Theoretical part

1. Purpose and features of waveguide slot antennas

The waveguide-slot antenna (WSA) belongs to the class of linear (flat) multi-element antennas. The radiating elements of such antennas are slots cut in the walls of waveguides, cavity resonators or metal bases of strip lines. In practice, VSCHA with a directional pattern (DP) fixed in space is used, as well as VSCHA with mechanical, electromechanical and electrical scanning.

The advantages of VSCHA include:

The absence of protruding parts, which allows their radiating surface to be combined with the outer surface of the aircraft body, without introducing additional aerodynamic drag;

A relatively simple exciting device and easy to operate.

The main disadvantage of VSCHA is the limited range properties. When the frequency changes in a non-scanning VSC, the beam deviates from the specified position in space, which is accompanied by a change in the width of the pattern and a violation of the coordination of the antenna with the supply feeder.

2. Basic parameters of the slot in the waveguide

A slit cut into a waveguide will be excited if its wide side crosses currents flowing along the inner walls. When constructing a VSC based on a rectangular waveguide with the main wave H 10, it is necessary to take into account that in the wide wall of the waveguide there are longitudinal and transverse components of the surface current, and in the narrow wall there are only transverse ones. Slots can be cut in wide and narrow walls of the waveguide.

Let us consider a slot located on the wide wall of the waveguide longitudinally relative to the axial (middle) line of the wide wall (Fig. 1).

Such a gap is excited by the transverse component of the current if it is displaced relative to midline at a distance x 1. At x 1 =0 there is no radiation from the gap. By changing the magnitude of the slit displacement x 1, the intensity of its radiation can be adjusted.

When the slot is excited by currents flowing along the inner walls of the waveguide, electromagnetic energy is emitted both into the external space and into the waveguide. To analyze the operation of the gap, the concepts of external and internal conductivity of the gap are introduced, determined by the external and internal radiation of the gap, respectively. Knowing the values ​​of these conductivities, it is possible to determine the resonant frequency of slits of different lengths and trace its dependence on the location on the wall of the waveguide.

As is known, a slit cut in a waveguide disrupts its operating mode, causing reflection of energy: part of it is emitted, the rest passes further along the waveguide. Thus, we can consider that the slot serves as a load for the waveguide, on which part of the power equivalent to the radiation power is dissipated. Therefore, to simplify the analysis, you can replace the waveguide with an equivalent two-wire line, into which loads are connected in parallel or in series, depending on the type of slot (a longitudinal slot is equivalent to a parallel connection, a transverse slot is equivalent to a serial connection).

3. Varieties of VSCHA

According to the principle on which the operation of the VSC is based, a distinction is made between resonant and non-resonant waveguide slot antennas.

In resonant antennas, the distance between adjacent slits is chosen equal to l B (slots in-phase connected to the waveguide field) or l B /2 (slots in-phase connected to the waveguide field), where l B is the wavelength in the waveguide, and at the end of the waveguide install a short-circuiting piston. Thus, resonant antennas are in phase and, therefore, the direction of their maximum radiation coincides with the normal to the longitudinal axis of the antenna. In-phase excitation of longitudinal slots located on different sides relative to the center line is ensured by an additional 180° phase shift caused by opposite currents on both sides of the axial line of the wide wall of the waveguide.

The resonant antenna can be well matched with the supply feeder in a fairly narrow frequency band. Indeed, since each slot is not separately matched with the waveguide, all the waves reflected from the slots add up at the antenna input in phase and the reflection coefficient of the system becomes large. Therefore, they usually abandon the common-mode excitation of individual slits and choose the distance between them d¹l V /2.

A characteristic feature of the non-resonant waveguide-slot antenna (NVSA) obtained in this way is a wider frequency band, within which there is good matching, since individual reflections with a large number of emitters are almost completely compensated. However, the difference between the distance between the slits and l B /2 leads to their out-of-phase excitation by the incident wave and a deviation of the direction of the main maximum of radiation from the normal to the antenna axis. To eliminate reflection from the end of the waveguide, a termination load is usually installed.

As stated above, NVShchA has good coordination with the feeder over a fairly wide range. The exception is the case when d»l B /2; in this case, the reflected waves add up in phase and the traveling wave coefficient (TWC) in the waveguide drops sharply. This type of change in the BV as the distance between the slits approaches the value l B /2 is called the normal effect.

The disadvantage of NVShCHA is that it has a smaller coefficient than that of resonant antennas. useful action(to increase it, the intensity of slot excitation should be increased) and irremovable amplitude distortions (to reduce them, the intensity of slot excitation should be reduced). Based on this, the intensity of excitation must be chosen based on compromise considerations.

4. Features of antennas for Doppler measurement of aircraft speed and drift angle (DISS antennas)

The task of determining the true location of an aircraft in space when exposed to meteorological factors can be solved if the longitudinal and transverse components of its speed are known. These quantities are usually determined indirectly by measuring Doppler frequencies. It is known that a radio signal with frequency f, reflected from an object (for example, from an aircraft) moving in space with speed V, receives an additional frequency increment

,

where a is the angle between the velocity vector and the radial direction on the aircraft. The sign of the Doppler increment is positive if the object is moving towards the radio source, and negative if the object is moving away from it.

DISS antennas allow, by measuring Doppler components, to determine the longitudinal and transverse speeds of the aircraft, and the speed of its movement in the vertical direction. Such antennas form four beams as shown in Fig. 2.

Since the Doppler components caused by the movement of the aircraft at a certain speed in the front and rear beams have different sign, and the random (interference) components in them are approximately the same, then by subtracting the signals from the second pair of beams from the signals of the first pair, it is possible to compensate for the interference and, therefore, increase the accuracy of measuring the aircraft speed.

Antennas for Doppler measurement of aircraft speed and drift angle are often built on the basis of VSCHA arrays. To protect from precipitation and dust, the opening of the antenna arrays is covered with a dielectric plate or the entire radiating system is placed in a radio-transparent radome.

antenna waveguide slot Doppler

5. Calculation of VShchA

5.1 Calculation of the wide wall of the waveguide

Let's solve the system of equations from which we find a and lcr.

and it is necessary to choose such that the wavelength in the waveguide is 0.9 of the critical wavelength.

5.2 Calculation of the distance between the slits d, take μmax = -20 degrees, d will be found by solving the equation.

a short-circuited quarter-wave section of a two-wire line is formed. Having a high input resistance, it does not allow currents to branch off to the outer shell of the feeder. Since the resistance between points “a” and “b” is high, the arms of the vibrator at the radiation frequency are electrically isolated, despite the galvanic connection between them. The edges of the slots are usually made widening to ensure matching of the wave impedance of the feeder with the input impedance of the vibrator.

			λ /2					U-elbow (Fig. 3.20). This
								curved	coaxial feeder
								length λ /2,	to the internal pro-
								whose water is connected
								vibrator shoulders. External
								the feeder tray for feeding the shoulders is not
								used and grounded. On the-
								voltages and currents at points "a" and
			λ /2					"b" are equal in size and opposite
								are opposite in phase, as required
								available for symmetrical
aerial power supply. Except							symmetry		U-knee reduces

The input impedance of the vibrator is 4 times. In this regard, it is convenient to use it to power the Pistelkors loop vibrator, the input impedance of which is 300 Ohms, with a standard feeder with ρ f = 75 Ohms.

3. 2. Slot antennas

3.2.1. Types of slot antennas. Features of their design

A slot antenna is a narrow slit cut into metal surface screen, resonator shell or waveguide. Slot width d<<λ , длина обычно близка к половине волны. Щели прорезаются так, чтобы они пересекали линии поверхностного тока, текущего по внутренней стенке волновода или резонатора (рис. 3.21). Возможны различные положения щелей (см. рис. 3.21): поперечная (1), продольная (2), наклонная (3), и разнообразные их формы: прямолинейные, уголковые, гантельные, крестообразные (рис. 3.22).

A high-frequency surface current, crossing the gap, induces alternating charges (voltage) along its edges, and on the reverse (outer) side

It is not the surface that currents are excited. The electric field in the gap and currents on the surface are sources of radiation and form in space

		electromagnetic field.
			The simplest
		are
		different sizes with a slot,
		resonator slot
		and waveguide-slit
			Excitation
		half-wave slits in the ex-
			carried out in
		meter		range
		using symmetrical
		two-wire line, and

and in decimeter - using a coaxial transmission line. In this case, the outer conductor is connected to one edge of the slot, and the inner conductor is connected to the other. To match the transmission line with the antenna, the feed point is shifted from the middle of the slot to its edge. Such an antenna can radiate into both hemispheres. In the centimeter range and the adjacent part of the decimeter range, resonator and waveguide-slot antennas are used (see Fig. 3.21, 3.22). In coaxial waveguides, only transverse or inclined slots are excited; in rectangular waveguides, various slot placement options are possible (see Fig. 3.21).

The slot width affects the active and reactive parts of the input resistance. Both components increase with increasing slit width. Therefore, to compensate for Xin, it is necessary to reduce the length of the slot (shorten it). An increase in Rin leads to an expansion of the slot antenna's bandwidth. Typically, the slot width d is selected in the range (0.03...0.15)λ. To further expand the bandwidth, dumbbell slots and special designs of exciting devices are used.

In addition to the range, the choice of slot width is influenced by the condition for ensuring electrical strength. The concentration of electric charges at the edges of the gap leads to local overvoltages and the occurrence of electrical

where E ь max is the electric field strength at the antinode. Taking E ь max = E μ (breakdown voltage, for dry air E μ = 30 kV/m), we find

d min= U ы max/ E pr.

In practice, choose d ≥ K spare d min, where K spare =2…4 is the reserve coefficient

Slots of more complex shapes than rectangular ones can be considered as combinations of simple ones. They are used to produce electromagnetic waves with the required polarization properties. For example, a cross-shaped slot allows you to obtain an antenna with elliptical and circular polarization. The direction of rotation depends on the direction of displacement of the slit from the axis of the wide wall of the waveguide.

Slot antennas are distinguished by their simple design, high reliability and the absence of protruding parts, which allows them to be used in aircraft and ground antenna systems as independent antennas, feeds for complex antenna systems and elements of antenna arrays.

3.2.2. Single slot. Pistelkors' principle of duality

Let's consider the characteristics and parameters of the so-called ideal slot antenna, i.e. a single slit cut into a perfectly conducting flat screen. Calculating the field of such an antenna using the equations of electrodynamics presents significant difficulties. It is greatly simplified if we use the principle of duality formulated by Pistelkors in 1944. This principle is based on the permutational duality of Maxwell's equations, known from the theory of the electromagnetic field. For a gap these equations have the form:

If the screen is removed and the slit is replaced by an ideal flat vibrator of the same dimensions as the slit (Fig. 3.23), and with the same current distribution as the voltage distribution along the slit (an equivalent vibrator cut from the screen to form the slit), then the field emitted they will also

will satisfy Maxwell's equations

rotHr B = iωε 0 EB ,

rotEB = − iωμ 0 H B ,

but under other boundary conditions:

in place of the screen - E τ

≠ 0, H τ = 0 ; on the vibrator - E τ B = 0, H τ B ≠ 0. (3.29)

Comparing the boundary conditions of the slot (3.27) and the equivalent vibrator (3.29), we can verify that the structures of the electric field near the slot and the magnetic field near the vibrator coincide. The boundary conditions for the equivalent vibrator are obtained from the boundary conditions for the slot by rearranging E ↔ H. Taking into account the above, for the complete field in the entire space we can write:

E r = C 1 H B , H = C 2 E B ,

where C 1 and C 2 are constant coefficients.

In practice, half-wave slits are usually used. In this case, regardless of the excitation method, the amplitude of the electric field in the gap is maximum in the center and decreases towards the edges, i.e. corresponds to the law of current distribution in a half-wave vibrator. For a narrow slit (thin vibrator), the boundary conditions, and therefore the constant coefficients, can be expressed as

voltage at the center of the slot U 0 and current at the center of the vibrator I 0 (see Fig. 3.23):

	U 0 , H				Where does C = 2 U 0 come from.

Then the first expression in (3.31) will be rewritten as:

E =			H B .

Thus, the principle of duality as applied to slot antennas is formulated as follows: the electric field of a slot antenna, up to a constant factor, coincides with the magnetic field of an additional vibrator of the same dimensions as the slot and with the same amplitude distribution.

This means that the EMF of the slot and the equivalent vibrator are different

between themselves only by rotating the corresponding vectors E r ы and E B by 90°,

H r sch and H B .

Applying the principle of duality, we can write for the radiation patterns:

F u (θ ) H = F B (θ ) E ;

F u(θ) E = F B (θ) H,

where F sch (θ ) H , F sch (θ ) E - normalized DN gaps in the planes H and E corresponding

responsibly; F B (θ ) H , F B (θ ) E are the corresponding normalized patterns of the half-wave vibrator.

When the angle θ is measured from the normal to the slit plane, the radiation pattern of the half-wave slit will be written in accordance with equality (3.33) in the form:

	cos(π sinθ )
F ы(θ ) H =				F ы (θ )E = 1.y				screen measures exist
					DN form, and their sub-
					rectify
					planes.

The resistance of the slit, as well as the vibrator, is complex and depends on its dimensions (length 2l and width d). The values ​​of Rw in and X w in are calculated for different values ​​of l / λ and are given in the form of graphs in reference and educational literature. The reactive component of the gap is capacitive in nature. However, the gap can also be adjusted by shortening it. The amount of shortening is calculated using the formula:

							ln(2λ π d )

As follows from (3.35), wider slits are shortened by a larger amount.

The input resistance of the slot is related to the input resistance of the vibrator complementing it. It is more convenient to express this relationship in terms of the complex input gap conductance:

Z inv

(60π )2

Thus, the input conductivity of the gap is determined by the expression

(60π )2

where ρ A = 120 ln

− 0,577

Wave impedance of the slot.

π d

Complex input conductance of a half-wave slot

Radio magazine, number 9, 1999.

Judging by foreign amateur radio literature, the skeleton-slot antenna is popular at frequencies above 20 MHz. The published article attempts to answer the question - to what extent its directional coefficient stated in the literature corresponds to reality.

In books on VHF antennas, the so-called skeleton-slot antenna has been repeatedly described, and all publications, without exception, reported on its very high parameters, large directivity coefficient (DA), wide frequency band and ease of tuning. The idea of ​​the antenna was proposed by J. Ramsey back in 1949, its design is shown in Fig. 1,borrowed from . The active element of the antenna consists of three parallel half-wave dipoles located three levels above each other.

To reduce the size of the antenna, the ends of the upper and lower dipoles are bent at right angles towards the middle dipole and connected to it. This is what gets them excited. The middle dipole is made split and connected to a matching quarter-wave two-wire line, which also serves to mount the reflector. The reflector is designed like a wave channel in the form of a single vibrator, the electrical length of which is slightly greater than a half-wave. The dimensions of the antenna in wavelengths and the values ​​of the shortening coefficient k, depending on the diameter of the conductors (tubes) d, are shown in Fig. 1. By moving the feed point XX along the two-wire line, you can change the input impedance of the antenna from zero (near the reflector) to approximately 400 Ohms (at point YY near the active element).

The current distribution in the active element is shown in Fig. 2. It can be seen that the antinodes (maxima) of the current are located exactly in the middle of the horizontal parts of the element, forming a three-story in-phase system. In the vertical parts of the active element, the currents are small and directed towards each other. In addition, there are four current nodes here, so there is no far-field radiation from the vertical parts. Let us recall that in the far zone the antenna radiation pattern is almost completely formed. The distance to the far zone is several wavelengths. The greater the antenna efficiency, the greater it is.

The active element of a skeleton-slot antenna can also be considered as two squares, combined with one side and feed points. However, compared to two full-size squares, the perimeter of the active element of the skeleton-slot antenna is somewhat smaller, probably due to the shortening effect of the capacitance between the vertical conductors of the element. A similar antenna was proposed by K. Kharchenko, but in it two squares are fed from the corners and combined with feed points.

A simple skeleton-slot antenna has a reflector that is not efficient enough. This drawback can be eliminated by constructing the reflector in exactly the same way as the active element (in the form of the same three-story structure of vibrators). Two-wire lines can no longer be placed between the elements, but no one bothers to draw them in the plane of each element to the point with zero potential in the middle of the lower horizontal vibrator.

What happens after this modification is shown in Fig. 3. The dimensions of the elements themselves remain the same, and the distance between the active element and the reflector is reduced to 0.18. This antenna has one more advantage. By moving short-circuiting jumpers along two-wire lines, the elements can be adjusted to the desired frequency, and by moving the reflector jumper, it is easy to adjust the antenna to the maximum efficiency or forward-backward radiation ratio.

For such a two-element antenna, described in [and], an unusually high efficiency of 14...16 dB is reported! If the second of the books mentioned was not a serious publication, then one could still give up and not take this figure seriously. But this book is overall very good and contains almost no errors. Its author, of course, could not test all the many constructions given in it. Therefore, if this is an error, then it appeared earlier, in some other publications, and it is now difficult to find the original source. It is quite clear that an in-phase system of vibrators should give greater efficiency than a single vibrator, but the question is - how much? Although on p. 100 and it is stated that the antenna “... is actually a six-element, three-story in-phase antenna,” but the vibrators are quite close to each other, and also shortened. This is bound to reduce efficiency. Thus, there were more questions than answers. In addition, radio amateurs familiar to the author were planning to build just such an antenna for the 10-meter range and were ready to spend money on the material, which is not cheap these days!

To get a clear and precise answer to the question about the directivity factor, an experiment was conducted in the 432 MHz range. The elements were bent in accordance with Fig. 3 pieces of enameled copper wire with a diameter of 1.5 mm, the connections are soldered, and the line conductors in the places where the closing jumpers are installed and the cable is connected are stripped of insulation. The entire structure was assembled on a wooden frame made of dry thin slats. The power cable ran from the power points along the two-wire line conductor to which the braid was connected, vertically down and connected directly to the output of the standard signal generator. The field indicator was a half-wave dipole with a detector and a microammeter. It was located on a tripod at a distance of several meters from the antenna. The antenna was also mounted on a primitive rotating tripod, which made it possible to change its orientation.

The antenna was tuned quite easily and quickly, just for maximum radiation in the main direction. With the indicated dimensions at a frequency of 432 MHz, the distances of the closing jumpers from the base of the two-wire lines for the tuned antenna turned out to be as follows: for the reflector - 43 mm, for the active element - 28 mm. The distance to the connection point of the 50-ohm cable was 70 mm.

When adjusted to maximum directivity, a small back lobe is detected. By adjusting the reflector, it can be suppressed almost completely. There was no sideways, up or down radiation.

The efficiency, or more precisely, the gain of the antenna, equal to the product of the efficiency and efficiency, was determined as follows: the signal level created by the antenna in the main direction was noted on the indicator, then, instead of the antenna, a half-wave dipole located at the same point in space was connected to the power cable. The signal level from the generator increased enough to obtain the same readings on the indicator. The change in signal level measured by the generator attenuator is numerically equal to the gain of the antenna relative to the half-wave dipole. For this antenna it turned out to be 7 dBd. Compared to an isotropic (omnidirectional) emitter, it will be 2.15 dB more and will be about 9.2 dBi.

Pay attention to the letters d and i in the designation of decibels - in the literature on antennas this is how it is customary to indicate relative to which emitter the directivity is measured. The width of the radiation pattern at half power was about 60° in the horizontal plane (in azimuth), and about 90° in the vertical plane (in elevation). Having this data, the directivity can be calculated in one more way: the solid angle into which the antenna radiates is equal to the product of linear angles corresponding to the width of the diagram and expressed in radians. We get a value of about 1.5 steradians. At the same time, an isotropic antenna radiates into a solid angle of 4, or 12.6 steradians. The directivity, by definition, is the ratio of these solid angles and is 12.6/1.5 = 8.4 or 9.2 dBi.

Having obtained such a good agreement between the directivity values ​​determined by the two methods, the author decided that there was nothing more to measure and, with slight disappointment, he was once again convinced that miracles do not happen in antenna technology. Nevertheless, the antenna works very well and, despite its small dimensions (330x120x120 mm in the 432 MHz range), provides a very decent gain.

• Translation

The article for translation was proposed by alessandro893. The material is taken from an extensive reference site, describing, in particular, the principles of operation and design of radars.

An antenna is an electrical device that converts electricity into radio waves and vice versa. The antenna is used not only in radars, but also in jammers, radiation warning systems and communications systems. During transmission, the antenna concentrates the energy of the radar transmitter and forms a beam directed in the desired direction. When receiving, the antenna collects the returning radar energy contained in the reflected signals and transmits them to the receiver. Antennas often vary in beam shape and efficiency.

On the left is an isotropic antenna, on the right is a directional antenna

Dipole antenna

A dipole antenna, or dipole, is the simplest and most popular class of antennas. Consists of two identical conductors, wires or rods, usually with bilateral symmetry. For transmitting devices, current is supplied to it, and for receiving devices, a signal is received between the two halves of the antenna. Both sides of the feeder at the transmitter or receiver are connected to one of the conductors. Dipoles are resonating antennas, that is, their elements serve as resonators in which standing waves pass from one end to the other. So the length of the dipole elements is determined by the length of the radio wave.

Directional pattern

Dipoles are omnidirectional antennas. For this reason, they are often used in communication systems.

Antenna in the form of an asymmetric vibrator (monopole)

An asymmetrical antenna is half of a dipole antenna, and is mounted perpendicular to the conducting surface, a horizontal reflecting element. The directivity of a monopole antenna is twice that of a double-length dipole antenna because there is no radiation underneath the horizontal reflective element. In this regard, the efficiency of such an antenna is twice as high, and it is capable of transmitting waves further using the same transmission power.

Directional pattern

Wave channel antenna, Yagi-Uda antenna, Yagi antenna

Directional pattern

Corner antenna

A type of antenna often used on VHF and UHF transmitters. It consists of an irradiator (this can be a dipole or a Yagi array) mounted in front of two flat rectangular reflective screens connected at an angle, usually 90°. A sheet of metal or a grating (for low-frequency radars) can act as a reflector, reducing weight and reducing wind resistance. Corner antennas have a wide range, and the gain is about 10-15 dB.

Directional pattern

Vibrator log-periodic (logarithmic periodic) antenna, or log-periodic array of symmetrical vibrators

A log-periodic antenna (LPA) consists of several half-wave dipole emitters of gradually increasing length. Each consists of a pair of metal rods. The dipoles are attached closely, one behind the other, and connected to the feeder in parallel, with opposite phases. This antenna looks similar to the Yagi antenna, but it works differently. Adding elements to a Yagi antenna increases its directivity (gain), and adding elements to an LPA increases its bandwidth. Its main advantage over other antennas is its extremely wide range of operating frequencies. The lengths of the antenna elements relate to each other according to a logarithmic law. The length of the longest element is 1/2 the wavelength of the lowest frequency, and the shortest is 1/2 the wavelength of the highest frequency.

Directional pattern

Helix antenna

A helical antenna consists of a conductor twisted into a spiral. They are usually mounted above a horizontal reflective element. The feeder is connected to the bottom of the spiral and the horizontal plane. They can operate in two modes - normal and axial.

Normal (transverse) mode: The helix dimensions (diameter and inclination) are small compared to the wavelength of the transmitted frequency. The antenna operates in the same way as a shorted dipole or monopole, with the same radiation pattern. The radiation is linearly polarized parallel to the axis of the spiral. This mode is used in compact antennas for portable and mobile radios.

Axial mode: the dimensions of the spiral are comparable to the wavelength. The antenna works as a directional one, transmitting the beam from the end of the spiral along its axis. Emits radio waves of circular polarization. Often used for satellite communications.

Directional pattern

Rhombic antenna

A diamond antenna is a broadband directional antenna consisting of one to three parallel wires fixed above the ground in the shape of a diamond, supported at each vertex by towers or poles to which the wires are attached using insulators. All four sides of the antenna are the same length, usually at least the same wavelength, or longer. Often used for communication and operation in the decameter wave range.

Directional pattern

Two-dimensional antenna array

Multi-element array of dipoles used in the HF bands (1.6 - 30 MHz), consisting of rows and columns of dipoles. The number of rows can be 1, 2, 3, 4 or 6. The number of columns can be 2 or 4. The dipoles are horizontally polarized and a reflective screen is placed behind the dipole array to provide an amplified beam. The number of dipole columns determines the width of the azimuthal beam. For 2 columns the width of the radiation pattern is about 50°, for 4 columns it is 30°. The main beam can be tilted 15° or 30° for maximum coverage of 90°.

The number of rows and the height of the lowest element above the ground determines the elevation angle and the size of the serviced area. An array of two rows has an angle of 20°, and an array of four has an angle of 10°. The radiation from a two-dimensional array usually approaches the ionosphere at a slight angle, and due to its low frequency, is often reflected back to the earth's surface. Since radiation can be reflected many times between the ionosphere and the ground, the antenna's action is not limited to the horizon. As a result, such an antenna is often used for long-distance communications.

Directional pattern

Horn antenna

A horn antenna consists of an expanding horn-shaped metal waveguide that collects radio waves into a beam. Horn antennas have a very wide range of operating frequencies; they can operate with a 20-fold gap in its boundaries - for example, from 1 to 20 GHz. The gain varies from 10 to 25 dB, and they are often used as feeds for larger antennas.

Directional pattern

Parabolic antenna

One of the most popular radar antennas is the parabolic reflector. The feed is located at the focus of the parabola, and the radar energy is directed to the surface of the reflector. Most often, a horn antenna is used as a feed, but both a dipole and a helical antenna can be used.

Since the point source of energy is at the focus, it is converted into a wavefront of constant phase, making the parabola well suited for use in radar. By changing the size and shape of the reflective surface, beams and radiation patterns of various shapes can be created. The directivity of parabolic antennas is much better than that of a Yagi or dipole; the gain can reach 30-35 dB. Their main drawback is their inability to handle low frequencies due to their size. Another thing is that the irradiator can block part of the signal.

Directional pattern

Cassegrain antenna

A Cassegrain antenna is very similar to a conventional parabolic antenna, but uses a system of two reflectors to create and focus the radar beam. The main reflector is parabolic, and the auxiliary reflector is hyperbolic. The irradiator is located at one of the two foci of the hyperbola. The radar energy from the transmitter is reflected from the auxiliary reflector onto the main one and focused. The energy returning from the target is collected by the main reflector and reflected in the form of a beam converging at one point onto the auxiliary one. It is then reflected by an auxiliary reflector and collected at the point where the irradiator is located. The larger the auxiliary reflector, the closer it can be to the main one. This design reduces the axial dimensions of the radar, but increases the shading of the aperture. A small auxiliary reflector, on the contrary, reduces shading of the opening, but it must be located away from the main one. Advantages compared to a parabolic antenna: compactness (despite the presence of a second reflector, the total distance between the two reflectors is less than the distance from the feed to the reflector of a parabolic antenna), reduced losses (the receiver can be placed close to the horn emitter), reduced side lobe interference for ground radars. Main disadvantages: the beam is blocked more strongly (the size of the auxiliary reflector and feed is larger than the size of the feed of a conventional parabolic antenna), does not work well with a wide range of waves.

Directional pattern

Antenna Gregory

On the left is the Gregory antenna, on the right is the Cassegrain antenna

The Gregory parabolic antenna is very similar in structure to the Cassegrain antenna. The difference is that the auxiliary reflector is curved in the opposite direction. Gregory's design can use a smaller secondary reflector compared to a Cassegrain antenna, resulting in less of the beam being blocked.

Offset (asymmetric) antenna

As the name suggests, the emitter and auxiliary reflector (if it is a Gregory antenna) of an offset antenna are offset from the center of the main reflector so as not to block the beam. This design is often used on parabolic and Gregory antennas to increase efficiency.

Cassegrain antenna with flat phase plate

Another design designed to combat beam blocking by an auxiliary reflector is the flat plate Cassegrain antenna. It works taking into account the polarization of waves. An electromagnetic wave has 2 components, magnetic and electric, which are always perpendicular to each other and the direction of movement. The polarization of the wave is determined by the orientation of the electric field, it can be linear (vertical/horizontal) or circular (circular or elliptical, twisted clockwise or counterclockwise). The interesting thing about polarization is the polarizer, or the process of filtering the waves, leaving only waves polarized in one direction or plane. Typically, the polarizer is made of a material with a parallel arrangement of atoms, or it can be a lattice of parallel wires, the distance between which is less than the wavelength. It is often assumed that the distance should be approximately half the wavelength.

A common misconception is that the electromagnetic wave and polarizer work in a similar way to an oscillating cable and a plank fence - that is, for example, a horizontally polarized wave must be blocked by a screen with vertical slits.

In fact, electromagnetic waves behave differently than mechanical waves. A lattice of parallel horizontal wires completely blocks and reflects a horizontally polarized radio wave and transmits a vertically polarized one - and vice versa. The reason is this: when an electric field, or wave, is parallel to a wire, it excites electrons along the length of the wire, and since the length of the wire is many times greater than its thickness, the electrons can easily move and absorb most of the energy of the wave. The movement of electrons will lead to the appearance of a current, and the current will create its own waves. These waves will cancel out the transmission waves and behave like reflected waves. On the other hand, when the electric field of the wave is perpendicular to the wires, it will excite electrons across the width of the wire. Since the electrons will not be able to actively move in this way, very little energy will be reflected.

It is important to note that although in most illustrations radio waves have only 1 magnetic field and 1 electric field, this does not mean that they oscillate strictly in the same plane. In fact, one can imagine that electric and magnetic fields consist of several subfields that add up vectorially. For example, for a vertically polarized wave from two subfields, the result of adding their vectors is vertical. When two subfields are in phase, the resulting electric field will always be stationary in the same plane. But if one of the subfields is slower than the other, then the resulting field will begin to rotate around the direction the wave is moving (this is often called elliptical polarization). If one subfield is slower than the others by exactly a quarter of a wavelength (the phase differs by 90 degrees), then we get circular polarization:

To convert linear polarization of a wave into circular polarization and back, it is necessary to slow down one of the subfields relative to the others by exactly a quarter of the wavelength. For this, a grating (quarter-wave phase plate) of parallel wires with a distance between them of 1/4 wavelength, located at an angle of 45 degrees to the horizontal, is most often used.
For a wave passing through the device, linear polarization turns into circular, and circular into linear.

A Cassegrain antenna with a flat phase plate operating on this principle consists of two reflectors of equal size. The auxiliary reflects only horizontally polarized waves and transmits vertically polarized waves. The main one reflects all waves. The auxiliary reflector plate is located in front of the main one. It consists of two parts - a plate with slits running at an angle of 45°, and a plate with horizontal slits less than 1/4 wavelength wide.

Let's say the feed transmits a wave with circular polarization counterclockwise. The wave passes through the quarter-wave plate and becomes a horizontally polarized wave. It is reflected from horizontal wires. It passes through the quarter-wave plate again, on the other side, and for it the plate wires are already oriented mirror-image, that is, as if rotated by 90°. The previous change in polarization is reversed, so that the wave again becomes circularly polarized counterclockwise and travels back to the main reflector. The reflector changes polarization from counterclockwise to clockwise. It passes through the horizontal slits of the auxiliary reflector without resistance and leaves in the direction of the targets, vertically polarized. In receive mode, the opposite happens.

Slot antenna

Although the described antennas have fairly high gain relative to the aperture size, they all have common disadvantages: high side-lobe susceptibility (susceptibility to nuisance reflections from the earth's surface and sensitivity to targets with a low effective scattering area), reduced efficiency due to beam blocking (small radars, which can be used on aircraft, have a problem with blocking; large radars, where the problem with blocking is less, cannot be used in the air). As a result, a new antenna design was invented - a slot antenna. It is made in the form of a metal surface, usually flat, in which holes or slots are cut. When it is irradiated at the desired frequency, electromagnetic waves are emitted from each slot - that is, the slots act as individual antennas and form an array. Since the beam coming from each slot is weak, their side lobes are also very small. Slot antennas are characterized by high gain, small side lobes and low weight. They may have no protruding parts, which in some cases is their important advantage (for example, when installed on aircraft).

Directional pattern

Passive phased array antenna (PFAR)

Radar with MIG-31

Since the early days of radar development, developers have been plagued by one problem: the balance between accuracy, range and scan time of the radar. It arises because radars with a narrower beam width increase accuracy (increased resolution) and range at the same power (power concentration). But the smaller the beam width, the longer the radar scans the entire field of view. Moreover, a high-gain radar will require larger antennas, which is inconvenient for fast scanning. To achieve practical accuracy at low frequencies, the radar would require antennas so huge that they would be mechanically difficult to rotate. To solve this problem, a passive phased array antenna was created. It relies not on mechanics, but on the interference of waves to control the beam. If two or more waves of the same type oscillate and meet at one point in space, the total amplitude of the waves adds up in much the same way as waves on water add up. Depending on the phases of these waves, interference can strengthen or weaken them.

The beam can be shaped and controlled electronically by controlling the phase difference of a group of transmitting elements - thus controlling where amplification or attenuation interference occurs. It follows from this that the aircraft radar must have at least two transmitting elements to control the beam from side to side.

Typically, a PFAR radar consists of 1 feed, one LNA (low noise amplifier), one power distributor, 1000-2000 transmitting elements and an equal number of phase shifters.

Transmitting elements can be isotropic or directional antennas. Some typical types of transmission elements:

On the first generations of fighter aircraft, patch antennas (strip antennas) were most often used because they were the easiest to develop.

Modern active phase arrays use groove emitters due to their wideband capabilities and improved gain:

Regardless of the type of antenna used, increasing the number of radiating elements improves the radar's directivity characteristics.

As we know, for the same radar frequency, increasing the aperture leads to a decrease in beam width, which increases range and accuracy. But for phased arrays, it is not worth increasing the distance between the emitting elements in an attempt to increase the aperture and reduce the cost of the radar. Because if the distance between the elements is greater than the operating frequency, side lobes may appear, significantly degrading the radar's performance.

The most important and expensive part of the PFAR is the phase shifters. Without them, it is impossible to control the signal phase and beam direction.

They come in different types, but generally they can be divided into four types.

Phase shifters with time delay

The simplest type of phase shifters. It takes time for a signal to travel through a transmission line. This delay, equal to the phase shift of the signal, depends on the length of the transmission line, the frequency of the signal, and the phase velocity of the signal in the transmitting material. By switching a signal between two or more transmission lines of a given length, the phase shift can be controlled. Switching elements are mechanical relays, pin diodes, field-effect transistors or microelectromechanical systems. Pin diodes are often used because of their high speed, low loss, and simple bias circuits that provide resistance changes from 10 kΩ to 1 Ω.

Delay, sec = phase shift ° / (360 * frequency, Hz)

Their disadvantage is that the phase error increases with increasing frequency and increases in size with decreasing frequency. Also, the phase change varies with frequency, so they are not applicable for very low and high frequencies.

Reflective/quadrature phase shifter

Typically this is a quadrature coupling device that splits the input signal into two signals 90° out of phase, which are then reflected. They are then combined in phase at the output. This circuit works because signal reflections from conductive lines can be out of phase with respect to the incident signal. The phase shift varies from 0° (open circuit, zero varactor capacitance) to -180° (shorted circuit, infinite varactor capacitance). Such phase shifters have a wide range of operation. However, the physical limitations of varactors mean that in practice the phase shift can only reach 160°. But for a larger shift it is possible to combine several such chains.

Vector IQ modulator

Just like a reflective phase shifter, here the signal is split into two outputs with a 90-degree phase shift. The unbiased input phase is called the I-channel, and the quadrature with a 90-degree offset is called the Q-channel. Each signal is then passed through a biphasic modulator capable of shifting the phase of the signal. Each signal is phase shifted by 0° or 180°, allowing any pair of quadrature vectors to be selected. The two signals are then recombined. Since the attenuation of both signals can be controlled, not only the phase but also the amplitude of the output signal is controlled.

Phase shifter on high/low pass filters

It was manufactured to solve the problem of time delay phase shifters not being able to operate over a large frequency range. It works by switching the signal path between high-pass and low-pass filters. Similar to a time delay phase shifter, but uses filters instead of transmission lines. The high-pass filter consists of a series of inductors and capacitors that provide phase advance. Such a phase shifter provides a constant phase shift in the operating frequency range. It is also much smaller in size than the previous phase shifters listed, which is why it is most often used in radar applications.

To summarize, compared to a conventional reflective antenna, the main advantages of PFAR will be: high scanning speed (increasing the number of tracked targets, reducing the likelihood of the station detecting an radiation warning), optimization of the time spent on the target, high gain and small side lobes (difficult to jam and detect), random scan sequence (harder to jam), ability to use special modulation and detection techniques to extract signal from noise. The main disadvantages are high cost, the inability to scan wider than 60 degrees in width (the field of view of a stationary phase array is 120 degrees, a mechanical radar can expand it to 360).

Active phased array antenna

Outside, AFAR (AESA) and PFAR (PESA) are difficult to distinguish, but inside they are radically different. PFAR uses one or two high-power amplifiers to transmit a single signal, which is then divided into thousands of paths for thousands of phase shifters and elements. An AFAR radar consists of thousands of reception/transmission modules. Since the transmitters are located directly in the elements themselves, it does not have a separate receiver and transmitter. The differences in architecture are shown in the picture.

In AFAR, most of the components, such as a weak signal amplifier, a high-power amplifier, a duplexer, and a phase shifter, are reduced in size and assembled in one housing called a transmit/receive module. Each of the modules is a small radar. Their architecture is as follows:

Although AESA and PESA use wave interference to shape and deflect the beam, the unique design of AESA provides many advantages over PFAR. For example, a small signal amplifier is located close to the receiver, before the components where part of the signal is lost, so it has a better signal-to-noise ratio than a PFAR.

Moreover, with equal detection capabilities, AFAR has a lower duty cycle and peak power. Also, since individual APAA modules do not rely on a single amplifier, they can transmit signals at different frequencies simultaneously. As a result, AFAR can create several separate beams, dividing the array into subarrays. The ability to operate on multiple frequencies brings multitasking and the ability to deploy electronic jamming systems anywhere in relation to the radar. But forming too many simultaneous beams reduces the radar's range.

The two main disadvantages of AFAR are high cost and limited field of view to 60 degrees.

Hybrid electronic-mechanical phased array antennas

The very high scanning speed of the phased array is combined with a limited field of view. To solve this problem, modern radars place phased arrays on a movable disk, which increases the field of view. Do not confuse the field of view with the width of the beam. Beam width refers to the radar beam, and field of view refers to the overall size of the space being scanned. Narrow beams are often needed to improve accuracy and range, but a narrow field of view is usually not necessary.

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in the supercritical mode, when they propagate between parallel metal plates, the distance between the protrusions can be determined; d 0 (Fig. 5.12), their length is 1(/and thickness - \ - ., \ ^

In Fig. 5.13 and 5.14 show examples of the design of waveguide-slot non-resonant

antennas with inclined slots on a narrow waveguide wall when the antenna is fed by a rectangular waveguide (Fig. 5.13) and with longitudinal slots on a wide wall when fed by a coaxial cable (Fig. 5.14).

An example of the design of a waveguide slot antenna with electromechanical beam swing (with a removable upper slot wall) is shown in Fig. 5.15. The purpose of the individual antenna elements is indicated in the same figure.

In Fig. 5.1-6a shows one of the variants of a two-dimensional waveguide-slot antenna [L 11], consisting of eight parallel aluminum waveguides, in each of which ten dumbbell slots are cut. Dumbbell slots have a greater bandwidth than conventional rectangular slots [LO 9]. A special feature of the antenna is that the even and odd waveguides are fed from different sides using power dividers and the entire aperture is used to form four beams, the spatial arrangement of which is shown by the dotted line in Fig. 5.16.6, Such antennas are used, for example, * in aircraft Doppler autonomous navigation devices designed to determine the speed and drift angle of the aircraft.

A set of several linear*waveguide-slot antennas located along the generatrices of the conical part of the aircraft (Fig. 5.17) / can be used to form the required shape of the radiation pattern [LO 7]..

To protect from atmospheric precipitation and dust, the opening of the waveguide-slot antenna must be covered with a dielectric plate, or the entire radiating system must be placed in a radio-transparent radome. /у.-"-; ;7 ";;>■-■

5.9. Approximate procedure for calculating waveguide-slot

When developing or designing slot antennas, the initial data can be:

Width of pattern in two main planes or in one

20q 5 and side lobe level;

Directional coefficient £) 0 ;

Amplitude: or amplitude-phase distribution over the antenna and the number of emitters N; frequency range

Let us dwell on the calculation procedure for the following two options:

Option 1. The amplitude distribution over the antenna aperture and the number of emitters N are specified.

Option 2. The width of the radiation pattern in one or two main planes and the level of lateral radiation are specified.

First, the type of waveguide-slot antenna is selected. If the angular position of the main maximum DN 0 GL is specified and the antenna must ensure operation in the frequency band, a non-resonant antenna is selected. If, according to the design instructions, the antenna is narrow-band, but must have a high efficiency value, a resonant antenna is preferable.

Option 1. For a given law of amplitude changes according to the antenna aperture, the distance between the emitters d in the waveguide of a given frequency range selected for constructing the antenna is initially determined: In a resonant antenna with variable-phase slots In a non-resonant antenna, the value of d can be chosen in two ways. If the position of the main maximum of the pattern in space 6 No. is given, then the required value of rf is found using formula (5.26). If the Angle angle is not specified, then the distance between the emitters is selected d^\"k B /2 and, moreover, so that at the extreme frequencies of the given range there is no resonant excitation of the antenna [formula (5.22)]: Next, the calculation is carried out in the following order.

Ts Taking into account the general equivalent circuit of the antenna (see Fig. 5.8.6), the equivalent normalized conductivities g n (or resistance g n) of all N slots of the antenna are calculated (see § 5.4).

2. Knowing the value of gv or g p / by: formulas table. 5.1 (§ 5.2) determine the displacement of the center of the slits relative to the middle of the wide wall of the waveguide, or the angle of their inclination 6 in the side wall.

P 3. Having calculated the conductivity of the radiation of the slot in the waveguide (i.e., external conductivity), f from the known value of the power at the input, (in the case of a transmitting antenna) determine the voltage at the antinode of the slot U m [formula (5.3)], and therefore, and slit width di [formula (5.4)].

4. Given the known location of the slits on the wall of the waveguide and their width, according to the data in § 5.2, find the resonant length of the slits in the waveguide.

5. Calculate the antenna pattern (see § 5.7) ^ its k.n. d. and k.u.

Option 2. First, find the distance between the emitters similar to the first calculation option. Then the amplitude distribution over the antenna is selected, ensuring

10* 147 starting pattern with a given level of side lobes. Next, using the now known amplitude distribution, the length of the antenna (and, accordingly, the number of emitters) is found, providing the required width of the pattern at a level of 0.5 power (formulas in Table 5.2 § 5.7). Further calculation coincides with paragraphs. 1-5 of the previous calculation option.

In addition to the electrical calculation of the antenna itself, the supply line and exciter are calculated, the required type of rotating joint is selected when required by the design specifications, and its main characteristics are determined.

Literature

G. Kyu n PV Microwave antennas. TTur. With; German edited by M. P. Dolukhanova. Publishing house "Shipbuilding", 1967.

"2. Pietol'kor with A.A. General theory of diffraction antennas. ZhTP, 1944, vol. XIV, No. 12, ZhTF, 1946, vol. XVI, (Nb 1.

3. "Manual for course design of antennas." VZEIS, 1967.

4. Yatsuk L.P., Smirnova N.! B. Internal conductivities of non-resonant slots in a rectangular waveguide. “News of universities”, Radio engineering, 1967, vol. X, 4.

"5. Veshch"Nikova I.E., Evetroiyov G.A. Theory of matched slot emitters. "Radio engineering and electronics", 1965, vol. X, No. Ш

6. E in s t r. o i o in G. A., Ts a r a p k i n S. A. Study of waveguide-slot antennas: with identical resonant emitters. "Radio Engineering and Electronics", 1965, vol. X, no. 9.

7. Evstropov G.A., Tsarailkin S. “A: Calculation of wave-bottom-slot antennas taking into account the interaction of emitters along the fundamental wave. “Radio engineering and electronics”, 1966, vol. XI, no. 5.

8. Shubarin Yu. V. Antennas of ultrahigh frequencies. Kharkov University Publishing House, 1960.

9. "Microwave Scanning Antenna Systems", vol. I. Transl. from English, ed. G. T. Markov and A. F. Chaplin. Publishing house "Soviet Radio", 1966.

10. Shyrman Ya. D. Radio fiber guides and volumetric resonators. Svyazizdat, 1959.

11. Reznikov G. B. Aircraft antennas. Publishing house "Soviet Radio", 1962.

HORN ANTENNAS

6.1. Main characteristics of horn antennas

Waveguide horn antennas are the simplest antennas in the centimeter wave range.

They can form radiation patterns with a width from 100-140° (when opening a special shape) to 10-520° in pyramidal horns. The possibility of further narrowing the horn pattern is limited by the need to sharply increase its length.

Waveguide horn antennas are broadband devices and provide approximately one and a half range coverage. The possibility of changing the operating frequency within even greater limits is limited by the excitation and propagation of higher types of waves in the supply waveguides. The efficiency of the horn is high (about 100%). Horn antennas are easy to manufacture. A relatively minor complication (inclusion of a phasing section in the waveguide path) ensures the creation of a field with circular polarization.

The disadvantages of horn antennas are: a) bulky design, limiting the possibility of obtaining narrow radiation patterns; b) difficulties in regulating the amplitude-phase distribution of the field in the aperture, which limit the possibility of reducing the level of side lobes and creating radiation patterns of a special shape.

Horn radiators can be used as independent antennas or, like the open ends of waveguides, as elements of more complex antenna devices. As independent antennas, horns are used in radio relay lines, in weather service stations, very widely in radio measuring equipment, as well as in some special-purpose stations. Widely - small horns are used. and open ends of waveguides as feeds

parabolic mirrors and lenses. Feeders in the form of a line of horns or open ends of waveguides can be used to form specially shaped radiation patterns, controlled patterns, or, for example, using the same paraboloid to create pencil and cosecant radiation patterns. A four-horn or eight-horn emitter can be used for: Monopulse direction finding method. Sectorial horns with higher pitches can be used for the same purpose. : wave types (#yu, Nsch #zo). To form narrow radiation patterns, two-dimensional arrays made from the open ends of waveguides or small horns can be used. It is possible to construct flat or convex phased arrays.

Paragraphs 6.2-6.9 are devoted to consideration of methods. calculation of horn emitters. Paragraphs 6.10-6.12 outline some features of the design of horn-waveguide phased arrays.

6.2. Calculation method

The calculation of horn antennas is based on the results of their analysis, i.e., they are initially tentatively specified; " the geometric dimensions of the antenna, and then determine its electrical parameters. If the dimensions are unsuccessful, then the calculation is repeated again.

Radiation field of a horn antenna; like all microwave antennas, it is determined by an approximate method. The essence of approach; is that despite the connection between the field inside and outside the horn, the internal problem is solving the external one, and obtained from. this

solving the field value in the plane of the horn opening is used to solve the external Problem [DO 1, LO 13].

The amplitude distribution of the field in the horn aperture is assumed to be the same as in the waveguide feeding it. For example, . when excited.;, horn with a rectangular WAVEGUIDE WITH wave #10, along the X-axis (passing in the H plane) the distribution of the field amplitude is cosine, and along the Y axis (passing in the E plane) the amplitude distribution is uniform. Due to the fact that the wave front in the horn does not remain flat, but is transformed into a cylindrical one in a sectorial horn and into a spherical one in a pyramidal and conical one, the phase of the field along the opening changes according to a quadratic law.

The described amplitude and phase distributions of the field along the aperture are approximate. Some clarification is provided by taking into account reflection from the opening of at least only the main type of wave. It should be borne in mind that the reflection coefficient G decreases with increasing aperture.

The radiation pattern of a horn antenna based on a known field in the aperture can be calculated by the wave optics method based on the Huygens principle and the Kirchhoff formula [LO 13, JIO 11, J10 1]. The application of Kirchhoff's formula to the electromagnetic field is not strict. A number of authors have made clarifications that take into account the characteristics of the electromagnetic field of the antenna. Because of this, in the literature for calculating the radiation pattern there are several different, but similar formulas that give similar results. Calculation formulas will be given below in § 6.5. Having an expression for the radiation pattern, one can find the directional coefficient of the antenna, the dependence of the width of the radiation pattern on the size of the aperture, and other characteristics of the antenna.

6.3. Selection of geometric dimensions of the horn and waveguide emitter

Horn antenna (Fig. 6.1) consists of horn I, waveguide and exciting device 3

If the generator feeding the antenna * has a coaxial output, then the antenna waveguide 2 is most often excited by a pin located perpendicular to the wide wall j of the waveguide; the excitation is supplied to the pin by a coaxial cable. If the generator feeding the antenna has a waveguide output, then the feeder path is usually made in the form of a rectangular waveguide with an H 10 wave. The waveguide feeder directly passes into the waveguide 2, exciting the horn. Calculation of the exciting device in the form; an asymmetrical pin will be given in the next paragraph.

Selecting Waveguide Sizes

The choice of cross-sectional dimensions of a rectangular waveguide a and b is made from the condition of propagation of only the main type of wave #у in the waveguide:

Relationship (6.1) is presented in the graph in Fig. 6.2, which can be used to find the dimensions of a. Dimension b must satisfy condition b

Let us present some considerations for calculating probe transfer (see Fig. 6.3).

The input impedance of a pin in a waveguide, as well as an asymmetrical vibrator in free space, is in the general case a complex quantity. The active part of the input resistance depends: mainly on the length of the pin, the reactive part - on the length and thickness. In contrast to free space, the input impedance of a pin in a waveguide depends on the field structure in the waveguide near the pin.

Calculation; the reactive component of the input resistance gives inaccurate results and does not make sense. To ensure matching, the reactive component of the input resistance must be equal to zero. The active component of the input resistance can be considered equal to the resistance of the Radiation pin in the waveguide. It should; be equal!

The radiation resistance of a pin in a rectangular waveguide in the traveling wave mode is determined by the following relation:

In the presence of a reflected wave in a rectangular one; waveguide, the resistance of the pin changes slightly:-

wave impedance of the feeder.

reactive parts of conductivity to the right and left of the pin, namely:

In the given formulas, the following notations are adopted: a and bSh are the dimensions of the cross-section of the waveguide; X\ - position of the pin on the wide wall of the waveguide, more often; In total, the pin is located in the middle of the wide wall, i.e. Xi = a/2; Zi.-- distance from the pin to the short-circuiting wall of the waveguide; dsh is the distance from the pin to the nearest voltage node; k.b. V. - coefficient of the traveling wave in the waveguide; X^f is the wavelength in the waveguide; r in -4 waveguide impedance

/g d - effective height of the pin in the wave

water, the geometric height of which is /, is determined by the formula

Given the values ​​x\ and, using formulas (6.18), (6.19) and (6.21) we can find the height of the pin / at which the required /? In x.

For complete coordination, the designs must provide two adjustment elements. For example, you can adjust the height of the pin / and the position of the short-circuiting wall in the waveguide U (see Fig. 6.3) or the dimensions k and S (see Fig. 6.4,6). In some cases, to simplify the design, they are limited to one; adjustment and allow some* mismatch in the supply coaxial.

6.5. Reflection coefficient calculation

Reflection in a horn antenna occurs in two sections: in the horn aperture (1\) and in its neck (G 2).

Let us briefly consider each of the reflection coefficients. The reflection coefficient from the aperture T\ is a complex value; its modulus and phase depend on the size of the aperture. A rigorous solution to the problem for the open end of a waveguide sandwiched between two infinite planes, carried out by L. A. Weinstein; allows us to establish that the modulus of the reflection coefficient decreases with increasing size of the aperture, and the phase approaches zero.

Approximately the modulus of the reflection coefficient from the aperture for the main type of wave can be determined from the relation

Propagation constant in a rectangular waveguide, the cross section of which is equal to the horn aperture;/" d*// r: . ? \ ^

The propagation constant in a circular waveguide whose diameter is equal to the diameter of the aperture of a conical horn.

The reflection coefficient along the length of the horn from the aperture to the neck changes not only in phase, but also in amplitude. With opening sizes of several lengths

The reflection coefficient fi from the open end of a rectangular waveguide (23X10) mm 2 at a wavelength of 3.2 cm, measured experimentally, is equal to

Let's consider the reflection coefficient from the throat of the horn G2.

When determining the coefficient G2, it is assumed that

a traveling wave was established in the horn. The problem is solved by combining fields >at the junction of the waveguide

Selecting Horn Sizes

The dimensions of the opening of a pyramidal or sectorial horn a p and b p (see Fig. 6.1) are selected according to the required width of the radiation pattern in the corresponding plane or according to the k.n. d.

The width of the radiation pattern is related to the aperture dimensions a v and b v by the following ratios: