диафрагмированные волноводные фильтры / 94330a3d-60f8-4c40-be15-3ed08830ab12

Mykhailo Omelianenko

National Technical University of Ukraine

"Igor Sikorsky Kyiv Polytechnic Institute"

Kyiv, Ukraine email: oltur@meta.ua

Abstract—This paper presents E-plane stepped-impedance

bandpass filter with wide stopband. In comparison with the well-known E-plane filters on homogeneous resonators, the stopband of proposed structure is much wider and has higher attenuation. Significant improvement of these characteristics was achieved by a slight change in the topology of the filter resonators - the implementation of each resonator was realized using fin-lines of significantly different slot widths. These changes in topology dramatically change the frequency response of the resonators. In resonators with a significant predominance of the length of the low-impedance fin-line section, an increase in the bandwidth between the main and high order resonances can exceed 50% compared to homogeneous resonator. This is accompanied by a significant increase in the attenuation level in this frequency band and the appearance on the attenuation pole, the frequency of which can vary over a wide range by changing the impedance of the lowimpedance section. The filter synthesis procedure is based on the use of a modified technique with K-inverters. The size of the elements required to implement the inverter specifications were calculated using a FDTD simulation. The two-resonator filter with a central frequency of 17.25 GHz, with a bandwidth of 300 MHz was calculated and manufactured; it showed losses in the passband of the order of 1 dB, losses of higher than 30 dB up to 29.5 GHz in the stopband, and a maximum attenuation of 45 dB in the stopband. In comparison, the calculated values for a two-resonator filter using homogeneous resonators with the same specifications produces the same stopband losses only up to 21 GHz, a maximum loss of 32 dB, and moreover, the proposed filter has a reduction in size of 25%.

Keywords—bandpass filters, millimeter waves, microwave hybrid integrated circuits, stepped-impedance resonators.

I. INTRODUCTION

The E-plane waveguide filter is a convenient, functionally flexible structure that can effectively solve many important problems when developing telecommunication systems up to the frequencies of the short millimeter wavelength range [1], [2]. One of the disadvantages of the simplest and most widely used configuration of such filters — inductive strip filters — is the narrow frequency band between the main and next passbands, which is of the order of 1.4f0, and the low attenuation introduced into it. Although a considerable number of works [3], [4], [5] were devoted to the elimination of this drawback at different times, the improvement, as a rule, was achieved due to a significant complication of their design. The advantage of the topology of the E-plane waveguide bandpass filter proposed in this work is a minimal change in the filter design as a whole, which consists of only a modification of its metal-dielectric planar structure. Physically, the filter differs in that its resonators are made inhomogeneous — consisting of two sections based on fin-lines with very different slot widths. Thus, the filter is built on stepped impedance resonators (SIR). Although the microstrip structures of such resonators

Taras Romanenko

National Technical University of Ukraine

"Igor Sikorsky Kyiv Polytechnic Institute"

Kyiv, Ukraine email: hohner_@ukr.net

are well known and have been successfully used in microstrip filters with extended stopbands in the centimeter waves [6], [7], [8], the proposed E-plane SIR has a number of important features that are studied in detail in this work. In particular, it was found that the frequency response of the SIR with dimensions close to optimal for the stopband, has an attenuation pole. The position of it can be changed on the frequency axis by choosing the slot width of the lowimpedance section of the resonator. In addition, it was shown that such an E-plane SIR, despite the complexity of the configuration, can be fairly accurately calculated based on the parameters of the individual elements that make up its topology. This formed the basis for the synthesis of the proposed E-plane SIR filter.

II. THE PROPOSED E-PLANE STEPPED IMPEDANCE RESONATORS.

The topology of the proposed E-plane stepped impedance resonators is shown in Fig. 1. The figure shows that the resonator consists of two sections formed by fin-lines with different slot widths. In the high-impedance part, the width of the fin-line slot is set to equal to the height of the waveguide “b”. The simplified equivalent circuit of a weakly coupled resonator (Fig. 2) neglects the parasitic effect at the junction of the sections. However, it takes into account the influence of the reactances of the resonator, which can be characterized by the reflection coefficients

equation for finding the resonator frequencies takes the form

Equation (1) enables the calculation of ratio of the two resonant frequencies = ⁄ , where and are the first and second resonant frequencies. If the dispersion of the phase velocity in the sections of the resonator is small, and

Fig. 1. Geometry of a proposed E-plane SIR.

Fig. 2. Simplified equivalent circuit of E-plane SIR.

ratio “m” can be found from the following equation

"m" is greater than unity, and minimized. The calculated

normalized length of the low-impedance section are given in Fig. 3. The calculations were performed for phase values

φ = 2.97 rad; φ = 2.61 rad; – which are typical for strongly reflecting (|Г| 0.98) strips of SIR (Fig.1).

Fig. 3. Calculated values of normalized resonator length and frequency ratio versus normalized length of low-impedance section.

It can be seen that in the approximation of this rough model, even with a moderate difference in section impedances, which is practically achievable in the E-plane SIR, it is possible to obtain approximately 40% band expansion between the two lower resonance frequencies. In this case, the length of the lowimpedance part of the resonator should exceed the length of its highimpedance section.

These features of the simplified resonator model also appear for a real E-plane SIR. Fig. 4a, Fig. 5a shows the frequency response of two resonators calculated by FDTD simulation (all simulated results obtained by commercial software CST Microwave Studio, Transient Solver Analysis with Adaptive mesh refinement, delta 0.01). All calculations were performed for structures based on metallized substrates

a × b = 11 × 5.5 mm. Weak coupling of the resonators was ensured by the proper choice of the strip widths S1 = 2 mm and S2 = 3 mm (Fig. 1), at which the reflection coefficient was greater than 0.98 at a given fundamental resonance

frequency f1 = 17 GHz. The characteristics are depicted for two values of the slot widths of the low-impedance part of the resonator indicated in the figures. The different characteristics in the figures relate to different values of the length of the low-impedance section l1. In this case, the length of the high-impedance section was selected each time

in order to ensure a given fundamental frequency f1 of the resonator. It should be noted that the curves related to the value of l1 = 0.01 mm are characteristics of homogeneous inductive strip resonators and are given for comparison with the frequency characteristics of the E-plane SIR. The presented results show that the previously considered model describes the real behavior of SIR only qualitatively: a reduction in the size of the resonator and an increase in the

ratio ⁄ occurs only when the length of resonator is dominated by the length of the low-impedance section. The simplified model gives an estimate of the magnitude of this dominance which is incorrect, since (Fig. 3) the maximum

value of the frequency ratio ⁄ in the terms of this model is achieved with the length of the low-impedance part only slightly exceeding half the total resonator length. In reality, the indicated ratio of frequencies monotonically increases, despite the decreasing value of in comparison to . This can be seen from Figs.4b, 5b, which shows the calculated values of the frequency ratio and the normalized total cavity

show two important features of the E-plane SIR when the low-impedance section dimensions are optimal.

Fig. 4a. Simulated characteristics of SIRs with w1 = 1mm for: 1 – l1=0.01

mm, l2 = 11.5 mm; 2 – l1 = 3.0 mm, l2 = 9 mm; 3 – l1 = 5.5 mm, l2 = 1.07 mm.

Fig. 4b. Simulated values of frequency ratio (1) and normalized resonator length (2) versus high-impedance to low-impedance section length ratio for SIRs with w1 = 1 mm.

Fig. 5a. Simulated characteristics of SIRs with w1=0.5mm for: 1– l1 = 0.01

mm, l2 = 11.5 mm; 2 – l1 = 3.5mm, l2 = 7.7 mm; 3 – l1 = 4.8 mm, l2 = 1.1 mm.

First, unlike a homogeneous resonator, its frequency response near the second resonance is strongly distorted, and the second resonance itself is also distorted. Secondly, for all considered values of the slot width of the low-impedance

Fig. 5b. Simulated values of frequency ratio (1) and normalized resonator length (2) versus high-impedance to low-impedance section length ratio for SIRs with w1 = 0.5 mm.

part of the resonator, in the frequency band between the first and second resonances there is a attenuation pole, the frequency of which depends on the width of the slot. The presence of a pole makes the selective properties of a homogeneous resonator and a E-plane SIR generally incomparable. Since with a proper choice of the slot width, the introduced SIR losses at the frequency of the second resonance of the homogeneous resonator can be made extremely large.

Despite the inconsistency of the results obtained by the simplified representation of SIR and its electrodynamics modeling, it seems reasonable to refine the model of the resonator in terms of circuit theory in order to establish the possibility of calculating SIR without involving its full electrodynamics model. This will make it possible to significantly reduce the synthesis time of resonators and filters by using look-up tables of parameters of the elements of the resonator. For this purpose, the resonator was presented in the form of a cascade connection of S- matrices,

as shown in Fig. 6. In this figure, the matrices ( ), ( ),

( ) are the single-wave scattering matrices of the strips and the jump in the resonator slot width. These matrices are calculated using electrodynamic calculations. The matrices

calculated in this way with selected dimensions of slot width

w1 = 0.5 mm and section lengths l1 = 4.8 mm, l2 = 1.1 mm is shown in Fig. 7 (curve 1). For comparison (curve 2), the resonator characteristic calculated via FDTD simulation is given. It can be seen that the characteristics coincide with graphic accuracy in the frequency region adjacent to the resonant frequency f1. This important fact suggests the possibility of using circuit theory for the synthesis of resonators. Detailed calculations show

Fig.6. Modified equivalent circuit of E-plane SIR.

Fig. 7. Comparison of characteristics of SIR according modified model (1) and full resonator analysis (2); l1 = 4.3 mm, l2 = 1.16 mm.

that the difference in frequency response far from f1 for a resonator with a parameter close to the maximum value f2/f1 is explained by the interaction between the transition region

( ( )) and the strip ( ( )). This occurs when the highimpedance part of the SIR has a short length. Such a mutual influence of closely located inhomogeneities, obviously, cannot be taken into account in the single-mode approximation.

III. E-PLANE SIR FILTERS.

The E-plane SIRs proposed and considered in this work were used to implement bandpass filters with extended stopbands in the short-wavelength part of the centimeter wave domain. As an example, here we consider the topology of a Chebyshev two resonator filter with a ripple level of 0.5 dB between the passband frequencies fL = 17.1 GHz and fН = 17.4 GHz. The planar structure of the filter is manufactured on a substrate with a thickness of d = 140 μm with two-sided 35 μm metallization and a dielectric constant ε = 2.2, placed in a waveguide with dimensions a × b = 11 × 5.5 mm. The synthesis of the filter, the topology of which is shown in Fig. 8, was carried out by a technique based on the use of K-inverters. In this case, the sizes of the coupling elements of the resonator S1 and S2, which can be calculated from the required inversion coefficients, were calculated using a package of programs for electrodynamic modeling; the size of the slot of the low-

impedance section and the length of the high-impedance part of the resonator were fixed (w1 = 1mm, l2 = 1 mm), and the length the low-impedance section l1 was calculated based on the refined model of the resonator as described above. The results are: S1 = 3.8mm, S2 = 2.18 mm, l1 = 5.4 mm. The calculated filter response is shown in Fig. 9 (thin solid line). The obtained sizes were refined using an iterative procedure. The obtained sizes are S1 = 3.27 mm, S2 = 1.49 mm, l1 = 5.38 mm; the calculated frequency response is shown in Fig. 9 as the bold line. As expected, the selective properties of the proposed E-plane SIR filter are significantly superior to those for a

Fig. 8. Geometry of a proposed E-plane SIR filter.

Fig.9. Simulated frequency responses of E-plane SIR filter calculated by

standard filter with the same number of resonators and bandwidth requirements (the characteristic is shown by a dashed line): at the frequencies of the second passband of the standard filter, the losses of the new filter are about 45dB, and its second passband is generally weakly expressed.

IV. EXPERIMENTAL RESULTS

The characteristics of the calculated and manufactured samples of the resonator and two resonator filter were measured experimentally (Fig. 10, Fig. 11, respectively). Loss measurements are shown by dots; whilst the thick black line shows the results of the simulation for comparison. The filter characteristics coincide with the accuracy necessary for practical use.

Fig.10. Measured ( ) and simulated ( ) characteristics of E-plane SIR; l1 = 5.6 mm, l2 = 1 mm, w1 = 1 mm, S1 = 3 mm, S2 = 2 mm.

Fig.11. Measured ( ) and simulated ( ) characteristics of two resonator E-plane SIR filter; l1 = 5.38 mm, l2 = 1 mm, w1 = 1 mm, S1 = 3.27 mm, S2 = 1.49 mm.

V. CONCLUSION

The proposed E-plane stepped impedance resonators and bandpass filters, while preserving the simplicity and manufacturability of E-plane waveguide hybrid integrated circuit on homogeneous resonators, have significantly wider stopbands and stopband attenuation. At the same time, the reduction in size of the developed two resonator filter is almost 25%. The E-plane technology of the proposed filters allows them to be used at frequencies of the millimeter wavelength range.

ACKNOWLEDGMENT

The authors would like to thank Robert Christopher Jones for helpful discussion support and contribution.

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