диафрагмированные волноводные фильтры / 61386d77-950e-48f6-bd43-d1b3d65f759f

Abstract— The possibility of using traditional (scalar) models of band-pass filters (BPF) of the millimeter range on "all-metal inserts" in design of three-dimensional modifications of such a BPF is estimated. The complication of the filter geometry is associated with the introduction of narrow grooves in each of the resonators, which provide a number of technological advantages in fabrication. It is proved that with all-metal inserts with a thickness of not more than

λ/100, the results of the “vector” and “scalar” models completely coincide.

Keywords: band-pass filters, all-metal insert filter, optimization

I. INTRODUCTION

One of the first band-pass filters intended for use in the mm range was a filter on a longitudinal metal insert, first described in [1, 2]. It contained a number of rectangular holes with a total height equal to the height of the waveguide and with lengths that determine the frequencies of the resonators in the in-line filter circuit. Being inserted into two halves of the filter housing (Fig. 1), such an insert organizes a chain of resonators separated by longitudinal strips dividing the cross section into two below cutoff sections. Their lengths determine the coupling between adjacent resonators. After the first publication, a lot of work appeared on the synthesis and optimization of such filters and their various applications. The IRE team made a certain contribution in this direction, bringing the matter to a series of problem-oriented programs for the design of the filters themselves, as well as various diplexers and multiplexers based on them [3 - 5].

Such filters gained particular relevance with an increase in the operating frequencies of designed devices for the following reasons:

mechanical rigidity (work under severe overloads);

manufacturability of the design, providing the minimum requirements for equipment;

relatively large size, which allows increasing the tolerances for the manufacture of the structure and reduces the field strength in the filter cavities providing greater resistance to breakdown at high powers.

The advantages of these filters include simple algorithms of their synthesis and accurate electromagnetic calculation.

Fig. 1. Construction of a filter on all-metal insert

The main disadvantage of such filters is the limited bandwidth associated with the fact that the longitudinal iris has a limit of adjustment of the reflection coefficient, which cannot be arbitrarily small [6].

It should be said that the high manufacturability of such filters still gives rise to new proposals in the development of the original idea, especially when using longitudinal inserts on a dielectric substrate.

The reason for this investigation was the design of a millimeter-wave diplexer with increased requirements for the isolation between the channels implemented on the branching of the waveguide in the E-plane.

The described design was chosen because of its convenience to use one longitudinal insert for both channels of the filter. It was necessary to include ten resonators in order to satisfy the high requirements of this device.

Since the structure synthesized in the single-wave model was suitable only for the initial approximation, the final optimization required a full-wave model that takes into account many evanescent modes. In this case, taking into account the geometry of the connecting unit and the number of resonators in the filters, the total number of optimized parameters (the dimension of the optimization space) has reached several tens.

Since the procedure for analyzing (calculating the frequency response) of such a device on commercial packages reached many hours, then we were not talking about multidimensional optimization using them.

Designing was possible owing to the use of special algorithms based on the mode matching technique developed in the IRE as a part of the electromagnetic simulation system MWD [7], taking into account:

analytical representation of waveguide element bases;

symmetry of the structure;

two-dimensionality of the scattering problems for channel filters and the possibility of their local optimization, which reduces the dimension of the optimization space;

the procedure of scalarization - vectorization that allows S-matrix assembling the common junction with channel filters.

In addition, using the multi-stage global optimization procedure, gradually (pyramidal) increasing the optimization space dimension by gradually including channel filters elements that are more and more distant from the common junction, we achieved the solution of the device design problem with the required characteristics [4,5] in a time comparable to its frequency response calculation with commercial packages.

However, in the manufacture of such devices, questions arose of the suitability of the design model for the technology. Since in the manufacture of a longitudinal insert, only a milling cutter with a minimum radius of 0.5 mm for a waveguide size of 7.2x3.4 mm2 could be used.

It was necessary to estimate the error introduced by the longitudinal grooves in rectangular waveguides and, most importantly, to prove using a strict model the possibility of design of the filters with narrow longitudinal grooves in the resonators using software designed for two-dimensional problems.

II. CALCULATION

Since it is known that a narrow longitudinal slit along a wide waveguide wall weakly affects the field inside it,

G. I. Khlopov proposed to hide the rounding windows in allmetal insert inside the waveguide wall.

The width of the slit was taken 0.1 mm in accordance with the thickness of the plate used in the manufacture of the insert, and the depth was equal to the radius of the cutter (0.5 mm).

Figure 2 shows that a segment of a rectangular waveguide serving as a resonator is transformed over most of its length into a grooved waveguide. The problem of calculating such geometry became the full-wave vector problem in contrast to the traditional scalar configuration, which is calculated completely in the basis of TEq0 waves. Here, accurate calculation of the multimode projection basis of a grooved waveguide and the S-matrix of plane-junctions of a grooved waveguide and a pair of narrow rectangular waveguides is required.

For a comparative analysis of the influence of the grooves on the characteristics of the device, the resonators shown in Fig.2e,f were calculated.

Fig. 2. Design of a separate resonator used in the filter: a) longitudinal view of a rectangular resonator, b) longitudinal view of a produced resonator, c) longitudinal view of a grooved resonator (without rounding of the longitudinal insert), d) transversal view of a grooved waveguide, e) isometric view of a rectangular resonator, f) isometric view of a grooved resonator.

Taking into account the highest sensitivity to simulation accuracy, the highest-quality resonator in the channel filters of the designed diplexer was chosen as a test object.

The complexity of the problem was that the grooved waveguide basis was calculated numerically by searching for hundreds (!) of the roots of the dispersion equation. Thus, its mode bases cannot be considered a priori reliable, as in the two-dimensional problem. The frequency responses

different models and in different approximations are shown in Fig. 3 and 4. As can be seen, the vector model (with a groove) and the scalar one (only TEq0 modes) give a relatively small difference even at fcut = 100 GHz (Fig. 3). However, the resonant frequency itself turned out to be somewhat shifted down in frequency.

Here the accuracy parameter fcut determines the size of projection bases in the mode matching technique. It defines the maximum cutoff frequency of the waveguide modes included in the projection basis. The value fcut = 100 GHz corresponds to 17 TE and TM modes taken into account in the calculations.

At the same time, it turned out that for such high-quality resonators, the result of the response calculation stabilizes only at fcut > 450 GHz. Indeed, Fig. 4 confirms the complete coincidence of the frequency response for the two types of resonators both in the Q - factor and in the center frequency.

To assess the dependence of the frequency response of the resonator under consideration on the groove depth, a two-dimensional distribution of the return loss in the coordinates ―frequency –groove depth‖ was calculated (Fig. 5). Positive values of depth h correspond to grooved waveguide, negative values are for rigged waveguide, and h = 0 corresponds to rectangular waveguide.

Frequency, GHz

Fig. 3. Comparison of the frequency response of the resonators shown in Fig. 2e and Fig. 2f (fcut=100 GHz).

The brightness of the points on the graph corresponds to the transmission coefficient in decibels. Analysis of this graph allows us to draw the following conclusions:

The field does not penetrate deep into a narrow longitudinal slit; therefore, it is convenient to hide possible manufacturing errors in grooves behind the walls of the waveguide; above h > 0.1 mm, the cavity

―does not notice‖ the presence of a groove;

The ridge inside the resonator dramatically changes its characteristic and, at first, the frequency of such a resonator increases almost linearly with increasing h.

Frequency, GHz

718

Analyzing the figure, we can conclude that the scalar model shown in Fig. 3e can be used for optimization of the design shown in Fig. 3f.

Fig. 5. The return loss versus the frequency and the groove size.

Rectangular Resonators

Grooved Rectangular Resonators

Frequency, GHz

Fig. 6. Comparison of the frequency response of the filters with grooved and rectangular resonators

Fig. 4. Comparison of the frequency response of the resonators shown in Fig. 2e and Fig. 2f (fcut=500 GHz).

Finally, we compare the characteristics of a threeresonator filter, similar to that shown in Fig. 1, calculated using the scalar model with rectangular resonators (Fig. 3a,e), with a filter calculated using the vector model with grooved waveguide resonators (Fig. 3f). The comparison results are presented in Fig. 6.

As can be seen from the figure, the curves of reflection coefficients are actually superimposed on each other, so a curve representing their difference is added. Noticeable differences are observed only in the areas of transmission resonances.

Based on the presented results, the following conclusions can be drawn:

since the field does not penetrate into the narrow gap along the wide wall of the waveguide, some technological errors can be hidden inside it;

the algorithms and filter synthesis programs based on the ―scalar‖ solutions of the type considered above and various diplexers based on them can well be used in the presence of narrow grooves in resonators with a depth of at least λ/100.

REFERENCES

[1]Y. Konoshi and K. Uenakada, ―The design of a bandpass filter with inductive strip-planar circuit mounted in waveguide‖, ibid., MTT-22, pp. 869-873, 1974.

[2]Y. Tajima and Y. Sawayama, ―Design and analysis of a waveguidesandwich microwave filter‖, ibid., MTT-22, pp. 83984, 1974.

[3]A. A. Kirilenko, S. L. Senkevich, V. I. Tkachenko, and B. G. Tysik, ―Microwave diplexer and multiplexer design‖, IEEE MTT, vol. 42, No. 4, pp. 1393-1396, 1994.

[4] A. A. Kirilenko, V. I. Tkachenko, and L. A. Rud, ―Design of E-tee diplexers having closely spaced frequency channels in the upper part of a waveguide operating range‖, Proc. of 12th Int. Conf. on Microwaves and Radars (MIKON-98), Krakow, Poland, vol. 1, pp. 43-57, May 20-22 1998.

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[5]A. A. Kirilenko, V. I. Tkachenko, and L. A. Rud, ―A systematic approach for computer aided design of waveguide E-plane diplexers‖,

Int. J. RF and Microwave CAE 9, pp. 104-116, 1999.

[6]Y.-C. Shih, ―Design of waveguide E-plane filters with all-metal inserts‖, IEEE Trans. Microwave Theory Tech., vol. MTT-32, pp. 695-704, July 1984.

[7]A. A. Kirilenko, D. Yu. Kulik, and V. I. Tkachenko, ―The automatic mode-matching solver application by the example of complicated shape cavities design‖, European Conference on Numerical Methods in Electromagnetism Conf. Proc., Toulouse, France, CD-ROM, pp. 1- 3, 2003.

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