Work satellite dishes, in particular those who take television signal, is based on the optical property of the parabola. A parabola is the locus of points equidistant from a straight line (called the directrix) and from a point not lying on the directrix (called the focus). From the above definition of a parabola, it is not difficult to get a "school" one: a parabola is a graph of a quadratic function y=ax^2+bx+c (in particular, y=x^2).

Let us formulate the mentioned optical property of the parabola. If a point source of light (a light bulb) is placed at the focus of the parabola and turned on, then the rays, reflected from the parabola, will go parallel to the axis of symmetry of the parabola, and the leading edge will be perpendicular to the axis.

The reverse is also true - if a stream of rays parallel to the axis of symmetry falls on a parabola, then, reflected from the parabola, the rays will come into focus, and at the same time, if the leading edge of the stream of rays is perpendicular to the axis.

When a parabola rotates around its axis of symmetry, a paraboloid of revolution is obtained - a surface of the second order. For any section of the paraboloid by planes passing through the axis of symmetry, equal parabolas with a common focus are obtained, therefore the paraboloid also has an optical property. If you place the emitter in focus, then the rays, reflected from the surface, will go parallel to the axis of rotation. And if rays parallel to its axis fall on a paraboloid, then after reflection they all gather in focus.

The optical property is the fundamental basis of parabolic antennas. Antennas can rotate, for example - parabolic antennas at airports, shaped like "slices" of huge paraboloids, they both transmit and receive a signal. Antennas may be fixed. The latter type includes household satellite television antennas("dish"): they are aimed at a relay satellite high above the Earth in geostationary orbit, after which their position is fixed.

Since the satellite is far from the surface, the rays coming from it at the point of reception by the antenna can be considered parallel. At the focus of the satellite dish is the receiver, from which the signal is sent via cable to the TV.

The same idea is used to create searchlights for railway locomotives, car headlights, it can even be used for cooking in the field. The optical property of the parabola "knows" the world of wildlife. For example, some northern flowers, living in conditions of short summer and lack of sunlight, open their petals in the form of a paraboloid, so that the "heart" of the flower is warmer. "Parabolic" are such alpine and arctic flowers as alpine backache, glacial bekvichia, polar poppy. Due to the optical property of the parabola, seed ripening is accelerated in such flowers. Another useful consequence of their parabolic property for flowers is the attraction of insects that like to “soak up” in the flower bowl, and this affects the process of pollen transfer (pollination).

APPENDIX 10

PARABOLIC DIRROR ANTENNA

Parabolic reflector antennas consist of two parts: a mirror and a feed.

The irradiator emits an electromagnetic wave towards the mirror. The wave front in space is formed as a result of the reflection of an electromagnetic wave from the surface of a mirror (reflector).

Mirror antennas are widely used, starting from the decimeter wavelength range. They are used in various radio engineering systems: radars, radio relay lines, radio astronomy, etc.

The initial data for calculating the reflector antenna are: wavelength https://pandia.ru/text/78/045/images/image002_222.gif" width="41" height="28 src=">.gif" alt="( !LANG:Signature: Fig. A10.2" align="left" width="253" height="220">!} .gif" width="87" height="25">.

For a given antenna gain, the mirror radius can be determined from the expression

, (A10.1)

where RO mirror opening radius; ν - coefficient of use of the surface of the mirror (KPI), - efficiency of the antenna.

On fig. 10.2 shows the dependence on the angle. In real parabolic antennas, the antenna efficiency (product) ranges from 0.45 to 0.6..gif" width="145" height="24 src=">. (A10.2)

In the event that the width of the antenna radiation pattern is given, then to select the size of the mirror, you can use the data in Table. P10.1.

Data for selecting the dimensions of the antenna mirror Table A10.1

			Sidelobe suppression
H-plane	E-plane

2. The parameters of a given type of irradiator are calculated.

It is necessary to design the irradiator so that it has unidirectional radiation. The radiation pattern should have axial symmetry with a minimum level of side lobes.

The phase center of the irradiator is at the focus of the mirror. The irradiator should obscure the mirror to a minimum extent.

Vibrator irradiator

The irradiator in the form of a symmetrical vibrator with a counter-reflector is used in the decimeter and long-wavelength part of the centimeter wave range (https://pandia.ru/text/78/045/images/image019_43.gif "alt="(!LANG: Signature:" align="left" width="278 height=247" height="247">ство щелевого типа.!}

The radiation pattern of a half-wave vibrator with a counter-reflector in a plane perpendicular to the vibrator axis (in the H-plane) is calculated by the formula

where d- distance from the vibrator to the counter-reflector,

The distance from the vibrator to the counterreflector, equal to , is necessary for the field reflected from the counterreflector to be in phase with the field that is radiated by the vibrator towards the mirror.

The radiation pattern of a half-wave vibrator with a counterreflector in the plane passing through the vibrator axis (and the mirror axis) is described by the expression

https://pandia.ru/text/78/045/images/image024_35.gif" width="107" height="41">; , where is the length of one arm of the vibrator, and h- the distance between the vibrator and its mirror image.

, Ohm, https://pandia.ru/text/78/045/images/image029_27.gif" width="65" height="23">, Ohm, a, Ohm

To match the irradiator with the supply feeder, it is necessary that the input impedance of the vibrator be purely active and equal to the wave impedance of the supply feeder.

The reactive component of the input resistance can be compensated either by a reactive loop, or by some shortening of the vibrator arms. Since in this case coaxial feeder, then its wave impedance is equal to

https://pandia.ru/text/78/045/images/image032_27.gif" width="23" height="18">- inner diameter of the outer conductor; d- outer diameter of the inner conductor; - relative permittivity of the material filling the coaxial feeder.

Usually set by the diameter of the vibrator arms 2 ... 4 mm and an equal diameter d and determine by the formula (A10.6) the value D. After choosing the dimensions of the coaxial line, it must be checked for a breakdown condition

KV/cm, (A10.7)

here P is the power passing through the line in kW; d- in cm; W- in Ohm; SWR should be taken equal to 1.2 ... 1.4.

If condition (A10.7) is not met, then it is necessary to increase the inner diameter of the coaxial line and the diameter of the vibrator arms in order to reduce the concentration of the electric field near the surface of a small curvature radius.

The coaxial line ends with a high-frequency connector for connecting a cable with a standard wave resistance(= 50, 75 ohms). If the coaxial line has, then a quarter-wave impedance matching transformer should be used, which is usually structurally performed in the section of the coaxial line.

double slit irradiator

An irradiator of this type is usually used at wavelengths shorter than 5 ... 6 cm. It is based on E- planar waveguide T- splitter. Branching in this case is carried out in the plane of the vector E waves H10(Fig. A10.4).

The development of the irradiator begins with the choice of a standard waveguide for a given operating wavelength range. The slot length is chosen equal to (0.47...0.48). Distance d1 from the slots to the walls should be equal. Distance between slots d2 is selected as in conventional antenna arrays, most often or. The slot width is selected from the condition of the absence of electrical breakdown at a given value of radiation power

, (A10.8)

where EPROB is the breakdown value of the field strength in the slot material. For air EPROB= 3 106 V/m. Max voltage equal to the gap

. (P10.9)

https://pandia.ru/text/78/045/images/image043_17.gif" width="128" height="25">,

where https://pandia.ru/text/78/045/images/image045_17.gif" width="108" height="27">,B

The radiation patterns of a double-slit irradiator are calculated by the formulas:

, in the plane E,(P10.11)

, in the plane N.(P10.12)

corners q and j are counted from the normal to the slot location plane..gif" width="83" height="21 src=">.

Horn irradiator

Horn feeds are used mainly in the centimeter and millimeter wavelengths https://pandia.ru/text/78/045/images/image051_15.gif" width="37" height="21"> and equal to 0.3 at q (j) = 50 ° ... 70 °, find the size of the opening of the horn.

In-plane horn directivity E can be estimated by the simplified formula

https://pandia.ru/text/78/045/images/image055_13.gif" width="323" height="41 src=">, (P10.14)

where the angles https://pandia.ru/text/78/045/images/image057_11.gif" width="20" height="18"> are measured from the normal to the horn opening plane.

Equations (A10.13) and (A10.14) are transcendental in relation to the dimensions of the horn opening and are solved by the selection method.

The length of the horn is usually taken equal to R = (1,2 … 1,3) ar, at which the wave front is spherical.

3. The antenna pattern is calculated.

The directivity characteristic of the antenna can be calculated by the approximate formula

https://pandia.ru/text/78/045/images/image059_11.gif" width="55" height="24"> – Bessel function of the first kind of the first order.

More precisely, the radiation pattern of a reflector antenna is calculated through the amplitude distribution of the field along the opening. To do this, the focus of the mirror is built in polar system coordinates of the irradiator radiation pattern, and along it the amplitude distribution of the field along the mirror (see Fig. A10.5).

https://pandia.ru/text/78/045/images/image061_12.gif" width="27" height="18">= 0; 0.5; 1.0, which are called interpolation nodes.

The approximating function is represented by a polynomial of the form

https://pandia.ru/text/78/045/images/image063_11.gif" width="57" height="22"> and the actual order function.

Lambda function can be expressed in terms of the Bessel function of the first kind of the same order

.

Values ​​of lambda functions are tabulated, their values ​​are given in Appendix 20.

The first factor in the expression (A10.20), which depends on the angle , has the form and is the radiation field of the elementary area - the Huygens element. The second factor, determined by the sum, is the grating factor, which characterizes the directional properties of the emitter system. The influence of the first factor when changing the angle can be neglected, since the radiation pattern of the Huygens element is much wider than the radiation pattern of a reflector antenna. Then the normalized antenna pattern is given by

https://pandia.ru/text/78/045/images/image081_7.gif" width="267" height="45 src=">. (P10.22)

In general, radiation patterns should be calculated for two planes: E and H. However, if the radiation pattern of the irradiator in the planes E and H approximately the same, then we can assume that the formula (A10.22) describes the directional properties of the reflector antenna in both planes..gif" width="93" height="44 src=">, (A10.23)

where DOBL- coefficient of directional action of the irradiator (usually 3 ... 6);

f- focal length.

5. The efficiency of the antenna-feeder path is calculated.

6. A constructive calculation of the antenna is carried out and its sketch is made.

The principle of operation of a parabolic antenna

A parabolic antenna is used to create highly directional radiation in the microwave range, when the dimensions of the antenna are many times greater than the operating wavelength. The antenna consists of a metal mirror (reflector) of a parabolic shape and a feed located at its focus. In this paper, we study an antenna with a mirror in the form of a paraboloid of revolution (Figure 1) with an aperture having the shape of a circle with a diameter of 2R. The straight line, perpendicular to the plane of the aperture and passing through its center, is the axis of the mirror, the point O of the intersection of the axis with the surface of the mirror is its apex. The distance f from the top of the mirror to the focus F is called the focal length. The following figure shows the path of rays in a parabolic antenna.

Figure 1 - Scheme of a parabolic antenna.

Figure 2 - The path of the rays in a parabolic antenna.

The choice of geometric dimensions of the parabolic mirror

To calculate the diameter of the mirror opening, we use the formula from radar:

We know all the values, then we express from the formula G - the antenna gain:

Knowing that G=D ?a, where D is the directivity of the antenna (assuming?a=1 - efficiency), G=D.

As a result, D=7127.

Where S is the geometric size of the mirror opening (S=?r2); ? - the mirror utilization factor, which indicates how efficiently the entire surface of the mirror is used, is usually 0.64 × 0.65 (0.7).

The aperture diameter of the mirror is a function of the required beamwidth, and also depends somewhat on the amplitude and phase response in the aperture of the mirror. The distribution law of the field amplitudes along the surface of the mirror opening is determined by the radiation pattern of the irradiator, if we neglect the losses during reflection from the mirror. For most feeds used, the distribution of amplitudes in one of the planes (horizontal or vertical) along the mirror opening can be approximated with sufficient accuracy by the law (1-x2) p, where x is the coordinate plotted from the antenna axis; p = 0,1,2,3 - some integer.

Let us calculate the radius of the convex part of the mirror. To do this, plot the function of the opening radius on the distance y(x) = (4f x) 0.5, where f is the distance to the focus. The result is a graph shown in Figure 12.

Figure 3 - The dependence of the opening radius on the distance.

The radius of the parabolic part of the mirror is 0.9m. As a result, the geometric dimensions of the mirror are completely determined.

The choice of irradiator, and its calculation

For further calculations, it is required to choose an irradiator that would satisfy this antenna. One of important parts parabolic antenna is the primary feed placed at the focus of the mirror. Ideally, the following requirements are imposed on it: 1) the irradiator should not radiate energy in the direction opposite to the direction to the mirror, since this radiation is not focused by the mirror and therefore distorts the main radiation pattern; 2) the irradiator diagram must ensure uniform irradiation of the mirror and thus obtain the maximum directivity; 3) the irradiator diagram should be such that the phase of the field in the mirror opening is constant. An irradiator that fully satisfies these requirements practically does not exist. When designing parabolic antennas, feeds are used in the form of a half-wave vibrator, the open end of the waveguide, a horn and a slot, although they only partially satisfy the listed requirements.

Let us consider in more detail some types of irradiators.

Antennas parabolic antennas also play an important role in cellular communication. The main area of ​​​​their application is the organization of transport channels for the base station (). As a rule, they are used in radio relay lines () communications, much less often in satellite ones. However, in both cases, the principle of operation remains unchanged. A parabolic antenna consists of two main elements: a parabolic mirror and an emitter at some distance from the mirror, which transmits and receives the emitted signal. The principle of operation of a parabolic antenna is based on the fact that all rays falling on the mirror are focused at a single point - the focus of the parabola, where the signal receiver is located. At the same time, all rays emitted from the focus will be transmitted in the same direction. Main Feature A parabolic antenna is a needle-shaped radiation pattern characterized by a long and narrow main lobe.

By design, parabolic antennas can be quite different from each other. This is influenced by many parameters such as the frequency range used, the radiated power, the distance between objects, the capacity of the communication channel, and many others. In the event that a parabolic antenna is used in, then the antenna is usually placed in a special protective plastic case that prevents external negative conditions. The diameter of the mirror of a parabolic antenna can be from 30 cm to several meters. The frequency can also be selected from a wide range ranging from 3 to 40 GHz. Usually guided by the rule: the longer the span, the lower the frequency used and the larger the diameter of the antenna. A radio module is attached to the rear of the antenna using a waveguide, which converts the high-frequency signal of the gigahertz range used to transmit information through open space into a medium frequency signal of the megahertz range, transmitted to the internal module of the system.

Types of parabolic antennas

Parabolic antennas for satellite communications have a slightly different design. Usually, in such antennas, the radiator is located not in the center of the antenna, but with some offset, i.e. the focus of the parabola is offset from its axis. This is necessary in order not to create additional shading obstacles in the path of the received signal. Antennas for satellite communication are usually larger in diameter and not enclosed in a protective housing. Otherwise, the principle of their operation is similar to antennas.

Reception of satellite television signals is carried out by special receivers, an integral part of which is the antenna. Parabolic antennas are the most popular for professional and amateur transmissions from satellites, due to the property of a paraboloid of revolution to reflect the rays incident on its aperture, parallel to the axis, to one point, called the focus. The aperture is the part of the plane bounded by the edge of the paraboloid of revolution.

A paraboloid of revolution, which is used as an antenna reflector, is formed by rotating a flat parabola around its axis. A parabola is the locus of points equidistant from given point(focus) and a given straight line (directrix) (Fig. 6.1). Point F is the focus and line AB is the directrix. Point M with coordinates x, y is one of the points of the parabola. The distance between the focus and the directrix is ​​called the parameter of the parabola and is denoted by the letter p. Then the coordinates of the focus F are: (p/2, 0). The origin of coordinates (point 0) is called the vertex of the parabola.

By definition of a parabola, the segments MF and PM are equal. According to the Pythagorean theorem MF^2 =FK^2+ MK^2. At the same time FK = x - p/2, KM = y and PM = x + p/2, then (x - p/2)^2 + y^2 = (x + p/2)^2.

Squaring the expressions in brackets and bringing like terms, we finally obtain the canonical equation of the parabola:

y^2 = 2px, or y = (2px)^0.5. (6.1)

According to this classic formula, millions of antennas are made to receive signals. satellite television. What is it about this antenna?

Parallel to the axis of the paraboloid, the rays (radio waves) from the satellite, reflected from the aperture to the focus, pass the same (focal length). Conventionally, two beams (1 and 2) fall on the opening area of ​​the paraboloid at different points (Fig. 6.2). However, the reflected signals of both beams pass to the focus F same distance. This means that distance A+B=C+D. Thus, all the rays emitted by the transmitting antenna of the satellite and to which the paraboloid mirror is directed are concentrated in phase at the focus F. This fact is proved mathematically (Fig. 6.3).

The choice of the parabola parameter determines the depth of the paraboloid, i.e. the distance between the vertex and the focus. With the same aperture diameter, short-focus paraboloids have a large depth, which makes it extremely inconvenient to install the irradiator in focus. In addition, in short-focus paraboloids, the distance from the feed to the top of the mirror is much less than to its edges, which leads to uneven amplitudes at the feed for waves reflected from the edge of the paraboloid and from the zone close to the top.

Long-focus paraboloids have a shallower depth, the irradiator installation is more convenient and the amplitude distribution becomes more uniform. So, with an aperture diameter of 1.2 m and a parameter of 200 mm, the depth of the paraboloid is 900 mm, and with a parameter of 750 mm - only 240 mm. If the parameter exceeds the aperture radius, the focus, in which the feed should be located, is located outside the volume bounded by the paraboloid and the aperture. The optimal option is when the parameter is slightly larger than the aperture radius.

A satellite dish is the only amplifying element of the receiving system that does not introduce its own noise and does not degrade the signal and, consequently, the image. Antennas with a mirror in the form of a paraboloid of revolution are divided into two main classes: symmetrical parabolic reflector and asymmetric (Fig. 6.4, 6.5). The first type of antennas is usually called direct focus, the second - offset.

The offset antenna is, as it were, a cut out segment of a parabola. The focus of such a segment is located below the geometric center of the antenna. This eliminates the shading of the usable area of ​​the antenna by the feed and its supports, which increases its coefficient beneficial use for the same mirror area with an axisymmetric antenna. In addition, the feed is installed below the center of gravity of the antenna, thereby increasing its stability under wind loads.

It is this design of the antenna that is most common in the individual reception of satellite television, although other principles for constructing terrestrial satellite antennas are currently used.

It is advisable to use offset antennas if the antenna size up to 1.5 m is required for stable reception of the programs of the selected satellite, since with an increase in the total area of ​​the antenna, the mirror shading effect becomes less significant.

The offset antenna is mounted almost vertically. Depending on the geographical latitude the angle of its inclination changes slightly. This position excludes the collection of atmospheric precipitation in the antenna bowl, which greatly affects the quality of reception.

The principle of operation (focusing) of direct focus (axisymmetric) and offset (asymmetric) antennas is shown in fig. 6.6.

For antennas, directional characteristics are of particular importance. Thanks to the ability to use antennas with high spatial selectivity, satellite television is received. The most important characteristics of antennas are gain and radiation pattern.

The gain of a parabolic antenna depends on the diameter of the paraboloid: the larger the diameter of the mirror, the higher the gain.

The dependence of the parabolic antenna gain on the diameter is shown below.

The role of the parabolic antenna gain can be analyzed using a light bulb (Fig. 6.7, a). The light is evenly scattered into the surrounding space, and the observer's eye perceives a certain level of illumination corresponding to the power of the light bulb.

However, if a light source is placed at the focus of a paraboloid with a gain of 300 times (Fig. 6.7, b), its rays, after reflection by the surface of the paraboloid, will be parallel to its axis, and the color strength will be equivalent to a source with a power of 13,500 watts. The observer's eyes cannot perceive such illumination. On this property, in particular, the principle of operation of the spotlight is based.

Thus, the antenna paraboloid, strictly speaking, is not an antenna in its understanding of the transformation of the electromagnetic field strength into a signal voltage. A paraboloid is only a reflector of radio waves, concentrating them at a focus, where the active antenna (feeder) should be placed.

The antenna pattern (Fig. 6.8) characterizes the dependence of the amplitude of the electric field strength E, created at a certain point, on the direction to this point. In this case, the distance from the antenna to this point remains constant.

An increase in the gain of the antenna entails a narrowing of the main lobe of the radiation pattern, and narrowing it to less than 1 ° leads to the need to supply the antenna with a tracking system, since geostationary satellites oscillate around their stationary position in orbit. An increase in the width of the radiation pattern leads to a decrease in the gain, and hence to a decrease in the signal power at the receiver input. Based on this, the optimal width of the main lobe of the radiation pattern is a width of 1 ... 2 °, provided that the transmitting satellite antenna is kept in orbit with an accuracy of ± 0.1 °.

The presence of side lobes in the radiation pattern also reduces the gain of the antenna and increases the possibility of receiving interference. In many ways, the width and configuration of the radiation pattern depend on the shape and diameter of the receiving antenna mirror.

most important characteristic parabolic antenna is shape accuracy. It should repeat the shape of a paraboloid of revolution with minimal errors. Shape accuracy determines the gain of the antenna and its radiation pattern.

It is almost impossible to make an antenna with a perfect paraboloid surface. Any deviation from the real shape of the parabolic mirror from the ideal one affects the characteristics of the antenna. Phase errors occur, which degrade the quality of the received image, and the antenna gain decreases. Shape distortion also occurs during the operation of antennas: under the influence of wind and precipitation; gravity; as a result of uneven heating of the surface by the sun's rays. Taking into account these factors, the allowable total deviation of the antenna profile is determined.

The quality of the material also affects the characteristics of the antenna. For the manufacture of satellite dishes, steel and duralumin are mainly used.

Steel antennas are cheaper than aluminum ones, but heavier and more prone to corrosion, so anti-corrosion treatment is especially important for them. The fact is that a very thin near-surface metal layer participates in the reflection of an electromagnetic signal from the surface. If it is damaged by rust, the efficiency of the antenna is significantly reduced. It is better to first cover a steel antenna with a thin protective layer of some non-ferrous metal (for example, zinc), and then paint it.

With aluminum antennas, these problems do not arise. However, they are somewhat more expensive. The industry also produces plastic antennas. Their mirrors with a thin metal coating are subject to shape distortion due to various external influences: temperature, wind loads and a number of other factors. There are mesh antennas that are resistant to wind loads. They have good weight characteristics, but have proven themselves poorly when receiving Ki-band signals. It is advisable to use such antennas for receiving C-band signals.

A parabolic antenna at first glance seems like a rough piece of metal, but nevertheless it requires careful handling during storage, transportation and installation. Any distortion of the shape of the antenna leads to a sharp decrease in its efficiency and a deterioration in the quality of the image on the TV screen. When buying an antenna, you need to pay attention to the presence of distortion of the working surface of the antenna. Sometimes it happens that when anti-corrosion and decorative coatings are applied to the antenna mirror, it “leads” and it takes the form of a propeller. You can check this by placing the antenna on a flat floor: the edges of the antenna should touch the surface everywhere.