1926:. As receiving antennas, they are much more sensitive to radio waves coming from a preferred direction compared to waves coming from other directions (which would be considered interference). As transmitting antennas, most of their power is radiated in a particular direction at the expense of other directions. Although antenna gain and effective aperture are functions of direction, when no direction is specified, these are understood to refer to their maximal values, that is, in the direction(s) of the antenna's intended use (also referred to as the antenna's
2309:
33:
4301:, be it in free-space or transmitted electrically. Since there is only a single connection to the resistor, the resistor itself represents a single mode. And an antenna, also having a single electrical connection, couples to one mode of the electromagnetic field according to its average effective cross-section of
1948:
The fraction of the power delivered to a transmitting antenna that is received by a receiving antenna is proportional to the product of the apertures of both the antennas and inversely proportional to the squared values of the distance between the antennas and the wavelength. This is given by a form
154:
of an antenna is defined as "In a given direction, the ratio of the available power at the terminals of a receiving antenna to the power flux density of a plane wave incident on the antenna from that direction, the wave being polarization matched to the antenna." Of particular note in this definition
1168:
a measure of received power (but does not directly specify voltage or current). For instance, a half-wave dipole has a much longer effective length than a short dipole. However the effective area of the short dipole is almost as great as it is for the half-wave antenna, since (ideally), given an
3351:
997:
Most antenna designs are not defined by a physical area but consist of wires or thin rods; then the effective aperture bears no clear relation to the size or area of the antenna. An alternate measure of antenna response that has a greater relationship to the physical length of such antennas is
1231:
of the gain in those directions. But since changing the physical size of an antenna inevitably changes the impedance (often by a great factor), the effective length is not by itself a useful figure of merit for describing an antenna's peak directivity and is more of theoretical importance. In
141:
of an antenna is defined as "A surface, near or on an antenna, on which it is convenient to make assumptions regarding the field values for the purpose of computing fields at external points. The aperture is often taken as that portion of a plane surface near the antenna, perpendicular to the
1467:
is a dimensionless parameter between 0 and 1 that measures how close the antenna comes to using all the radio wave power intersecting its physical aperture. If the aperture efficiency were 100%, then all the wave's power falling on its physical aperture would be converted to electrical power
3771:
3562:
828:
4113:
We thus find that for a hypothetical isotropic antenna, thermodynamics demands that the effective cross-section of the receiving antenna to have an area of λ/4π. This result could be further generalized if we allow the integral over frequency to be more general. Then we find that
4047:
3388:
However, that radiation is unpolarized, whereas the antenna is only sensitive to one polarization, reducing it by a factor of 2. To find the total power from black-body radiation accepted by the antenna, we must integrate that quantity times the assumed cross-sectional area
3141:
2049:
3003:
1909:
1163:
The longer the effective length, the greater is the voltage appearing at its terminals. However, the actual power implied by that voltage depends on the antenna's feedpoint impedance, so this cannot be directly related to antenna gain, which
1733:
428:
1516:
aperture size, there may be a strong motivation to reduce these (while achieving a specified antenna gain) by maximizing the aperture efficiency. Aperture efficiencies of typical aperture antennas vary from 0.35 to well over 0.70.
3163:
3601:
2704:
4214:
4253:
will still flow in opposite directions, even though the voltage and currents seen at the antenna and resistor's terminals will differ. The spectral density of the power flow in either direction will still be given by
906:
2790:
1655:, that is, a hypothetical antenna that receives power equally well from all directions. It can be seen that (for antennas at a given frequency) gain is also equal to the ratio of the apertures of these antennas:
3406:
2852:
681:
2526:
4108:
620:
1458:
1794:
3904:
1087:
3009:
1506:
2385:
4348:
3574:
is independent of angle, so the integration over solid angles is trivial, introducing a factor of 4π. And again we can take the simple case of a narrowband electronic filter function
2255:
4295:
3822:
1959:
301:
2888:
1309:
from the original beam. That power removed from the plane wave can be actually received by the antenna (converted into electrical power), reflected or otherwise scattered, or
1307:
1368:
1277:
185:
1649:
1225:
1194:
1026:
223:
3886:
2169:
2140:
2111:
2082:
1622:
1555:
1398:
535:
485:
458:
328:
253:
2597:
1829:
649:
3838:
at the same temperature, we expect no net transfer of power between the cavities. Otherwise one cavity would heat up and the other would cool down in violation of the
3383:
2558:
2297:
1817:
1661:
1341:
1149:
1120:
975:
948:
508:
336:
2345:
2275:
2211:
2191:
1589:
669:
1571:
of an antenna, its ability to direct radio waves preferentially in one direction or receive preferentially from a given direction, is expressed by a parameter
1169:
ideal impedance-matching network, it can receive almost as much power from that wave. Note that for a given antenna feedpoint impedance, an antenna's gain or
3346:{\displaystyle {\text{P}}_{f,A,\Omega }(f)={\frac {2hf^{3}}{c^{2}}}{\frac {1}{e^{hf/k_{\text{B}}T}-1}}={\frac {2f^{2}}{c^{2}}}\,k_{\text{B}}T\,\eta (f),}
3766:{\displaystyle P_{A}=2\pi P_{f,A,\Omega }(f)A_{\text{eff}}\,B_{1}={\frac {4\pi \,k_{\text{B}}T\,\eta (f_{1})}{\lambda _{1}^{2}}}A_{\text{eff}}B_{1},}
2394:, the basis of the definition of gain above, can be derived on the basis of consistency with thermodynamics. Suppose that an ideal isotropic antenna
1512:, as well as other scattering or loss mechanisms, this is not achieved in practice. Since a parabolic antenna's cost and wind load increase with the
1530:. Outside of aperture antennas, most antennas consist of thin wires or rods with a small physical cross-sectional area (generally much smaller than
155:
is that both effective area and power flux density are functions of incident angle of a plane wave. Assume a plane wave from a particular direction
2605:
4157:
839:
1232:
practice, the effective length of a particular antenna is often combined with its impedance and loss to become the realized effective length.
3557:{\displaystyle P_{A}=\int _{0}^{\infty }\int _{4\pi }\,{\frac {P_{f,A,\Omega }(f)}{2}}A_{\text{eff}}(\Omega ,f)\,F_{\nu }(f)\,d\Omega \,df.}
2854:
can be found by integrating the above equation for the spectral density of mean-squared noise voltage over frequencies passed by the filter
919:, an antenna's directivity in receiving and transmitting are identical, so the power transmitted by an antenna in different directions (the
823:{\displaystyle P_{\text{O}}=\eta P_{\text{R}}=\eta A|{\vec {S}}\cdot {\hat {a}}|=\eta A\|{\vec {S}}(\theta ,\phi )\|\cos \theta \cos \phi ,}
4613:(whose gain is 1.64), since the half-wave dipole can be used as an empirical reference antenna. Such antenna gain figures are expressed in
2738:
2798:
2454:
4570:
4053:
4042:{\displaystyle {\frac {4\pi \,k_{\text{B}}T\,\eta (f_{1})}{\lambda _{1}^{2}}}A_{\text{eff}}B_{1}=k_{\text{B}}T\,\eta (f_{1})\,B_{1},}
540:
1406:
1744:
97:
4474:
69:
3146:
This power due to
Johnson noise from the resistor is received by the antenna, which radiates it into the closed system CA.
4223:, the same as the resistor, can also be relaxed. In principle, any antenna impedance (that isn't totally reactive) can be
225:; this is the amount of power passing through a unit area normal to the direction of the plane wave of one square meter.
50:
4526:
1034:
76:
4553:
3136:{\displaystyle \qquad ={\frac {4k_{\text{B}}TR\,\eta (f_{1})\,B_{1}}{4{\text{R}}}}=k_{\text{B}}T\,\eta (f_{1})\,B_{1}.}
1526:, a measure which applies to all antennas (not just aperture antennas) and accounts only for the gain reduction due to
1279:
which is opaque to such radiation, essentially casting a shadow from a plane wave and thus removing an amount of power
4410:
4400:
116:
1471:
83:
4464:
1370:, as it accounts only for the portion of that wave actually received as electrical power. An aperture antenna's
2350:
916:
258:
to the transmission line connected to its output terminals when irradiated by a uniform field of power density
54:
17:
4304:
4133:
isotropic (that is, any real antenna). Since the angle of arriving electromagnetic radiation only enters into
2216:
4359:
4257:
1240:
In general, the aperture of an antenna cannot be directly inferred from its physical size. However so-called
65:
3839:
2044:{\displaystyle {\frac {P_{\text{r}}}{P_{\text{t}}}}={\frac {A_{\text{r}}A_{\text{t}}}{d^{2}\lambda ^{2}}},}
3779:
2998:{\displaystyle P_{R}={\frac {\int _{0}^{\infty }4k_{\text{B}}TR\,\eta (f)\,F_{\nu }(f)\,df}{4{\text{R}}}}}
1738:
As shown below, the aperture of a lossless isotropic antenna, which by this definition has unity gain, is
1950:
1943:
4219:
Although the above is sufficient proof, we can note that the condition of the antenna's impedance being
261:
3153:, receives a spectral radiance (power per unit area per unit frequency per unit solid angle) given by
1282:
3835:
2441:
2407:
1346:
1255:
158:
2399:
1627:
1203:
1172:
1004:
193:
1904:{\displaystyle G={\frac {A_{\text{e}}}{A_{\text{iso}}}}={\frac {4\pi A_{\text{e}}}{\lambda ^{2}}}.}
4121:
for the same antenna must vary with frequency according to that same formula, using λ =
3848:
2147:
2118:
2089:
2060:
1600:
1533:
1376:
513:
463:
436:
306:
231:
4298:
43:
2567:
1728:{\displaystyle G={\frac {P_{\text{o}}}{P_{\text{iso}}}}={\frac {A_{\text{e}}}{A_{\text{iso}}}}.}
1227:, so that the effective length for an antenna relative to different wave directions follows the
625:
2213:
large enough to ensure a plane wave front at the receive antenna, sufficiently approximated by
1520:
Note that when one simply speaks of an antenna's "efficiency", what is most often meant is the
4543:
3359:
2534:
2282:
1802:
90:
4578:
4236:
4617:
using the notation dBd rather than dBi, where the gain is relative to an isotropic antenna.
2433:
1522:
1468:
delivered to the load attached to its output terminals, so these two areas would be equal:
1319:
1127:
1098:
953:
926:
672:
493:
488:
423:{\displaystyle A_{\text{e}}(\theta ,\phi )={\frac {P_{O}}{\|{\vec {S}}(\theta ,\phi )\|}}.}
651:
is the unit vector normal to the array aperture, multiplied by the physical aperture area
8:
4297:, and in fact this is the very thermal-noise power spectral density associated with one
4507:
2714:
2330:
2260:
2196:
2176:
1652:
1574:
654:
142:
direction of maximum radiation, through which the major part of the radiation passes."
4633:
4549:
4470:
4406:
4224:
2391:
1931:
1915:
1245:
920:
4511:
4129:. Moreover, the integral over solid angle can be generalized for an antenna that is
460:
accepted by the antenna (the power at the antenna terminals) is less than the power
4610:
4499:
4439:
2722:
2445:
2303:
992:
130:
3154:
2308:
187:, which are the azimuth and elevation angles relative to the array normal, has a
134:
4503:
4427:
1152:
986:
1343:
is always less than (or equal to) the area of the antenna's physical aperture
4627:
4232:
4443:
4140:
in the above integral, we arrive at the simple but powerful result that the
2699:{\displaystyle \eta (f)={\frac {hf/k_{\text{B}}T}{e^{hf/k_{\text{B}}T}-1}}.}
4209:{\displaystyle {\overline {A_{\text{eff}}}}={\frac {\lambda ^{2}}{4\pi }}.}
1593:
1249:
4428:"Unified frequency and time-domain antenna modeling and characterization"
1567:
901:{\displaystyle A_{\text{e}}(\theta ,\phi )=\eta A\cos \theta \cos \phi .}
4577:. US National Radio Astronomy Observatory (NRAO) website. Archived from
1923:
1820:
1527:
1310:
4386:
IEEE Std 145-2013, IEEE Standard for
Definitions of Terms for Antennas
3149:
The same antenna, being bathed in black-body radiation of temperature
1624:
received by that antenna from waves in a given direction to the power
2785:{\displaystyle P={\frac {{\text{v}}_{\text{rms}}^{2}}{4{\text{R}}}}.}
2422:. In between may be inserted an arbitrary lossless electronic filter
1927:
1509:
1122:
is the open-circuit voltage appearing across the antenna's terminals,
4490:
Friis, H. T. (May 1946). "A Note on a Simple
Transmission Formula".
2414:. We connect the antenna terminals to a resistor also of resistance
32:
4614:
2847:{\displaystyle {\overline {v_{n}^{2}}}={\text{v}}_{\text{rms}}^{2}}
2709:
The amount of power supplied by an electrical source of impedance
2521:{\displaystyle {\overline {v_{n}^{2}}}=4k_{\text{B}}TR\,\eta (f),}
4103:{\displaystyle A_{\text{eff}}={\frac {\lambda _{1}^{2}}{4\pi }}.}
3898:, the cross-sectional area intercepted by the isotropic antenna:
3396:
of the antenna over all solid angles Ω and over all frequencies
2304:
Derivation of antenna aperture from thermodynamic considerations
2193:
is the distance between antennas (the formula is only valid for
1028:
measured in metres, which is defined for a receiving antenna as
3842:. Therefore, the power flows in both directions must be equal:
2084:
is the power fed into the transmitting antenna input terminals,
615:{\displaystyle |S(\theta ,\phi )|=|{\vec {S}}\cdot {\hat {a}}|}
1453:{\displaystyle e_{\text{a}}={\frac {A_{e}}{A_{\text{phys}}}}.}
2113:
is the power available at receiving antenna output terminals,
1789:{\displaystyle A_{\text{iso}}={\frac {\lambda ^{2}}{4\pi }},}
911:
The effective area of an antenna or aperture is based upon a
4609:
Note that antenna gain is also often measured relative to a
3824:
is the free-space wavelength corresponding to the frequency
537:
is equal to the power density of the electromagnetic energy
2432:
Each cavity is in thermal equilibrium and thus filled with
2277:
is the largest linear dimension of either of the antennas),
1508:. But due to nonuniform illumination by a parabolic dish's
1156:
255:
1914:
So antennas with large effective apertures are considered
1597:. This is most commonly defined as the ratio of the power
1252:, have a large (relative to the wavelength) physical area
4548:. Springer Science and Business Media. pp. 134–135.
2440:. The resistor, due to that temperature, will generate
1557:) for which "aperture efficiency" is not even defined.
4151:
over all angles at wavelength λ must also be given by
2418:
inside a second closed system CR, also at temperature
4307:
4260:
4160:
4056:
3907:
3851:
3782:
3604:
3409:
3362:
3166:
3012:
2891:
2882:, in which case that integral simplifies as follows:
2801:
2741:
2608:
2570:
2560:
is a quantum-mechanical factor applying to frequency
2537:
2457:
2353:
2333:
2285:
2263:
2219:
2199:
2179:
2150:
2121:
2092:
2063:
1962:
1832:
1805:
1747:
1664:
1630:
1603:
1577:
1536:
1474:
1409:
1379:
1349:
1322:
1285:
1258:
1206:
1175:
1130:
1101:
1037:
1007:
956:
929:
842:
684:
671:. The incoming radiation is assumed to have the same
657:
628:
543:
516:
496:
466:
439:
339:
309:
303:
watts per square meter, the antenna's effective area
264:
234:
196:
161:
2564:; at normal temperatures and electronic frequencies
57:. Unsourced material may be challenged and removed.
4531:. London: Oxford University Press. pp. 23–24.
4342:
4289:
4208:
4102:
4041:
3880:
3816:
3765:
3556:
3377:
3345:
3135:
2997:
2846:
2784:
2698:
2591:
2552:
2520:
2379:
2339:
2291:
2269:
2249:
2205:
2185:
2171:is the effective area of the transmitting antenna,
2163:
2134:
2105:
2076:
2043:
1903:
1811:
1788:
1727:
1643:
1616:
1583:
1549:
1500:
1452:
1392:
1362:
1335:
1301:
1271:
1219:
1188:
1143:
1114:
1082:{\displaystyle l_{\text{eff}}=V_{0}/E_{\text{s}},}
1081:
1020:
969:
942:
900:
822:
663:
643:
614:
529:
502:
479:
452:
422:
322:
295:
247:
217:
179:
330:for the direction of that plane wave is given by
4625:
2444:with an open-circuit voltage whose mean-squared
4524:
2327:. If both cavities are at the same temperature
2142:is the effective area of the receiving antenna,
4432:IEEE Transactions on Antennas and Propagation
4425:
3567:Since we have assumed an isotropic radiator,
1937:
977:is understood to refer to its maximal value.
923:) is also proportional to the effective area
4568:
4541:
1501:{\displaystyle A_{\text{e}}=A_{\text{phys}}}
1400:is defined as the ratio of these two areas:
796:
766:
411:
381:
212:
197:
4419:
4274:
4025:
4005:
3931:
3917:
3702:
3688:
3665:
3595:. The double integral then simplifies to
3544:
3537:
3517:
3451:
3327:
3313:
3119:
3099:
3059:
3039:
2975:
2955:
2942:
2717:(that is, something with an impedance of
2502:
2380:{\displaystyle P_{\text{A}}=P_{\text{R}}}
2320:in thermal cavities, connected by filter
2299:is the wavelength of the radio frequency.
117:Learn how and when to remove this message
4525:Pawsey, J. L.; Bracewell, R. N. (1955).
4343:{\displaystyle \lambda _{1}^{2}/(4\pi )}
2429:passing only some frequency components.
2307:
2250:{\displaystyle d\gtrsim 2a^{2}/\lambda }
4542:Rohlfs, Kristen; Wilson, T. L. (2013).
4462:
4290:{\displaystyle k_{\text{B}}T\,\eta (f)}
2861:. For simplicity, let us just consider
1922:), which have relatively small angular
14:
4626:
4469:. Technical Publications. p. 51.
4456:
4380:
4378:
4376:
4374:
1313:(converted to heat). In this case the
1235:
228:By definition, if an antenna delivers
4569:Condon, J. J.; Ransom, S. M. (2016).
4562:
4545:Tools of Radio Astronomy, 4th Edition
4535:
4518:
4489:
4405:. Vol. 1. USA: IET. p. 24.
4398:
3581:which only passes power of bandwidth
4483:
4392:
3817:{\displaystyle \lambda _{1}=c/f_{1}}
2868:as a narrowband filter of bandwidth
1560:
55:adding citations to reliable sources
26:
4426:Sullivan, P.; Scott, A. D. (2005).
4371:
4231:by inserting a suitable (lossless)
2721:, such as the antenna in CA) whose
1651:that would be received by an ideal
980:
24:
3641:
3541:
3505:
3472:
3433:
3186:
2918:
2406:sits within a closed system CA in
950:. When no direction is specified,
296:{\displaystyle |S(\theta ,\phi )|}
25:
4645:
145:
4575:Essential Radio Astronomy course
1302:{\displaystyle A_{\text{phys}}S}
31:
4144:of the effective cross-section
3013:
1363:{\displaystyle A_{\text{phys}}}
1272:{\displaystyle A_{\text{phys}}}
180:{\displaystyle (\theta ,\phi )}
42:needs additional citations for
4603:
4402:The Handbook of Antenna Design
4337:
4328:
4284:
4278:
4022:
4009:
3948:
3935:
3719:
3706:
3652:
3646:
3534:
3528:
3514:
3502:
3483:
3477:
3372:
3366:
3337:
3331:
3197:
3191:
3116:
3103:
3056:
3043:
2972:
2966:
2952:
2946:
2618:
2612:
2580:
2574:
2547:
2541:
2512:
2506:
1644:{\displaystyle P_{\text{iso}}}
1220:{\displaystyle l_{\text{eff}}}
1189:{\displaystyle A_{\text{eff}}}
1021:{\displaystyle l_{\text{eff}}}
865:
853:
793:
781:
775:
753:
746:
731:
721:
635:
608:
601:
586:
576:
568:
564:
552:
545:
487:received by an antenna by the
408:
396:
390:
362:
350:
289:
285:
273:
266:
218:{\displaystyle \|{\vec {S}}\|}
206:
174:
162:
13:
1:
4365:
4360:Surface equivalence principle
2599:, but in general is given by
4173:
3881:{\displaystyle P_{A}=P_{R}.}
3840:second law of thermodynamics
2819:
2475:
2164:{\displaystyle A_{\text{t}}}
2135:{\displaystyle A_{\text{r}}}
2106:{\displaystyle P_{\text{r}}}
2077:{\displaystyle P_{\text{t}}}
1617:{\displaystyle P_{\text{o}}}
1550:{\displaystyle A_{\text{e}}}
1393:{\displaystyle e_{\text{a}}}
530:{\displaystyle P_{\text{R}}}
480:{\displaystyle P_{\text{R}}}
453:{\displaystyle P_{\text{O}}}
323:{\displaystyle A_{\text{e}}}
248:{\displaystyle P_{\text{O}}}
7:
4353:
1944:Friis transmission equation
1196:increases according to the
675:as the antenna. Therefore,
10:
4650:
4504:10.1109/JRPROC.1946.234568
2592:{\displaystyle \eta (f)=1}
1951:Friis transmission formula
1941:
1938:Friis transmission formula
1159:per metre, at the antenna.
990:
984:
644:{\displaystyle {\hat {a}}}
3836:thermodynamic equilibrium
2875:around central frequency
2795:The mean-squared voltage
2408:thermodynamic equilibrium
1823:of the radio waves. Thus
915:antenna. However, due to
4596:
4466:Antennas And Propagation
4235:. Since that network is
3834:Since each system is in
3378:{\displaystyle \eta (f)}
2725:open-circuit voltage is
2553:{\displaystyle \eta (f)}
2292:{\displaystyle \lambda }
1812:{\displaystyle \lambda }
1155:of the radio signal, in
4463:Narayan, C. P. (2007).
4444:10.1109/TAP.2005.850760
4399:Rudge, Alan W. (1982).
2400:driving-point impedance
66:"Aperture" antenna
4571:"Antenna Fundamentals"
4438:(7). IEEE: 2284–2291.
4344:
4291:
4210:
4104:
4043:
3891:We can then solve for
3882:
3818:
3767:
3558:
3379:
3347:
3137:
2999:
2848:
2786:
2700:
2593:
2554:
2522:
2387:
2381:
2341:
2293:
2271:
2251:
2207:
2187:
2165:
2136:
2107:
2078:
2045:
1905:
1813:
1790:
1729:
1645:
1618:
1585:
1551:
1502:
1454:
1394:
1364:
1337:
1303:
1273:
1221:
1190:
1145:
1116:
1083:
1022:
971:
944:
902:
824:
665:
645:
616:
531:
504:
481:
454:
424:
324:
297:
249:
219:
181:
4345:
4292:
4211:
4105:
4044:
3883:
3819:
3768:
3559:
3380:
3348:
3138:
3000:
2849:
2787:
2701:
2594:
2555:
2523:
2442:Johnson–Nyquist noise
2382:
2342:
2311:
2294:
2272:
2252:
2208:
2188:
2166:
2137:
2108:
2079:
2046:
1906:
1814:
1791:
1730:
1646:
1619:
1586:
1552:
1503:
1455:
1395:
1365:
1338:
1336:{\displaystyle A_{e}}
1304:
1274:
1222:
1191:
1146:
1144:{\displaystyle E_{s}}
1117:
1115:{\displaystyle V_{0}}
1084:
1023:
972:
970:{\displaystyle A_{e}}
945:
943:{\displaystyle A_{e}}
903:
825:
666:
646:
617:
532:
505:
503:{\displaystyle \eta }
482:
455:
425:
325:
298:
250:
220:
182:
4305:
4299:electromagnetic mode
4258:
4158:
4054:
3905:
3849:
3780:
3602:
3407:
3360:
3164:
3010:
2889:
2799:
2739:
2606:
2568:
2535:
2455:
2434:black-body radiation
2351:
2331:
2283:
2261:
2217:
2197:
2177:
2148:
2119:
2090:
2061:
1960:
1830:
1803:
1745:
1662:
1628:
1601:
1575:
1534:
1523:radiation efficiency
1472:
1407:
1377:
1347:
1320:
1283:
1256:
1204:
1173:
1128:
1099:
1035:
1005:
954:
927:
840:
682:
655:
626:
541:
514:
494:
489:radiation efficiency
464:
437:
337:
307:
262:
232:
194:
159:
51:improve this article
4581:on 1 September 2018
4322:
4086:
3966:
3737:
3437:
3356:using the notation
2922:
2843:
2818:
2766:
2474:
2436:due to temperature
2390:The aperture of an
2312:Diagram of antenna
1465:aperture efficiency
1372:aperture efficiency
1236:Aperture efficiency
4340:
4308:
4287:
4206:
4100:
4072:
4039:
3952:
3878:
3814:
3763:
3723:
3554:
3423:
3375:
3343:
3133:
2995:
2908:
2844:
2827:
2804:
2782:
2750:
2696:
2589:
2550:
2518:
2460:
2388:
2377:
2337:
2289:
2267:
2247:
2203:
2183:
2161:
2132:
2103:
2074:
2041:
1916:high-gain antennas
1901:
1809:
1786:
1725:
1641:
1614:
1581:
1547:
1498:
1450:
1390:
1360:
1333:
1315:effective aperture
1299:
1269:
1217:
1186:
1141:
1112:
1079:
1018:
967:
940:
898:
820:
661:
641:
612:
527:
500:
477:
450:
420:
320:
293:
245:
215:
189:power flux density
177:
4476:978-81-8431-176-1
4268:
4225:impedance-matched
4201:
4176:
4170:
4095:
4064:
3999:
3976:
3967:
3925:
3747:
3738:
3696:
3662:
3588:around frequency
3499:
3490:
3321:
3311:
3279:
3264:
3233:
3171:
3093:
3081:
3078:
3030:
2993:
2990:
2933:
2836:
2831:
2822:
2777:
2774:
2759:
2754:
2691:
2676:
2645:
2493:
2478:
2392:isotropic antenna
2374:
2361:
2340:{\displaystyle T}
2270:{\displaystyle a}
2206:{\displaystyle d}
2186:{\displaystyle d}
2158:
2129:
2100:
2071:
2036:
2010:
2000:
1985:
1982:
1972:
1896:
1882:
1861:
1858:
1848:
1781:
1755:
1720:
1717:
1707:
1693:
1690:
1680:
1653:isotropic antenna
1638:
1611:
1584:{\displaystyle G}
1561:Aperture and gain
1544:
1495:
1482:
1445:
1442:
1417:
1387:
1357:
1293:
1266:
1242:aperture antennas
1214:
1183:
1073:
1045:
1015:
921:radiation pattern
850:
778:
749:
734:
708:
692:
664:{\displaystyle A}
638:
604:
589:
524:
510:of the antenna.
474:
447:
415:
393:
347:
317:
242:
209:
127:
126:
119:
101:
16:(Redirected from
4641:
4618:
4611:half-wave dipole
4607:
4591:
4590:
4588:
4586:
4566:
4560:
4559:
4539:
4533:
4532:
4522:
4516:
4515:
4487:
4481:
4480:
4460:
4454:
4453:
4451:
4450:
4423:
4417:
4416:
4396:
4390:
4389:
4382:
4349:
4347:
4346:
4341:
4327:
4321:
4316:
4296:
4294:
4293:
4288:
4270:
4269:
4266:
4233:matching network
4227:to the resistor
4215:
4213:
4212:
4207:
4202:
4200:
4192:
4191:
4182:
4177:
4172:
4171:
4168:
4162:
4109:
4107:
4106:
4101:
4096:
4094:
4085:
4080:
4071:
4066:
4065:
4062:
4048:
4046:
4045:
4040:
4035:
4034:
4021:
4020:
4001:
4000:
3997:
3988:
3987:
3978:
3977:
3974:
3968:
3965:
3960:
3951:
3947:
3946:
3927:
3926:
3923:
3909:
3887:
3885:
3884:
3879:
3874:
3873:
3861:
3860:
3823:
3821:
3820:
3815:
3813:
3812:
3803:
3792:
3791:
3772:
3770:
3769:
3764:
3759:
3758:
3749:
3748:
3745:
3739:
3736:
3731:
3722:
3718:
3717:
3698:
3697:
3694:
3680:
3675:
3674:
3664:
3663:
3660:
3645:
3644:
3614:
3613:
3563:
3561:
3560:
3555:
3527:
3526:
3501:
3500:
3497:
3491:
3486:
3476:
3475:
3453:
3450:
3449:
3436:
3431:
3419:
3418:
3384:
3382:
3381:
3376:
3352:
3350:
3349:
3344:
3323:
3322:
3319:
3312:
3310:
3309:
3300:
3299:
3298:
3285:
3280:
3278:
3271:
3270:
3266:
3265:
3262:
3256:
3236:
3234:
3232:
3231:
3222:
3221:
3220:
3204:
3190:
3189:
3172:
3169:
3142:
3140:
3139:
3134:
3129:
3128:
3115:
3114:
3095:
3094:
3091:
3082:
3080:
3079:
3076:
3070:
3069:
3068:
3055:
3054:
3032:
3031:
3028:
3018:
3004:
3002:
3001:
2996:
2994:
2992:
2991:
2988:
2982:
2965:
2964:
2935:
2934:
2931:
2921:
2916:
2906:
2901:
2900:
2853:
2851:
2850:
2845:
2842:
2837:
2834:
2832:
2829:
2823:
2817:
2812:
2803:
2791:
2789:
2788:
2783:
2778:
2776:
2775:
2772:
2765:
2760:
2757:
2755:
2752:
2749:
2705:
2703:
2702:
2697:
2692:
2690:
2683:
2682:
2678:
2677:
2674:
2668:
2651:
2647:
2646:
2643:
2637:
2625:
2598:
2596:
2595:
2590:
2559:
2557:
2556:
2551:
2527:
2525:
2524:
2519:
2495:
2494:
2491:
2479:
2473:
2468:
2459:
2446:spectral density
2386:
2384:
2383:
2378:
2376:
2375:
2372:
2363:
2362:
2359:
2346:
2344:
2343:
2338:
2298:
2296:
2295:
2290:
2276:
2274:
2273:
2268:
2256:
2254:
2253:
2248:
2243:
2238:
2237:
2212:
2210:
2209:
2204:
2192:
2190:
2189:
2184:
2170:
2168:
2167:
2162:
2160:
2159:
2156:
2141:
2139:
2138:
2133:
2131:
2130:
2127:
2112:
2110:
2109:
2104:
2102:
2101:
2098:
2083:
2081:
2080:
2075:
2073:
2072:
2069:
2050:
2048:
2047:
2042:
2037:
2035:
2034:
2033:
2024:
2023:
2013:
2012:
2011:
2008:
2002:
2001:
1998:
1991:
1986:
1984:
1983:
1980:
1974:
1973:
1970:
1964:
1910:
1908:
1907:
1902:
1897:
1895:
1894:
1885:
1884:
1883:
1880:
1867:
1862:
1860:
1859:
1856:
1850:
1849:
1846:
1840:
1818:
1816:
1815:
1810:
1795:
1793:
1792:
1787:
1782:
1780:
1772:
1771:
1762:
1757:
1756:
1753:
1734:
1732:
1731:
1726:
1721:
1719:
1718:
1715:
1709:
1708:
1705:
1699:
1694:
1692:
1691:
1688:
1682:
1681:
1678:
1672:
1650:
1648:
1647:
1642:
1640:
1639:
1636:
1623:
1621:
1620:
1615:
1613:
1612:
1609:
1590:
1588:
1587:
1582:
1556:
1554:
1553:
1548:
1546:
1545:
1542:
1507:
1505:
1504:
1499:
1497:
1496:
1493:
1484:
1483:
1480:
1459:
1457:
1456:
1451:
1446:
1444:
1443:
1440:
1434:
1433:
1424:
1419:
1418:
1415:
1399:
1397:
1396:
1391:
1389:
1388:
1385:
1369:
1367:
1366:
1361:
1359:
1358:
1355:
1342:
1340:
1339:
1334:
1332:
1331:
1308:
1306:
1305:
1300:
1295:
1294:
1291:
1278:
1276:
1275:
1270:
1268:
1267:
1264:
1246:parabolic dishes
1226:
1224:
1223:
1218:
1216:
1215:
1212:
1195:
1193:
1192:
1187:
1185:
1184:
1181:
1151:is the electric
1150:
1148:
1147:
1142:
1140:
1139:
1121:
1119:
1118:
1113:
1111:
1110:
1088:
1086:
1085:
1080:
1075:
1074:
1071:
1065:
1060:
1059:
1047:
1046:
1043:
1027:
1025:
1024:
1019:
1017:
1016:
1013:
1000:effective length
993:Effective height
981:Effective length
976:
974:
973:
968:
966:
965:
949:
947:
946:
941:
939:
938:
907:
905:
904:
899:
852:
851:
848:
829:
827:
826:
821:
780:
779:
771:
756:
751:
750:
742:
736:
735:
727:
724:
710:
709:
706:
694:
693:
690:
670:
668:
667:
662:
650:
648:
647:
642:
640:
639:
631:
621:
619:
618:
613:
611:
606:
605:
597:
591:
590:
582:
579:
571:
548:
536:
534:
533:
528:
526:
525:
522:
509:
507:
506:
501:
486:
484:
483:
478:
476:
475:
472:
459:
457:
456:
451:
449:
448:
445:
429:
427:
426:
421:
416:
414:
395:
394:
386:
379:
378:
369:
349:
348:
345:
329:
327:
326:
321:
319:
318:
315:
302:
300:
299:
294:
292:
269:
254:
252:
251:
246:
244:
243:
240:
224:
222:
221:
216:
211:
210:
202:
186:
184:
183:
178:
131:electromagnetics
122:
115:
111:
108:
102:
100:
59:
35:
27:
21:
4649:
4648:
4644:
4643:
4642:
4640:
4639:
4638:
4624:
4623:
4622:
4621:
4608:
4604:
4599:
4594:
4584:
4582:
4567:
4563:
4556:
4540:
4536:
4528:Radio Astronomy
4523:
4519:
4488:
4484:
4477:
4461:
4457:
4448:
4446:
4424:
4420:
4413:
4397:
4393:
4384:
4383:
4372:
4368:
4356:
4323:
4317:
4312:
4306:
4303:
4302:
4265:
4261:
4259:
4256:
4255:
4252:
4245:
4217:
4193:
4187:
4183:
4181:
4167:
4163:
4161:
4159:
4156:
4155:
4150:
4139:
4120:
4087:
4081:
4076:
4070:
4061:
4057:
4055:
4052:
4051:
4030:
4026:
4016:
4012:
3996:
3992:
3983:
3979:
3973:
3969:
3961:
3956:
3942:
3938:
3922:
3918:
3910:
3908:
3906:
3903:
3902:
3897:
3869:
3865:
3856:
3852:
3850:
3847:
3846:
3830:
3808:
3804:
3799:
3787:
3783:
3781:
3778:
3777:
3754:
3750:
3744:
3740:
3732:
3727:
3713:
3709:
3693:
3689:
3681:
3679:
3670:
3666:
3659:
3655:
3628:
3624:
3609:
3605:
3603:
3600:
3599:
3594:
3587:
3579:
3573:
3522:
3518:
3496:
3492:
3459:
3455:
3454:
3452:
3442:
3438:
3432:
3427:
3414:
3410:
3408:
3405:
3404:
3395:
3385:defined above.
3361:
3358:
3357:
3318:
3314:
3305:
3301:
3294:
3290:
3286:
3284:
3261:
3257:
3252:
3245:
3241:
3240:
3235:
3227:
3223:
3216:
3212:
3205:
3203:
3173:
3168:
3167:
3165:
3162:
3161:
3124:
3120:
3110:
3106:
3090:
3086:
3075:
3071:
3064:
3060:
3050:
3046:
3027:
3023:
3019:
3017:
3011:
3008:
3007:
2987:
2983:
2960:
2956:
2930:
2926:
2917:
2912:
2907:
2905:
2896:
2892:
2890:
2887:
2886:
2881:
2874:
2866:
2859:
2838:
2833:
2828:
2813:
2808:
2802:
2800:
2797:
2796:
2771:
2767:
2761:
2756:
2751:
2748:
2740:
2737:
2736:
2731:
2673:
2669:
2664:
2657:
2653:
2652:
2642:
2638:
2633:
2626:
2624:
2607:
2604:
2603:
2569:
2566:
2565:
2536:
2533:
2532:
2490:
2486:
2469:
2464:
2458:
2456:
2453:
2452:
2427:
2410:at temperature
2371:
2367:
2358:
2354:
2352:
2349:
2348:
2332:
2329:
2328:
2325:
2306:
2284:
2281:
2280:
2262:
2259:
2258:
2239:
2233:
2229:
2218:
2215:
2214:
2198:
2195:
2194:
2178:
2175:
2174:
2155:
2151:
2149:
2146:
2145:
2126:
2122:
2120:
2117:
2116:
2097:
2093:
2091:
2088:
2087:
2068:
2064:
2062:
2059:
2058:
2029:
2025:
2019:
2015:
2014:
2007:
2003:
1997:
1993:
1992:
1990:
1979:
1975:
1969:
1965:
1963:
1961:
1958:
1957:
1946:
1940:
1890:
1886:
1879:
1875:
1868:
1866:
1855:
1851:
1845:
1841:
1839:
1831:
1828:
1827:
1804:
1801:
1800:
1773:
1767:
1763:
1761:
1752:
1748:
1746:
1743:
1742:
1714:
1710:
1704:
1700:
1698:
1687:
1683:
1677:
1673:
1671:
1663:
1660:
1659:
1635:
1631:
1629:
1626:
1625:
1608:
1604:
1602:
1599:
1598:
1576:
1573:
1572:
1563:
1541:
1537:
1535:
1532:
1531:
1492:
1488:
1479:
1475:
1473:
1470:
1469:
1439:
1435:
1429:
1425:
1423:
1414:
1410:
1408:
1405:
1404:
1384:
1380:
1378:
1375:
1374:
1354:
1350:
1348:
1345:
1344:
1327:
1323:
1321:
1318:
1317:
1290:
1286:
1284:
1281:
1280:
1263:
1259:
1257:
1254:
1253:
1238:
1211:
1207:
1205:
1202:
1201:
1180:
1176:
1174:
1171:
1170:
1135:
1131:
1129:
1126:
1125:
1106:
1102:
1100:
1097:
1096:
1070:
1066:
1061:
1055:
1051:
1042:
1038:
1036:
1033:
1032:
1012:
1008:
1006:
1003:
1002:
995:
989:
983:
961:
957:
955:
952:
951:
934:
930:
928:
925:
924:
847:
843:
841:
838:
837:
770:
769:
752:
741:
740:
726:
725:
720:
705:
701:
689:
685:
683:
680:
679:
656:
653:
652:
630:
629:
627:
624:
623:
607:
596:
595:
581:
580:
575:
567:
544:
542:
539:
538:
521:
517:
515:
512:
511:
495:
492:
491:
471:
467:
465:
462:
461:
444:
440:
438:
435:
434:
385:
384:
380:
374:
370:
368:
344:
340:
338:
335:
334:
314:
310:
308:
305:
304:
288:
265:
263:
260:
259:
239:
235:
233:
230:
229:
201:
200:
195:
192:
191:
160:
157:
156:
148:
123:
112:
106:
103:
60:
58:
48:
36:
23:
22:
15:
12:
11:
5:
4647:
4637:
4636:
4620:
4619:
4601:
4600:
4598:
4595:
4593:
4592:
4561:
4555:978-3662053942
4554:
4534:
4517:
4498:(5): 254–256.
4482:
4475:
4455:
4418:
4411:
4391:
4369:
4367:
4364:
4363:
4362:
4355:
4352:
4339:
4336:
4333:
4330:
4326:
4320:
4315:
4311:
4286:
4283:
4280:
4277:
4273:
4264:
4250:
4243:
4205:
4199:
4196:
4190:
4186:
4180:
4175:
4166:
4153:
4148:
4137:
4118:
4111:
4110:
4099:
4093:
4090:
4084:
4079:
4075:
4069:
4060:
4049:
4038:
4033:
4029:
4024:
4019:
4015:
4011:
4008:
4004:
3995:
3991:
3986:
3982:
3972:
3964:
3959:
3955:
3950:
3945:
3941:
3937:
3934:
3930:
3921:
3916:
3913:
3895:
3889:
3888:
3877:
3872:
3868:
3864:
3859:
3855:
3828:
3811:
3807:
3802:
3798:
3795:
3790:
3786:
3774:
3773:
3762:
3757:
3753:
3743:
3735:
3730:
3726:
3721:
3716:
3712:
3708:
3705:
3701:
3692:
3687:
3684:
3678:
3673:
3669:
3658:
3654:
3651:
3648:
3643:
3640:
3637:
3634:
3631:
3627:
3623:
3620:
3617:
3612:
3608:
3592:
3585:
3577:
3571:
3565:
3564:
3553:
3550:
3547:
3543:
3540:
3536:
3533:
3530:
3525:
3521:
3516:
3513:
3510:
3507:
3504:
3495:
3489:
3485:
3482:
3479:
3474:
3471:
3468:
3465:
3462:
3458:
3448:
3445:
3441:
3435:
3430:
3426:
3422:
3417:
3413:
3393:
3374:
3371:
3368:
3365:
3354:
3353:
3342:
3339:
3336:
3333:
3330:
3326:
3317:
3308:
3304:
3297:
3293:
3289:
3283:
3277:
3274:
3269:
3260:
3255:
3251:
3248:
3244:
3239:
3230:
3226:
3219:
3215:
3211:
3208:
3202:
3199:
3196:
3193:
3188:
3185:
3182:
3179:
3176:
3144:
3143:
3132:
3127:
3123:
3118:
3113:
3109:
3105:
3102:
3098:
3089:
3085:
3074:
3067:
3063:
3058:
3053:
3049:
3045:
3042:
3038:
3035:
3026:
3022:
3016:
3005:
2986:
2981:
2978:
2974:
2971:
2968:
2963:
2959:
2954:
2951:
2948:
2945:
2941:
2938:
2929:
2925:
2920:
2915:
2911:
2904:
2899:
2895:
2879:
2872:
2864:
2857:
2841:
2826:
2821:
2816:
2811:
2807:
2793:
2792:
2781:
2770:
2764:
2747:
2744:
2729:
2707:
2706:
2695:
2689:
2686:
2681:
2672:
2667:
2663:
2660:
2656:
2650:
2641:
2636:
2632:
2629:
2623:
2620:
2617:
2614:
2611:
2588:
2585:
2582:
2579:
2576:
2573:
2549:
2546:
2543:
2540:
2529:
2528:
2517:
2514:
2511:
2508:
2505:
2501:
2498:
2489:
2485:
2482:
2477:
2472:
2467:
2463:
2425:
2370:
2366:
2357:
2336:
2323:
2305:
2302:
2301:
2300:
2288:
2278:
2266:
2246:
2242:
2236:
2232:
2228:
2225:
2222:
2202:
2182:
2172:
2154:
2143:
2125:
2114:
2096:
2085:
2067:
2052:
2051:
2040:
2032:
2028:
2022:
2018:
2006:
1996:
1989:
1978:
1968:
1942:Main article:
1939:
1936:
1912:
1911:
1900:
1893:
1889:
1878:
1874:
1871:
1865:
1854:
1844:
1838:
1835:
1808:
1797:
1796:
1785:
1779:
1776:
1770:
1766:
1760:
1751:
1736:
1735:
1724:
1713:
1703:
1697:
1686:
1676:
1670:
1667:
1634:
1607:
1580:
1562:
1559:
1540:
1491:
1487:
1478:
1461:
1460:
1449:
1438:
1432:
1428:
1422:
1413:
1383:
1353:
1330:
1326:
1298:
1289:
1262:
1237:
1234:
1210:
1179:
1161:
1160:
1153:field strength
1138:
1134:
1123:
1109:
1105:
1090:
1089:
1078:
1069:
1064:
1058:
1054:
1050:
1041:
1011:
987:Antenna factor
985:Main article:
982:
979:
964:
960:
937:
933:
909:
908:
897:
894:
891:
888:
885:
882:
879:
876:
873:
870:
867:
864:
861:
858:
855:
846:
831:
830:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
777:
774:
768:
765:
762:
759:
755:
748:
745:
739:
733:
730:
723:
719:
716:
713:
704:
700:
697:
688:
660:
637:
634:
610:
603:
600:
594:
588:
585:
578:
574:
570:
566:
563:
560:
557:
554:
551:
547:
520:
499:
470:
443:
431:
430:
419:
413:
410:
407:
404:
401:
398:
392:
389:
383:
377:
373:
367:
364:
361:
358:
355:
352:
343:
313:
291:
287:
284:
281:
278:
275:
272:
268:
238:
214:
208:
205:
199:
176:
173:
170:
167:
164:
152:effective area
147:
146:Effective area
144:
125:
124:
39:
37:
30:
18:Effective area
9:
6:
4:
3:
2:
4646:
4635:
4632:
4631:
4629:
4616:
4612:
4606:
4602:
4580:
4576:
4572:
4565:
4557:
4551:
4547:
4546:
4538:
4530:
4529:
4521:
4513:
4509:
4505:
4501:
4497:
4493:
4486:
4478:
4472:
4468:
4467:
4459:
4445:
4441:
4437:
4433:
4429:
4422:
4414:
4412:0-906048-82-6
4408:
4404:
4403:
4395:
4387:
4381:
4379:
4377:
4375:
4370:
4361:
4358:
4357:
4351:
4334:
4331:
4324:
4318:
4313:
4309:
4300:
4281:
4275:
4271:
4262:
4249:
4242:
4239:, the powers
4238:
4234:
4230:
4226:
4222:
4216:
4203:
4197:
4194:
4188:
4184:
4178:
4164:
4152:
4147:
4143:
4136:
4132:
4128:
4124:
4117:
4097:
4091:
4088:
4082:
4077:
4073:
4067:
4058:
4050:
4036:
4031:
4027:
4017:
4013:
4006:
4002:
3993:
3989:
3984:
3980:
3970:
3962:
3957:
3953:
3943:
3939:
3932:
3928:
3919:
3914:
3911:
3901:
3900:
3899:
3894:
3875:
3870:
3866:
3862:
3857:
3853:
3845:
3844:
3843:
3841:
3837:
3832:
3827:
3809:
3805:
3800:
3796:
3793:
3788:
3784:
3760:
3755:
3751:
3741:
3733:
3728:
3724:
3714:
3710:
3703:
3699:
3690:
3685:
3682:
3676:
3671:
3667:
3656:
3649:
3638:
3635:
3632:
3629:
3625:
3621:
3618:
3615:
3610:
3606:
3598:
3597:
3596:
3591:
3584:
3580:
3570:
3551:
3548:
3545:
3538:
3531:
3523:
3519:
3511:
3508:
3493:
3487:
3480:
3469:
3466:
3463:
3460:
3456:
3446:
3443:
3439:
3428:
3424:
3420:
3415:
3411:
3403:
3402:
3401:
3399:
3392:
3386:
3369:
3363:
3340:
3334:
3328:
3324:
3315:
3306:
3302:
3295:
3291:
3287:
3281:
3275:
3272:
3267:
3258:
3253:
3249:
3246:
3242:
3237:
3228:
3224:
3217:
3213:
3209:
3206:
3200:
3194:
3183:
3180:
3177:
3174:
3160:
3159:
3158:
3156:
3152:
3147:
3130:
3125:
3121:
3111:
3107:
3100:
3096:
3087:
3083:
3072:
3065:
3061:
3051:
3047:
3040:
3036:
3033:
3024:
3020:
3014:
3006:
2984:
2979:
2976:
2969:
2961:
2957:
2949:
2943:
2939:
2936:
2927:
2923:
2913:
2909:
2902:
2897:
2893:
2885:
2884:
2883:
2878:
2871:
2867:
2860:
2839:
2824:
2814:
2809:
2805:
2779:
2768:
2762:
2745:
2742:
2735:
2734:
2733:
2728:
2724:
2720:
2716:
2712:
2693:
2687:
2684:
2679:
2670:
2665:
2661:
2658:
2654:
2648:
2639:
2634:
2630:
2627:
2621:
2615:
2609:
2602:
2601:
2600:
2586:
2583:
2577:
2571:
2563:
2544:
2538:
2515:
2509:
2503:
2499:
2496:
2487:
2483:
2480:
2470:
2465:
2461:
2451:
2450:
2449:
2447:
2443:
2439:
2435:
2430:
2428:
2421:
2417:
2413:
2409:
2405:
2401:
2397:
2393:
2368:
2364:
2355:
2334:
2326:
2319:
2316:and resistor
2315:
2310:
2286:
2279:
2264:
2244:
2240:
2234:
2230:
2226:
2223:
2220:
2200:
2180:
2173:
2152:
2144:
2123:
2115:
2094:
2086:
2065:
2057:
2056:
2055:
2038:
2030:
2026:
2020:
2016:
2004:
1994:
1987:
1976:
1966:
1956:
1955:
1954:
1952:
1945:
1935:
1933:
1929:
1925:
1921:
1920:beam antennas
1917:
1898:
1891:
1887:
1876:
1872:
1869:
1863:
1852:
1842:
1836:
1833:
1826:
1825:
1824:
1822:
1806:
1783:
1777:
1774:
1768:
1764:
1758:
1749:
1741:
1740:
1739:
1722:
1711:
1701:
1695:
1684:
1674:
1668:
1665:
1658:
1657:
1656:
1654:
1632:
1605:
1596:
1595:
1578:
1570:
1569:
1558:
1538:
1529:
1525:
1524:
1518:
1515:
1511:
1489:
1485:
1476:
1466:
1447:
1436:
1430:
1426:
1420:
1411:
1403:
1402:
1401:
1381:
1373:
1351:
1328:
1324:
1316:
1312:
1296:
1287:
1260:
1251:
1250:horn antennas
1247:
1243:
1233:
1230:
1208:
1199:
1177:
1167:
1158:
1154:
1136:
1132:
1124:
1107:
1103:
1095:
1094:
1093:
1076:
1067:
1062:
1056:
1052:
1048:
1039:
1031:
1030:
1029:
1009:
1001:
994:
988:
978:
962:
958:
935:
931:
922:
918:
914:
895:
892:
889:
886:
883:
880:
877:
874:
871:
868:
862:
859:
856:
844:
836:
835:
834:
817:
814:
811:
808:
805:
802:
799:
790:
787:
784:
772:
763:
760:
757:
743:
737:
728:
717:
714:
711:
702:
698:
695:
686:
678:
677:
676:
674:
658:
632:
598:
592:
583:
572:
561:
558:
555:
549:
518:
497:
490:
468:
441:
417:
405:
402:
399:
387:
375:
371:
365:
359:
356:
353:
341:
333:
332:
331:
311:
282:
279:
276:
270:
257:
236:
226:
203:
190:
171:
168:
165:
153:
143:
140:
136:
132:
121:
118:
110:
107:December 2009
99:
96:
92:
89:
85:
82:
78:
75:
71:
68: –
67:
63:
62:Find sources:
56:
52:
46:
45:
40:This article
38:
34:
29:
28:
19:
4605:
4583:. Retrieved
4579:the original
4574:
4564:
4544:
4537:
4527:
4520:
4495:
4491:
4485:
4465:
4458:
4447:. Retrieved
4435:
4431:
4421:
4401:
4394:
4385:
4247:
4240:
4228:
4220:
4218:
4154:
4145:
4141:
4134:
4130:
4126:
4122:
4115:
4112:
3892:
3890:
3833:
3825:
3775:
3589:
3582:
3575:
3568:
3566:
3397:
3390:
3387:
3355:
3155:Planck's law
3150:
3148:
3145:
2876:
2869:
2862:
2855:
2794:
2732:is given by
2726:
2718:
2715:matched load
2710:
2708:
2561:
2530:
2448:is given by
2437:
2431:
2423:
2419:
2415:
2411:
2403:
2395:
2389:
2321:
2317:
2313:
2053:
1947:
1919:
1913:
1798:
1737:
1594:antenna gain
1592:
1566:
1564:
1521:
1519:
1513:
1464:
1462:
1371:
1314:
1241:
1239:
1228:
1197:
1165:
1162:
1091:
999:
996:
912:
910:
832:
673:polarization
432:
227:
188:
151:
149:
138:
137:theory, the
128:
113:
104:
94:
87:
80:
73:
61:
49:Please help
44:verification
41:
1924:beam widths
1568:directivity
1229:square root
917:reciprocity
4449:2024-06-24
4366:References
1821:wavelength
991:See also:
433:The power
77:newspapers
4585:22 August
4335:π
4310:λ
4276:η
4198:π
4185:λ
4174:¯
4092:π
4074:λ
4007:η
3954:λ
3933:η
3915:π
3785:λ
3725:λ
3704:η
3686:π
3642:Ω
3622:π
3542:Ω
3524:ν
3506:Ω
3473:Ω
3447:π
3440:∫
3434:∞
3425:∫
3364:η
3329:η
3273:−
3187:Ω
3101:η
3041:η
2962:ν
2944:η
2919:∞
2910:∫
2820:¯
2685:−
2610:η
2572:η
2539:η
2504:η
2476:¯
2287:λ
2245:λ
2224:≳
2027:λ
1932:boresight
1928:main lobe
1888:λ
1873:π
1807:λ
1778:π
1765:λ
913:receiving
893:ϕ
890:
884:θ
881:
872:η
863:ϕ
857:θ
815:ϕ
812:
806:θ
803:
797:‖
791:ϕ
785:θ
776:→
767:‖
761:η
747:^
738:⋅
732:→
715:η
699:η
636:^
602:^
593:⋅
587:→
562:ϕ
556:θ
498:η
412:‖
406:ϕ
400:θ
391:→
382:‖
360:ϕ
354:θ
283:ϕ
277:θ
213:‖
207:→
198:‖
172:ϕ
166:θ
4634:Antennas
4628:Category
4615:decibels
4512:51630329
4492:IRE Proc
4354:See also
4237:lossless
2257:, where
1514:physical
1311:absorbed
1244:such as
622:, where
139:aperture
4388:. IEEE.
4142:average
2713:into a
2398:with a
1949:of the
1819:is the
1591:called
135:antenna
91:scholar
4552:
4510:
4473:
4409:
3776:where
2531:where
2054:where
1799:where
1528:losses
1198:square
1092:where
93:
86:
79:
72:
64:
4597:Notes
4508:S2CID
1157:volts
256:watts
98:JSTOR
84:books
4587:2018
4550:ISBN
4471:ISBN
4407:ISBN
4246:and
1918:(or
1565:The
1510:feed
1494:phys
1463:The
1441:phys
1356:phys
1292:phys
1265:phys
1248:and
833:and
150:The
133:and
70:news
4500:doi
4440:doi
4169:eff
4149:eff
4138:eff
4131:not
4119:eff
4063:eff
3975:eff
3896:eff
3746:eff
3661:eff
3572:eff
3498:eff
3394:eff
2835:rms
2758:rms
2730:rms
2723:rms
2402:of
1934:).
1930:or
1857:iso
1754:iso
1716:iso
1689:iso
1637:iso
1213:eff
1200:of
1182:eff
1044:eff
1014:eff
887:cos
878:cos
809:cos
800:cos
129:In
53:by
4630::
4573:.
4506:.
4496:34
4494:.
4436:53
4434:.
4430:.
4373:^
4350:.
3831:.
3400::
3157::
2347:,
1953::
1166:is
4589:.
4558:.
4514:.
4502::
4479:.
4452:.
4442::
4415:.
4338:)
4332:4
4329:(
4325:/
4319:2
4314:1
4285:)
4282:f
4279:(
4272:T
4267:B
4263:k
4251:R
4248:P
4244:A
4241:P
4229:R
4221:R
4204:.
4195:4
4189:2
4179:=
4165:A
4146:A
4135:A
4127:f
4125:/
4123:c
4116:A
4098:.
4089:4
4083:2
4078:1
4068:=
4059:A
4037:,
4032:1
4028:B
4023:)
4018:1
4014:f
4010:(
4003:T
3998:B
3994:k
3990:=
3985:1
3981:B
3971:A
3963:2
3958:1
3949:)
3944:1
3940:f
3936:(
3929:T
3924:B
3920:k
3912:4
3893:A
3876:.
3871:R
3867:P
3863:=
3858:A
3854:P
3829:1
3826:f
3810:1
3806:f
3801:/
3797:c
3794:=
3789:1
3761:,
3756:1
3752:B
3742:A
3734:2
3729:1
3720:)
3715:1
3711:f
3707:(
3700:T
3695:B
3691:k
3683:4
3677:=
3672:1
3668:B
3657:A
3653:)
3650:f
3647:(
3639:,
3636:A
3633:,
3630:f
3626:P
3619:2
3616:=
3611:A
3607:P
3593:1
3590:f
3586:1
3583:B
3578:ν
3576:F
3569:A
3552:.
3549:f
3546:d
3539:d
3535:)
3532:f
3529:(
3520:F
3515:)
3512:f
3509:,
3503:(
3494:A
3488:2
3484:)
3481:f
3478:(
3470:,
3467:A
3464:,
3461:f
3457:P
3444:4
3429:0
3421:=
3416:A
3412:P
3398:f
3391:A
3373:)
3370:f
3367:(
3341:,
3338:)
3335:f
3332:(
3325:T
3320:B
3316:k
3307:2
3303:c
3296:2
3292:f
3288:2
3282:=
3276:1
3268:T
3263:B
3259:k
3254:/
3250:f
3247:h
3243:e
3238:1
3229:2
3225:c
3218:3
3214:f
3210:h
3207:2
3201:=
3198:)
3195:f
3192:(
3184:,
3181:A
3178:,
3175:f
3170:P
3151:T
3131:.
3126:1
3122:B
3117:)
3112:1
3108:f
3104:(
3097:T
3092:B
3088:k
3084:=
3077:R
3073:4
3066:1
3062:B
3057:)
3052:1
3048:f
3044:(
3037:R
3034:T
3029:B
3025:k
3021:4
3015:=
2989:R
2985:4
2980:f
2977:d
2973:)
2970:f
2967:(
2958:F
2953:)
2950:f
2947:(
2940:R
2937:T
2932:B
2928:k
2924:4
2914:0
2903:=
2898:R
2894:P
2880:1
2877:f
2873:1
2870:B
2865:ν
2863:F
2858:ν
2856:F
2840:2
2830:v
2825:=
2815:2
2810:n
2806:v
2780:.
2773:R
2769:4
2763:2
2753:v
2746:=
2743:P
2727:v
2719:R
2711:R
2694:.
2688:1
2680:T
2675:B
2671:k
2666:/
2662:f
2659:h
2655:e
2649:T
2644:B
2640:k
2635:/
2631:f
2628:h
2622:=
2619:)
2616:f
2613:(
2587:1
2584:=
2581:)
2578:f
2575:(
2562:f
2548:)
2545:f
2542:(
2516:,
2513:)
2510:f
2507:(
2500:R
2497:T
2492:B
2488:k
2484:4
2481:=
2471:2
2466:n
2462:v
2438:T
2426:ν
2424:F
2420:T
2416:R
2412:T
2404:R
2396:A
2373:R
2369:P
2365:=
2360:A
2356:P
2335:T
2324:ν
2322:F
2318:R
2314:A
2265:a
2241:/
2235:2
2231:a
2227:2
2221:d
2201:d
2181:d
2157:t
2153:A
2128:r
2124:A
2099:r
2095:P
2070:t
2066:P
2039:,
2031:2
2021:2
2017:d
2009:t
2005:A
1999:r
1995:A
1988:=
1981:t
1977:P
1971:r
1967:P
1899:.
1892:2
1881:e
1877:A
1870:4
1864:=
1853:A
1847:e
1843:A
1837:=
1834:G
1784:,
1775:4
1769:2
1759:=
1750:A
1723:.
1712:A
1706:e
1702:A
1696:=
1685:P
1679:o
1675:P
1669:=
1666:G
1633:P
1610:o
1606:P
1579:G
1543:e
1539:A
1490:A
1486:=
1481:e
1477:A
1448:.
1437:A
1431:e
1427:A
1421:=
1416:a
1412:e
1386:a
1382:e
1352:A
1329:e
1325:A
1297:S
1288:A
1261:A
1209:l
1178:A
1137:s
1133:E
1108:0
1104:V
1077:,
1072:s
1068:E
1063:/
1057:0
1053:V
1049:=
1040:l
1010:l
963:e
959:A
936:e
932:A
896:.
875:A
869:=
866:)
860:,
854:(
849:e
845:A
818:,
794:)
788:,
782:(
773:S
764:A
758:=
754:|
744:a
729:S
722:|
718:A
712:=
707:R
703:P
696:=
691:O
687:P
659:A
633:a
609:|
599:a
584:S
577:|
573:=
569:|
565:)
559:,
553:(
550:S
546:|
523:R
519:P
473:R
469:P
446:O
442:P
418:.
409:)
403:,
397:(
388:S
376:O
372:P
366:=
363:)
357:,
351:(
346:e
342:A
316:e
312:A
290:|
286:)
280:,
274:(
271:S
267:|
241:O
237:P
204:S
175:)
169:,
163:(
120:)
114:(
109:)
105:(
95:·
88:·
81:·
74:·
47:.
20:)
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