Radiation_pattern - Wikiparency

# Radiation pattern A **radiation pattern**, also called an antenna pattern, describes how strongly an antenna sends or receives radio waves as a function of direction, plotted as the field strength, the power, or the phase measured at a fixed large distance from the antenna as that direction sweeps around it. Close to the antenna, in what is called the near field, the pattern's shape still depends on distance as well as direction; far enough away, in the far field this article is chiefly about, the shape stops changing with distance and becomes a fixed function of angle alone, usually shown as a polar plot with the antenna at the centre. The same function describes an antenna whether it is transmitting or receiving: a reciprocity property of Maxwell's equations, proved below, guarantees that an [[Antenna_(radio)|antenna]]'s transmitting pattern and its receiving pattern are identical, so a pattern measured the easier way, often by receiving a known signal rather than by transmitting one, describes both directions of use without further assumption. A sharply peaked pattern concentrates power, or receiving sensitivity, into a narrow range of directions, which is exactly the property the sibling article on [[Directivity|directivity]] turns into a single number. Elsewhere on this page, a three.js companion sketch renders an antenna's pattern as cuts through two perpendicular planes, conventionally called the E-plane and the H-plane, the same pair of slices an antenna datasheet almost always plots instead of the full three-dimensional surface; the sketches carried by the neighbouring [[Radar]], [[Doppler_effect]] and [[Sonar]] articles show, in their own systems, what a real antenna or transducer's directional sensitivity does to a moving or distant target's signal. ## Reciprocity Reciprocity is the statement that an [[Antenna_(radio)|antenna]]'s transmitting pattern and its receiving pattern, over the same frequency and polarization, are exactly the same function of direction. Physically, this follows from a general property of linear, passive electromagnetic systems: the antenna itself does not know, and does not need to know, which direction power is flowing when it launches or collects a wave, because the same currents and fields that a transmitted wave sets up on the antenna's conductors are exactly the currents and fields that an incoming wave from the same direction would induce there. The term borrows its name from the reciprocity theorems of general linear circuit and field theory, the same family of results that also gives the reciprocal relationship between a two-port network's forward and reverse transfer functions in ordinary [[Electronics|circuit theory]]. The practical consequence, exploited constantly in antenna measurement, is that a pattern can be measured in whichever direction is more convenient: a large or expensive antenna, such as a satellite dish or a broadcast tower array, is far easier to characterize by receiving a known signal from a rotating source than by transmitting from itself and measuring the received field at every angle around it, yet the resulting pattern describes the antenna equally well as a transmitter. Reciprocity holds for the antenna alone; it says nothing about the rest of a communication link, where a transmitter's power amplifier and a receiver's low-noise amplifier are entirely different, non-reciprocal devices, so a reciprocal antenna pattern does not imply a reciprocal overall [[Link_budget|link budget]]. ## Typical patterns An isotropic radiator, a hypothetical antenna radiating exactly the same power in every direction, has no pattern to speak of at all: on a polar plot it is simply a circle, and every real antenna's directivity, covered in the companion article, is defined relative to this unreachable reference. An omnidirectional pattern is the practical case closest to it: a simple [[Dipole_antenna|dipole]] or [[Monopole_antenna|monopole]] radiates equally in every direction around its own axis, so its pattern is a circle in the plane perpendicular to the antenna, but it is not isotropic, since the pattern pinches toward zero along the antenna's own axis, where a doughnut-shaped three-dimensional pattern narrows to a point. A directional, or pencil-beam, pattern instead concentrates most of the radiated power into one comparatively narrow main lobe, with much weaker side lobes at other angles and, often, a small back lobe directly opposite the main one; a parabolic dish, a [[Yagi–Uda_antenna|Yagi–Uda antenna]], or an electronically steered [[Antenna_array|antenna array]] using [[Beamforming|beamforming]] are all designed chiefly to trade an omnidirectional or broad pattern for a narrow one. The angular width of the main lobe between the two points where the radiated power falls to half its peak value, the half-power beamwidth, is the single number most often quoted to describe how narrow a directional pattern is, and it shrinks as an antenna is made physically larger relative to a wavelength, the same trade this article's sibling on directivity expresses as a single ratio rather than as an angle. Nulls, the angles at which the pattern drops to a deep minimum rather than merely a weak one, matter in their own right: a null steered deliberately toward a source of interference can reject it far more effectively than the sidelobe level elsewhere in the pattern would suggest is possible. Patterns are commonly plotted in [[Decibel|decibels]] relative to the peak, which compresses the enormous dynamic range between a strong main lobe and a sidelobe or null many orders of magnitude weaker into a chart that remains readable, and a full three-dimensional surface is more often reduced to the two orthogonal planar cuts named above, since a complete solid pattern is harder to read at a glance than two flat curves. ## Proof of reciprocity The formal proof treats an antenna as a linear circuit element with one extra "port" opening onto free space instead of a second pair of wires, and applies the general reciprocity theorem that already governs any passive, linear circuit: if a current source at port A produces a voltage at port B, then the same current source moved to port B produces the identical voltage back at port A. Extending that theorem from a two-wire network to one port replaced by a radiated field requires the Lorentz reciprocity theorem of electromagnetics, which relates two independent solutions of [[Maxwell's_equations|Maxwell's equations]] sharing the same linear medium; applied to an antenna, it shows that the field the antenna radiates in a given direction, when driven by a unit current, equals the open-circuit voltage that antenna would develop at its terminals if a distant unit-amplitude plane wave arrived from that same direction. Because that equality holds at every direction independently, it holds for the whole pattern at once: the transmitting pattern, plotted as radiated field versus angle, and the receiving pattern, plotted as terminal response versus the angle of an incoming wave, are the same function. The proof requires only that the antenna and the medium around it be linear and made of ordinary, non-magnetized materials; an antenna containing a magnetized ferrite element, of the kind used in a one-way [[Microwave|microwave]] isolator, breaks the assumption and is a genuine exception to reciprocity, though such non-reciprocal antennas are rare enough that the reciprocal case above may fairly be called the general rule. ### Practical consequences One direct consequence is a measurement shortcut used throughout the antenna industry: because the transmitting and receiving patterns are identical, an antenna designed to transmit can be fully characterized in an anechoic chamber by receiving a known test signal from a scanned or rotated source, which is almost always easier to arrange precisely than transmitting from the antenna under test and moving a receiver, or many receivers, all the way around it. A second, quite different consequence appears in radio astronomy and in any [[Radio_receiver|receiver]] that must account for the noise the surrounding sky itself contributes. An antenna aimed at the sky collects thermal radiation from every direction its pattern is sensitive to, not only from the direction it is nominally pointed, and reciprocity is what justifies computing that collected noise, the antenna temperature, using the antenna's ordinary transmitting-mode directivity `D` as the receiving-mode weighting function: `T_A = (1/(4*pi)) * integral T_B * D dOmega`, integrating the sky's brightness temperature `T_B` over the whole sphere.[^ell-ta-formula] The brightness behind that integral spans an enormous range: the cosmic microwave background contributes a nearly uniform 2.7 kelvin, a quiet Sun can reach 1,000 to 1,000,000 kelvin depending on frequency, and the Moon and ordinary terrain sit at only a few hundred kelvin, so a pattern narrow enough to exclude the Sun, or wide enough to include it, changes the resulting antenna temperature by orders of magnitude.[^ell-brightness] Below a few hundred megahertz, galactic background noise adds still more, falling off with frequency roughly as `f^-2.55`, and near the ground, man-made noise from electrical equipment can exceed all of the above by a wide margin in a city compared with a quiet rural site at the same frequency.[^ell-galactic][^ell-manmade] None of this is [[Noise_(electronics)|noise]] the receiver's own electronics generate; it is noise the antenna's pattern collects from the world outside, and reciprocity is precisely why a pattern measured for transmission describes that collection accurately. ## Microsims This article carries no p5.js sketch of its own. A three.js companion elsewhere on this page instead renders an antenna's pattern as two perpendicular cuts, the E-plane and the H-plane, the same pair of slices an antenna datasheet almost always plots, so the omnidirectional, directional and lobed shapes described above can be compared cut by cut rather than only in words. *Try:* in the [[Radar]] sketch, press space to freeze the rotating beam and note that the simulated echo only ever appears while that narrow wedge points at the target — a receive-mode demonstration of the same pattern the antenna would radiate on transmit, exactly the reciprocity proved above. *Try:* in the [[Sonar]] sketch, find the "listening" label the same transducer carries right after it sends out a ping — a working example of reciprocity in hardware, since one physical element serves as both the transmitting and the receiving antenna for exactly the reason its transmit and receive patterns are identical. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Radiation_pattern) : [Wikitube](https://en.wikitube.io/wiki/Radiation_pattern) Skeleton mirrored at revision 1343410001. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Directivity]] - [[Antenna_(radio)]] - [[Yagi–Uda_antenna]] - [[Beamforming]] - [[Antenna_array]] - [[Radar]] ## References Standard antenna theory — the definitions of isotropic, omnidirectional and directional patterns, half-power beamwidth, and the reciprocity theorem's derivation from Maxwell's equations — is covered in essentially every antenna-engineering textbook and is not separately footnoted here, per the Wikitube style guide §6.1. Page numbers below are PDF pages of the open edition linked below. [^ell-ta-formula]: Ellingson, S. *Radio Systems Engineering*, Revised First Edition. 2023, p. 105 (PDF page). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell-brightness]: Ellingson, S. *Radio Systems Engineering*, Revised First Edition. 2023, pp. 104-105 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell-galactic]: Ellingson, S. *Radio Systems Engineering*, Revised First Edition. 2023, p. 105 (PDF page). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell-manmade]: Ellingson, S. *Radio Systems Engineering*, Revised First Edition. 2023, pp. 106-107 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. ## External links This article carries no sketch of its own yet. The three.js companion named in the lead is placed on the live page by the site's build process and will list its own link here once published.