In this paper, an approach to the development of small-sized phased antenna arrays on ferrite phase shifters is considered. The paper presents examples of predicting the radiation characteristics of phased antenna arrays and processing their measured characteristics using mathematical models. On the basis of a phased array antenna for an unmanned aerial vehicle, the influence of the design features of such an antenna on its radiation characteristics is shown. The radiation characteristics of a phased array antenna for an unmanned aerial vehicle developed at V. V. Tikhomirov Scientific Research Institute of Instrument Design are presented.

Рассмотрены особенности разработки малогабаритных фазированных антенных решеток на ферритовых фазовращателях. Приведены примеры прогнозирования характеристик излучения фазированной антенной решетки и обработки измеренных характеристик фазированной антенной решетки с помощью математической модели. На примере фазированной антенной решетки для беспилотного летательного аппарата показано влияние конструктивных особенностей антенны на излучающие характеристики. Приведены характеристики излучения разработанной и изготовленной в АО «НИИП им. В. В. Тихомирова» фазированной антенной решетки для беспилотного летательного аппарата.

Development of complex microwave systems, such as active and passive antenna arrays, is a labour- and capital-intensive process involving state-of-the-art technologies. To reduce expenses, the developer strives to minimize the scope of works associated with mocking-up and full-scale experiments. Currently, one of the minimization methods is the full-fledged use of mathematical modelling means at all stages of development, manufacturing, setup and testing. At that, the more sophisticated is the device being developed, the higher is the efficiency of using mathematical modelling means. V. Tikhomirov Scientific-Research Institute of Instrument Design, JSC widely uses mathematical models describing the radiating and distributing systems of an antenna array (AA), using the break-down principle. The antenna system (AS) is broken down into several simpler assemblies that can be modelled using numerical methods subject to some simplifications. The mathematical model of a complex system, such as phased antenna array (PAA), becomes too complicated for calculation, unless we assume that all AA radiating elements are identical, metals have perfect conductivity and there are no losses in the dielectric materials.

The antenna system mathematical model, developed by A. N. Gribanov at V. Tikhomirov Scientific-Research Institute of Instrument Design, JSC, has the following break-down block diagram (Fig. 1).

The above mathematical model is original, it has been designed and developed within V. Tikhomirov Scientific-Research Institute of Instrument Design, JSC for several decades. Its functionality makes it possible not just to predict AS parameters, but also to analyse experimental data. Our colleagues, being its immediate authors, have made numerous publications about the peculiarities and capabilities of developed mathematical model for the PAA and APAA design [

Fig. 1. Block diagram of PAA mathematical model break-down

Fig. 2. Appearance of PAA developed and manufactured at V. Tikhomirov Scientific-Research Institute of Instrument Design, JSC for unmanned aerial vehicle

The considered PAA is distinguished from most known PAA by its small electrical size of about 10-15 wave lengths, and small number of radiating elements. The antenna emission system is designed in the form of an array of waveguide radiating elements with an increment of 16 mm in the azimuthal plane and 20.5 mm in the elevation plane. The energy distribution system is a waveguide system. The phasing system is based on Reggia - Spencer ferrite phase shifters [2, 3] with the use of control device designed based on PLIC, composite transistor switches and powerful MOSFET-transistors for control of inductive load.

The listed set of technical solutions provides for small dimensions, maximum AG, low level of background radiation; however, it sets the task of enhancing the accuracy of phase front implementation to a few degrees through elimination of all potential causes of amplitude and phase errors in the PAA aperture.

The design features and accuracy of antenna system and its elements manufacturing have the same level of importance. It is known that, at random distribution of phase errors in the PAA aperture, the background radiation level can be estimated using formula 1 [

(1)

where σ is root mean square implementation error of phase distribution in radians; N is number of PAA elements.

At the same time, if due to some design or methodological solutions the errors are of periodic nature, then the level of side lobes increases by dozens of times due to this periodicity. Unfortunately, this effect could not be avoided in the first PAA prototype.

When measuring radiation characteristics of an antenna, such an increase of the side lobe was revealed at upper frequencies in the radiation pattern (RP) of the azimuthal plane within the range from 70 to 90 and from -70 to -90° (Fig. 3).

To reveal the origin of this lobe, the mathematical model of a small-size PAA was used [

As a result of analysis of RP obtained using mathematical modelling (Fig. 5) and equivalent line (Fig. 6) built based on the amplitude and phase distribution measured by channels (Fig. 7), the version about errors of phase distribution of the PAA aperture was not confirmed.

Fig. 3. Radiation pattern in the azimuth plane of PAA prototype for a UAV

Fig. 4. Modelled equivalent line of phase distribution of PAA by measured RP

Fig. 6. Equivalent line of phase distribution of PAA by measured phase distribution

Fig. 7. Measured phase distribution of PAA aperture

The next step for revealing the lobe origin in the range of 70-90 and -70..._90ه in the azimuth plane consisted in recording the amplitude and phase distribution in the PAA aperture plane using the near-field scanner (Fig. 8). This data made it possible to determine and measure the shift of phase centres of the radiating panel (Fig. 9) relative to their geometric centres.

Fig. 8. Phase distribution of a fragment of the aperture of PAA prototype for a UAV

Fig. 9. Design of the radiating panel of PAA for a UAV

To simplify the manufacturing technology, the considered antenna included the radiating panel of a double row structure, where the wide walls of waveguides bended along the external sides of the radiating panels. This bend causes an increase in the size of the narrow wall of radiating element in the antenna aperture area and, therefore, a shift of phase centres of the radiating panel relative to the geometric centres of PAA elements.

The adjusted mathematical model of PAA, where the radiating panel design features were taken into account (Fig. 10), confirms that the main reason for the side lobe increase in the range from 70 to 90 and from -70 to -90° is the shift of phase centres of the radiating panel relative to the geometric centres. Therefore, further use of the double-row structure of the radiating panel requires its modification.

Table 1

Radiation characteristics at fcp of PAA for a UAV

Parameter name Azimuth Elevation Beam width (by -3 dB level) 3.8° 8° SLL -28.5 dB -22 dB Implemented phase distribution RMSD 4.3°

The considered PAA has an amplification gain exceeding 28 dB and a zero depth of less than -30 dB at fcp, other characteristics are specified in Table 1, and RPs are shown in Figures 11 and 12 and in 3D format in Figure 13.

Fig. 12. a - RP in the azimuth plane of PAA prototype for a UAV in various angular positions; b - RP in the elevation plane of PAA prototype for a UAV in various angular positions

Fig. 13. а - 3D RP of PAA prototype for a UAV; b - spatial RP of PAA prototype for a UAV

To sum up, it is to be noted that, by virtue of mathematical modelling, already the first prototype of a small-size PAA was successful in terms of radiation characteristics that met all the requirements of SOW, in spite of both technical and technological complexity of antenna system developed at V. Tikhomirov Scientific-Research Institute of Instrument Design, JSC.

The authors declare that there are no conflicts of interest present.