Methods for mathematical modeling of waveguide phased arrays are well developed [1]. There are a lot of works devoted to studying arrays with emitters in the form of open endings of circular and rectangular waveguides and also waveguides with a more complex form of the cross-section. Nevertheless, there is almost no works where you could find the results of a numeric study of characteristics of phased arrays with coaxial waveguide emitters.

The aim of the articles is to study scanning characteristics, possibilities of matching the mentioned emitters on the basis of design features and the traditional methods, for example, with the help of electrical insertions.

When designing the mathematical model of phased arrays with coaxial waveguide emitters, we used the technique described in [1]. The mentioned mathematical model is realized in the form of a computer program GuidesArray Coaxial. The results of numerical experiment are given below.

Fig.1

Fig.2

In fig.1 you can see the set of curves representing the dependence of the reflection coefficient at the entry point of an emitter on the radius of the external conductor of a coaxial waveguide. The mentioned set is true for an array with emitters located in the nodes of a square net. The parameter of the set is the radius of the internal conductor of a coaxial waveguide. The array spacing is ==0,7142. The phasing direction coincides with the direction of the normal to the array plane. The graphs show that nearly complete matching can be achieved without using any additional elements, but just by choosing the appropriate values and . Any value
has some optimum , minimizing the reflection coefficient. Calculation error estimated by the intrinsic convergence of numerical procedure does not exceed 1..3% when using the basis function corresponding to modes *Т*, , ,
. (Further on we give those intrinsic modes of the coaxial waveguide, taking into the consideration the one that gave the stated accuracy.)

In fig.2 you can see partial diagrams of the directivity of coaxial waveguide emitters in *Е-* and *H-*planes (curves 1 and 2 respectively) in an array with the triangular grid of the location of emitting elements. The array spacing is *d*=0,7142. The sizes of the coaxial waveguides are =0,14,
=0,34. During the calculation we took modes *Т*, , in the coaxial waveguide emitters into account. Arrows in fig.2 indicate phasing directions when the diffraction maxima of higher order are on the border between actual and imaginary angles. The graphs show that the direction of the array dazzling in the plane *H* is shifted relative to the above-mentioned direction towards the normal. The numerical
experiment shows that this shift is determined by the excitation in the area of the aperture of the waveguide for the in the supercritical mode. If this mode is excluded from the waveguide waves taken into account, the direction of the array dazzling
coincides with the phasing direction, when the diffraction maximum is on the border between actual and imaginary angles (curve 3). The array spacing in the plane under consideration is less than . The mode excitation is equal to the applying a reactive loading to the point of the waveguide location. The mentioned loadings and the screen form a structure capable of maintaining surface waves, it creates the shift in the direction of dazzling towards the normal.

Fig.3

Fig.4

In fig.3 you can see graphs showing how the reflection coefficient depends on the scanning angle in *Е-* and *H-*planes (curves 1 and 2 respectively) when matching emitters with the help of dielectrical insertions towards the normal at the angle of 30° relative to the normal (curve 3), and also the dependence of the amplitude of *Т-*mode appearing at the aperture of the waveguide, related to the amplitude of an incident wave (curve 4). Curves 1 and 2 represent the insertions with the thickness *t*=0,142, placed at the distance of *l*=0,2121 from the aperture of the waveguides. The dielectric permeability of the insertions is =3,376. Before matching, the reflection coefficient in the direction towards the normal to the array plane is *|R|*=0,622. Curve 3 represents the insertion with the parameters *t*=0,1185,
*l*=0,2166, =4,729. Before matching, the reflection coefficient in the direction towards matching is *|R|*=0,721. The above-mentioned curves correspond to the triangular array of placing emitters with the array spacing *d*=0,7142, the sizes of the coaxial waveguide are =0,275, =0,33. Modes *T*, , were taken into account. The numerical experiment showed that the presence of dielectric insertions leaded to the result when the shift of the dazzling direction to the normal in *H-*plane was almost absent and the dazzling of the array occurs when the direction of diffractional maximum coincided with the border between actual and imaginary angles. The graphs in the fig.3 show that dielectric insertions ensure effective matching, as it is the case with arrays having circular and rectangular waveguides. The difference is that in our case the insertions can be used as constructive elements supporting the central conductor of the coaxial waveguide.

In the fig. 4 you can see the graphs showing the dependence between the modules of wave reflection coefficients , of modes providing the circular polarization of the array emanation field when phasing towards the normal (curves 1,2), as well as the dependence of the axial ratio (curve 3) and the slope angle of the polarizing ellipse (curve 4) on the scanning direction for the array with the triangular grid location of emitters. The emitter array is
*d*=0,7142, the sizes of coaxial waveguides are =0,14, =0,34. Waveguide modes *Т*, ,
were taken into account. The scanning plane corresponds to the *Е-* and *H-* planes of the emitter, excited by waves, the reflection coefficients of which are and
, respectively. The graphs show that in the selected array geometry decreasing the axial ratio to -3dB occurs when the ray diverges from the normal to the array plane for 40°.

__Conclusion.__

The results of the numerical experiment confirm the possibility of the effective use of coaxial waveguide emitters as emitting elements of phased arrays.