En la ingeniería de radio , una antena o antena es la interfaz entre las ondas de radio que se propagan a través del espacio y las corrientes eléctricas que se mueven en conductores metálicos, que se utilizan con un transmisor o receptor . [1] En la transmisión , un transmisor de radio suministra una corriente eléctrica a los terminales de la antena y la antena irradia la energía de la corriente en forma de ondas electromagnéticas (ondas de radio). En recepción , una antena intercepta parte de la potencia de una onda de radio para producir una corriente eléctrica en sus terminales, que se aplica a un receptor para ser amplificada.. Las antenas son componentes esenciales de todos los equipos de radio .
Una antena es una matriz de conductores ( elementos ), conectados eléctricamente al receptor o transmisor. Las antenas pueden diseñarse para transmitir y recibir ondas de radio en todas las direcciones horizontales por igual ( antenas omnidireccionales ) o preferentemente en una dirección particular ( antenas direccionales , de alta ganancia o de “haz”). Una antena puede incluir componentes no conectados al transmisor, reflectores parabólicos , bocinas o elementos parásitos , que sirven para dirigir las ondas de radio hacia un haz u otro patrón de radiación deseado .
Las primeras antenas fueron construidas en 1888 por el físico alemán Heinrich Hertz en sus experimentos pioneros para demostrar la existencia de ondas predichas por la teoría electromagnética de James Clerk Maxwell . Hertz colocó antenas dipolo en el punto focal de los reflectores parabólicos tanto para transmitir como para recibir. [2] A partir de 1895, Guglielmo Marconi comenzó a desarrollar antenas prácticas para telegrafía inalámbrica de larga distancia, por lo que recibió un premio Nobel. [3]
Terminología
Las palabras antena y antena se utilizan indistintamente. Ocasionalmente, el término equivalente "antena" se utiliza para referirse específicamente a una antena de cable horizontal elevada. El origen de la palabra antena en relación con los aparatos inalámbricos se atribuye al pionero de la radio italiana Guglielmo Marconi . En el verano de 1895, Marconi comenzó a probar su sistema inalámbrico al aire libre en la finca de su padre cerca de Bolonia y pronto comenzó a experimentar con largas "antenas" de alambre suspendidas de un poste. [3] En italiano, un poste de tienda se conoce como l'antenna centrale , y el poste con el alambre se llama simplemente l'antenna . Hasta entonces, los elementos transmisores y receptores inalámbricos radiantes se conocían simplemente como "terminales". Debido a su prominencia, el uso de Marconi de la palabra antena se extendió entre los investigadores y entusiastas de la tecnología inalámbrica, y más tarde entre el público en general. [4] [5] [6]
Antena puede referirse en términos generales a un conjunto completo, incluida la estructura de soporte, el gabinete (si lo hubiera), etc., además de los componentes funcionales reales. Una antena receptora puede incluir no solo los elementos receptores metálicos pasivos, sino también un preamplificador o mezclador integrado , especialmente en y por encima de las frecuencias de microondas .
Descripción general
Cualquier receptor o transmisor de radio requiere antenas para acoplar su conexión eléctrica al campo electromagnético. [8] Las ondas de radio son ondas electromagnéticas que transportan señales a través del aire (o del espacio) a la velocidad de la luz sin casi ninguna pérdida de transmisión .
Las antenas se pueden clasificar como omnidireccionales , que irradian energía aproximadamente por igual en todas las direcciones, o direccionales , donde la energía irradia más en una dirección que en otras. (Las antenas son recíprocas, por lo que ocurre el mismo efecto para la recepción de ondas de radio). Una antena omnidireccional completamente uniforme no es físicamente posible. Algunos tipos de antenas tienen un patrón de radiación uniforme en el plano horizontal, pero envían poca energía hacia arriba o hacia abajo. Una antena "direccional" generalmente está destinada a maximizar su acoplamiento al campo electromagnético en la dirección de la otra estación.
Una antena vertical o una antena de látigo irradia en todas las direcciones horizontalmente, pero envía menos energía hacia arriba o hacia abajo. De manera similar, una antena dipolo orientada horizontalmente envía poca energía en vectores de dirección paralelos al conductor; esta región se llama antena nula.
La antena dipolo, que es la base para la mayoría de los diseños de antenas, es un componente balanceado , con tensiones y corrientes iguales pero opuestas aplicadas en sus dos terminales. La antena vertical es una antena monopolo , no balanceada con respecto a tierra. La tierra (o cualquier superficie conductora grande) juega el papel del segundo conductor de un dipolo. Dado que las antenas monopolo dependen de una superficie conductora, se pueden montar con un plano de tierra para aproximar el efecto de estar montadas en la superficie de la Tierra.
Las antenas más complejas aumentan la directividad de la antena. Los elementos adicionales en la estructura de la antena, que no necesitan conectarse directamente al receptor o transmisor, aumentan su direccionalidad. La "ganancia" de la antena describe la concentración de energía radiada en un ángulo sólido particular del espacio. "Ganancia" es quizás un término elegido por desgracia, en comparación con "ganancia" de amplificador, que implica un aumento neto de potencia. Por el contrario, para la "ganancia" de la antena, la potencia aumentada en la dirección deseada es a expensas de la potencia reducida en direcciones no deseadas. A diferencia de los amplificadores, las antenas son dispositivos eléctricamente " pasivos " que conservan la potencia total, y no hay un aumento en la potencia total por encima de la suministrada por la fuente de alimentación (el transmisor), solo una mejor distribución de ese total fijo.
Una matriz en fase consta de dos o más antenas simples que están conectadas entre sí a través de una red eléctrica. Esto a menudo implica una serie de antenas dipolo paralelas con un cierto espaciado. Dependiendo de la fase relativa introducida por la red, la misma combinación de antenas dipolo puede funcionar como un "conjunto de banda ancha" (direccional normal a una línea que conecta los elementos) o como un "conjunto de fuego final" (direccional a lo largo de la línea que conecta el elementos). Los conjuntos de antenas pueden emplear cualquier tipo de antena básica (omnidireccional o débilmente direccional), como antenas dipolo, de bucle o de ranura. Estos elementos suelen ser idénticos.
Una red de dipolos log-periódica consta de varios elementos de dipolos de diferentes longitudes para obtener una antena algo direccional que tiene un ancho de banda extremadamente amplio. Las antenas dipolo que lo componen se consideran "elementos activos" ya que están todos conectados eléctricamente entre sí (ya la línea de transmisión). Una antena Yagi-Uda (o simplemente "Yagi"), tiene un solo elemento dipolo con una conexión eléctrica; los otros elementos parásitos interactúan con el campo electromagnético para realizar una antena direccional en un ancho de banda estrecho. Puede haber varios denominados "directores" delante del elemento activo en la dirección de propagación, y uno o más "reflectores" en el lado opuesto del elemento activo.
Se puede obtener una mayor direccionalidad utilizando técnicas de formación de haz como un reflector parabólico o una bocina. Dado que la alta directividad en una antena depende de que sea grande en comparación con la longitud de onda, los haces estrechos de este tipo se logran más fácilmente en las frecuencias de UHF y microondas.
A bajas frecuencias (como la transmisión de AM ), se utilizan conjuntos de torres verticales para lograr la direccionalidad [9] y ocuparán grandes áreas de tierra. Para la recepción, una antena de bebidas larga puede tener una directividad significativa. Para uso portátil no direccional, una antena vertical corta o una antena de bucle pequeño funcionan bien, y el principal desafío de diseño es la adaptación de impedancia . Con una antena vertical, se puede emplear una bobina de carga en la base de la antena para cancelar la componente reactiva de la impedancia ; Las antenas de bucle pequeño están sintonizadas con condensadores en paralelo para este propósito.
Una entrada de antena es la línea de transmisión , o línea de alimentación , que conecta la antena a un transmisor o receptor. La " alimentación de antena " puede referirse a todos los componentes que conectan la antena al transmisor o receptor, como una red de adaptación de impedancia además de la línea de transmisión. En una llamada "antena de apertura", como una bocina o un plato parabólico, la "alimentación" también puede referirse a una antena radiante básica incrustada en todo el sistema de elementos reflectantes (normalmente en el foco del plato parabólico o en el garganta de una bocina) que podría considerarse el único elemento activo en ese sistema de antena. También se puede alimentar una antena de microondas directamente desde una guía de ondas en lugar de una línea de transmisión (conductora) .
Un contrapeso de antena , o plano de tierra , es una estructura de material conductor que mejora o sustituye a la tierra. Puede estar conectado o aislado del suelo natural. En una antena monopolo, esto ayuda en la función del suelo natural, particularmente cuando las variaciones (o limitaciones) de las características del suelo natural interfieren con su función adecuada. Una estructura de este tipo está normalmente conectada a la conexión de retorno de una línea de transmisión desequilibrada, como el blindaje de un cable coaxial .
Un refractor de ondas electromagnéticas en algunas antenas de apertura es un componente que debido a su forma y posición funciona para retrasar o hacer avanzar selectivamente porciones del frente de ondas electromagnéticas que lo atraviesan. El refractor altera las características espaciales de la onda en un lado con respecto al otro lado. Puede, por ejemplo, enfocar la onda o alterar el frente de onda de otras formas, generalmente para maximizar la directividad del sistema de antena. Este es el equivalente de radio de una lente óptica .
Una red de acoplamiento de antena es una red pasiva (generalmente una combinación de elementos de circuito inductivos y capacitivos) que se utiliza para igualar la impedancia entre la antena y el transmisor o receptor. Esto puede usarse para mejorar la relación de ondas estacionarias con el fin de minimizar las pérdidas en la línea de transmisión y presentar al transmisor o receptor con una impedancia resistiva estándar que espera ver para un funcionamiento óptimo.
Reciprocidad
Es una propiedad fundamental de las antenas que las características eléctricas de una antena descritas en la siguiente sección, como ganancia , patrón de radiación , impedancia , ancho de banda , frecuencia resonante y polarización , sean las mismas ya sea que la antena esté transmitiendo o recibiendo . [10] [11] Por ejemplo, el " patrón de recepción " (sensibilidad en función de la dirección) de una antena cuando se utiliza para la recepción es idéntico al patrón de radiación de la antena cuando se activa y funciona como un radiador. Esta es una consecuencia del teorema de reciprocidad de los electromagneticos. [11] Por lo tanto, en las discusiones sobre las propiedades de la antena no se suele hacer distinción entre la terminología de recepción y transmisión, y la antena puede verse como transmisora o receptora, lo que sea más conveniente.
Una condición necesaria para la propiedad de reciprocidad antes mencionada es que los materiales en la antena y el medio de transmisión sean lineales y recíprocos. Recíproco (o bilateral ) significa que el material tiene la misma respuesta a una corriente eléctrica o campo magnético en una dirección, que al campo o corriente en la dirección opuesta. La mayoría de los materiales utilizados en las antenas cumplen estas condiciones, pero algunas antenas de microondas utilizan componentes de alta tecnología, como aisladores y circuladores , hechos de materiales no recíprocos como la ferrita . [10] [11] Estos pueden usarse para darle a la antena un comportamiento diferente en la recepción que en la transmisión, [10] lo cual puede ser útil en aplicaciones como el radar .
Antenas resonantes
La mayoría de los diseños de antenas se basan en el principio de resonancia . Esto se basa en el comportamiento de los electrones en movimiento, que se reflejan en las superficies donde cambia la constante dieléctrica , de una manera similar a la forma en que se refleja la luz cuando cambian las propiedades ópticas. En estos diseños, la superficie reflectante se crea por el extremo de un conductor, normalmente un alambre o varilla de metal delgado, que en el caso más simple tiene un punto de alimentación en un extremo donde está conectado a una línea de transmisión . El conductor, o elemento , está alineado con el campo eléctrico de la señal deseada, lo que normalmente significa que es perpendicular a la línea desde la antena a la fuente (o receptor en el caso de una antena de transmisión). [12]
El componente eléctrico de la señal de radio induce un voltaje en el conductor. Esto hace que una corriente eléctrica comience a fluir en la dirección del campo instantáneo de la señal. Cuando la corriente resultante llega al final del conductor, se refleja, lo que equivale a un cambio de fase de 180 grados. Si el conductor tiene 1 ⁄ 4 de longitud de onda, la corriente desde el punto de alimentación sufrirá un cambio de fase de 90 grados cuando llegue al final del conductor, se reflejará 180 grados y luego otros 90 grados a medida que regrese. Eso significa que ha sufrido un cambio de fase total de 360 grados, devolviéndolo a la señal original. La corriente en el elemento se suma a la corriente que se crea a partir de la fuente en ese instante. Este proceso crea una onda estacionaria en el conductor, con la máxima corriente en la alimentación. [13]
El dipolo ordinario de media onda es probablemente el diseño de antena más utilizado. Este consta de dos Elementos de 1 ⁄ 4 de longitud de onda dispuestos de extremo a extremo y que se encuentran esencialmente a lo largo del mismo eje (o colineal ), cada uno de los cuales alimenta un lado de un cable de transmisión de dos conductores. La disposición física de los dos elementos los coloca 180 grados fuera de fase, lo que significa que en un instante dado uno de los elementos está impulsando corriente hacia la línea de transmisión mientras que el otro la extrae. La antena monopolo es esencialmente la mitad del dipolo de media onda, un solo Elemento de 1 ⁄ 4 de longitud de onda con el otro lado conectado a tierra o un plano de tierra equivalente(o contrapeso ). Los monopolos, que tienen la mitad del tamaño de un dipolo, son comunes para las señales de radio de longitud de onda larga donde un dipolo sería impracticablemente grande. Otro diseño común es el dipolo plegado que consta de dos (o más) dipolos de media onda colocados uno al lado del otro y conectados en sus extremos, pero solo uno de los cuales es impulsado.
Las formas de onda estacionaria con este patrón deseado a la frecuencia de funcionamiento de diseño, f O , y las antenas están normalmente diseñados para ser de este tamaño. Sin embargo, alimentar ese elemento con 3 f 0 (cuya longitud de onda es 1 / 3 que de f o ) también dará lugar a un patrón de onda estacionaria. Por lo tanto, un elemento de antena también esresonante cuando su longitud es 3 ⁄ 4 de longitud de onda. Esto es cierto para todos los múltiplos impares de 1 ⁄ 4 de longitud de onda. Esto permite cierta flexibilidad de diseño en términos de longitudes de antena y puntos de alimentación. Se sabe que las antenas utilizadas de esta manera funcionan armónicamente . [14] Las antenas resonantes generalmente usan un conductor lineal (o elemento ), o un par de tales elementos, cada uno de los cuales tiene aproximadamente un cuarto de la longitud de onda (un múltiplo impar de un cuarto de longitud de onda también será resonante). Las antenas que deben ser pequeñas en comparación con la eficiencia de sacrificio de longitud de onda y no pueden ser muy direccionales. Dado que las longitudes de onda son tan pequeñas en frecuencias más altas ( UHF , microondas ), por lo general no es necesario intercambiar el rendimiento para obtener un tamaño físico más pequeño.
Distribución de corriente y tensión
Los elementos de cuarto de onda imitan un elemento eléctrico resonante en serie debido a la onda estacionaria presente a lo largo del conductor. En la frecuencia de resonancia, la onda estacionaria tiene un pico de corriente y un nodo de voltaje (mínimo) en la alimentación. En términos eléctricos, esto significa que el elemento tiene una reactancia mínima , generando la corriente máxima para un voltaje mínimo. Ésta es la situación ideal, porque produce la máxima salida para la mínima entrada, produciendo la mayor eficiencia posible. A diferencia de un circuito resonante en serie ideal (sin pérdidas), permanece una resistencia finita (correspondiente al voltaje relativamente pequeño en el punto de alimentación) debido a la resistencia a la radiación de la antena, así como a las pérdidas eléctricas reales.
Recuerde que una corriente se reflejará cuando haya cambios en las propiedades eléctricas del material. Para transferir eficientemente la señal recibida a la línea de transmisión, es importante que la línea de transmisión tenga la misma impedancia que su punto de conexión en la antena; de lo contrario, parte de la señal se reflejará hacia atrás en el cuerpo de la antena; Asimismo, parte de la potencia de la señal del transmisor se reflejará de regreso al transmisor, si hay un cambio en la impedancia eléctrica donde la línea de alimentación se une a la antena. Esto lleva al concepto de adaptación de impedancia , el diseño del sistema general de antena y línea de transmisión para que la impedancia sea lo más cercana posible, reduciendo así estas pérdidas. La adaptación de impedancia se logra mediante un circuito llamado sintonizador de antena o red de adaptación de impedancia entre el transmisor y la antena. La coincidencia de impedancia entre la línea de alimentación y la antena se mide mediante un parámetro llamado relación de onda estacionaria (SWR) en la línea de alimentación.
Considere un dipolo de media onda diseñado para trabajar con señales con una longitud de onda de 1 m, lo que significa que la antena estaría aproximadamente a 50 cm de punta a punta. Si el elemento tiene una relación de longitud a diámetro de 1000, tendrá una impedancia inherente de aproximadamente 63 ohmios resistivos. Usando el cable de transmisión apropiado o balun, igualamos esa resistencia para asegurar una mínima reflexión de la señal. Alimentar esa antena con una corriente de 1 amperio requerirá 63 voltios, y la antena irradiará 63 vatios (ignorando las pérdidas) de potencia de radiofrecuencia. Consideremos ahora el caso en el que la antena recibe una señal con una longitud de onda de 1,25 m; en este caso, la corriente inducida por la señal llegaría al punto de alimentación de la antena fuera de fase con la señal, provocando que la corriente neta caiga mientras el voltaje permanece igual. Eléctricamente, esto parece ser una impedancia muy alta. La antena y la línea de transmisión ya no tienen la misma impedancia y la señal se reflejará nuevamente en la antena, reduciendo la salida. Esto podría solucionarse cambiando el sistema de adaptación entre la antena y la línea de transmisión, pero esa solución solo funciona bien en la nueva frecuencia de diseño.
El resultado final es que la antena resonante alimentará de manera eficiente una señal en la línea de transmisión solo cuando la frecuencia de la señal fuente esté cerca de la frecuencia de diseño de la antena, o una de las múltiples resonantes. Esto hace que los diseños de antenas resonantes sean intrínsecamente de banda estrecha: solo son útiles para un pequeño rango de frecuencias centradas alrededor de la (s) resonancia (s).
Antenas eléctricamente cortas
Es posible utilizar técnicas simples de adaptación de impedancia para permitir el uso de antenas monopolo o dipolo sustancialmente más cortas que las 1 ⁄ 4 o 1 ⁄ 2 de longitud de onda, respectivamente, a la que resuenan. A medida que estas antenas se acortan (para una frecuencia determinada), su impedancia pasa a estar dominada por una reactancia capacitiva (negativa) en serie; mediante la adición de un tamaño apropiado “ bobina de carga ” - una inductancia en serie con la reactancia igual y opuesta (positiva) - reactancia capacitiva de la antena puede ser cancelada dejando sólo una resistencia pura. A veces, la frecuencia de resonancia eléctrica resultante (más baja) de dicho sistema (antena más red de adaptación) se describe utilizando el concepto de longitud eléctrica , por lo que una antena utilizada a una frecuencia más baja que su frecuencia de resonancia se denomina antena eléctricamente corta [15]
For example, at 30 MHz (10 m wavelength) a true resonant 1⁄4 wavelength monopole would be almost 2.5 meters long, and using an antenna only 1.5 meters tall would require the addition of a loading coil. Then it may be said that the coil has lengthened the antenna to achieve an electrical length of 2.5 meters. However, the resulting resistive impedance achieved will be quite a bit lower than that of a true 1⁄4 wave (resonant) monopole, often requiring further impedance matching (a transformer) to the desired transmission line. For ever shorter antennas (requiring greater "electrical lengthening") the radiation resistance plummets (approximately according to the square of the antenna length), so that the mismatch due to a net reactance away from the electrical resonance worsens. Or one could as well say that the equivalent resonant circuit of the antenna system has a higher Q factor and thus a reduced bandwidth,[15] which can even become inadequate for the transmitted signal's spectrum. Resistive losses due to the loading coil, relative to the decreased radiation resistance, entail a reduced electrical efficiency, which can be of great concern for a transmitting antenna, but bandwidth is the major factor[dubious ][dubious ] that sets the size of antennas at 1 MHz and lower frequencies.
Arrays and reflectors
The amount of signal received from a distant transmission source is essentially geometric in nature due to the inverse-square law, and this leads to the concept of effective area. This measures the performance of an antenna by comparing the amount of power it generates to the amount of power in the original signal, measured in terms of the signal's power density in Watts per square metre. A half-wave dipole has an effective area of . If more performance is needed, one cannot simply make the antenna larger. Although this would intercept more energy from the signal, due to the considerations above, it would decrease the output significantly due to it moving away from the resonant length. In roles where higher performance is needed, designers often use multiple elements combined together.
Returning to the basic concept of current flows in a conductor, consider what happens if a half-wave dipole is not connected to a feed point, but instead shorted out. Electrically this forms a single 1⁄2 wavelength element. But the overall current pattern is the same; the current will be zero at the two ends, and reach a maximum in the center. Thus signals near the design frequency will continue to create a standing wave pattern. Any varying electrical current, like the standing wave in the element, will radiate a signal. In this case, aside from resistive losses in the element, the rebroadcast signal will be significantly similar to the original signal in both magnitude and shape. If this element is placed so its signal reaches the main dipole in-phase, it will reinforce the original signal, and increase the current in the dipole. Elements used in this way are known as “passive elements”.
A Yagi-Uda array uses passive elements to greatly increase gain. It is built along a support boom that is pointed toward the signal, and thus sees no induced signal and does not contribute to the antenna's operation. The end closer to the source is referred to as the front. Near the rear is a single active element, typically a half-wave dipole or folded dipole. Passive elements are arranged in front (directors) and behind (reflectors) the active element along the boom. The Yagi has the inherent quality that it becomes increasingly directional, and thus has higher gain, as the number of elements increases. However, this also makes it increasingly sensitive to changes in frequency; if the signal frequency changes, not only does the active element receive less energy directly, but all of the passive elements adding to that signal also decrease their output as well and their signals no longer reach the active element in-phase.
It is also possible to use multiple active elements and combine them together with transmission lines to produce a similar system where the phases add up to reinforce the output. The antenna array and very similar reflective array antenna consist of multiple elements, often half-wave dipoles, spaced out on a plane and wired together with transmission lines with specific phase lengths to produce a single in-phase signal at the output. The log-periodic antenna is a more complex design that uses multiple in-line elements similar in appearance to the Yagi-Uda but using transmission lines between the elements to produce the output.
Reflection of the original signal also occurs when it hits an extended conductive surface, in a fashion similar to a mirror. This effect can also be used to increase signal through the use of a reflector, normally placed behind the active element and spaced so the reflected signal reaches the element in-phase. Generally the reflector will remain highly reflective even if it is not solid; gaps less than 1⁄10 generally have little effect on the outcome. For this reason, reflectors often take the form of wire meshes or rows of passive elements, which makes them lighter and less subject to wind-load effects, of particular importance when mounted at higher elevations with respect to the surrounding structures. The parabolic reflector is perhaps the best known example of a reflector-based antenna, which has an effective area far greater than the active element alone.
Modelado de antenas con ecuaciones lineales
The equations governing the flow of current in wire antennas are identical to the telegrapher's equations,[16]:7–10 [17]:232 so antenna segments can be modeled as a two-way, single-conductor transmission lines. The antenna is broken into multiple line segments, each segment having approximately constant primary line parameters, R, L, C, and G, and current dividing at each junction based on impedance.[a]
At the tip of the antenna wire, the transmission-line impedance is essentially infinite (equivalently, the admittance is almost zero) and the wave injected at the feedpoint reverses direction, flowing back towards the feedpoint. The combination of the overlapping, oppositely-directed waves form the familiar standing waves most often considered for practical antenna-building. Further, partial reflections occur within the antenna where ever there is a mismatched impedance at the junction of two or more elements, and these reflected waves also contribute to standing waves along the length of the wire(s).[16][17] When the antenna is resonant, the standing waves are fixed in position; when non-resonant, the current and voltage waves drift across each other, always with zero current at the tip, but otherwise with complicated phase relationships that shift along the wire over time.
Caracteristicas
The antenna's power gain (or simply "gain") also takes into account the antenna's efficiency, and is often the primary figure of merit. Antennas are characterized by a number of performance measures which a user would be concerned with in selecting or designing an antenna for a particular application. A plot of the directional characteristics in the space surrounding the antenna is its radiation pattern.
Bandwidth
The frequency range or bandwidth over which an antenna functions well can be very wide (as in a log-periodic antenna) or narrow (as in a small loop antenna); outside this range the antenna impedance becomes a poor match to the transmission line and transmitter (or receiver). Use of the antenna well away from its design frequency affects its radiation pattern, reducing its directive gain.
Generally an antenna will not have a feed-point impedance that matches that of a transmission line; a matching network between antenna terminals and the transmission line will improve power transfer to the antenna. A non-adjustable matching network will most likely place further limits the usable bandwidth of the antenna system. It may be desirable to use tubular elements, instead of thin wires, to make an antenna; these will allow a greater bandwidth. Or, several thin wires can be grouped in a cage to simulate a thicker element. This widens the bandwidth of the resonance.
Amateur radio antennas that operate at several frequency bands which are widely separated from each other may connect elements resonant at those different frequencies in parallel. Most of the transmitter's power will flow into the resonant element while the others present a high impedance. Another solution uses traps, parallel resonant circuits which are strategically placed in breaks created in long antenna elements. When used at the trap's particular resonant frequency the trap presents a very high impedance (parallel resonance) effectively truncating the element at the location of the trap; if positioned correctly, the truncated element makes a proper resonant antenna at the trap frequency. At substantially higher or lower frequencies the trap allows the full length of the broken element to be employed, but with a resonant frequency shifted by the net reactance added by the trap.
The bandwidth characteristics of a resonant antenna element can be characterized according to its Q where the resistance involved is the radiation resistance, which represents the emission of energy from the resonant antenna to free space.
The Q of a narrow band antenna can be as high as 15. On the other hand, the reactance at the same off-resonant frequency of one using thick elements is much less, consequently resulting in a Q as low as 5. These two antennas may perform equivalently at the resonant frequency, but the second antenna will perform over a bandwidth 3 times as wide as the antenna consisting of a thin conductor.
Antennas for use over much broader frequency ranges are achieved using further techniques. Adjustment of a matching network can, in principle, allow for any antenna to be matched at any frequency. Thus the small loop antenna built into most AM broadcast (medium wave) receivers has a very narrow bandwidth, but is tuned using a parallel capacitance which is adjusted according to the receiver tuning. On the other hand, log-periodic antennas are not resonant at any frequency but can be built to attain similar characteristics (including feedpoint impedance) over any frequency range. These are therefore commonly used (in the form of directional log-periodic dipole arrays) as television antennas.
Gain
Gain is a parameter which measures the degree of directivity of the antenna's radiation pattern. A high-gain antenna will radiate most of its power in a particular direction, while a low-gain antenna will radiate over a wide angle. The antenna gain, or power gain of an antenna is defined as the ratio of the intensity (power per unit surface area) radiated by the antenna in the direction of its maximum output, at an arbitrary distance, divided by the intensity radiated at the same distance by a hypothetical isotropic antenna which radiates equal power in all directions. This dimensionless ratio is usually expressed logarithmically in decibels, these units are called "decibels-isotropic" (dBi)
A second unit used to measure gain is the ratio of the power radiated by the antenna to the power radiated by a half-wave dipole antenna ; these units are called "decibels-dipole" (dBd)
Since the gain of a half-wave dipole is 2.15 dBi and the logarithm of a product is additive, the gain in dBi is just 2.15 decibels greater than the gain in dBd
High-gain antennas have the advantage of longer range and better signal quality, but must be aimed carefully at the other antenna. An example of a high-gain antenna is a parabolic dish such as a satellite television antenna. Low-gain antennas have shorter range, but the orientation of the antenna is relatively unimportant. An example of a low-gain antenna is the whip antenna found on portable radios and cordless phones. Antenna gain should not be confused with amplifier gain, a separate parameter measuring the increase in signal power due to an amplifying device placed at the front-end of the system, such as a low-noise amplifier.
Effective area or aperture
The effective area or effective aperture of a receiving antenna expresses the portion of the power of a passing electromagnetic wave which the antenna delivers to its terminals, expressed in terms of an equivalent area. For instance, if a radio wave passing a given location has a flux of 1 pW / m2 (10−12 Watts per square meter) and an antenna has an effective area of 12 m2, then the antenna would deliver 12 pW of RF power to the receiver (30 microvolts RMS at 75 Ohms). Since the receiving antenna is not equally sensitive to signals received from all directions, the effective area is a function of the direction to the source.
Due to reciprocity (discussed above) the gain of an antenna used for transmitting must be proportional to its effective area when used for receiving. Consider an antenna with no loss, that is, one whose electrical efficiency is 100%. It can be shown that its effective area averaged over all directions must be equal to λ2/4π, the wavelength squared divided by 4π. Gain is defined such that the average gain over all directions for an antenna with 100% electrical efficiency is equal to 1. Therefore, the effective area Aeff in terms of the gain G in a given direction is given by:
For an antenna with an efficiency of less than 100%, both the effective area and gain are reduced by that same amount. Therefore, the above relationship between gain and effective area still holds. These are thus two different ways of expressing the same quantity. Aeff is especially convenient when computing the power that would be received by an antenna of a specified gain, as illustrated by the above example.
Radiation pattern
The radiation pattern of an antenna is a plot of the relative field strength of the radio waves emitted by the antenna at different angles in the far-field. It is typically represented by a three-dimensional graph, or polar plots of the horizontal and vertical cross sections. The pattern of an ideal isotropic antenna, which radiates equally in all directions, would look like a sphere. Many nondirectional antennas, such as monopoles and dipoles, emit equal power in all horizontal directions, with the power dropping off at higher and lower angles; this is called an omnidirectional pattern and when plotted looks like a torus or donut.
The radiation of many antennas shows a pattern of maxima or "lobes" at various angles, separated by "nulls", angles where the radiation falls to zero. This is because the radio waves emitted by different parts of the antenna typically interfere, causing maxima at angles where the radio waves arrive at distant points in phase, and zero radiation at other angles where the radio waves arrive out of phase. In a directional antenna designed to project radio waves in a particular direction, the lobe in that direction is designed larger than the others and is called the "main lobe". The other lobes usually represent unwanted radiation and are called "sidelobes". The axis through the main lobe is called the "principal axis" or "boresight axis".
The polar diagrams (and therefore the efficiency and gain) of Yagi antennas are tighter if the antenna is tuned for a narrower frequency range, e.g. the grouped antenna compared to the wideband. Similarly, the polar plots of horizontally polarized yagis are tighter than for those vertically polarized.[18]
Field regions
The space surrounding an antenna can be divided into three concentric regions: The reactive near-field (also called the inductive near-field), the radiating near-field (Fresnel region) and the far-field (Fraunhofer) regions. These regions are useful to identify the field structure in each, although the transitions between them are gradual, and there are no precise boundaries.
The far-field region is far enough from the antenna to ignore its size and shape: It can be assumed that the electromagnetic wave is purely a radiating plane wave (electric and magnetic fields are in phase and perpendicular to each other and to the direction of propagation). This simplifies the mathematical analysis of the radiated field.
Efficiency
Efficiency of a transmitting antenna is the ratio of power actually radiated (in all directions) to the power absorbed by the antenna terminals. The power supplied to the antenna terminals which is not radiated is converted into heat. This is usually through loss resistance in the antenna's conductors, or loss between the reflector and feed horn of a parabolic antenna.
Antenna efficiency is separate from impedance matching, which may also reduce the amount of power radiated using a given transmitter. If an SWR meter reads 150 W of incident power and 50 W of reflected power, that means 100 W have actually been absorbed by the antenna (ignoring transmission line losses). How much of that power has actually been radiated cannot be directly determined through electrical measurements at (or before) the antenna terminals, but would require (for instance) careful measurement of field strength. The loss resistance and efficiency of an antenna can be calculated once the field strength is known, by comparing it to the power supplied to the antenna.
The loss resistance will generally affect the feedpoint impedance, adding to its resistive component. That resistance will consist of the sum of the radiation resistance Rr and the loss resistance Rloss. If a current I is delivered to the terminals of an antenna, then a power of I2 Rr will be radiated and a power of I2 Rloss will be lost as heat. Therefore, the efficiency of an antenna is equal to Rr⁄(Rr + Rloss). Only the total resistance Rr + Rloss can be directly measured.
According to reciprocity, the efficiency of an antenna used as a receiving antenna is identical to its efficiency as a transmitting antenna, described above. The power that an antenna will deliver to a receiver (with a proper impedance match) is reduced by the same amount. In some receiving applications, the very inefficient antennas may have little impact on performance. At low frequencies, for example, atmospheric or man-made noise can mask antenna inefficiency. For example, CCIR Rep. 258-3 indicates man-made noise in a residential setting at 40 MHz is about 28 dB above the thermal noise floor. Consequently, an antenna with a 20 dB loss (due to inefficiency) would have little impact on system noise performance. The loss within the antenna will affect the intended signal and the noise/interference identically, leading to no reduction in signal to noise ratio (SNR).
Antennas which are not a significant fraction of a wavelength in size are inevitably inefficient due to their small radiation resistance. AM broadcast radios include a small loop antenna for reception which has an extremely poor efficiency. This has little effect on the receiver's performance, but simply requires greater amplification by the receiver's electronics. Contrast this tiny component to the massive and very tall towers used at AM broadcast stations for transmitting at the very same frequency, where every percentage point of reduced antenna efficiency entails a substantial cost.
The definition of antenna gain or power gain already includes the effect of the antenna's efficiency. Therefore, if one is trying to radiate a signal toward a receiver using a transmitter of a given power, one need only compare the gain of various antennas rather than considering the efficiency as well. This is likewise true for a receiving antenna at very high (especially microwave) frequencies, where the point is to receive a signal which is strong compared to the receiver's noise temperature. However, in the case of a directional antenna used for receiving signals with the intention of rejecting interference from different directions, one is no longer concerned with the antenna efficiency, as discussed above. In this case, rather than quoting the antenna gain, one would be more concerned with the directive gain, or simply directivity which does not include the effect of antenna (in)efficiency. The directive gain of an antenna can be computed from the published gain divided by the antenna's efficiency. In equation form, gain = directivity × efficiency.
Polarization
The polarization of an antenna refers to the orientation of the electric field of the radio wave transmitted by it, and is determined by the physical structure of the antenna and its orientation. For instance, an antenna composed of a linear conductor (such as a dipole or whip antenna) oriented vertically will result in vertical polarization; if turned on its side the same antenna's polarization will be horizontal.
Reflections generally affect polarization. Radio waves reflected off the ionosphere can change the wave's polarization. For line-of-sight communications or ground wave propagation, horizontally or vertically polarized transmissions generally remain in about the same polarization state at the receiving location. Using a vertically polarized antenna to receive a horizontally polarized wave (or visa-versa) results in relatively poor reception.
An antenna's polarization can sometimes be inferred directly from its geometry. When the antenna's conductors viewed from a reference location appear along one line, then the antenna's polarization will be linear in that very direction. In the more general case, the antenna's polarization must be determined through analysis. For instance, a turnstile antenna mounted horizontally (as is usual), from a distant location on earth, appears as a horizontal line segment, so its radiation received there is horizontally polarized. But viewed at a downward angle from an airplane, the same antenna does not meet this requirement; in fact its radiation is elliptically polarized when viewed from that direction. In some antennas the state of polarization will change with the frequency of transmission. The polarization of a commercial antenna is an essential specification.
In the most general case, polarization is elliptical, meaning that over each cycle the electric field vector traces out an ellipse. Two special cases are linear polarization (the ellipse collapses into a line) as discussed above, and circular polarization (in which the two axes of the ellipse are equal). In linear polarization the electric field of the radio wave oscillates along one direction. In circular polarization, the electric field of the radio wave rotates around the axis of propagation. Circular or elliptically polarized radio waves are designated as right-handed or left-handed using the "thumb in the direction of the propagation" rule. Note that for circular polarization, optical researchers use the opposite right hand rule[citation needed] from the one used by radio engineers.
It is best for the receiving antenna to match the polarization of the transmitted wave for optimum reception. Otherwise there will be a loss of signal strength: when a linearly polarized antenna receives linearly polarized radiation at a relative angle of θ, then there will be a power loss of cos2θ. A circularly polarized antenna can be used to equally well match vertical or horizontal linear polarizations, suffering a 3 dB signal reduction. However it will be blind to a circularly polarized signal of the opposite orientation!
Impedance matching
Maximum power transfer requires matching the impedance of an antenna system (as seen looking into the transmission line) to the complex conjugate of the impedance of the receiver or transmitter. In the case of a transmitter, however, the desired matching impedance might not correspond to the dynamic output impedance of the transmitter as analyzed as a source impedance but rather the design value (typically 50 Ohms) required for efficient and safe operation of the transmitting circuitry. The intended impedance is normally resistive but a transmitter (and some receivers) may have additional adjustments to cancel a certain amount of reactance in order to "tweak" the match. When a transmission line is used in between the antenna and the transmitter (or receiver) one generally would like an antenna system whose impedance is resistive and near the characteristic impedance of that transmission line in order to minimize the standing wave ratio (SWR) and the increase in transmission line losses it entails, in addition to matching the impedance that the transmitter (or receiver) expects.
Antenna tuning, in the context of modifying the antenna itself, generally refers only to cancellation of any reactance seen at the antenna terminals, leaving only a resistive impedance which might or might not be exactly the desired impedance (that of the transmission line). Although an antenna may be designed to have a purely resistive feedpoint impedance (such as a dipole 97% of a half wavelength long) this might not be exactly true at the frequency that it is eventually used at. In some cases the physical length of the antenna can be "trimmed" to obtain a pure resistance. On the other hand, the addition of a series inductance or parallel capacitance can be used to cancel a residual capacitative or inductive reactance, respectively. Antenna tuning used in the context of an impedance matching device called an antenna tuner involves both removal of reactance, and transforming the remaining resistance to be a match for the radio or feedline.
In some cases this is done in a more extreme manner, not simply to cancel a small amount of residual reactance, but to resonate an antenna whose resonance frequency is quite different from the intended frequency of operation. For instance, a "whip antenna" can be made significantly shorter than 1⁄4 wavelength long, for practical reasons, and then resonated using a so-called loading coil. This physically large inductor at the base of the antenna has an inductive reactance which is the opposite of the capacitative reactance that a short vertical antenna has at the desired operating frequency. The result is a pure resistance seen at feedpoint of the loading coil; that resistance is somewhat lower than would be desired to match commercial coax.[citation needed]
An additional problem is matching the remaining resistive impedance to the characteristic impedance of the transmission line. A general matching network (an antenna tuner or ATU) will have at least two adjustable elements to correct both components of impedance. Matching networks will have losses, and power restrictions when used for transmitting. Commercial antennas are generally designed to get an approximate match to standard coaxial cables, merely using a matching network to "tweak" any residual mismatch. Antennas of any kind may include a balun at their feedpoint to transform the resistive part of the impedance for a nearer match to the feedline.
Another extreme case of impedance matching occurs when using a small loop antenna (usually, but not always, for receiving) at a relatively low frequency where it appears almost as a pure inductor. Resonating such an inductor with a capacitor at the frequency of operation not only cancels the reactance but greatly magnifies the very small radiation resistance of such a loop.[citation needed] This is implemented in most AM broadcast receivers, with a small ferrite loop antenna resonated by a capacitor which is varied along with the receiver tuning in order to maintain resonance over the AM broadcast band
Efecto del suelo
Ground reflections is one of the common types of multipath.[19][20][21]
The radiation pattern and even the driving point impedance of an antenna can be influenced by the dielectric constant and especially conductivity of nearby objects. For a terrestrial antenna, the ground is usually one such object of importance. The antenna's height above the ground, as well as the electrical properties (permittivity and conductivity) of the ground, can then be important. Also, in the particular case of a monopole antenna, the ground (or an artificial ground plane) serves as the return connection for the antenna current thus having an additional effect, particularly on the impedance seen by the feed line.
When an electromagnetic wave strikes a plane surface such as the ground, part of the wave is transmitted into the ground and part of it is reflected, according to the Fresnel coefficients. If the ground is a very good conductor then almost all of the wave is reflected (180° out of phase), whereas a ground modeled as a (lossy) dielectric can absorb a large amount of the wave's power. The power remaining in the reflected wave, and the phase shift upon reflection, strongly depend on the wave's angle of incidence and polarization. The dielectric constant and conductivity (or simply the complex dielectric constant) is dependent on the soil type and is a function of frequency.
For very low frequencies to high frequencies (< 30 MHz), the ground behaves as a lossy dielectric,[22] thus the ground is characterized both by a conductivity[23] and permittivity (dielectric constant) which can be measured for a given soil (but is influenced by fluctuating moisture levels) or can be estimated from certain maps. At lower frequencies the ground acts mainly as a good conductor, which AM middle wave broadcast (0.5–1.6 MHz) antennas depend on.
At frequencies between 3 and 30 MHz, a large portion of the energy from a horizontally polarized antenna reflects off the ground, with almost total reflection at the grazing angles important for ground wave propagation. That reflected wave, with its phase reversed, can either cancel or reinforce the direct wave, depending on the antenna height in wavelengths and elevation angle (for a sky wave).
On the other hand, vertically polarized radiation is not well reflected by the ground except at grazing incidence or over very highly conducting surfaces such as sea water.[24] However the grazing angle reflection important for ground wave propagation, using vertical polarization, is in phase with the direct wave, providing a boost of up to 6 dB, as is detailed below.
At VHF and above (> 30 MHz) the ground becomes a poorer reflector. However it remains a good reflector especially for horizontal polarization and grazing angles of incidence. That is important as these higher frequencies usually depend on horizontal line-of-sight propagation (except for satellite communications), the ground then behaving almost as a mirror.
The net quality of a ground reflection depends on the topography of the surface. When the irregularities of the surface are much smaller than the wavelength, the dominant regime is that of specular reflection, and the receiver sees both the real antenna and an image of the antenna under the ground due to reflection. But if the ground has irregularities not small compared to the wavelength, reflections will not be coherent but shifted by random phases. With shorter wavelengths (higher frequencies), this is generally the case.
Whenever both the receiving or transmitting antenna are placed at significant heights above the ground (relative to the wavelength), waves specularly reflected by the ground will travel a longer distance than direct waves, inducing a phase shift which can sometimes be significant. When a sky wave is launched by such an antenna, that phase shift is always significant unless the antenna is very close to the ground (compared to the wavelength).
The phase of reflection of electromagnetic waves depends on the polarization of the incident wave. Given the larger refractive index of the ground (typically n ≈ 2) compared to air (n = 1), the phase of horizontally polarized radiation is reversed upon reflection (a phase shift of radians or 180°). On the other hand, the vertical component of the wave's electric field is reflected at grazing angles of incidence approximately in phase. These phase shifts apply as well to a ground modeled as a good electrical conductor.
This means that a receiving antenna "sees" an image of the emitting antenna but with 'reversed' currents (opposite in direction/phase) if the emitting antenna is horizontally oriented (and thus horizontally polarized). However, the received current will be in the same absolute direction/phase if the emitting antenna is vertically oriented/polarized.
The actual antenna which is transmitting the original wave then also may receive a strong signal from its own image from the ground. This will induce an additional current in the antenna element, changing the current at the feedpoint for a given feedpoint voltage. Thus the antenna's impedance, given by the ratio of feedpoint voltage to current, is altered due to the antenna's proximity to the ground. This can be quite a significant effect when the antenna is within a wavelength or two of the ground. But as the antenna height is increased, the reduced power of the reflected wave (due to the inverse square law) allows the antenna to approach its asymptotic feedpoint impedance given by theory. At lower heights, the effect on the antenna's impedance is very sensitive to the exact distance from the ground, as this affects the phase of the reflected wave relative to the currents in the antenna. Changing the antenna's height by a quarter wavelength, then changes the phase of the reflection by 180°, with a completely different effect on the antenna's impedance.
The ground reflection has an important effect on the net far field radiation pattern in the vertical plane, that is, as a function of elevation angle, which is thus different between a vertically and horizontally polarized antenna. Consider an antenna at a height h above the ground, transmitting a wave considered at the elevation angle θ. For a vertically polarized transmission the magnitude of the electric field of the electromagnetic wave produced by the direct ray plus the reflected ray is:
Thus the power received can be as high as 4 times that due to the direct wave alone (such as when θ = 0), following the square of the cosine. The sign inversion for the reflection of horizontally polarized emission instead results in:
where:
- is the electrical field that would be received by the direct wave if there were no ground.
- θ is the elevation angle of the wave being considered.
- is the wavelength.
- is the height of the antenna (half the distance between the antenna and its image).
For horizontal propagation between transmitting and receiving antennas situated near the ground reasonably far from each other, the distances traveled by the direct and reflected rays are nearly the same. There is almost no relative phase shift. If the emission is polarized vertically, the two fields (direct and reflected) add and there is maximum of received signal. If the signal is polarized horizontally, the two signals subtract and the received signal is largely cancelled. The vertical plane radiation patterns are shown in the image at right. With vertical polarization there is always a maximum for θ = 0, horizontal propagation (left pattern). For horizontal polarization, there is cancellation at that angle. Note that the above formulae and these plots assume the ground as a perfect conductor. These plots of the radiation pattern correspond to a distance between the antenna and its image of 2.5 λ . As the antenna height is increased, the number of lobes increases as well.
The difference in the above factors for the case of θ = 0 is the reason that most broadcasting (transmissions intended for the public) uses vertical polarization. For receivers near the ground, horizontally polarized transmissions suffer cancellation. For best reception the receiving antennas for these signals are likewise vertically polarized. In some applications where the receiving antenna must work in any position, as in mobile phones, the base station antennas use mixed polarization, such as linear polarization at an angle (with both vertical and horizontal components) or circular polarization.
On the other hand, analog television transmissions are usually horizontally polarized, because in urban areas buildings can reflect the electromagnetic waves and create ghost images due to multipath propagation. Using horizontal polarization, ghosting is reduced because the amount of reflection in the horizontal polarization off the side of a building is generally less than in the vertical direction. Vertically polarized analog television have been used in some rural areas. In digital terrestrial television such reflections are less problematic, due to robustness of binary transmissions and error correction.
Impedancia mutua e interacción entre antenas
Current circulating in one antenna generally induces a voltage across the feedpoint of nearby antennas or antenna elements. Such interactions can greatly affect the performance of a group of antennas.
With a particular geometry, it is possible for the mutual impedance between nearby antennas to be zero. This is the case, for instance, between the crossed dipoles used in the turnstile antenna.
Tipos de antenas
Antennas can be classified by operating principles or by their application.
Ver también
- Category:Radio frequency antenna types
- Category:Radio frequency propagation
- Cellular repeater
- DXing
- Electromagnetism
- Mobile broadband modem
- Numerical Electromagnetics Code
- Radial (radio)
- Radio masts and towers
- RF connector
- Smart antenna
- TETRA
- Shortwave broadband antenna
- Personal RF safety monitor
Notas al pie
- ^ Since voltage lost due to radiation is typically small compared to the voltages required due to the antenna's surge impedance, and since dry air is a very good insulator, the antenna is often modeled as lossless: R = G = 0 . The essential loss or gain of voltage due to transmission or reception is usually inserted post-hoc, after the transmission line solutions, although it can be modeled as a small value of R at the expense of working with complex numbers.
Referencias
- ^ Graf, Rudolf F., ed. (1999). "Antenna". Modern Dictionary of Electronics. Newnes. p. 29. ISBN 978-0750698665.
- ^ Hertz, H. (1889). "[no title cited]". Annalen der Physik und Chemie. 36.
- ^ a b Marconi, G. (11 December 1909). "Wireless Telegraphic Communication". Nobel Lecture. Archived from the original on 4 May 2007.
"Physics 1901–1921". Nobel Lectures. Amsterdam: Elsevier Publishing Company. 1967. pp. 196–222, 206. - ^ Slyusar, Vadym (20–23 September 2011). The history of radio engineering's term "antenna" (PDF). VIII International Conference on Antenna Theory and Techniques (ICATT’11). Kyiv, Ukraine. pp. 83–85. Archived (PDF) from the original on 24 February 2014.
- ^ Slyusar, Vadym (21–24 February 2012). An Italian period on the history of radio engineering's term "antenna" (PDF). 11th International Conference Modern Problems of Radio Engineering, Telecommunications, and Computer Science (TCSET’2012). Lviv-Slavske, Ukraine. p. 174. Archived (PDF) from the original on 24 February 2014.
- ^ Slyusar, Vadym (June 2011). "Антенна: история радиотехнического термина" [The Antenna: A history of radio engineering’s term] (PDF). ПЕРВАЯ МИЛЯ / Last Mile: Electronics: Science, Technology, Business (in Russian). No. 6. pp. 52–64. Archived (PDF) from the original on 24 February 2014.
- ^ "Media Advisory: Apply now to attend the ALMA Observatory inauguration". ESO press release. Archived from the original on 6 December 2012. Retrieved 4 December 2012.
- ^ Elliott, Robert S. (1981). Antenna Theory and Design (1st ed.). Wyle. p. 3.
- ^ Smith, Carl (1969). Standard Broadcast Antenna Systems. Cleveland, Ohio: Smith Electronics. p. 2-1212.
- ^ a b c Lonngren, Karl Erik; Savov, Sava V.; Jost, Randy J. (2007). Fundamentals of Electomagnetics With Matlab (2nd ed.). SciTech Publishing. p. 451. ISBN 978-1891121586.
- ^ a b c Stutzman, Warren L.; Thiele, Gary A. (2012). Antenna Theory and Design (3rd ed.). John Wiley & Sons. pp. 560–564. ISBN 978-0470576649.
- ^ Hall, Gerald, ed. (1991). The ARRL Antenna Book (15th ed.). ARRL. p. 24. ISBN 978-0-87259-206-3.
- ^ Hall 1991, p. 25.
- ^ Hall 1991, pp. 31-32.
- ^ a b Slyusar, V. I. (17–21 September 2007). 60 Years of Electrically Small Antenna Theory (PDF). 6th International Conference on Antenna Theory and Techniques. Sevastopol, Ukraine. pp. 116–118. Archived (PDF) from the original on 28 August 2017. Retrieved 2 September 2017.
- ^ a b Raines, Jeremy Keith (2007). Folded Unipole Antennas: Theory and applications. Electronic Engineering (1st ed.). McGraw Hill. ISBN 978-0-07-147485-6.ISBN 0-07-147485-4
- ^ a b Schelkunoff, Sergei A.; Friis, Harald T. (July 1966) [1952]. Antennas: Theory and practice. John Wiley & Sons. LCCN 52-5083.
- ^ "Aerial Polar Response Diagrams". ATV/Fracarro.
- ^ Fixed Broadband Wireless System Design, p. 130, at Google Books
- ^ Monopole Antennas, p. 340, at Google Books
- ^ Wireless and Mobile Communication, p. 37, at Google Books
- ^ Silver, H. Ward, ed. (2011). ARRL Antenna Book. Newington, Connecticut: American Radio Relay League. p. 3-2. ISBN 978-0-87259-694-8.
- ^ "M3 Map of Effective Ground Conductivity in the United States (a Wall-Sized Map), for AM Broadcast Stations". fcc.gov. 11 December 2015. Archived from the original on 18 November 2015. Retrieved 6 May 2018.
- ^ Silver 2011, p. 3-23
The dictionary definition of antenna at Wiktionary