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!Español!!Ingles
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=Introducción=
Una fórmula de transmisión una fórmula de transmisión simple para un circuito de radio es encontrada. Se hace hincapié en la utilidad de la fórmula y se discuten sus limitaciones<br />
Línea 23 ⟶ 15:
'''Área efectiva'''<br />
El área efectiva de cualquier antena ya sea emisora o receptora, se define para la condición en la que la antena se usa para recibir una onda electromagnética plana polarizada linealmente. El área efectiva se define como la relación entre la potencia recibida y la densidad de potencia incidente en una antena.
'''(Ítem A )(formula 2 y 3) '''<br />
Línea 62 ⟶ 35:
<math>A_{dip}</math>=<math>\frac{P_r}{P_0}=\frac{3\lambda ^2}{8\pi}= 0.1193\lambda ^2</math>[0.3cm] <math>P_o=E^2/120\pi</math>
<br />
<math>Pr=\frac{E^2 a^2}{4(80\pi^2 a^2/ \lambda ^2 )}</math> = <math>\frac{\lambda^2 E^2 a^2}{320\pi a^2}</math>= <math>\frac{\lambda^2 E^2}{320\pi^2}</math><br />
<math>A_{dip}=\frac{\frac{\lambda^2 E^2}{320\pi^2}}{\frac{E^2}{120\pi}} = \frac{ 120 \pi \lambda^2 E^2}{320\pi^2E^2}=\frac{3\lambda^2}{8\pi}</math><br />
[[File:Area efectiva de una circunferencia.png|centro|miniaturadeimagen|300x300px|Área efectiva de una circunferencia]]
'''Área efectiva de un rectángulo'''
Línea 128 ⟶ 65:
<math>r=\sqrt{\frac{A}{\pi}}</math><br />
<math>r=\sqrt{\frac{466.29}{\pi}}=12.1829</math><br />
'''(Ítem D)
Línea 184 ⟶ 79:
El área efectiva de una antena isotrópica la podemos tomar como si estuviéramos hablando de una antena dipolo pequeña.<br />
Un dipolo pequeño equivale a <math>L=\frac{\alpha}{10}</math><br />
<br />
'''ANTENAS DE BOCINA:'''<br />
Línea 210 ⟶ 95:
[[File:Polarizaciones.png|centro|miniaturadeimagen|300x300px|Polarización]]
[[File:RADIOELACES.cmap.cmap.pdf|centro|miniaturadeimagen|700x700px|Último párrafo (Héctor Javier Vega Lozano)]]
'''DE FRIIS A RAPPAPORT Y DE RAPPAPORT A FRIIS '''<br />
Línea 324 ⟶ 155:
<math>d:</math>Distancia entre antenas.<br />
<math>\lambda:</math> Longitud de onda.<br />
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= Introduction =
'''Abstract—A simple transmission formula for a radio circuit
is derived. The utility of the formula is emphasized and its
limitations are discussed.'''
This note emphasizes the utility of the following simple transmission formula for a radio circuit made up of a transmitting antenna and a receiving antenna in free space:<br />
<math>\frac{P_{r}}{P_{t}}=\frac{A_{r}A_{t}}{d^{2}\lambda ^{2}}</math><br />
where<br />
Pt= power fed into the transmitting antenna at its input terminals.<br />
Pr=power available at the output terminals of the receiving antenna.<br />
Ar=effective area of the receiving antenna.<br />
At=effective area of the transmitting antenna<br />
d=distance between antennas.<br />
<math>\lambda</math>= wavelength<br />
The effective areas appearing in (1) are discussed in the next section and this is followed by a derivation of the formula and a discussion of its limitations.<br />
'''EFFECTIVE AREAS'''<br />
The effective area of any antenna, whether transmitting or receiving, is defined for the condition in which the antenna is used to receive a linearly polarized, plane electromagnetic wave. The author suggests the adoption of the following definition:<br />
<br />
<math>A_{eff.}=\frac{P_r}{P_0}</math><br />
or<br />
<math>P_r=P_0 A_{eff.}</math><br />
Where Pr is the received power as defined above and Po is the power flow per unit area of the incident field at the antenna. In words, (3) states that the received power is equal to the power flow through an area that is equal to the effective area of the antenna. Note that the definition does not impose the condition of no heat loss in the antenna. Equation (3) shows that the effective area of an antenna is proportional to its power gain. The effective areas of antennas of special interest are given in the following:<br />
'''A.Small Dipole with No Heat Loss'''<br />
For a small uniform current element the available output power is equal to the induced voltage squared divided by four times the radiation resistance. Thus<br />
<math>P_r=\frac{E^2a^2}{4R_{rad}}</math><br />
where<br />
E=effective value of the electric field of the wave.<br />
a=length of the current element.<br />
Rrad. = radiation resistance of the current element<br />
<math>R_{rad}=80\pi ^2a^2/\lambda ^2</math> Since the power flow per unit area is equal to the electric field squared divided by the impedance of free space,<br />
i.e., <math>P_o=E^2/120\pi</math>, we have<br />
<math>A_{dip}=\frac{P_r}{P_0}=\frac{3\lambda ^2}{8\pi}=0.1193\lambda ^2</math><br />
The effective area of a half-wavelength dipole with no heat loss is only 9.4 per cent, 0.39 decibels,2 larger than the effective area of the small dipole. Therefore<br />
<math>A_{0.5\lambda }=0.1305\lambda ^2</math>
The area of a rectangle with one-half wavelength and one-quarter wavelength sides is <math>0.125\lambda ^2 </math> and it is, therefore, a good approximation for the effective areas of small dipoles and half-wavelength dipoles.
<math>A_{0.5}=0.1305\lambda^2</math><br />
<math>0.1305\lambda^2 = \pi r^2</math><br />
<math>\frac{0.1305}{\pi} \lambda^2 = r^2</math><br />
<math>0.04154 \lambda^2 = r^2 </math><br />
<math>\sqrt{0.04152 \lambda^2} =\sqrt{r^2}</math><br />
<math>r=0.2038\lambda</math>
'''B. Isotropic Antenna with No Heat Loss'''<br />
The hypothetical isotropic antenna has the same radiation intensity in all directions. It has two thirds of the gain’ or effective area of the small dipole. Therefore<br />
<math>A_{isotr.}=\frac{\lambda ^2}{4\pi}.</math> .<br />
'''(Ítem C Arrays ) '''<br />
[[File:Dimensiones en Lambda.png||centro|miniaturadeimagen|300x300px|Dimensiones en Lambda]]
[[File:Vista Frontal.png||centro|miniaturadeimagen|300x300px|Vista Frontal]]
[[File:Orden de los dipolos.png||centro|miniaturadeimagen|300x300px|Orden de los dipolos]]
<math>A_{pinetree}=n*0.5\lambda * 0.5\lambda</math><br />
'''C. Broadside Arrays (Pine- Tree Antennas)'''<br />
The effective area of an antenna array made up of a curtain of rows of half-wave dipoles spaced half a wavelength was calculated several years ago by the method of Pistolkors. Equal amplitude and phase of the currents in all the dipoles and no heat loss were assumed. The effective area of such an array with a reflector that doubled the gain was found to be approximately equal to the actual area occupied by the array; thus<br />
<math>A_{pire-tree} \approx n\times 0.5\lambda \times 0.5\lambda</math><br />
where n is the total number of half-wave dipoles in the front curtain. Formula (7) is a good approximation for large antennas. For example, an antenna of 6 rows of 17 dipoles each gave a calculated effective area only 3 per cent below the value obtained by (7). It should be pointed out that the heat loss in the connecting transmission lines will reduce the effective areas in actual antennas.<br />
[[File:N=102_dipolos_Ares(pineetree)_=_n_∗_0,_5λ_∗_0,_5λ.png||centro|miniaturadeimagen|300x300px| n=102 dipolos Ares(pineetree) = n ∗ 0, 5λ ∗ 0, 5λ]]
<math>Apt=102*0.5\lambda *0.5\lambda =\frac{51\lambda^2}{2}</math><br />
<math>A_{circulo}=\pi r^2----A_{pinetree}= 25.5\lambda ^2</math><br />
[[File:Radios.png||centro|miniaturadeimagen|300x300px|Radio]]
<math>\pi r^2 = 25.5\lambda</math><br />
<math>r^2 = \frac{25.5\lambda}{\pi}</math><br />
<math>r^2 = 8.117\lambda ^2</math><br />
<math>r= \sqrt{8.117\lambda^2}</math><br />
<math>r=2.849\lambda</math><br />
[[File:Diopole.png||centro|miniaturadeimagen|300x300px|Dipolo]]
.<br />
'''D. Parabolic Reflectors'''<br />
The effective area of the parabolic type of antenna with a proper feed has been found experimentally to be approximately two thirds of the projected area of the reflector.<br />
.<br />
'''(Ítem E)'''<br />
'''E. Electric Horns-Aperture Sides <math>>> \lambda</math>'''<br />
The effective area of a very long horn with small aperture dimensions is 81 per cent of the area of the aperture. For an optimum horn, where the aperture is dimensioned to give maximum gain for a given length of the horn, the effective area is approximately 50 per cent of the area of the aperture.<br />
.<br />
'''DERIVATION OF TRANSMISSION FORMULA (1)'''<br />
Having defined the effective area of an antenna, it is a simple matter to derive (1). As shown in Fig. 1, consider a radio circuit made up of an isotropic transmitting<br />
[[File:Explicacion figura.png|centro|miniaturadeimagen|300x300px|]]
antenna and a receiving antenna with effective area Ar. The power flow per unit area at the distance d from the transmitter is<br />
<math>P_0=\frac{P_t}{4\pi d^2}.</math><br />
Assuming a plane wave front at the distance d, definition (2) for the effective area and formula (8) give<br />
<math>\frac{P_r}{P_t}=\frac{A_r}{4\pi d^2}</math><br />
Replacing the isotropic transmitting antenna in the illustration with a transmitting antenna with effective area At will increase the received power by the ratio <math>At/A_isotr</math>, and we obtain<br />
<math>\frac{P_r}{P_t}=\frac{A_r}{4\pi d^2 A_{isotr}}</math><br />
Introducing the effective area (6) for the isotropic antenna, we have (1).<br />
'''LIMITATIONS OF TRANSMISSION FORMULA (1)'''<br />
In deriving (1), a plane wave front was assumed at the distance d. Formula (1), therefore, should not be used when d is small. W. D. Lewis, of these Laboratories, has made a theoretical study of transmission between large antennas of equal areas with plane phase fronts at their apertures and he finds that (1) is correct to within a few per cent when<br />
<math>d\geq \frac{2a^2}{\lambda }</math><br />
where a is the largest linear dimension of either of the antennas.<br />
Formula (1) applies to free space only, a condition which designers of microwave circuits seek to approximate. Application of the formula to other conditions may require corrections for the effect of the “ground,” and for absorption in the transmission medium, which are beyond the scope of this note.<br />
he advantage of (1) over other formulations is that, fortunately, it has no numerical coefficients. It is so simple that it may be memorized easily. Almost 7 years of intensive use has proved its utility in transmission calculations involving wavelengths up to several meters, and it may become useful also at longer wavelengths. It is suggested that radio engineers hereafter give the radiation from a transmitting antenna in terms of the power flow per unit area which is equal to <math>P_t A_t / \lambda^2 d^2 </math>, instead of giving the field strength in volts per meter. It is also suggested that an antenna be characterized by its effective area, instead of by its power gain or radiation resistance. The ratio of the effective area to the actual area of the aperture of an antenna is also of importance in antenna design, since it gives an indication of how efficiently the antenna is utilizing the physical space it occupies. *The directional pattern, which has not been discussed in this note,is, of course, always an important characteristic of an antenna.
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