RU2541206C2 - Method of determining radio characteristics of large-size antennae for spacecraft without direct measurement thereof - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: invention relates to radio engineering and can be used to determine radio characteristics of large-size antennae for spacecraft without direct measurement thereof. The method includes constructing a three-dimensional model of a reflector using a high-precision contactless laser scanner Leica Lazer Radar LR200, constructing three-dimensional amplitude and phase directional patterns of the irradiator based on the measured principal cross-sections of the amplitude and phase directional patterns, calculating energy characteristics of the large-size antennae using a developed program-algorithm system.

EFFECT: high reliability of measurements of radio characteristics of large-size antennae for spacecraft in conditions exposed to the Earth's gravity, enabling investigation of the relationship between required accuracy of the reflector profile and the operating frequency range without direct measurements in the far zone.

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Description

The invention relates to radio engineering and can be used to determine the radio technical characteristics of large antennas for spacecraft without their direct measurements.

Currently, various stands, methods and devices are known (see patents and applications for inventions of the Russian Federation No. 2276793, 2284535, 2370781) for measuring the radio characteristics of antennas. The proposed methods and devices are based on the use of:

- a device that automates the control of the process of measuring the antenna pattern and improves the accuracy of measurements;

- a broadband sounding signal to expand the range of frequency measurements to tens and hundreds of GHz;

- a stand for measuring reflector parameters in an anechoic chamber using a system of irradiators.

A device is known (patent RU 2370781 C1) for measuring the antenna pattern. According to the device, the technical result consists in automating the control of the process of measuring the antenna radiation pattern and increasing accuracy. The device contains a signal generator connected to the input of the auxiliary antenna, a mixer connected in series, the input of which is connected to the output of the antenna under study mounted on a rotary stand, an intermediate frequency amplifier, a peak detector, the input of which is connected to an intermediate frequency amplifier, a sampling-storage unit, a oscillating oscillator frequency, the first output of which is connected to the second input of the mixer, and the second output to the input "Reset" of the peak detector and the input "Sample" block sampling-storage, as well as e series-connected analog-to-digital converter (ADC), control unit, computer. Moreover, the ADC input is connected to the output of the sample-storage unit, and the output is connected to a computer, the first computer control port is connected to a control unit connected in series to a rotary stand, and the second computer control port is connected to a signal generator.

The disadvantage of this device is the difficulty of measuring the radio characteristics of large antennas for spacecraft. According to the device, it is necessary to perform full-scale measurements of the characteristics of the prototypes of the antennas, however, this requires significant production areas to accommodate large-sized structures and the formation of the far zone of the measured antenna, which is not always possible to implement. In addition, the process of full-scale measurements requires considerable time, since in the process of adjusting the profiles of large-sized antennas from a metallized mesh sheet, it is constantly necessary to measure radio-technical characteristics to obtain the parameters specified in the guidance documents, which also limits the scope of this device.

Also known is a method (patent RU 2284535 C2) of microwave antenna measurements. This method is intended for the study of radiation patterns and amplitude-frequency characteristics (AFC) of antennas. A microwave monochromatic signal is used as a probe, and when receiving, a desynchronized stroboscopic receiver is used, the maximum instantaneous values of the received signal are isolated, according to which the frequency response of the measured antenna is estimated. The technical result is to ensure a rapid transition from ultra-wideband (UWB) to monochromatic measurements, due to which it is possible to expand the frequency domain of measurements to tens and hundreds of GHz, increase the calibration of UWB measurements, and also increase the visibility of the measurement process.

The disadvantage of this method is the difficulty of organizing the process of ground-based experimental testing of large-sized antennas for spacecraft. Due to the peculiarities of manufacturing a large-sized reflector from a metallized net-sheet, mining must be carried out in an anechoic chamber. Accordingly, the maximum size of the developed antenna will be limited by the size of the camera, taking into account the requirements for the formation of the far zone of the antenna pattern. In addition, ground-based experimental testing will require a lot of time due to the need to constantly adjust the reflector profile and repeat the process of measuring the radio characteristics of the antenna.

An analysis of information sources, patent and scientific and technical literature showed that the closest is a stand for measuring reflector parameters (patent RU 2276793 C2), consisting of an anechoic chamber including a reflector, a receiving technological antenna and a system of transmitting horn irradiators, which is equipped with a tension system and adjusting cables made of their elastic radiolucent material. A receiving technological antenna is fixed on the cables with the possibility of movement by adjusting the length of the cables, the optical axis of which is directed perpendicular to the phase front of the electromagnetic wave reflected by the reflector. The system of transmitting horn irradiators is connected to the control cable and mounted on the console, which is made of durable hard radio-transparent material and is mounted on the wall of the anechoic chamber.

A disadvantage of the known stand is the limitation of the maximum size of the measured antenna reflectors by the dimensions of the anechoic chamber, in addition, for conducting ground experimental testing, a large number of experiments are required to measure the reflector parameters in the process of adjusting its profile to obtain the required antenna characteristics, which will lead to a significant increase in the cost and duration of testing created antenna samples.

The objective of the present invention is to eliminate the disadvantages of analogues and prototype associated with:

- the need to create large anechoic chambers to ensure the far zone when measuring the radio characteristics of the antenna;

- high cost and long terms of ground-based experimental testing when tuning the characteristics of large antennas.

The problem is solved as follows.

First, the coordinates of the set of points of the profile of the reflector are measured using a high-precision non-contact laser scanner, the accuracy of its execution relative to the theoretical profile is estimated with the calculation of the parameters characterizing it. A three-dimensional model of the reflector is constructed using series of Zernike functions, then the main sections of the amplitude and phase radiation patterns of the irradiator are measured. Next, an approximation is made using power polynomials of the volume amplitude and phase radiation patterns of the irradiator, after which the energy characteristics of the large-sized antenna are calculated. To achieve the required antenna parameters, the reflector profile is tuned and the energy characteristics of the large antenna are calculated again.

In parallel or in advance, measurements are made of the directivity characteristics of the irradiator of a given reflector in at least two principal planes, sets of coefficients are calculated that determine the models of its amplitude and phase radiation patterns (MD) for any direction of observation.

Then, using the developed software and algorithmic complex, mathematical models of the reflector and the beam of the irradiator are combined and the radio-technical characteristics of a large antenna are calculated.

To assess the accuracy of the reflector profile in the form of an axisymmetric paraboloid of rotation, a model has been developed that allows you to set a rotation paraboloid with the orientation of the focal axis θ _o , φ _o , taking the origin of the coordinate system Δx, Δy, Δz and the standard deviation of the surface σ, and then solve the inverse problem - evaluate the values of θ _o , φ _o , Δx, Δy, Δz, F _opt according to the set of measured coordinates (x _k , y _k , z _k ).

Consider the algorithm for solving the problem. The general equation of a second-order surface describing a rotated and displaced paraboloid has the form:

$$a_{\text{eleven}}{\text{x}}^{\text{2}}+a_{\text{22}}{\text{y}}^{\text{2}}+a_{\text{33}}{\text{<figure-callout id="2" label="z" filenames="00000030.png" state="{{state}}">z</figure-callout>}}^{\text{2}}+\text{2}{a}_{\text{12}}\text{xy}+\text{2}{a}_{\text{13}}\text{xz}+\text{2}{a}_{\text{23}}\text{yz}+\text{2}{a}_{\text{fourteen}}\text{x}+\text{2}{a}_{\text{24}}\text{y}+\text{2}{a}_{\text{34}}\text{z}+a_{\text{44}}=\text{0}\text{. (one)}$$

Figure 1 shows the original paraboloid, the rotated and offset paraboloid and approximating paraboloid (the best match paraboloid - PNS) is the result of solving the problem.

However, such stable results are obtained if the paraboloid is given in its entirety - in the sector of angles φ = 0 ÷ 360 °. If a “cut” from a paraboloid, for example, a 90 ° sector, is specified, then a nonlinear problem is required to evaluate the accuracy of the reflector profile in the form of a “cut” from a rotation paraboloid, because the estimated parameters θ, φ _o , Δx, Δy, Δz, F are included in the coefficients a _{ij of} equation (1), which describes the rotated and shifted paraboloid, as non-linear dependencies.

Deviations of the reflector surface ΔZ from the PNS (residual deformations) are laid out in a row according to the special Zernike polynomial-harmonic functions:

$$\begin{array}{cc}\begin{array}{l}\Delta Z\left(r,\varphi \right)={\displaystyle \sum _{l=0}^L{\displaystyle \sum _{m=\left(0,\mathrm{one}\right)}^{\min \left(l,M\right),2}}}{a}_l^m{R}_l^m\left(q\right)\cos m\varphi +{\displaystyle \sum _{l=0}^L{\displaystyle \sum _{m=\left(\mathrm{one},2\right)}^{\min \left(l,M\right),2}}}{b}_l^m{R}_l^m\left(q\right)\sin m\varphi =\\ {\displaystyle \sum _{l=0}^{L,2}{a}_l^o{R}_l^o\left(q\right)++}{\displaystyle \sum _{l=\mathrm{one}}^L{\displaystyle \sum _{m=\left(\mathrm{one},2\right)}^{\min \left(l,M\right),2}}}{R}_l^m\left(q\right)\left\{a_l^m\cos m\varphi +b_l^m\sin m\varphi \right\},\end{array}& \left(2\right)\end{array}$$

where L, M are given integers (respectively, the maximum degree and order of the Zernike function), bounding in the general case infinite series (M≤L by definition);

min {1, M} - designation of the operation of choosing the minimum of two numbers:

..., 2 - change the index in increments of 2;

m = {0,1} -m = 0 for even l, m = l for odd l;

m = {1,2} -m = 2 for even l, m = l for odd l:

, $$b_l^m$$

- набор коэффициентов, определяющих отклонения профиля измеренного рефлектора от ПНС в системе координат (СК) ПНС; $$a_l^m$$

, $$b_l^m$$

- a set of coefficients that determine the deviation of the profile of the measured reflector from the PNS in the coordinate system (SK) of the PNS;

R (φ) is the boundary of the aperture in the general case of complex shape;

generalized polar radius of the reflector surface point in the aperture;

r, φ are the values of the radius and polar angle of the reflector surface point in the polar SC of its aperture relative to some point of its center of the aperture (X _c , Y _c );

$$\varphi =arctg\begin{array}{c}{Y}_{Pn\mathrm{from}}-Y_c-\\ X_{Pn\mathrm{from}}-Y_c\end{array}\left(\mathrm{four}\right)$$

- радиальные полиномы Зернике, определяемые следующим образом: $$R_l^m\left(q\right)$$

- Radial Zernike polynomials defined as follows:

$$\begin{array}{cc}{R}_l^m\left(q\right){\displaystyle \sum _{\text{k}=\text{0}}^{\begin{array}{l}l-m\\ 2\end{array}}{\left(\text{-one}\right)}^k}& \begin{array}{l}\\ \stackrel{\text{(lk)!}}{\text{k! (}\underset{\text{2}}{\stackrel{\text{l}+\text{m}}{}}-k)!\text{(}\underset{\text{2}}{\stackrel{\text{l}-\text{m}}{}}-k){!}^{q^{l-2k}}}\end{array}\end{array}\left(5\right)$$

l≥0, 0≤m≤l, (l + m) is an even value.

The developed software was tested when processing the data of the measurement results of the profile of two types of antennas:

1) a reflector in the form of a cut from a paraboloid of revolution ⌀12 m with a focal length F = 8.3 m, the number of measurement points n = 732 (see figure 2);

2) a reflector in the form of a cut from a paraboloid of revolution ⌀0.6 m with a focal length F = 0.297 m, the number of measurement points n = 8600 (see Fig. 3).

Analysis of the results presented in figure 2, 3, shows a good agreement between the results, which allows us to conclude that the developed mathematical models and software are correct.

Next, modeling the directional characteristics of the antenna feed is performed.

, $${\Phi }_{1,2}^{XOZ}\left(\theta \right)$$

, $$A_{1,2}^{YOZ}\left(\theta \right)$$

, $${\Phi }_{1,2}^{YOZ}\left(\theta \right)$$

- измеренные в наборе углов амплитудная и фазовая диаграммы направленности в главных плоскостях (индекс 1 соответствует ДН, измеренным при X-ориентации линейно-поляризованной измерительной антенны, индекс 2 соответствует ДН, измеренным при Y-ориентации линейно-поляризованной измерительной антенны). $$A_{\mathrm{one},2}^{XOZ}\left(\theta \right)$$

, $${\Phi }_{\mathrm{one},2}^{XOZ}\left(\theta \right)$$

, $$A_{\mathrm{one},2}^{YOZ}\left(\theta \right)$$

, $${\Phi }_{\mathrm{one},2}^{YOZ}\left(\theta \right)$$

- the amplitude and phase radiation patterns measured in the set of angles in the main planes (index 1 corresponds to the DNs measured at the X-orientation of the linearly polarized measuring antenna, index 2 corresponds to the DNs measured at the Y-orientation of the linearly polarized measuring antenna).

The bottom of the irradiator is a weakly oscillating angular function. Based on this, for its approximation it is advisable to use the usual polynomial series:

$$\text{y}=a_{\text{n}}{\text{x}}^{\text{n}}+a_{\text{n-1}}{\text{x}}^{\text{n-1}}+...+a_{\mathrm{one}}{\text{x}}^{\text{one}}+a_{\text{o}}\text{. (6)}$$

For linearly X-polarized irradiators, the volume amplitude MD can be approximated in the form:

$$\overrightarrow{A}\left(\theta ,\varphi \right)={\overrightarrow{i}}_0{A}_l^{XOZ}\left(\theta \right)\cos \varphi -{\overrightarrow{i}}_{\varphi }{A}_l^{YOZ}\left(\theta \right)\sin \varphi \left(7\right)$$

where: 0≤θ≤π; 0≤φ≤2π;

- амплитудная ДН в плоскости XOZ (плоскость вектора E); $$A_l^{XOZ}\left(\theta \right)$$

- the amplitude pattern in the XOZ plane (plane of the vector E);

- амплитудная ДН в плоскости YOZ (плоскость вектора H). $$A_l^{YOZ}\left(\theta \right)$$

- the amplitude pattern in the YOZ plane (plane of the vector H).

For linearly Y-polarized irradiators, the amplitude pattern can be approximated in the form:

$$\overrightarrow{A}\left(\theta ,\varphi \right)={\overrightarrow{i}}_0{A}_2^{YOZ}\left(\theta \right)\sin \varphi +{\overrightarrow{i}}_{\varphi }{A}_2^{XOZ}\left(\theta \right)\cos \varphi .\left(8\right)$$

- амплитудная ДН в плоскости YOZ (плоскость вектора E);Where $$A_2^{YOZ}\left(\theta \right)$$

- amplitude DN in the YOZ plane (plane of the vector E);

- амплитудная ДН в плоскости XOZ (плоскость вектора H). $$A_2^{XOZ}\left(\theta \right)$$

- amplitude MD in the XOZ plane (plane of the vector H).

, $${\Phi }_{1,2}^{YOZ}\left(\theta \right)$$

.In the case of an X- or Y-polarized irradiator, to approximate the volume PDN, the values of the PDN in the main planes are used $${\Phi }_{\mathrm{one},2}^{XOZ}\left(\theta \right)$$

, $${\Phi }_{\mathrm{one},2}^{YOZ}\left(\theta \right)$$

.

For irradiators with an elliptical (in the general case) polarization, the approximation of the volume pattern can be represented by a superposition of expressions (7) and (8) taking into account the complex nature of the field:

$$\begin{array}{l}\overrightarrow{A}\left(\theta ,\varphi \right)={\overrightarrow{i}}_0\left(A_l^{XOZ}\left(\theta \right)\cos \varphi \cdot e^{/F_{\mathrm{one}}\left(0\right)}+A_2^{YOZ}\left(\theta \right)\sin \varphi \cdot e^{/F_{\mathrm{one}}\left(0\right)}\right)+\\ +{\overrightarrow{i}}_{\varphi }\left(A_2^{XOZ}\left(\theta \right)\cos \varphi \cdot e^{/F_2\left(0\right)}-A_{\mathrm{one}}^{YOZ}\left(\theta \right)\sin \varphi \cdot e^{/F_{\mathrm{one}}\left(0\right)}\right)\text{.}\left(9\right)\end{array}$$

Thus, as the initial data, two main sections of the amplitude beam of the irradiator are set on one of the orthogonal field components (Fig. 4), where α is the azimuth and β is the elevation angle. Cross sections were measured in the same symmetric range of angles: [-α _max ... α _max ], [-β _max ... β _max ], α _max = β _max .

The approximation of the volume amplitude MD during the approximation of its main sections by fourth-order power polynomials is shown in Fig. 5, where the points show the initial data. The standard deviation of this model with respect to the initial data (main sections) in amplitude is σ = 0.003. In order to symmetry the obtained DN, it is enough in the calculated coefficient vector to equate to zero the coefficients for the terms of the series containing odd degrees.

The approximation of the volume phase phase beam (PD) of the irradiator and its individual sections is performed by the same methods as the approximation of the amplitude beam (see Fig. 6). The result of approximation of the model by fourth-order power polynomials is presented in Fig. 7.

The standard deviation (RMS) of the model relative to the initial data in this example was σ = 0.013.

To calculate the main and cross-polarization components of the field of a large-sized hybrid-mirror antenna (GZA) in the far zone, we obtained relations for the fields of linear and circular polarization of the field. For example, for the field of right circular polarization, they are calculated in accordance with (10) and (11):

$$F_{GL}\left(\theta ,\varphi \right)=\frac{\mathrm{one}}{\sqrt{2}}\left[F_{\theta }\left(\theta ,\varphi \right)+j{F}_{\varphi }\left(\theta ,\varphi \right)\right].\left(\mathrm{one}0\right)$$

$$F_{GL}\left(\theta ,\varphi \right)=\frac{\mathrm{one}}{\sqrt{2}}\left[j{F}_{\theta }\left(\theta ,\varphi \right)+F_{\varphi }\left(\theta ,\varphi \right)\right].\left(\mathrm{one}\mathrm{one}\right)$$

where F _θ (θ, φ) and F _φ (θ, φ) are the component fields along the orthogonal angular components.

The relationships for calculating the energy characteristics of GCA are represented by formulas (12), (13). Formula (12) shows the calculation of the coefficient of directional action on the main polarization of the GZA with linearly polarized emitters, formula (13) for emitters having circular polarization.

$$\mathrm{TO}N{D}_{GL}=\frac{\pi {\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">W</figure-callout>}}_0^2}{{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000030.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}^2}\cdot \frac{{\left|{\mathrm{<figure-callout\; id="0"\; label="F"\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">F</figure-callout>}}_{{\tilde{0}}_{\mathrm{one},2}}\left({\theta }_M,{\varphi }_M\right)\right|}^2}{{\displaystyle \underset{0}{\overset{2\pi }{\int }}{\displaystyle \underset{0}{\int }\left[U_{\mathrm{one}}^2\left(\theta \text{'}\text{'}\right){\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="00000030.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\varphi \text{'}\text{'}+{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="00000030.png"\; state="\{\{state\}\}">U</figure-callout>}}_2^2\left(\theta \text{'}\text{'}\right){\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="00000030.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\varphi \text{'}\text{'}\right]{\left|{\displaystyle \sum _{n=\mathrm{one}}^N{l}_{n}e{\text{'}\text{'}}^{k{R}_n\cos {\alpha }_n}}\right|}^2}\sin \theta \text{'}\text{'}d\theta \text{'}\text{'}d\varphi \text{'}\text{'}}}\left(12\right)$$

with emitters having circular polarization of the radiation field, -

$$\mathrm{TO}N{D}_{GL}=\frac{\pi {\mathrm{<figure-callout\; id="0"\; label="W"\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">W</figure-callout>}}_0^2}{{\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000030.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}^2}\cdot \frac{{\left|F_{GL}\left({\theta }_M,{\varphi }_M\right)\right|}^2}{{\displaystyle \underset{0}{\overset{2\pi }{\int }}{\displaystyle \underset{S_R}{\int }\left[U_{\mathrm{one}}^2\left(\theta \text{'}\text{'}\right)+{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="00000030.png"\; state="\{\{state\}\}">U</figure-callout>}}_2^2\left(\theta \text{'}\text{'}\right)\right]{\left|{\displaystyle \sum _{n=\mathrm{one}}^N{l}_{n}e{\text{'}\text{'}}^{k{R}_n\cos {\alpha }_n}}\right|}^2}\sin \theta \text{'}\text{'}d\theta \text{'}\text{'}d\varphi \text{'}\text{'}}}\left(13\right)$$

Relations (14), (15), (16) provide the calculation of the total coefficient of utilization of the surface of the GZA, the coefficient of interception by the reflector of the radiation power by the antenna array and the aperture coefficient of use of the surface of the GZA.

$$\eta =\frac{\mathrm{TO}N{D}_{GL}}{\mathrm{<figure-callout\; id="0"\; label="TO\; N\; D"\; filenames="00000030.png,00000031.png"\; state="\{\{state\}\}">TO\; </figure-callout>}N{D}_{}{}_0}=\frac{\mathrm{TO}N{D}_{GL}\cdot {\mathrm{<figure-callout\; id="2"\; label="\lambda "\; filenames="00000030.png"\; state="\{\{state\}\}">\lambda </figure-callout>}}^2}{\mathrm{four}\pi \cdot S_{R\mathrm{but}\mathrm{from}\mathrm{to}}}\left(\mathrm{fourteen}\right)$$

$$\eta ={\eta }_a\cdot {\eta }_p\cdot \eta \text{'}\text{'}\left(\text{fifteen}\right)$$

$${\eta }_p=\frac{P_{Refl}}{R_{\Sigma }}\left(\text{16}\right)$$

Here η _a is the aperture instrumentation of the GZA reflector, η _p is the interception coefficient equal to the ratio of the power incident on the reflector (P _refl ) to the total power radiated by the irradiating AR P _Σ , η ′ is the coefficient taking into account the influence of such factors on the GZA efficiency, as the difference between the real phase front of the irradiator and the spherical one, inaccuracy of manufacturing the reflector, heat loss in the reflector, etc. For preliminary calculations, η ′ can be taken equal to unity.

To achieve the required energy characteristics of the antenna, adjusting the profile of its reflector reduces its standard deviation and repeats the calculation procedure using the developed software-algorithm complex.

Achievable technical result is the development of a method that allows the most reliable measurement of the radio characteristics of large antennas for spacecraft under the influence of Earth's gravity, as well as allowing studies of the dependences of the required accuracy of the reflector profile on the operating frequency range without making direct measurements in the far zone.

Claims (1)

A method for determining the radio technical characteristics of large-sized antennas for spacecraft without directly measuring them using a stand for measuring reflector parameters, characterized in that the parameters of the large-sized reflector are first measured using a high-precision non-contact laser scanner, after which a three-dimensional model of the reflector is constructed using series of Zernike functions , then the main sections of the amplitude and phase radiation patterns of the irradiator are measured, sweat Using the power polynomials, they approximate the volume amplitude and phase radiation patterns of the irradiator, then use the developed software to calculate the vector radiation pattern of the large antenna, as well as the values of the field components in the far zone taking into account the relative position of the irradiator and reflector, and then evaluate the energy characteristics large-sized antenna, then to achieve the required parameters of the antennas, adjust the reflectance profile ra and repeat the calculation of the energy characteristics of a large antenna.

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