {\big (}2r_{mn}{\big )}}}}
1305:
4182:
4431:
2175:
1023:
65:. Directivity is an important measure because many antennas and optical systems are designed to radiate electromagnetic waves in a single direction or over a narrow-angle. By the principle of
3354:
4292:
3825:
4354:
3640:
Further studies on directivity expressions for various cases, like if the sources are omnidirectional (even in the array environment) like if the prototype element-pattern takes the form
2018:
1693:
167:
1568:, the directivity is equal to the inverse of the square of the 2-norm of the array weight vector, under the assumption that the weight vector is normalized such that its sum is unity.
3306:
2409:
1247:
3028:
1912:
3077:
2627:
2099:
1566:
3565:
3536:
3106:
1199:
988:
922:
2721:
1288:
coordinate combination divided by what the radiation intensity would have been had the antenna been an isotropic antenna radiating the same amount of total power into space.
1286:
1979:
1941:
1164:
1015:
953:
2328:{\textstyle D=A_{e}{\frac {4\pi }{\lambda ^{2}}}=Ndx\,dy\,\eta {\frac {4\pi }{\lambda ^{2}}}=N{\frac {\lambda }{2}}{\frac {\lambda }{2}}{\frac {4\pi }{\lambda ^{2}}}=N\pi }
4031:
4001:
3837:(in radians) in two perpendicular planes. The half-power beamwidth is simply the angle in which the radiation intensity is at least half of the peak radiation intensity.
2045:
3774:
3643:
1537:
the directivity is a complicated calculation in the general case. For a linear array the directivity will always be less than or equal to the number of elements. For a
2679:
2653:
2600:
2432:
1841:
1823:
is the "illumination efficiency" of the array that accounts for tapering and spacing of the elements in the array. For an un-tapered array with elements at less than
4660:
4125:
2359:
1867:
855:
739:
2582:. The actual result is 34.6380 dBi, just shy of the ideal 35.0745 dBi we expected. Why the difference from the ideal? If the spacing in the x and y dimensions is
2065:
1821:
875:
1701:
4211:
2967:
731:
188:
3361:
3963:{\displaystyle D\approx 4\pi {\frac {\left({\frac {180}{\pi }}\right)^{2}}{\Theta _{1d}\Theta _{2d}}}\approx {\frac {41253}{\Theta _{1d}\Theta _{2d}}},}
2575:{\textstyle D=A_{e}{\frac {4\pi }{\lambda ^{2}}}=Ndx\,dy\,\eta {\frac {4\pi }{\lambda ^{2}}}=N\lambda \,\lambda \,{\frac {4\pi }{\lambda ^{2}}}=4N\pi }
1574:
3833:
The beam solid angle can be approximated for antennas with one narrow major lobe and very negligible minor lobes by simply multiplying the half-power
3261:{\displaystyle \beta _{n}=-k(x_{n}\sin \theta _{\tau }\cos \phi _{\tau }+y_{n}\sin \theta _{\tau }\sin \phi _{\tau }+z_{n}\cos \theta _{\tau })}
4493:
is calculated in the same manner as gain, but considering only a certain polarization. It is similarly additive for orthogonal polarizations.
431:
437:
634:
426:
4042:
3572:
449:
2726:
For antenna arrays, the closed form expression for
Directivity for progressively phased array of isotropic sources will be given by,
696:
2411:
29.05 dBi? The elements around the edge of the array aren't as limited in their effective aperture as are the majority of elements.
4969:
4922:
4133:
132:
4369:
4993:
66:
2104:
1129:{\displaystyle P_{\text{tot}}=\int _{\phi =0}^{\phi =2\pi }\int _{\theta =0}^{\theta =\pi }U\sin \theta \,d\theta \,d\phi ;}
4301:, which radiates uniformly in all directions and hence has a directivity of 1. The calculation is therefore simplified to
560:
312:
297:
3313:
4223:
550:
3782:
4853:
4998:
4307:
387:
1984:
4988:
540:
1659:
4799:"Wide Scanning Characteristics of Sparse Phased Array Antennas Using an Analytical Expression for Directivity"
1652:
In the case of a uniformly weighted (un-tapered) SLA, this reduces to simply N, the number of array elements.
1294:, if a direction is not specified, is the maximal directive gain value found among all possible solid angles:
3273:
2364:
1208:
2974:
118:
with the same total radiated power. The directivity is defined as the ratio of the maximum signal strength
4442:
3035:
1872:
689:
651:
397:
25:
Diagram showing directivity: the highest power density of this antenna is in the direction of the red lobe
2605:
1538:
585:
442:
2077:
1544:
3541:
3512:
3082:
1169:
958:
892:
4875:
4810:
4755:
4700:
3730:{\textstyle \sin ^{\mu }\theta \cos ^{\nu }\theta ,\;\left(\mu >-1,\nu >-{\frac {1}{2}}\right)}
2684:
1259:
886:
570:
62:
2074:
Let's assume a 16Ă—16 un-tapered standard rectangular array (which means that elements are spaced at
1946:
1917:
1142:
993:
931:
4528:
4505:
925:
97:
4006:
3976:
2027:
214:
88:
4899:
4865:
4834:
4779:
4724:
4298:
3752:
530:
490:
332:
257:
47:
2661:
2632:
827:{\displaystyle D(\theta ,\phi )={\frac {U(\theta ,\phi )}{P_{\text{tot}}/\left(4\pi \right)}}.}
4965:
4918:
4891:
4826:
4771:
4716:
2585:
2417:
1826:
682:
590:
575:
565:
535:
470:
287:
198:
106:
93:
69:, the directivity of an antenna when receiving is equal to its directivity when transmitting.
4110:
2338:
1846:
1656:
directivity can be estimated using the universal ratio of effective aperture to directivity,
840:
4883:
4818:
4763:
4708:
1793:{\displaystyle D=A_{e}{4{\pi } \over \lambda ^{2}}=Ndx\,dy\,\eta {4\pi \over \lambda ^{2}}}
377:
322:
317:
247:
30:
4661:"Phased Array Antennas: Floquet Analysis, Synthesis, BFNs and Active Array Systems | Wiley"
2050:
1806:
860:
3830:
which simply calculates the ratio of the beam solid angle to the solid angle of a sphere.
656:
382:
327:
237:
206:
38:
4879:
4814:
4759:
4744:"A Generalized Closed Form Expression of Directivity of Arbitrary Planar Antenna Arrays"
4704:
4646:
4632:
4618:
4561:
4196:
4127:
degrees, then elementary integral calculus yields an expression for the directivity as
2952:
2629:, thus creating tiny regions in the overall array where photons are missed, leading to
716:
580:
545:
500:
252:
232:
173:
42:
3502:{\displaystyle r_{mn}={\sqrt {(x_{m}-x_{n})^{2}+(y_{m}-y_{n})^{2}+(z_{m}-z_{n})^{2}}}}
4982:
1534:
1256:
In other words, directivity is the radiation intensity of an antenna at a particular
882:
610:
372:
342:
292:
224:
4903:
4838:
4783:
4728:
4687:
Das, Sudipta; Mandal, Durbadal; Ghoshal, Sakti Prasad; Kar, Rajib (February 2017).
4485:
4033:
is the half-power beamwidth in a plane at a right angle to the other (in degrees).
878:
555:
480:
367:
302:
262:
242:
77:
58:
1642:{\displaystyle D_{\text{SLA}}={1 \over {\vec {w}}^{\textsf {H}}{\vec {w}}}\leq N}
3746:
620:
475:
337:
4798:
4743:
4742:
Das, Sudipta; Mandal, Durbadal; Kar, Rajib; Ghoshal, Sakti Prasad (July 2013).
4688:
4933:
2021:
625:
520:
4895:
4887:
4830:
4822:
4775:
4767:
4720:
4712:
4854:"Closed-Form Directivity Expression for Arbitrary Volumetric Antenna Arrays"
4552:
IEEE Std 145-2013, IEEE Standard for
Definitions of Terms for Antennas, IEEE
4512:
3834:
1202:
615:
495:
485:
347:
307:
4445:
is taken under consideration, three additional measures can be calculated:
3840:
The same calculations can be performed in degrees rather than in radians:
21:
16:
Measure of how much of an antenna's signal is transmitted in one direction
2681:
spacing. The result now should converge to N times the element gain, or
407:
2434:
spacing. From the above formula, we expect the directivity to peak at
1869:. Note that for an un-tapered standard rectangular array (SRA), where
1803:
where dx and dy are the element spacings in the x and y dimensions and
4359:
Another common reference antenna is the theoretical perfect half-wave
4363:, which radiates perpendicular to itself with a directivity of 1.64:
4360:
73:
3030:
represents the location of elements in
Cartesian co-ordinate system;
105:
that radiates maximum power along the z-axis, and the pattern of an
4870:
4093:{\displaystyle D\approx {\frac {32400}{\Theta _{1d}\Theta _{2d}}}.}
3630:{\textstyle \operatorname {sinc} (x)={\frac {1}{\pi x}}\sin(\pi x)}
665:
402:
392:
282:
72:
The directivity of an actual antenna can vary from 1.76 dBi for a
20:
2361:
because the array is un-tapered. Why the slight difference from
643:
4107:(or approximately conical) beam with a half-power beamwidth of
3737:, and not restricting to progressive phasing can be done from.
92:
Diagram illustrating how directivity is defined. It shows the
4944:
4689:"Generalization of Directivity Expressions for Antenna Arrays"
4460:, divided by the average power density for all directions and
4214:
51:
2723:+ 9 dBi = 33.1 dBi. The actual result is in fact, 33.1 dBi.
1943:. For an un-tapered standard rectangular array (SRA), where
4193:
The directivity is rarely expressed as the unitless number
2067:
is reduced because the array is not uniformly illuminated.
2020:. The directivity of a planar array is the product of the
1383:
4177:{\displaystyle D={\frac {2}{1-\cos {\frac {\theta }{2}}}}}
4003:
is the half-power beamwidth in one plane (in degrees) and
4297:
The reference antenna is usually the theoretical perfect
4426:{\displaystyle D_{\text{dBd}}\approx 10\log _{10}\left.}
1201:
integrated over a spherical surface. Since there are 4Ď€
4501:
The term directivity is also used with other systems.
3646:
3575:
3276:
2440:
2184:
2170:{\displaystyle 10\log _{10}(N)=10\log _{10}(256)=24.1}
2080:
1875:
1662:
1547:
4372:
4310:
4226:
4199:
4136:
4113:
4045:
4009:
3979:
3849:
3785:
3755:
3544:
3515:
3364:
3316:
3116:
3085:
3038:
2977:
2955:
2735:
2687:
2664:
2635:
2608:
2588:
2420:
2367:
2341:
2107:
2053:
2030:
1987:
1949:
1920:
1849:
1829:
1809:
1704:
1577:
1303:
1262:
1211:
1172:
1145:
1026:
996:
961:
934:
895:
863:
843:
742:
719:
176:
135:
4852:
Costa, Bruno Felipe; AbrĂŁo, Taufik (December 2018).
4456:is the power density in a particular direction and
4797:Kedar, Ashutosh; Ligthart, L. P. (February 2019).
4425:
4348:
4286:
4205:
4176:
4119:
4092:
4025:
3995:
3962:
3819:
3768:
3729:
3629:
3559:
3530:
3501:
3348:
3300:
3260:
3100:
3071:
3022:
2961:
2935:
2715:
2673:
2647:
2621:
2594:
2574:
2426:
2403:
2353:
2327:
2169:
2093:
2059:
2039:
2012:
1973:
1935:
1906:
1861:
1835:
1815:
1792:
1687:
1641:
1560:
1517:
1280:
1241:
1193:
1158:
1128:
1009:
982:
947:
916:
869:
849:
826:
725:
182:
161:
3349:{\displaystyle \{\theta _{\tau },\phi _{\tau }\}}
4945:AES Professional Audio Reference definition of Q
4548:
4546:
4544:
4287:{\displaystyle D_{\text{dB}}=10\log _{10}\left.}
3356:is the angular location of the far-field target;
2969:is the total number of elements on the aperture;
1318:
4960:Coleman, Christopher (2004). "Basic Concepts".
3820:{\displaystyle D={\frac {4\pi }{\Omega _{A}}},}
928:, which is the power per unit solid angle; and
122:radiated by the antenna to the signal strength
4962:An Introduction to Radio Frequency Engineering
4458:for a particular component of the polarization
4858:IEEE Transactions on Antennas and Propagation
4803:IEEE Transactions on Antennas and Propagation
4748:IEEE Transactions on Antennas and Propagation
4693:IEEE Transactions on Antennas and Propagation
4349:{\displaystyle D_{\text{dBi}}=10\log _{10}D.}
3268:is the phase component (progressive phasing);
3079:is the complex excitation coefficient of the
2925:
2902:
690:
57:An antenna's directivity is greater than its
8:
4934:App note, Mini-Circuits directional couplers
4036:In planar arrays, a better approximation is
3343:
3317:
3017:
2978:
2013:{\displaystyle D_{\text{max}}\approx 4N\pi }
955:is the total radiated power. The quantities
3682:
2602:, then the spacing along the diagonals is
1688:{\textstyle {\frac {\lambda ^{2}}{4\pi }}}
697:
683:
193:
162:{\displaystyle G={S \over S_{\text{iso}}}}
4869:
4406:
4393:
4377:
4371:
4331:
4315:
4309:
4269:
4260:
4247:
4231:
4225:
4198:
4161:
4143:
4135:
4112:
4075:
4062:
4052:
4044:
4014:
4008:
3984:
3978:
3945:
3932:
3922:
3907:
3894:
3883:
3869:
3862:
3848:
3806:
3792:
3784:
3760:
3754:
3712:
3667:
3651:
3645:
3594:
3574:
3550:
3549:
3543:
3521:
3520:
3514:
3491:
3481:
3468:
3452:
3442:
3429:
3413:
3403:
3390:
3381:
3369:
3363:
3337:
3324:
3315:
3283:
3275:
3249:
3233:
3220:
3204:
3188:
3175:
3159:
3143:
3121:
3115:
3091:
3090:
3084:
3061:
3053:
3043:
3037:
3011:
2998:
2985:
2976:
2954:
2924:
2923:
2914:
2901:
2900:
2883:
2870:
2859:
2849:
2839:
2829:
2818:
2808:
2797:
2786:
2775:
2765:
2754:
2742:
2734:
2695:
2686:
2663:
2634:
2612:
2607:
2587:
2552:
2538:
2537:
2533:
2516:
2502:
2498:
2491:
2471:
2457:
2451:
2439:
2419:
2399:
2375:
2366:
2340:
2308:
2294:
2284:
2274:
2260:
2246:
2242:
2235:
2215:
2201:
2195:
2183:
2143:
2115:
2106:
2081:
2079:
2052:
2029:
1992:
1986:
1948:
1919:
1894:
1874:
1848:
1828:
1808:
1782:
1768:
1764:
1757:
1737:
1727:
1721:
1715:
1703:
1669:
1663:
1661:
1619:
1618:
1612:
1611:
1610:
1599:
1598:
1591:
1582:
1576:
1548:
1546:
1498:
1491:
1458:
1453:
1440:
1435:
1416:
1409:
1379:
1341:
1335:
1325:
1304:
1302:
1261:
1222:
1216:
1210:
1205:on the surface of a sphere, the quantity
1171:
1150:
1144:
1116:
1109:
1085:
1074:
1055:
1044:
1031:
1025:
1001:
995:
960:
939:
933:
894:
862:
842:
797:
791:
764:
741:
718:
175:
151:
142:
134:
3301:{\textstyle k={\frac {2\pi }{\lambda }}}
2178:elements limits their directivity. So,
87:
4540:
205:
3509:is the Euclidean distance between the
2404:{\displaystyle 10\log _{10}(N\pi )={}}
1242:{\displaystyle P_{\text{tot}}/(4\pi )}
432:Wireless electronic devices and health
4682:
4680:
3023:{\displaystyle \{x_{n},y_{n},z_{n}\}}
2414:Now let's move the array elements to
1981:, this reduces to a maximum value of
1907:{\textstyle dx=dy={\lambda \over 2}}
644:Multiple-input multiple-output (MIMO)
438:International Telecommunication Union
7:
4647:"MATLAB Phased Array System Toolbox"
4633:"MATLAB Phased Array System Toolbox"
4619:"MATLAB Phased Array System Toolbox"
3072:{\displaystyle I_{n}e^{j\beta _{n}}}
463:Radiation sources / regions
427:Wireless device radiation and health
4217:comparison to a reference antenna:
2815:
2794:
2751:
2622:{\displaystyle \lambda {\sqrt {2}}}
450:World Radiocommunication Conference
4072:
4059:
4011:
3981:
3942:
3929:
3904:
3891:
3803:
3757:
2094:{\textstyle {\frac {\lambda }{2}}}
1561:{\textstyle {\frac {\lambda }{2}}}
1166:is the power per unit solid angle
1139:that is, the total radiated power
129:radiated by the isotropic antenna
14:
76:to as much as 50 dBi for a large
3560:{\displaystyle n^{\textrm {th}}}
3531:{\displaystyle m^{\textrm {th}}}
3101:{\displaystyle n^{\textrm {th}}}
1194:{\displaystyle U(\theta ,\phi )}
983:{\displaystyle U(\theta ,\phi )}
917:{\displaystyle U(\theta ,\phi )}
213:
2716:{\displaystyle 10\log _{10}(N)}
1541:, where the element spacing is
1281:{\displaystyle (\theta ,\phi )}
4964:. Cambridge University Press.
3624:
3615:
3588:
3582:
3488:
3461:
3449:
3422:
3410:
3383:
3255:
3136:
2889:
2863:
2710:
2704:
2393:
2384:
2158:
2152:
2130:
2124:
1974:{\displaystyle dx=dy=\lambda }
1936:{\displaystyle D\approx N\pi }
1624:
1604:
1479:
1467:
1401:
1389:
1275:
1263:
1236:
1227:
1188:
1176:
1159:{\displaystyle P_{\text{tot}}}
1010:{\displaystyle P_{\text{tot}}}
977:
965:
948:{\displaystyle P_{\text{tot}}}
911:
899:
782:
770:
758:
746:
1:
885:respectively in the standard
313:Low-noise block downconverter
4026:{\displaystyle \Theta _{2d}}
3996:{\displaystyle \Theta _{1d}}
3567:element on the aperture, and
2040:{\displaystyle >\lambda }
1253:power per unit solid angle.
298:Counterpoise (ground system)
4437:Accounting for polarization
3769:{\displaystyle \Omega _{A}}
1539:standard linear array (SLA)
551:Friis transmission equation
190:is much greater than one.
5015:
4483:
2674:{\displaystyle 10\lambda }
2648:{\displaystyle \eta <1}
388:Municipal wireless network
635:Bell Laboratories Layered
61:by an efficiency factor,
4888:10.1109/TAP.2018.2869243
4823:10.1109/TAP.2018.2880006
4768:10.1109/TAP.2013.2257652
4713:10.1109/TAP.2016.2632738
4605:Optimum Array Processing
4590:Optimum Array Processing
4575:Optimum Array Processing
2595:{\displaystyle \lambda }
2427:{\displaystyle \lambda }
1836:{\displaystyle \lambda }
4120:{\displaystyle \theta }
2354:{\displaystyle \eta =1}
1862:{\displaystyle \eta =1}
850:{\displaystyle \theta }
668:Multiple Access (WSDMA)
666:Wideband Space Division
4454:Partial directive gain
4449:Partial directive gain
4427:
4350:
4288:
4207:
4189:Expression in decibels
4178:
4121:
4103:For an antenna with a
4094:
4027:
3997:
3964:
3821:
3770:
3741:Relation to beam width
3731:
3631:
3561:
3532:
3503:
3350:
3302:
3262:
3102:
3073:
3024:
2963:
2937:
2834:
2813:
2770:
2717:
2675:
2649:
2623:
2596:
2576:
2428:
2405:
2355:
2335:. Note, in this case
2329:
2171:
2101:.) The array gain is
2095:
2061:
2041:
2014:
1975:
1937:
1908:
1863:
1837:
1817:
1794:
1689:
1643:
1562:
1519:
1282:
1243:
1195:
1160:
1130:
1011:
984:
949:
918:
871:
851:
828:
727:
398:Radio masts and towers
191:
184:
163:
26:
4994:Microphone technology
4428:
4351:
4289:
4208:
4179:
4122:
4095:
4028:
3998:
3965:
3822:
3771:
3732:
3632:
3562:
3533:
3504:
3351:
3303:
3263:
3103:
3074:
3025:
2964:
2938:
2814:
2793:
2750:
2718:
2676:
2650:
2624:
2597:
2577:
2429:
2406:
2356:
2330:
2172:
2096:
2062:
2060:{\displaystyle \eta }
2042:
2015:
1976:
1938:
1909:
1864:
1838:
1818:
1816:{\displaystyle \eta }
1795:
1690:
1644:
1563:
1520:
1283:
1244:
1196:
1161:
1131:
1017:satisfy the relation
1012:
985:
950:
919:
872:
870:{\displaystyle \phi }
852:
829:
728:
586:Signal-to-noise ratio
421:Safety and regulation
185:
164:
91:
37:is a parameter of an
24:
4506:directional couplers
4370:
4308:
4224:
4197:
4134:
4111:
4043:
4007:
3977:
3847:
3783:
3753:
3644:
3573:
3542:
3513:
3362:
3314:
3274:
3114:
3083:
3036:
2975:
2953:
2733:
2685:
2662:
2633:
2606:
2586:
2438:
2418:
2365:
2339:
2182:
2105:
2078:
2051:
2028:
1985:
1947:
1918:
1873:
1847:
1827:
1807:
1702:
1660:
1575:
1545:
1301:
1260:
1209:
1170:
1143:
1024:
994:
959:
932:
893:
887:spherical coordinate
861:
841:
740:
717:
571:Radiation resistance
174:
133:
63:radiation efficiency
4880:2018ITAP...66.7443C
4815:2019ITAP...67..905K
4760:2013ITAP...61.3909D
4705:2017ITAP...65..915D
4607:. pp. 247–249.
4592:. pp. 247–249.
4529:Directional antenna
4473:Partial directivity
4468:Partial directivity
1463:
1448:
1096:
1069:
926:radiation intensity
98:directional antenna
4423:
4346:
4299:isotropic radiator
4284:
4203:
4174:
4117:
4090:
4023:
3993:
3960:
3817:
3766:
3727:
3627:
3557:
3528:
3499:
3346:
3308:is the wavenumber;
3298:
3258:
3098:
3069:
3020:
2959:
2933:
2713:
2671:
2645:
2619:
2592:
2572:
2424:
2401:
2351:
2325:
2167:
2091:
2057:
2037:
2010:
1971:
1933:
1914:, this reduces to
1904:
1859:
1833:
1813:
1790:
1685:
1639:
1558:
1515:
1513:
1449:
1431:
1278:
1239:
1191:
1156:
1126:
1070:
1040:
1007:
980:
945:
914:
867:
847:
824:
723:
637:Space-Time (BLAST)
491:Near and far field
192:
180:
159:
48:isotropic radiator
27:
4999:Radio electronics
4864:(12): 7443–7448.
4577:. pp. 60–63.
4462:all polarizations
4414:
4380:
4318:
4275:
4272:
4234:
4206:{\displaystyle D}
4172:
4169:
4085:
3955:
3917:
3877:
3812:
3749:, represented as
3720:
3607:
3553:
3524:
3497:
3296:
3094:
2962:{\displaystyle N}
2931:
2617:
2558:
2522:
2477:
2314:
2292:
2282:
2266:
2221:
2089:
1995:
1902:
1788:
1743:
1683:
1631:
1627:
1614:
1607:
1585:
1556:
1529:In antenna arrays
1506:
1429:
1412:
1363:
1338:
1219:
1153:
1034:
1004:
942:
819:
794:
726:{\displaystyle D}
707:
706:
591:Spurious emission
576:Radio propagation
566:Radiation pattern
541:Equivalent radius
536:Electrical length
443:Radio Regulations
288:Block upconverter
183:{\displaystyle G}
157:
154:
107:isotropic antenna
94:radiation pattern
5006:
4989:Antennas (radio)
4975:
4947:
4942:
4936:
4931:
4925:
4914:
4908:
4907:
4873:
4849:
4843:
4842:
4794:
4788:
4787:
4754:(7): 3909–3911.
4739:
4733:
4732:
4684:
4675:
4674:
4672:
4671:
4657:
4651:
4650:
4643:
4637:
4636:
4629:
4623:
4622:
4615:
4609:
4608:
4603:Van Trees, H.L.
4600:
4594:
4593:
4588:Van Trees, H.L.
4585:
4579:
4578:
4573:Van Trees, H.L.
4570:
4564:
4562:Antenna Tutorial
4559:
4553:
4550:
4432:
4430:
4429:
4424:
4419:
4415:
4407:
4398:
4397:
4382:
4381:
4378:
4355:
4353:
4352:
4347:
4336:
4335:
4320:
4319:
4316:
4293:
4291:
4290:
4285:
4280:
4276:
4274:
4273:
4270:
4261:
4252:
4251:
4236:
4235:
4232:
4213:but rather as a
4212:
4210:
4209:
4204:
4183:
4181:
4180:
4175:
4173:
4171:
4170:
4162:
4144:
4126:
4124:
4123:
4118:
4099:
4097:
4096:
4091:
4086:
4084:
4083:
4082:
4070:
4069:
4053:
4032:
4030:
4029:
4024:
4022:
4021:
4002:
4000:
3999:
3994:
3992:
3991:
3969:
3967:
3966:
3961:
3956:
3954:
3953:
3952:
3940:
3939:
3923:
3918:
3916:
3915:
3914:
3902:
3901:
3888:
3887:
3882:
3878:
3870:
3863:
3826:
3824:
3823:
3818:
3813:
3811:
3810:
3801:
3793:
3775:
3773:
3772:
3767:
3765:
3764:
3736:
3734:
3733:
3728:
3726:
3722:
3721:
3713:
3672:
3671:
3656:
3655:
3636:
3634:
3633:
3628:
3608:
3606:
3595:
3566:
3564:
3563:
3558:
3556:
3555:
3554:
3551:
3537:
3535:
3534:
3529:
3527:
3526:
3525:
3522:
3508:
3506:
3505:
3500:
3498:
3496:
3495:
3486:
3485:
3473:
3472:
3457:
3456:
3447:
3446:
3434:
3433:
3418:
3417:
3408:
3407:
3395:
3394:
3382:
3377:
3376:
3355:
3353:
3352:
3347:
3342:
3341:
3329:
3328:
3307:
3305:
3304:
3299:
3297:
3292:
3284:
3267:
3265:
3264:
3259:
3254:
3253:
3238:
3237:
3225:
3224:
3209:
3208:
3193:
3192:
3180:
3179:
3164:
3163:
3148:
3147:
3126:
3125:
3107:
3105:
3104:
3099:
3097:
3096:
3095:
3092:
3078:
3076:
3075:
3070:
3068:
3067:
3066:
3065:
3048:
3047:
3029:
3027:
3026:
3021:
3016:
3015:
3003:
3002:
2990:
2989:
2968:
2966:
2965:
2960:
2942:
2940:
2939:
2934:
2932:
2930:
2929:
2928:
2922:
2921:
2906:
2905:
2893:
2892:
2888:
2887:
2875:
2874:
2854:
2853:
2844:
2843:
2833:
2828:
2812:
2807:
2791:
2790:
2785:
2781:
2780:
2779:
2769:
2764:
2743:
2722:
2720:
2719:
2714:
2700:
2699:
2680:
2678:
2677:
2672:
2654:
2652:
2651:
2646:
2628:
2626:
2625:
2620:
2618:
2613:
2601:
2599:
2598:
2593:
2581:
2579:
2578:
2573:
2559:
2557:
2556:
2547:
2539:
2523:
2521:
2520:
2511:
2503:
2478:
2476:
2475:
2466:
2458:
2456:
2455:
2433:
2431:
2430:
2425:
2410:
2408:
2407:
2402:
2400:
2380:
2379:
2360:
2358:
2357:
2352:
2334:
2332:
2331:
2326:
2315:
2313:
2312:
2303:
2295:
2293:
2285:
2283:
2275:
2267:
2265:
2264:
2255:
2247:
2222:
2220:
2219:
2210:
2202:
2200:
2199:
2176:
2174:
2173:
2168:
2148:
2147:
2120:
2119:
2100:
2098:
2097:
2092:
2090:
2082:
2066:
2064:
2063:
2058:
2046:
2044:
2043:
2038:
2019:
2017:
2016:
2011:
1997:
1996:
1993:
1980:
1978:
1977:
1972:
1942:
1940:
1939:
1934:
1913:
1911:
1910:
1905:
1903:
1895:
1868:
1866:
1865:
1860:
1842:
1840:
1839:
1834:
1822:
1820:
1819:
1814:
1799:
1797:
1796:
1791:
1789:
1787:
1786:
1777:
1769:
1744:
1742:
1741:
1732:
1731:
1722:
1720:
1719:
1694:
1692:
1691:
1686:
1684:
1682:
1674:
1673:
1664:
1648:
1646:
1645:
1640:
1632:
1630:
1629:
1628:
1620:
1617:
1616:
1615:
1609:
1608:
1600:
1592:
1587:
1586:
1583:
1567:
1565:
1564:
1559:
1557:
1549:
1524:
1522:
1521:
1516:
1514:
1507:
1505:
1462:
1457:
1447:
1439:
1430:
1428:
1417:
1414:
1413:
1410:
1408:
1404:
1380:
1372:
1368:
1364:
1362:
1361:
1357:
1345:
1340:
1339:
1336:
1326:
1287:
1285:
1284:
1279:
1248:
1246:
1245:
1240:
1226:
1221:
1220:
1217:
1200:
1198:
1197:
1192:
1165:
1163:
1162:
1157:
1155:
1154:
1151:
1135:
1133:
1132:
1127:
1095:
1084:
1068:
1054:
1036:
1035:
1032:
1016:
1014:
1013:
1008:
1006:
1005:
1002:
989:
987:
986:
981:
954:
952:
951:
946:
944:
943:
940:
923:
921:
920:
915:
876:
874:
873:
868:
856:
854:
853:
848:
833:
831:
830:
825:
820:
818:
817:
813:
801:
796:
795:
792:
785:
765:
732:
730:
729:
724:
699:
692:
685:
464:
378:Cellular network
318:Passive radiator
217:
194:
189:
187:
186:
181:
168:
166:
165:
160:
158:
156:
155:
152:
143:
116:
103:
31:electromagnetics
5014:
5013:
5009:
5008:
5007:
5005:
5004:
5003:
4979:
4978:
4972:
4959:
4956:
4954:Further reading
4951:
4950:
4943:
4939:
4932:
4928:
4915:
4911:
4851:
4850:
4846:
4796:
4795:
4791:
4741:
4740:
4736:
4686:
4685:
4678:
4669:
4667:
4659:
4658:
4654:
4645:
4644:
4640:
4631:
4630:
4626:
4617:
4616:
4612:
4602:
4601:
4597:
4587:
4586:
4582:
4572:
4571:
4567:
4560:
4556:
4551:
4542:
4537:
4525:
4499:
4488:
4482:
4470:
4451:
4439:
4402:
4389:
4373:
4368:
4367:
4327:
4311:
4306:
4305:
4265:
4256:
4243:
4227:
4222:
4221:
4195:
4194:
4191:
4148:
4132:
4131:
4109:
4108:
4071:
4058:
4057:
4041:
4040:
4010:
4005:
4004:
3980:
3975:
3974:
3941:
3928:
3927:
3903:
3890:
3889:
3865:
3864:
3845:
3844:
3802:
3794:
3781:
3780:
3756:
3751:
3750:
3743:
3687:
3683:
3663:
3647:
3642:
3641:
3599:
3571:
3570:
3545:
3540:
3539:
3516:
3511:
3510:
3487:
3477:
3464:
3448:
3438:
3425:
3409:
3399:
3386:
3365:
3360:
3359:
3333:
3320:
3312:
3311:
3285:
3272:
3271:
3245:
3229:
3216:
3200:
3184:
3171:
3155:
3139:
3117:
3112:
3111:
3086:
3081:
3080:
3057:
3049:
3039:
3034:
3033:
3007:
2994:
2981:
2973:
2972:
2951:
2950:
2910:
2879:
2866:
2855:
2845:
2835:
2792:
2771:
2749:
2745:
2744:
2731:
2730:
2691:
2683:
2682:
2660:
2659:
2631:
2630:
2604:
2603:
2584:
2583:
2548:
2540:
2512:
2504:
2467:
2459:
2447:
2436:
2435:
2416:
2415:
2371:
2363:
2362:
2337:
2336:
2304:
2296:
2256:
2248:
2211:
2203:
2191:
2180:
2179:
2139:
2111:
2103:
2102:
2076:
2075:
2049:
2048:
2026:
2025:
1988:
1983:
1982:
1945:
1944:
1916:
1915:
1871:
1870:
1845:
1844:
1825:
1824:
1805:
1804:
1778:
1770:
1733:
1723:
1711:
1700:
1699:
1675:
1665:
1658:
1657:
1597:
1596:
1578:
1573:
1572:
1543:
1542:
1531:
1512:
1511:
1421:
1415:
1385:
1382:
1381:
1370:
1369:
1350:
1346:
1331:
1330:
1321:
1311:
1299:
1298:
1258:
1257:
1249:represents the
1212:
1207:
1206:
1168:
1167:
1146:
1141:
1140:
1027:
1022:
1021:
997:
992:
991:
957:
956:
935:
930:
929:
891:
890:
859:
858:
839:
838:
806:
802:
787:
786:
766:
738:
737:
715:
714:
703:
674:
673:
670:
667:
661:
657:Spread spectrum
652:Reconfiguration
639:
636:
630:
605:
597:
596:
595:
515:
514:Characteristics
507:
506:
505:
465:
462:
455:
454:
446:
440:
422:
414:
413:
412:
362:
354:
353:
352:
277:
269:
268:
267:
227:
172:
171:
147:
131:
130:
128:
114:
110:
101:
86:
17:
12:
11:
5:
5012:
5010:
5002:
5001:
4996:
4991:
4981:
4980:
4977:
4976:
4970:
4955:
4952:
4949:
4948:
4937:
4926:
4909:
4844:
4809:(2): 905–914.
4789:
4734:
4699:(2): 915–919.
4676:
4652:
4638:
4624:
4610:
4595:
4580:
4565:
4554:
4539:
4538:
4536:
4533:
4532:
4531:
4524:
4521:
4498:
4497:In other areas
4495:
4484:Main article:
4481:
4478:
4469:
4466:
4450:
4447:
4438:
4435:
4434:
4433:
4422:
4418:
4413:
4410:
4405:
4401:
4396:
4392:
4388:
4385:
4376:
4357:
4356:
4345:
4342:
4339:
4334:
4330:
4326:
4323:
4314:
4295:
4294:
4283:
4279:
4268:
4264:
4259:
4255:
4250:
4246:
4242:
4239:
4230:
4202:
4190:
4187:
4186:
4185:
4168:
4165:
4160:
4157:
4154:
4151:
4147:
4142:
4139:
4116:
4101:
4100:
4089:
4081:
4078:
4074:
4068:
4065:
4061:
4056:
4051:
4048:
4020:
4017:
4013:
3990:
3987:
3983:
3971:
3970:
3959:
3951:
3948:
3944:
3938:
3935:
3931:
3926:
3921:
3913:
3910:
3906:
3900:
3897:
3893:
3886:
3881:
3876:
3873:
3868:
3861:
3858:
3855:
3852:
3828:
3827:
3816:
3809:
3805:
3800:
3797:
3791:
3788:
3763:
3759:
3742:
3739:
3725:
3719:
3716:
3711:
3708:
3705:
3702:
3699:
3696:
3693:
3690:
3686:
3681:
3678:
3675:
3670:
3666:
3662:
3659:
3654:
3650:
3638:
3637:
3626:
3623:
3620:
3617:
3614:
3611:
3605:
3602:
3598:
3593:
3590:
3587:
3584:
3581:
3578:
3568:
3548:
3519:
3494:
3490:
3484:
3480:
3476:
3471:
3467:
3463:
3460:
3455:
3451:
3445:
3441:
3437:
3432:
3428:
3424:
3421:
3416:
3412:
3406:
3402:
3398:
3393:
3389:
3385:
3380:
3375:
3372:
3368:
3357:
3345:
3340:
3336:
3332:
3327:
3323:
3319:
3309:
3295:
3291:
3288:
3282:
3279:
3269:
3257:
3252:
3248:
3244:
3241:
3236:
3232:
3228:
3223:
3219:
3215:
3212:
3207:
3203:
3199:
3196:
3191:
3187:
3183:
3178:
3174:
3170:
3167:
3162:
3158:
3154:
3151:
3146:
3142:
3138:
3135:
3132:
3129:
3124:
3120:
3109:
3089:
3064:
3060:
3056:
3052:
3046:
3042:
3031:
3019:
3014:
3010:
3006:
3001:
2997:
2993:
2988:
2984:
2980:
2970:
2958:
2944:
2943:
2927:
2920:
2917:
2913:
2909:
2904:
2899:
2896:
2891:
2886:
2882:
2878:
2873:
2869:
2865:
2862:
2858:
2852:
2848:
2842:
2838:
2832:
2827:
2824:
2821:
2817:
2811:
2806:
2803:
2800:
2796:
2789:
2784:
2778:
2774:
2768:
2763:
2760:
2757:
2753:
2748:
2741:
2738:
2712:
2709:
2706:
2703:
2698:
2694:
2690:
2670:
2667:
2644:
2641:
2638:
2616:
2611:
2591:
2571:
2568:
2565:
2562:
2555:
2551:
2546:
2543:
2536:
2532:
2529:
2526:
2519:
2515:
2510:
2507:
2501:
2497:
2494:
2490:
2487:
2484:
2481:
2474:
2470:
2465:
2462:
2454:
2450:
2446:
2443:
2423:
2398:
2395:
2392:
2389:
2386:
2383:
2378:
2374:
2370:
2350:
2347:
2344:
2324:
2321:
2318:
2311:
2307:
2302:
2299:
2291:
2288:
2281:
2278:
2273:
2270:
2263:
2259:
2254:
2251:
2245:
2241:
2238:
2234:
2231:
2228:
2225:
2218:
2214:
2209:
2206:
2198:
2194:
2190:
2187:
2166:
2163:
2160:
2157:
2154:
2151:
2146:
2142:
2138:
2135:
2132:
2129:
2126:
2123:
2118:
2114:
2110:
2088:
2085:
2056:
2036:
2033:
2009:
2006:
2003:
2000:
1991:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1932:
1929:
1926:
1923:
1901:
1898:
1893:
1890:
1887:
1884:
1881:
1878:
1858:
1855:
1852:
1832:
1812:
1801:
1800:
1785:
1781:
1776:
1773:
1767:
1763:
1760:
1756:
1753:
1750:
1747:
1740:
1736:
1730:
1726:
1718:
1714:
1710:
1707:
1681:
1678:
1672:
1668:
1650:
1649:
1638:
1635:
1626:
1623:
1606:
1603:
1595:
1590:
1581:
1555:
1552:
1530:
1527:
1526:
1525:
1510:
1504:
1501:
1497:
1494:
1490:
1487:
1484:
1481:
1478:
1475:
1472:
1469:
1466:
1461:
1456:
1452:
1446:
1443:
1438:
1434:
1427:
1424:
1420:
1407:
1403:
1400:
1397:
1394:
1391:
1388:
1384:
1378:
1375:
1373:
1371:
1367:
1360:
1356:
1353:
1349:
1344:
1334:
1329:
1324:
1320:
1317:
1314:
1312:
1310:
1307:
1306:
1277:
1274:
1271:
1268:
1265:
1238:
1235:
1232:
1229:
1225:
1215:
1190:
1187:
1184:
1181:
1178:
1175:
1149:
1137:
1136:
1125:
1122:
1119:
1115:
1112:
1108:
1105:
1102:
1099:
1094:
1091:
1088:
1083:
1080:
1077:
1073:
1067:
1064:
1061:
1058:
1053:
1050:
1047:
1043:
1039:
1030:
1000:
979:
976:
973:
970:
967:
964:
938:
913:
910:
907:
904:
901:
898:
866:
846:
835:
834:
823:
816:
812:
809:
805:
800:
790:
784:
781:
778:
775:
772:
769:
763:
760:
757:
754:
751:
748:
745:
722:
705:
704:
702:
701:
694:
687:
679:
676:
675:
672:
671:
664:
660:
659:
654:
648:
647:
646:
640:
633:
629:
628:
623:
618:
613:
607:
606:
603:
602:
599:
598:
594:
593:
588:
583:
581:Radio spectrum
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
523:
517:
516:
513:
512:
509:
508:
504:
503:
501:Vertical plane
498:
493:
488:
483:
478:
473:
467:
466:
461:
460:
457:
456:
453:
452:
447:
436:
434:
429:
423:
420:
419:
416:
415:
411:
410:
405:
400:
395:
390:
385:
380:
375:
370:
364:
363:
360:
359:
356:
355:
351:
350:
345:
340:
335:
330:
325:
320:
315:
310:
305:
300:
295:
290:
285:
279:
278:
275:
274:
271:
270:
266:
265:
260:
255:
253:Satellite dish
250:
245:
240:
235:
229:
228:
223:
222:
219:
218:
210:
209:
203:
202:
179:
150:
146:
141:
138:
126:
112:
85:
82:
43:optical system
15:
13:
10:
9:
6:
4:
3:
2:
5011:
5000:
4997:
4995:
4992:
4990:
4987:
4986:
4984:
4973:
4971:0-521-83481-3
4967:
4963:
4958:
4957:
4953:
4946:
4941:
4938:
4935:
4930:
4927:
4924:
4923:1-55937-833-6
4920:
4913:
4910:
4905:
4901:
4897:
4893:
4889:
4885:
4881:
4877:
4872:
4867:
4863:
4859:
4855:
4848:
4845:
4840:
4836:
4832:
4828:
4824:
4820:
4816:
4812:
4808:
4804:
4800:
4793:
4790:
4785:
4781:
4777:
4773:
4769:
4765:
4761:
4757:
4753:
4749:
4745:
4738:
4735:
4730:
4726:
4722:
4718:
4714:
4710:
4706:
4702:
4698:
4694:
4690:
4683:
4681:
4677:
4666:
4662:
4656:
4653:
4648:
4642:
4639:
4634:
4628:
4625:
4620:
4614:
4611:
4606:
4599:
4596:
4591:
4584:
4581:
4576:
4569:
4566:
4563:
4558:
4555:
4549:
4547:
4545:
4541:
4534:
4530:
4527:
4526:
4522:
4520:
4518:
4514:
4509:
4507:
4502:
4496:
4494:
4492:
4487:
4479:
4477:
4474:
4467:
4465:
4463:
4459:
4455:
4448:
4446:
4444:
4436:
4420:
4416:
4411:
4408:
4403:
4399:
4394:
4390:
4386:
4383:
4374:
4366:
4365:
4364:
4362:
4343:
4340:
4337:
4332:
4328:
4324:
4321:
4312:
4304:
4303:
4302:
4300:
4281:
4277:
4266:
4262:
4257:
4253:
4248:
4244:
4240:
4237:
4228:
4220:
4219:
4218:
4216:
4200:
4188:
4166:
4163:
4158:
4155:
4152:
4149:
4145:
4140:
4137:
4130:
4129:
4128:
4114:
4106:
4087:
4079:
4076:
4066:
4063:
4054:
4049:
4046:
4039:
4038:
4037:
4034:
4018:
4015:
3988:
3985:
3957:
3949:
3946:
3936:
3933:
3924:
3919:
3911:
3908:
3898:
3895:
3884:
3879:
3874:
3871:
3866:
3859:
3856:
3853:
3850:
3843:
3842:
3841:
3838:
3836:
3831:
3814:
3807:
3798:
3795:
3789:
3786:
3779:
3778:
3777:
3761:
3748:
3740:
3738:
3723:
3717:
3714:
3709:
3706:
3703:
3700:
3697:
3694:
3691:
3688:
3684:
3679:
3676:
3673:
3668:
3664:
3660:
3657:
3652:
3648:
3621:
3618:
3612:
3609:
3603:
3600:
3596:
3591:
3585:
3579:
3576:
3569:
3546:
3517:
3492:
3482:
3478:
3474:
3469:
3465:
3458:
3453:
3443:
3439:
3435:
3430:
3426:
3419:
3414:
3404:
3400:
3396:
3391:
3387:
3378:
3373:
3370:
3366:
3358:
3338:
3334:
3330:
3325:
3321:
3310:
3293:
3289:
3286:
3280:
3277:
3270:
3250:
3246:
3242:
3239:
3234:
3230:
3226:
3221:
3217:
3213:
3210:
3205:
3201:
3197:
3194:
3189:
3185:
3181:
3176:
3172:
3168:
3165:
3160:
3156:
3152:
3149:
3144:
3140:
3133:
3130:
3127:
3122:
3118:
3110:
3087:
3062:
3058:
3054:
3050:
3044:
3040:
3032:
3012:
3008:
3004:
2999:
2995:
2991:
2986:
2982:
2971:
2956:
2949:
2948:
2947:
2918:
2915:
2911:
2907:
2897:
2894:
2884:
2880:
2876:
2871:
2867:
2860:
2856:
2850:
2846:
2840:
2836:
2830:
2825:
2822:
2819:
2809:
2804:
2801:
2798:
2787:
2782:
2776:
2772:
2766:
2761:
2758:
2755:
2746:
2739:
2736:
2729:
2728:
2727:
2724:
2707:
2701:
2696:
2692:
2688:
2668:
2665:
2656:
2642:
2639:
2636:
2614:
2609:
2589:
2569:
2566:
2563:
2560:
2553:
2549:
2544:
2541:
2534:
2530:
2527:
2524:
2517:
2513:
2508:
2505:
2499:
2495:
2492:
2488:
2485:
2482:
2479:
2472:
2468:
2463:
2460:
2452:
2448:
2444:
2441:
2421:
2412:
2396:
2390:
2387:
2381:
2376:
2372:
2368:
2348:
2345:
2342:
2322:
2319:
2316:
2309:
2305:
2300:
2297:
2289:
2286:
2279:
2276:
2271:
2268:
2261:
2257:
2252:
2249:
2243:
2239:
2236:
2232:
2229:
2226:
2223:
2216:
2212:
2207:
2204:
2196:
2192:
2188:
2185:
2164:
2161:
2155:
2149:
2144:
2140:
2136:
2133:
2127:
2121:
2116:
2112:
2108:
2086:
2083:
2072:
2068:
2054:
2034:
2031:
2023:
2007:
2004:
2001:
1998:
1989:
1968:
1965:
1962:
1959:
1956:
1953:
1950:
1930:
1927:
1924:
1921:
1899:
1896:
1891:
1888:
1885:
1882:
1879:
1876:
1856:
1853:
1850:
1830:
1810:
1783:
1779:
1774:
1771:
1765:
1761:
1758:
1754:
1751:
1748:
1745:
1738:
1734:
1728:
1724:
1716:
1712:
1708:
1705:
1698:
1697:
1696:
1679:
1676:
1670:
1666:
1653:
1636:
1633:
1621:
1601:
1593:
1588:
1579:
1571:
1570:
1569:
1553:
1550:
1540:
1536:
1535:antenna array
1528:
1508:
1502:
1499:
1495:
1492:
1488:
1485:
1482:
1476:
1473:
1470:
1464:
1459:
1454:
1450:
1444:
1441:
1436:
1432:
1425:
1422:
1418:
1405:
1398:
1395:
1392:
1386:
1376:
1374:
1365:
1358:
1354:
1351:
1347:
1342:
1332:
1327:
1322:
1315:
1313:
1308:
1297:
1296:
1295:
1293:
1289:
1272:
1269:
1266:
1254:
1252:
1233:
1230:
1223:
1213:
1204:
1185:
1182:
1179:
1173:
1147:
1123:
1120:
1117:
1113:
1110:
1106:
1103:
1100:
1097:
1092:
1089:
1086:
1081:
1078:
1075:
1071:
1065:
1062:
1059:
1056:
1051:
1048:
1045:
1041:
1037:
1028:
1020:
1019:
1018:
998:
974:
971:
968:
962:
936:
927:
908:
905:
902:
896:
888:
884:
883:azimuth angle
880:
864:
844:
821:
814:
810:
807:
803:
798:
788:
779:
776:
773:
767:
761:
755:
752:
749:
743:
736:
735:
734:
720:
712:
700:
695:
693:
688:
686:
681:
680:
678:
677:
669:
663:
662:
658:
655:
653:
650:
649:
645:
641:
638:
632:
631:
627:
624:
622:
619:
617:
614:
612:
611:Beam steering
609:
608:
601:
600:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
518:
511:
510:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
468:
459:
458:
451:
448:
444:
439:
435:
433:
430:
428:
425:
424:
418:
417:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
384:
381:
379:
376:
374:
373:Amateur radio
371:
369:
366:
365:
358:
357:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
293:Coaxial cable
291:
289:
286:
284:
281:
280:
273:
272:
264:
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
230:
226:
221:
220:
216:
212:
211:
208:
204:
200:
196:
195:
177:
148:
144:
139:
136:
125:
121:
117:
108:
104:
99:
95:
90:
83:
81:
79:
75:
70:
68:
64:
60:
55:
53:
49:
44:
40:
36:
32:
23:
19:
4961:
4940:
4929:
4912:
4861:
4857:
4847:
4806:
4802:
4792:
4751:
4747:
4737:
4696:
4692:
4668:. Retrieved
4664:
4655:
4641:
4627:
4613:
4604:
4598:
4589:
4583:
4574:
4568:
4557:
4516:
4510:
4503:
4500:
4491:Partial gain
4490:
4489:
4486:Antenna gain
4480:Partial gain
4472:
4471:
4461:
4457:
4453:
4452:
4443:polarization
4440:
4358:
4296:
4192:
4104:
4102:
4035:
3972:
3839:
3832:
3829:
3744:
3639:
2945:
2725:
2657:
2413:
2073:
2069:
1802:
1654:
1651:
1532:
1291:
1290:
1255:
1250:
1138:
879:zenith angle
836:
710:
708:
525:
481:Ground plane
368:Antenna farm
225:Common types
123:
119:
109:
100:
78:dish antenna
74:short dipole
71:
56:
34:
28:
18:
3747:solid angle
1292:Directivity
711:directivity
621:Beamforming
526:Directivity
476:Focal cloud
338:Transmitter
67:reciprocity
50:is 1, or 0
35:directivity
4983:Categories
4871:1810.01487
4670:2022-05-29
4535:References
3835:beamwidths
2658:Now go to
2022:array gain
1203:steradians
626:Small cell
604:Techniques
531:Efficiency
521:Array gain
276:Components
258:Television
84:Definition
4896:1558-2221
4831:0018-926X
4776:1558-2221
4721:1558-2221
4665:Wiley.com
4513:acoustics
4400:
4384:≈
4338:
4271:reference
4254:
4164:θ
4159:
4153:−
4115:θ
4073:Θ
4060:Θ
4050:≈
4012:Θ
3982:Θ
3943:Θ
3930:Θ
3920:≈
3905:Θ
3892:Θ
3875:π
3860:π
3854:≈
3804:Ω
3799:π
3758:Ω
3745:The beam
3710:−
3704:ν
3695:−
3689:μ
3677:θ
3674:
3669:ν
3661:θ
3658:
3653:μ
3619:π
3613:
3601:π
3580:
3475:−
3436:−
3397:−
3339:τ
3335:ϕ
3326:τ
3322:θ
3294:λ
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3251:τ
3247:θ
3243:
3222:τ
3218:ϕ
3214:
3206:τ
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3198:
3177:τ
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3169:
3161:τ
3157:θ
3153:
3131:−
3119:β
3108:-element;
3059:β
2898:
2881:β
2877:−
2868:β
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2795:∑
2752:∑
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2422:λ
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2343:η
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2258:λ
2253:π
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2213:λ
2208:π
2150:
2122:
2084:λ
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1999:≈
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1780:λ
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1489:θ
1486:
1477:ϕ
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1234:π
1186:ϕ
1180:θ
1121:ϕ
1114:θ
1107:θ
1104:
1093:π
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1076:θ
1072:∫
1066:π
1057:ϕ
1046:ϕ
1042:∫
975:ϕ
969:θ
909:ϕ
903:θ
865:ϕ
845:θ
811:π
780:ϕ
774:θ
756:ϕ
750:θ
616:Beam tilt
496:Side lobe
486:Main lobe
471:Boresight
348:Twin-lead
308:Feed line
102:(R, grey)
4904:54196716
4839:59620334
4784:44492351
4729:19645584
4523:See also
2946:where,
889:angles;
877:are the
642:Massive
408:Wireless
323:Receiver
248:Monopole
207:Antennas
199:a series
197:Part of
115:, green)
4876:Bibcode
4811:Bibcode
4756:Bibcode
4701:Bibcode
4215:decibel
4105:conical
1251:average
924:is the
383:Hotspot
361:Systems
328:Rotator
238:Fractal
39:antenna
4968:
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4361:dipole
3973:where
1533:In an
561:Height
546:Factor
233:Dipole
4900:S2CID
4866:arXiv
4835:S2CID
4780:S2CID
4725:S2CID
4504:With
4441:When
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3925:41253
837:Here
403:Wi-Fi
393:Radio
343:Tuner
283:Balun
96:of a
4966:ISBN
4919:ISBN
4892:ISSN
4827:ISSN
4772:ISSN
4717:ISSN
4412:1.64
3707:>
3692:>
3577:sinc
3538:and
2895:sinc
2640:<
2165:24.1
2032:>
990:and
881:and
857:and
709:The
556:Gain
333:Stub
303:Feed
263:Whip
243:Loop
59:gain
4884:doi
4819:doi
4764:doi
4709:doi
4511:In
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4329:log
4317:dBi
4245:log
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3872:180
3665:cos
3649:sin
3610:sin
3240:cos
3211:sin
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1101:sin
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127:iso
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201:on
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