This paper describes the design of a dual-channel semi-open groove waveguide and a methodology for designing such structures. A method for forming a negative phase shift by shortening the lengths of the radiating inhomogeneities is demonstrated. Simulation experiments were performed using the Ansys HFSS package.

Emerging air attack weapons flying at ultra-high speeds pose a challenge of reducing the time available for their detection, lock-on and tracking. An increase of information refresh rate in all-round scanning radars can be achieved through higher antenna rotation speeds, however, in the course of modernisation it will be difficult to implement this approach due to capacity constraints imposed, as a rule, by the existing rotation system. At the same time, introduction of an additional channel into a radar system, as well as application of advanced methods and signal processing facilities may allow to obtain more information per antenna revolution, which is equivalent to increased scanning rate. Although such design modifications are quite extensive, they are rather accomplishable. At that, one of the challenges to be addressed is related to antenna system modernisation.

It is well known that some all-round scanning radars, such as 9S18М1-3 and 9S15МD, feature an element of phased array (PhAr), determining radiation pattern (RP) in the azimuthal plane, which is introduced in the form of a structure described in [1][2][3[4], which represents linear emitter based on a semi-open groove waveguide (W waveguide) with one end connected to the exciter and another end - to the matched load, with n number of metal irregularities having length l and arranged in staggered order on the bottom along the longitudinal axis (Fig. 1).

Fig. 1. Arrangement of irregularities on the bottom of emitter

In non-resonant travelling-wave antennas of such type a parasite mirror beam [5] may be excited resulting from a reflection from the opposite end. This is the reason why they feature the matched load; however, within the framework of the preset task an additional exciter can be arranged instead of the matched load (Fig. 2), the exciter will help to generate auxiliary mirror beam for the additional channel.

Fig. 2.1- dual-channel W waveguide section, 2 - the first exciter, 3 - the second exciter

The main requirements for such a device can include the maximum possible angle diversity of RP maximums of the main and auxiliary mirror beams from the normal (not less than 20° ± 1°) without sacrificing low side lobe level (SLL) of less than minus 30 dB (by power).

According to [4], in order to deflect RP maximum by angle θ the distance between irregularities shall satisfy the following condition

where λ is wavelength, λg - is waveguide wavelength, d is irregularities pitch (Fig. 1). However, at an increase of RP deflection angle θ value d increases until linear array no longer satisfies the requirement [6], which leads to RP subordinate maximums.

At the same time, value d decreases for negative values θ, and at irregularities length l = λg / 2 [3][4] their cross-strapping occurs violating the unbalance condition, which reduces the level of the emitted power. In this case, the length of the emitting element is selected based on its wave impedance matching with the main line [7].

Thus, in order to solve the preset task, i. e., to obtain RP with the required parameters, the case when irregularities length is defined as l = λg / р, subject to shorting coefficient p ≥ 2, needs to be considered.

It is known that the amplitude of an emitted wave of single irregularity, arranged in the W waveguide section (Fig. 3), is defined by the coupling coefficient function [3]

where к(h) is attenuation coefficient per unit length of wave passing over the irregularity with height h and length l:

Fig. 3. W waveguide cross-section

Waveguide wavelength λg(h) = λ / γ(h) is determined through wave slowing-down coefficient

Since application of this formula is confirmed only in case of irregularity length l = λg / р, where p = 2, it is required to verify its applicability for the cases when p > 2.

For this purpose, with the use of software package Ansys Electronics Desktop 2019, HFSS, a model (Fig. 4) of W waveguide was built based on the design described in [1][2][3][4], operating at frequency f0 = 4 GHz with dimensions a = 24 mm, b = 10 mm, t = 2 mm; and emitting properties of irregularities arranged inside the same were analysed.

Fig. 4. Model of W waveguide with single irregularity

The model includes excitation port - 1, load port - 2, receiving port - 3 with length λ/2, located at distance λ from emitting edge of W waveguide section - 4 with irregularity - 5. All elements of emitting W waveguide are made of aluminium, the rest space is filled with air. In the course of modelling, irregularity height h and length have varying values l(h) = λδ (h) /p.

Figure 5 shows the obtained dependency of the level of tapped power and coupling coefficients calculated by formula (2) on the emitter irregularity height.

Since the considered values are directly dependent on one another, let’s assume the value of tapped power of known irregularity with length λg (1 mm) / 2 to be their proportionality coefficient and compare them on one diagram.

According to the obtained results, formula (2) is only applicable in case when p = 2. To calculate coupling coefficients at р ≥ 2, let’s introduce empirically determined correction factors into (2):

then the dependency takes the form (Fig. 6).

Considering the above, let’s calculate and model the dual-channel linear emitter with amplitude distribution forSLL of minus 40 dB and main lobe deflection angle of minus 20°.

According to (1), for RP deflection by angle θ = –20° the distance between the elements shall be

At such value d, section with length 34 · λ can accommodate 75 irregularities. At that, to meet the condition of no cross-strapping, their length shall be l = λg (0) / 4 = 24.3. At this stage, wavelength in an empty waveguide is used in the calculations, since values hn are yet unknown.

To calculate irregularities height, let’s use formulas from [3]:

In the obtained distribution, irregularities height hn ≤8 mm (Fig. 7), at that maximum error α′ doesn’t exceed 0.2 dB (Fig. 6).

Fig. 7. Distribution of irregularity heights hn

If distribution in height is known, amplitude distribution can be re-established, including at emitter excitation from the opposite side (Fig. 8):

Fig. 8 shows that excitation from the opposite side distorts amplitude distribution by reducing the contribution of the far-end emitters. At the same time, the forecast radiation pattern (Fig. 9) is characterized by acceptable SLL and width, which may be applied in radars.

Using the obtained values of hn, d, l, the dual-channel linear emitter was modelled (Fig. 10), its excitation is carried out via the end face by port P1, the wall of the opposite end face acts as a load predetermined by port P2. To obtain the second radiation pattern, it is necessary to change ports emission direction. To determine the parameters of amplitude and phase of emission in the near zone, the emission limit is set in the form of a line located above the emitting part of W waveguide at height λ (Near Field Line).

Fig. 10. Model of dual-channel W waveguide

Fig. 11 shows radiation patterns of the model compared with the design data. As shown, RP are characterized by high SLL, and the position of the main forward and reverse lobes is shifted from the expected one by 5°, which is caused by phase distortion (Fig. 12) increasing as the wave propagates though irregularities. At that, the obtained amplitude distribution fairly accurately conforms to the design data, despite the simplification assumed for the calculation of l.

The question of compensating phase distortion in the aperture of such linear emitter was raised in [3]. Based on the consideration that in each point, where travelling wave taps via a waveguide, there is an incident, transmitted and tapped wave satisfying the condition for complex amplitudes Епад = Епр + Еотв, phase distortion introduced by each irregularity is represented as a combination of two types of distortion , the items of which can be represented by linear function of irregularity height h:

Thus, at a fixed irregularity length l = λg (h) / 2 phase distortions can be compensated by their non-uniform arrangement, which is defined by the ratio:

where y(0) is empty W waveguide slowing-down coefficient, u, v are coefficients calculated based on experimental phase distribution [3].

Let’s define value dn for the case of l = λg (h) / p at p ≥ 2. For this purpose, let’s express the phase of emitted wave of zero and the first irregularity as follows:

where п/p and 2n/p are phase progression to the centre and along the entire length of zero irregularity; δΦtr0 is phase distortion of a wave passing through zero irregularity; δΦrad0 and δΦrad1 are phase distortion of a wave emitted by the corresponding irregularity; п is account of phase reversal on the opposite side of W waveguide ridge [4];

- is phase progression on an empty section of waveguide.

For beam deflection by angle θ, condition Φrad1 - δΦrad0 = d1 sin θ shall be fulfilled, whence we obtain:

considering (3), interelement spacing between irregularities may be written as follows:

Thus, the obtained expression allows to calculate distribution dn to compensate phase distortion introduced by irregularities of any length determined as ln = λg (h) / р. In particular, at p = 2, we obtain expression (5).

To compensate phase distortion in functions (4) it is necessary to determine coefficients u and v, for which purpose expressions [3] can be used:

In this case, they are equal u = -35.181 m-1, v = 56.488 m-1. The obtained distribution dn is shown in Figure 13.

Рис. 13. Распределение расстояний между неоднородностями после компенсации фазовых искажений

Since the distribution of irregularities position dn has changed, values hn shall also change. In turn, irregularities length shall also be changed in accordance with ratio ln = λg (hn) / р.

As a result of correction, phase error reduces, which improves RP parameters (Fig. 14, 15), however, the preset task remains only partly accomplished.

At repeated phase correction following the described method, further reduction of phase distortion impact is achieved (Fig. 16, 17), at that, the obtained RP are characterized by correct deflection angle and low SLL not exceeding 30 dB.

The tendency towards phase distortion reduction persists during further iterations in a lesser extent and in the end it converges to the values differing little from the obtained ones, which is explained by a non-linear component of distortion described in [3]. However, strict consideration of these corrections following the method described in [3] is impossible due to reduction of irregularities length, which would be the focus of further study. Nevertheless, in practice even during the second iteration the result fairly satisfies the criteria of the preset task.

The work undertaken produced a structure of irregularities distribution on the bottom of semiopen groove waveguide which allows to implement emitter with two radiation patterns that are formed depending on excitation direction. The properties of obtained RP allow to consider this emitter as one of the main elements during development of dual-channel radar PhAr with increased scanning rate.