Rod antenna. Coursework: Designing a grid of dielectric rod antennas. Radiator pattern calculation

Dielectric rod antennas belong to traveling wave antennas with a slow phase velocity. They are used at the border of the centimeter and decimeter wave bands in the frequency band from 2 to 10 GHz.

On fig. 6 shows the most typical scheme of a dielectric rod antenna. It is a dielectric rod 1 excited by a round waveguide 2 with an exciter 3 and a feeder 4. Depending on the requirements for the antenna, the cross section of the rod, the exciter and its power supply may vary. The most commonly used are cylindrical and conical rods.

Dielectric rod antenna: 1-dielectric rod; 2-exciting device; 3-pathogen; 4-feeder.

Rice. 6

Spiral antennas.

Helical antennas belong to the class of traveling wave antennas. They are a metal spiral fed by a coaxial line. There are cylindrical, conical and flat helical antennas.

Examples of the practical use of helical antennas are shown in the photo. The first photo shows part of the Soviet space station "Venus" with a logarithmic two-way helical antenna mounted on it, wound from a flat metal tape on a dielectric frame. The second photo shows the antenna of a ground station for space communications, which is a grid of four cylindrical helical antennas.

Choice of dielectric material

For the manufacture of the emitter, we will choose polystyrene, the parameters of which have the following values:

The dielectric constant;

Dielectric loss tangent.

Determining the bar diameter

To ensure the conversion of most of the energy into a surface wave, the exciter rod is made thick, and then gradually reduced to bring the phase velocity xf closer to the speed of light. It is recommended to make rods with a diameter of:

At MHz m, then:

Deceleration Factor Calculation

According to the selected value () and according to the schedule from the methodological literature (2, p. 41), we find the deceleration coefficient, it is equal to:

At 0.83 1.205

Antenna rod length calculation

The length of the dielectric rod is selected based on the given width of the antenna pattern.

At =40…45 respectively L1.588…1.255 m.

On the other hand, the maximum directivity of the antenna is achieved with a rod length equal to

Hence L=1.723m.

From these expressions, we choose the optimal length of the rod: L m

Antenna directivity calculation

The directional action coefficient is determined by the formula:

Calculation of radiation patterns

When calculating the radiation pattern of a conical dielectric antenna, expressions are used to calculate the radiation pattern of a cylindrical antenna of average diameter, while it is assumed that the wave in the rod traveling with constant deceleration along its length and reflection from the end of the rod is neglected, then the expression for calculating the radiation pattern is obtained as a linear antenna with a continuous distribution of radiating elements, in which the distribution of currents along the length corresponds to the law of a traveling wave.

where is the wave number, is the angle between the antenna axis and the direction to the observation point.


Fig 2.


Fig 3.

dielectric rod antenna in polar coordinate system

dielectric antenna rod

Calculation of the matching device

For transmission with the least energy loss in a coaxial cable, a traveling wave mode should be created. To obtain a traveling wave mode, it is necessary to ensure the equality of the load resistance and the wave resistance of the line, i.e. match the line with the load. However, it is difficult to obtain such an agreement at which the traveling wave coefficient (TWV = 1) is obtained. It is almost already good if KBV = 0.8 h 0.9. At the same time, the deterioration of the line performance is insignificant.

To match the wave impedance of the coaxial cable W f with the input impedance of the antenna, it is necessary to find the desired value of the effective height of the exciter (pin) h d, at which R in =W.

The distance from the shorting wall to the axis of the pin z 1 is chosen equal to /4, where in is the wavelength in the waveguide with wave H 11 in the presence of a dielectric

and the wave impedance of a circular waveguide filled with a dielectric for the wave H 11 is equal to

417.034 ohm, hence 0.781 m and z1 0.195 m

Then the effective pin height can be found from the expression:

Let us take for calculation a coaxial cable with an outer conductor made of round wires in a PE sheath RK 50-33-17 with a maximum allowable power at frequencies of 100 MHz and 1 GHz of 5 kW and 0.9 kW, respectively. Its wave resistance is 50 ohms, then 0.059 m

The geometric height is found from the ratio:

The length of the circular waveguide from the vibrator to its opening z 2 is selected from the conditions for providing the necessary attenuation of higher types of waves. It is usually believed that the weakening of the field of the nearest higher wave E 01 should be at least 10 ... 20 dB (100 times in power). If we take the attenuation value equal to 20 dB, then

When calculating, it turned out that there is a negative number under the root, which means that the wave is in the subcritical mode and does not decay. In this case, it is necessary to exclude the possibility of its excitation, for this we will take the length of the exciter 0.75 0.206. In this case, supercritical attenuation must be ensured for the next wave of higher type c, then m

To match the emitter with the supply feeder, a quarter-wave matching transformer with a wave impedance equal to

Calculation of the maximum voltage in the supply feeder

When choosing a coaxial cable, one should take into account not only the attenuation coefficient at the maximum operating frequency, but also its reliability for electrical breakdown. For this purpose, it is checked for the admissibility of the maximum operating voltage with the maximum allowable voltage for a given brand of cable.

To check the reliability of work in terms of electrical breakdown of a coaxial cable, we define

KBV can be taken equal to (0.5 ... 0.7), let's take KBV = 0.5, then

The corona voltage of the coaxial cable RK is 50-33-17 kV, then 4250 V, which means the condition is met.

Calculation of feeder line efficiency

The length of the feeder line is selected from design considerations (10 ... 100 m), we take l= 10 m

Feeder attenuation coefficient, dB/m, found from reference values

where 0.03 dB at 100 MHz means 0.062 dB/m.

The damping coefficient value is substituted in Np/m from the formula

means = 0.007

The modulus of the reflection coefficient from the end of a cylindrical rod can be estimated from the formula

For a conical rod, the reflection coefficient is much lower (usually 2...5 times), let's take 0.068. Then the calculated efficiency according to the above formula is 0.868.

Calculation of the efficiency of the antenna-feeder device

The calculation is made according to the formula:

The efficiency of the antenna is determined mainly by losses in the dielectric and is approximately 0.5 ... 0.7. Let's take 0.7, then 0.521

Let us make a few more remarks related to the efficiency of a dielectric rod antenna.

First, we note that dielectric rod antennas themselves do not have resonant elements and in this sense are broadband (unless the deceleration factor is out of range). The width of the operating frequency band in a dielectric antenna is determined by the resonant properties of the exciting element, i.e., the vibrator in a metal waveguide.

Secondly, the dielectric of the antenna must have low losses, otherwise the efficiency will be low. In addition, the exciting vibrator in the metal waveguide must be located outside the dielectric. This leads to an increase in efficiency due to the fact that the higher types of waves excited by the vibrator decay near it and do not penetrate into the dielectric medium.

Antenna design

The design of the antenna corresponds to Fig. 1, the dielectric rod is made cone-shaped, the calculated geometric dimensions and materials accepted for calculation are selected.


Dielectric antennas are solid rods or tubes made of dielectric several waves long and with transverse dimensions comparable to a wave.

Dielectric antennas, like lens antennas, are based on the use of the features of radio wave propagation in dielectric media. However, their principle of operation is completely different.

It is known that during the transition of electromagnetic waves from a medium with one permittivity to a medium with a different permittivity, charges and currents (the so-called polarization currents) appear on the interface between the media. Such charges and currents also arise on the surface of the rods when electromagnetic waves propagate along them, and the phase and amplitude of the charges at each point of the rod surface depend on the wave propagation velocity. The electromagnetic field at any point in space outside the rod, created by charges and currents, depends on the law of their distribution on the surface of the rod.

If the dimensions of the rod and its material are selected so that the speed of propagation of radio waves along the dielectric antenna is close to the speed of light, then the maximum radiation of the antenna will be directed along the axis of the rod in the direction of the wave.

Here we have an analogy with a "wave channel" type antenna, in which the directors also ensure the phase delay of the wave in the direction from the active vibrator towards maximum radiation. In director antennas, the desired distribution of phases and current amplitudes is selected by choosing the location and length of the vibrators. In dielectric antennas, this is achieved by choosing their sizes.

When the diameter of the rod is large compared to the wave, then the speed of propagation of radio waves along the rod is close to the speed of propagation of radio waves in the dielectric, equal to , where With is the speed of light, and e D is the dielectric constant of the rod material.

As the diameter of the rod decreases, the propagation speed approaches the speed of light With.

Experimental studies show that such rods have the best directional properties, the cross-sectional area of ​​which S does not exceed S max = , but not less than S min = , where l 0 is the operating wave length in air.

With these dimensions, the speed of propagation of radio waves along the rod is very close to the speed of light.

An increase in the cross section of the rod above the value of Smax leads to an increase in the level of side lobes and does not increase the gain of the antenna. Reducing the cross section against the value of S min very quickly leads to the expansion of the main lobe of the radiation pattern, and therefore to a decrease in the gain of the antenna.

The length of the dielectric rod antennas is chosen in the range from 2 to 6 waves, depending on the required gain.

If the antenna in the form of a single rod does not provide the desired directivity, then in this case they do not go along the path of increasing its length, but along the path of using systems of several dielectric rods of the same type, fed in phase. This is done because a further increase in the length of the dielectric antenna over 6 waves no longer gives a noticeable gain.

On fig. 65 shows a dielectric antenna of four polystyrene rods arranged in one row, and shows the radiation patterns of this antenna. Since the individual dielectric rods are sufficiently range due to the non-criticality of their dimensions, then when the power supply system for individual rods is implemented according to the parallel circuit shown in Fig. 65, the antenna system as a whole also retains its properties over a wide wavelength range.

Often, dielectric rods are made cone-shaped with a narrowing in the direction of maximum radiation. In this case, they strive not to reduce the weight, but to improve the directional properties, since giving the rod a small taper reduces the intensity of the side lobes of the radiation pattern.

To reduce the cross section, dielectric rods are made from materials with a high dielectric constant, while paying attention to the amount of losses in this dielectric, since the use of a material with a high dielectric constant and a large loss angle leads to a sharp deterioration in the efficiency of the antenna.

Excitation (power) of dielectric antennas is carried out either by a vibrator perpendicular to the axis of the rod, or by a waveguide carrying the main transverse magnetic wave. In the first case, the vibrator to eliminate back radiation is placed in a metal box, in the open end of which a dielectric rod is embedded (see Fig. 65). Such a box is essentially a short waveguide.

The directional properties of dielectric rod antennas practically do not depend on the shape of their cross section, which can be round, square, etc. into the waveguide, automatically solves the problem of sealing its internal cavity.

For a visual representation of the directional properties of dielectric antennas in fig. 66 they are compared with antennas equivalent to them in directivity and gain.

Dielectric antennas are equivalent to:

a rod with a length of 1.8 waves - a planar in-phase antenna, consisting of eight half-wave vibrators with a reflector;

rods with a length of 3.3 waves - a conical horn with a length of 5 waves and a throat diameter of two waves;

an antenna system of four rods - a conical horn having twice the length and cross-sectional area.

In addition to rod antennas, antennas are used in the form of hollow dielectric tubes with a diameter of about a wave, excited similarly to a solid rod emitter. The wall thickness of such tubes is taken in accordance with the dielectric constant of the tube material, but never exceeds 0.1 of the operating wavelength. Dielectric hollow tube antennas are often referred to as shell.

Shell dielectric antennas turn out to be somewhat more bulky, but they have less weight, and due to their large transverse dimensions, narrower radiation patterns than rod antennas of the same length. On fig. Figure 67 shows for comparison the radiation patterns of a waveguide, a solid dielectric rod, and a dielectric shell system.

Dielectric antennas are used both as independent antennas and feeders, successfully replacing horn antennas. The weight of dielectric antennas is proportional to the cube of the operating wave, which makes it irrational to use them at waves exceeding 10-25 cm. At shorter wavelengths, dielectric rod and shell radiators have a number of advantages, which include small dimensions with good directivity, the possibility of their use in a very wide wavelength range, low weight and low windage.

The disadvantages of dielectric antennas include the complexity of the power supply system (when the antenna consists of a number of common-mode elements) and the presence of dielectric losses that can significantly reduce the efficiency of the antenna.

Description Characteristics Reviews Instructions About the brand

AN-05 is a rod antenna designed for GSM signals in the 900/1800 MHz frequency range. The device has a magnetic base. It is compatible with communication modules:

  • JA-60GSM;
  • GD-04;
  • CA-1202 and some others.

Features of AN-05

The Czech-made AN-05 antenna has a well-thought-out design. The product is compact, has a length of only 37 centimeters. Benefits include:

  • the presence of two LEDs that act as alarm indicators. They are at an angle of 180 degrees to each other;
  • the ability to operate in a wide temperature range: from -10 to +65 degrees Celsius;
  • protection class IP43 (operation is permissible at a humidity of 95%);
  • universal base base included in delivery;
  • minimum weight, which ensures ease of installation and transportation.
A typeAntenna
Weight, kg0.1

there is no data...

Czech

Founded in 1990 in the Czech town of Jablonec nad Nisou, Jablotron specializes in the design and manufacture of security systems for homes, offices and vehicles. Today, Jablotron has become one of the largest manufacturers of security systems in Central Europe. The JABLOTRON Group group of companies includes twenty-one enterprises. In 1993, a subsidiary company was formed in Taipei, which assists not only in the marketing of Jablotron products in Asia, but also in the supply of components. Jablotron products are now sold in more than 70 countries around the world. The company's products are certified according to the ISO9001 standard. The JABLOTRON quality policy includes continuous improvement of the company's products and services, systematic collection of customer comments and suggestions, and attention to business and network partners. All this ensures the long-term success of the company.

Assignment for term paper

Introduction

Calculation of the parameters and dimensions of the antenna

Operation of the antenna-feeder device

Bibliography

Annex 1

Assignment for term paper

Option 89

Data for calculation:

Dielectric rod antenna

Operating frequency range, MHz = 350…500.

Radiated power, kW = 0.90.

Beam width = 40…45.

Dielectric constant = 3.1.

Introduction

In the microwave range, antennas excited by surface waves are widely used. The advantage of surface wave antennas (SW) is their range, simplicity of design, and small size.

The good aerodynamic qualities of the APVs make it possible to use them as low protruding antennas for moving objects. The automatic reclosure consists of two parts: the exciter of electromagnetic waves (EMW) and the radiating surface. The radiating part of the antenna is a retarding structure, which contributes to an increase in the directivity of the radiation compared to the primary field of the exciter. Depending on the type of the guide surface, there are flat, rod and disk automatic reclosing devices.

The most widely used are rod-type APVs made of a dielectric, as well as in the form of metal rods with a dielectric shell.

Dielectric rod antennas are traveling wave antennas with a slow phase velocity (υ f< с). Они применяются на границе сантиметрового и дециметрового диапазонов волн в полосе частот от 2 до 10 ГГц.а рис. 1 приведена наиболее типичная схема диэлектрической стержневой антенны. Она представляет собой диэлектрический стержень 1, excited by a circular waveguide 2 with a pathogen 3 and feeder 4.

Depending on the requirements for the antenna, the cross section of the rod, the exciter and its power supply may vary. The most commonly used are cylindrical and conical rods.

Experimental studies show that conical rods allow to obtain greater attenuation of the side lobes of the radiation pattern than cylindrical rods. However, the length of the conical rods with the same width of the radiation pattern is greater than the length of the cylindrical ones.

Fig 1. Diagram of a dielectric rod antenna

The dielectric rod of an antenna can be considered as a segment of a dielectric waveguide. It is known from the theory of dielectric waveguides that both symmetric and asymmetric waves can propagate in them. Symmetric waves are generally not used in dielectric rod antennas because, due to axial symmetry, they do not radiate power along the rod axis. The main wave used for this purpose is an asymmetric wave of the HE11 type, similar in structure to the main wave of a round metal H11 waveguide. The only difference is that the HE11 field also exists in outer space.

With the help of one rod, it is possible to form radiation patterns with a width of 2θ 0.5 ° > 20°…25°. To obtain narrower radiation patterns, arrays are used in which dielectric rod antennas are separate radiators. Taking into account the directional properties of the radiators, the relationship between them and the influence of decisions on the input impedance is weaker than in arrays consisting of vibrators and slots, which facilitates tuning and control of the array.

The speed of wave propagation along the dielectric rod depends little on the wavelength. Therefore, dielectric rod antennas are broadband and their bandwidth is limited mainly by the range properties of the exciter. With a broadband exciter, it can reach 40-50% of f cf.

The advantage of dielectric antennas is the simplicity of design and small transverse dimensions. As with all traveling wave antennas with a slow phase velocity, their feature is that the narrowing of the radiation pattern occurs due to an increase not in the transverse dimensions of the antenna, but in the longitudinal dimensions with a small transverse one. This feature determines their application, in particular, in aircraft radio devices.

The disadvantage of dielectric rod antennas is the relatively low transmit power and low radiation directivity.

. Calculation of the parameters and dimensions of the antenna

Choice of dielectric material

For the manufacture of the emitter, we will choose polystyrene, the parameters of which have the following values:

the dielectric constant ;

dielectric loss tangent .

Determining the bar diameter

To ensure the conversion of most of the energy into a surface wave, the exciter rod is made thick, and then gradually reduced in order to bring the phase velocity υ f closer to the speed of light. It is recommended to make rods with a diameter of:


At MHz m means:

m

m

Deceleration Factor Calculation

According to the selected value ( ) and according to the schedule from the methodological literature (2, p. 41) we find the deceleration coefficient, it is equal to:

At 0.83 1.205

Antenna rod length calculation

The length of the dielectric rod is selected based on the given width of the antenna pattern.


At =40…45 respectively L1.588…1.255 m.

On the other hand, the maximum directivity of the antenna is achieved with a rod length equal to


Hence L=1.723m.

From these expressions, we choose the optimal length of the rod: L m

Antenna directivity calculation

The directional action coefficient is determined by the formula:

D0

Calculation of radiation patterns

When calculating the radiation pattern of a conical dielectric antenna, expressions are used to calculate the radiation pattern of a cylindrical antenna of average diameter, while it is assumed that the wave in the rod traveling with constant deceleration along its length and reflection from the end of the rod is neglected, then the expression for calculating the radiation pattern is obtained as a linear antenna with a continuous distribution of radiating elements, in which the distribution of currents along the length corresponds to the law of a traveling wave.

,

where is the wave number, is the angle between the antenna axis and the direction to the observation point.


Fig 2. Radiation pattern of a conical dielectric rod antenna in the Cartesian coordinate system

Fig 3. Cone radiation pattern

dielectric rod antenna in polar coordinate system

dielectric antenna rod

Calculation of the matching device

To match the wave impedance of the coaxial cable W f with the input impedance of the antenna, it is necessary to find the desired value of the effective height of the exciter (pin) h d, at which R in =W.

The distance from the shorting wall to the axis of the pin z 1 is chosen equal to l in /4, where l in is the wavelength in the waveguide with wave H 11 in the presence of a dielectric

and the wave impedance of a circular waveguide filled with a dielectric for the wave H 11 is equal to


417.034 Ohm, hence 0.781 m and z 1 0.195 m

Then the effective pin height can be found from the expression:


Let us take for calculation a coaxial cable with an outer conductor made of round wires in a PE sheath RK 50-33-17 with a maximum allowable power at frequencies of 100 MHz and 1 GHz of 5 kW and 0.9 kW, respectively. Its wave resistance is 50 ohms, then 0.059 m

The geometric height is found from the ratio:

The length of the circular waveguide from the vibrator to its opening z 2 is selected from the conditions for providing the necessary attenuation of higher types of waves. It is usually believed that the weakening of the field of the nearest higher wave E 01 should be at least 10 ... 20 dB (100 times in power). If we take the attenuation value equal to 20 dB, then


where

When calculating, it turned out that there is a negative number under the root, which means that the wave is in the subcritical mode and does not decay. In this case, it is necessary to exclude the possibility of its excitation, for this we will take the length of the exciter 0.75 0.206. In this case, supercritical attenuation must be ensured for the next higher-type wave with , then m

To match the emitter with the supply feeder, a quarter-wave matching transformer with a wave impedance equal to

Calculation of the maximum voltage in the supply feeder

When choosing a coaxial cable, one should take into account not only the attenuation coefficient at the maximum operating frequency, but also its reliability for electrical breakdown. For this purpose, it is checked for the admissibility of the maximum operating voltage with the maximum allowable voltage for a given brand of cable.

To check the reliability of work in terms of electrical breakdown of a coaxial cable, we define


KBV can be taken equal to (0.5 ... 0.7), let's take KBV = 0.5, then

424.264 V

Corona voltage of the coaxial cable RK 50-33-17 kV, then 4250 V, so the condition is met .

Calculation of feeder line efficiency


The length of the feeder line is selected from design considerations (10 ... 100 m), we take l= 10 m

Feeder attenuation coefficient, dB/m, found from reference values

,

where 0.03 dB at 100 MHz means 0.062 dB/m.

The damping coefficient value is substituted in Np/m from the formula

,

means = 0.007

The modulus of the reflection coefficient from the end of a cylindrical rod can be estimated from the formula

For a conical rod, the reflection coefficient is much lower (usually 2...5 times), let's take 0.068. Then the calculated efficiency according to the above formula is 0.868.

Calculation of the efficiency of the antenna-feeder device

The calculation is made according to the formula:

The efficiency of the antenna is determined mainly by losses in the dielectric and is approximately 0.5 ... 0.7. Let's take 0.7, then 0.521

Let us make a few more remarks related to the efficiency of a dielectric rod antenna.

First, we note that dielectric rod antennas themselves do not have resonant elements and in this sense are broadband (unless the deceleration factor is out of range). The width of the operating frequency band in a dielectric antenna is determined by the resonant properties of the exciting element, i.e., the vibrator in a metal waveguide.

Secondly, the dielectric of the antenna must have low losses, otherwise the efficiency will be low. In addition, the exciting vibrator in the metal waveguide must be located outside the dielectric. This leads to an increase in efficiency due to the fact that the higher types of waves excited by the vibrator decay near it and do not penetrate into the dielectric medium.

Antenna design

The design of the antenna corresponds to Fig. 1, the dielectric rod is made cone-shaped, the calculated geometric dimensions and materials accepted for calculation are selected.

Fig 4. Drawing of the calculated conical dielectric rod antenna

. Operation of the antenna-feeder device

The dielectric rod antenna has a high level of side and rear radiation. The radiation patterns of such antennas have fairly wide main lobes, so they are classified as weakly directional antennas. Therefore, dielectric rod antennas are most often used as feeds for reflector antennas and collimators.

The dielectric rod antenna is broadband, such a mode requires certain ratios between the dimensions of the antenna and the wavelength. These dimensions must be exactly maintained in order to ensure wideband operation.

Antenna installation must be carried out in accordance with the product passport, as well as various regulatory documents for antennas operating in the VHF band. For the normal mode, it is necessary to ensure the integrity of the mechanical parts of the antenna: the rigidity of the radiator mounting in the waveguide and the fixing of the coaxial cable. Damage to the elements leads to a deterioration in performance, a decrease in the quality of reception and transmission, a deterioration in the properties of broadband and an increase in the reflection coefficient.

The generator that provides power to the antenna must operate stably, without reducing its output voltage, in order to prevent a decrease in the radiation power. Overvoltage must also occur, the electrical properties of the antenna must not be violated.

The operation of the antenna is carried out in accordance with the regulatory documentation, which stipulates the timing of routine maintenance. Routine work is a list of necessary actions to check the accuracy of the antenna and its parameters, as well as mechanical and electrical properties.

An external inspection must be carried out constantly for the presence of mechanical and electrical damage. Regularly clean the antenna from dirt and dust, check the feeder path.

Bibliography

Sazonov D.M. "Antennas and Microwave Devices". - M.: Higher school, 1988

Nechaev E.E. Guidelines and assignments for coursework in the discipline "Antennas and radio wave propagation". - M.: MSTU GA, 1996

. "Antennas and Microwave Devices". Ed. DI. Resurrection. - M.: Radio engineering, 2006

Goncharenko V.M., Kamenev V.G. "Design of microwave antennas". Tutorial. - M., 2006

Efimov I.E., Shermina G.A. "Waveguide transmission lines". - M.: Communication, 1979

Belorussov N.I. "Electric cables, wires and cords". Ed.5. Directory. - M.: Energoatomizdat, 1988

Annex 1

Table for calculating the radiation pattern in the Cartesian coordinate system

0.057 0.057 0.057 0.057 0.057 0.058 0.058 0.059 0.059 0.06 0.061 0.061 0.062 0.063 0.064 0.065 0.066 0.066 0.067 0.068 0.069 0.069 0.07 0.07 0.071 0.071 0.071 0.071 0.07 0.07 0.069 0.068 0.066 0.065 0.062 0.06 0.057 0.054 0.051

0.047 0.042 0.038 0.033 0.027 0.021 0.015 8.996E-3 2.366E-3 -4.482E-30.012 -0.019 -0.02.040.033 -0.040.047 -0.054 -0.07 -0.066 -0.072.070.0810.085 -0.088 -0.09 -0.091 -0.091 -0.09 -0.088 -0.085 -0.081 -0.076 -0.07 -0.062 -0.054 -0.045 -0.035 -0.024 -0.013

6.84E-4 0.049 0.061 0.072 0.083 0.061 0.072 0.083 0.093 0.102 0.117 0.122 0.126 0.128 0.128 0.112 0.054 0.094 0.082 0.069 0.055 0.039 0.069 0.055 0.039 0.022 5.098E-3 -0.013 -0.031 -0.05 -0.068 -0.087 -0.105 -0.12 03.138 -0.153 -0.167 -0.18

0.191 -0.2 -0.207 -0.213 -0.216 -0.213 -0.216 -0.213 -0.208 -0.201 -0.192 -0.181 -0.168 -0.153 -0.136 -0.118 -0.098 -0.077 -0.054 -0.031 -6.077E-3 0.031 0.075 0.072 0.099 0.045 0.072 0.099 0.076 0.074 0.181 0.209 0.236 0.263 0.289 0.315 0.341 0.366 0.39 0.413 0.436 0.458

0.479 0.499 0.518 0.536 0.554 0.57 0.586 0.6 0.614 0.627 0.639 0.65 0.66 0.669 0.677 0.685 0.691 0.697 0.702 0.707 0.479 0.499 0.518 0.536 0.554 0.57 0.586 0.6 0.614 0.627 0.639 0.65 0.66 0.669 0.677 0.685 0.691 0.697 0.702

0.707 0.71 0.713 0.715 0.716 0.716 0.716 0.715 0.713 0.71 0.707 0.702 0.697 0.691 0.685 0.677 0.669 0.66 0.65 0.639 0.627 0.614 0.6 0.586 0.57 0.554 0.536 0.518 0.499 0.479 0.458 0.436 0.413 0.39 0.366 0.341 0.315 0.289 0.263

0.236 0.209 0.181 0.154 0.056 0.099 0.072 0.045 0.019 -6.077E-3-0.031 -0.054 -0.077 -0.098 -0.10.10.136 -0.153 -0.168 -0.181 -0.192 -0.20.208 -0.213 -0.216 -0.217 -0.216 -0.213 -0.207 -0.2 -0.191 -0.18 -0.167 -0.153 -0.138 -0.122 -0.105 -0.087 -0.068 -0.05

0.031 -0.013 5.098E-3 0.022 0.039 0.055 0.069 0.082 0.094 0.104 0.112 0.119 0.124 0.127 0.128 0.128 0.126 0.122 0.117 0.1.102 0.093 0.083 0.072 0.061 0.049 0.036 0.061 0.049 0.036 0.024 0.04 -6.84E-4 -0.013 -0.024 -0.035 -0.045 -0.054 -0.062 -0.07 -0.076 -0.081

0.085 -0.088 -0.09 -0.091 -0.091 -0.09 -0.088 -0.085 -0.081 -0.077 -0.072 -0.066 -0.06 -0.054 -0.047 -0.04 -0.033 -0.026 -0.019

0.012 -4.482e-3 2.366e-3 8.996e-3 0.015 0.021 0.027 0.033 0.038 0.042 0.047 0.051 0.054 0.057 0.06 0.062 0.065 0.066 0.068

0.069 0.07 0.07 0.071 0.071 0.071 0.071 0.07 0.07 0.069 0.069 0.068 0.067 0.066 0.066 0.065 0.064 0.063 0.062

0.061 0.061 0.06 0.059 0.059 0.058 0.058 0.057 0.057 0.057 0.057 0.057


Table for calculating the radiation pattern in the polar coordinate system

180 -179 -178 -177 -176 -175 -174 -173 -172 -171 -170 -169 -168 -167 -166 -165 -164 -163 -162 -161 -160 -159 -158 -157 -156 -155 -154 -153 -152 -151 -150 -149 -148 -147 -146 -145 -144 -143 -142

0.042 0.057 -0.086 -0.205 0.71 -0.194 -0.079 0.062 0.015 0.048 0.549 0.153 0.09 0.07 0.07 0.095 0.167 0.54 0.056 0.018 0.063 -0.076 -0.189 0.708 -0.201 -0.085 0.057 -0.045 -0.105 0.663 -0.069 -0.012 0.069 0.052 0.125 0.392 0.356 0.128 0.057

141 -140 -139 -138 -137 -136 -135 -134 -133 -132 -131 -130 -129 -128 -127 -126 -125 -124 -123 -122 -121 -120 -119 -118 -117 -116 -115 -114 -113 -112 -111 -110 -109 -108 -107 -106 -105 -104 -103

0.07 6.506E-3.0333 0.648 -0.078 -0.035 0.058 -0.089 -0.211 0.713 -0.203 -0.084 0.062 8.081E-3 0.032 0.071 0.066 0.08 0.071 0.069 0.07 0.195 0.522 0.07 0.024 0.064 -0.07 -0.177 0.064 -0.192 -0.081 0.057 - 0.052 -0.123 0.672 -0.091 -0.023 0.068 0.049

102 -101 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64

0.12 0.416 0.07 0.019 -8.547E-3.02.636 -0.059 -0.027 0.058 -0.091 -0.215 0.0615 -0.21 -0.087 0.061 1.321E-3 0.061 0.582 0.098 0.068 0.071 0.068 0.112 0.071 0.068 0.112 0.023 0.064 0.083 0.029 0.064 -0.062 -0.164 0.7 - 0.062 -0.164 0.7 0.181 -0.076 0.057 -0.059 -0.139

63 -62 -61 -60 -59 -58 -57 -56 -55 -54 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25

0.68 -0.111 -0.034 0.067 0.044 0.113 0.062 0.071 0.032 0.062 0.071 -0.04 -0.02 0.059 -0.091 -0.217 0.716 -0.215 -0.09 0.06 -5.656E-3 -3.198E-3 0.071 0.07 0.057 0.071 0.066 0.057 0.071 0.066 0.058 0.071 0.066 0.095 0.035 0.065 -0.054 -0.148 0.694

24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6

5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0.022 -0.013 0.059 -0.091 -0.217 0.716 -0.217 -0.091 0.059 -0.013 -0.022 0.611 0.043 0.044 0.071 0.065 0.123 0.277 0.461 0.105 0.04 0.066 -0.045 -0.13 0.687 -0.154 -0.065 0.057 -0.071 -0.168 0.694 -0.148 -0.054 0.065 0.035 0.095 0.482 0.25 0.118

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

0.066 0.071 0.057 0.07 0.597 -3.198E-3 -5.656E-3 0.06 -0.09 -0.215 0.716 -0.217 -0.091 0.059 -0.02.044 0.624 0.017 0.032 0.071 0.062 0.032 0.071 0.062 0.127 0.304 0.067 0.113 0.044 0.067 -0.034 -0.111 0.68 -0.139 -0.059 0.057 -0.076 -0.181 0.7 -0.164 -0.062 0.064

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

0.029 0.083 0.502 0.223 0.112 0.068 0.071 0.068 0.098 0.582 0.015 1.321e-3 0.061 -0.087 -0.21 0.715 -0.215 -0.091 0.058 -0.027 -0.059 0.636 -8.547e-3 0.019 0.07 0.06 0.128 0.33 0.416 0.12 0.049 0.068 -0.023 -0.091 0.672 -0.123 -0.052 0.057 -0.081

112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

0.192 0.704 -0.177 -0.07 0.064 0.024 0.07 0.522 0.195 0.104 0.069 0.071 0.08 0.126 0.566 0.032 8.081e-3 0.062 -0.084

131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149

0.203 0.713 -0.211 -0.089 0.058 -0.035 -0.078 0.648 -0.033 6.506e-3 0.07 0.057 0.128 0.356 0.392 0.125 0.052 0.069 -0.012

150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

0.069 0.663 -0.105 -0.045 0.057 -0.085 -0.201 0.708 -0.189 -0.076 0.063 0.018 0.056 0.54 0.167 0.095 0.07 0.07 0.09

169 170 171 172 173 174 175 176 177 178 179 180

0.153 0.549 0.048 0.015 0.062 -0.079 -0.194 0.71 -0.205 -0.086 0.057 -0.042

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