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Wang Dan, Wei Bin, Heng Yong, Cao Bi-Song. High-temperature superconducting filter using self-embedding asymmetric stepped impedance resonator with wide stopband performance and miniaturized size. Chinese Physics B, 2017, 26(10): 108502  
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High-temperature superconducting filter using self-embedding asymmetric stepped impedance resonator with wide stopband performance and miniaturized size
Wang Dan1, Wei Bin1, †, Heng Yong2, Cao Bi-Song1
State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
Beijing Institute of Electronic System Engineering, Beijing 100854, China

 

† Corresponding author. E-mail: weibin@mail.tsinghua.edu.cn

Abstract

In this study, a novel self-embedding asymmetric stepped impedance resonator (SE-ASIR) topology is proposed. By embedding asymmetric stepped impedance resonators in themselves, circuit sizes of ASIRs can be reduced effectively, while the ability to control spurious modes of ASIRs remains. Therefore, SE-ASIRs are suitable for being used to design filters with wide stopbands and miniaturized sizes. Furthermore, the construction process of the SE-ASIR is described in detail, and an equivalent model of the SE-ASIR is proposed. For demonstration, a high-temperature superconducting bandpass filter centered at 1112 MHz is designed and fabricated. The measured result agrees well with the simulation result and shows that the out-of-band rejection is better than 60 dB up to 4088 MHz, which is about 3.7 times the center frequency. The filter circuit size is 31 mm × 13 mm or , where is the guided wavelength at 1112 MHz.

PACS: 85.25.-j
Keyword:high-temperature superconducting;bandpass filter;microstrip filter;wide stopband
1. Introduction

Microstrip filters are extensively used in modern wireless communications systems because of their simple fabricating procedures and compact sizes.[1–3] However, as planar devices, microstrip filters suffer unwanted spurious bands.[4] To solve this problem, bandpass filters with small sizes, wide stopbands and high rejection levels are demanded. Many resonators have been proposed to construct wide stopband filters, such as half-wavelength resonators,[5] quasi-lumped element resonators,[6] modified line resonators,[7] defected grounded structures resonators,[8] and stepped-impedance resonators (SIRs).[9–14]

Among the methods, SIRs are attractive due to simple theoretical models and convenient fabrications. The basic principle of SIRs is presented in Ref. [9]. The fundamental frequency f0 and the first spurious frequency of an SIR can be tuned by adjusting the structural parameters of SIR, and the ratio of an SIR is proportional to its impedance ratio. As a result, to shift up the ratio of SIRs, low impedance lines of SIRs are usually large, which restricts the application of SIRs. To address this issue, several methods have been developed to reduce the circuit size or further enhance the spurious suppression features of SIR filters. Introducing transmission zeros is a popular method to improve wide stopband performance.[10–13] In Refs. [10]–[12], transmission zeros are introduced by tapping stubs on SIR filters. In Ref. [13], couplings between SIRs are used to provide transmission zeros. These transmission zeros are properly located to attenuate the spurious harmonics of filters. Because the transmission zeros cannot eliminate spurious frequencies directly, the stopbands of these filters are usually wide but not very deep. At the same time, grounded quarter-wavelength structures are also used to design wide stopband SIR filters,[5,14,15] because the grounding can reduce circuit sizes and eliminate the even order spurious harmonics of SIR filters simultaneously. For example, in Ref. [15], stub-loaded SIRs with multiple transmission zeros and quarter-wavelength are proposed to design wide stopband filters. However, the grounding structures will increase the insertion loss and fabrication difficulty of a filter. In addition, use of multi-layers structures are beneficial to the decrease of circuit sizes of SIR filters. For example, in Ref. [16], SIRs are embedded on the middle layer of a bandpass filter, which can achieve spurious suppression, with no modification of the entire circuit size. However, the fabrication of multi-layer filters are usually difficult.

Recently, the interest in planar asymmetric SIR (ASIR) wide stopband filters has been aroused. ASIRs are used to enhance the spurious suppression performances of multi-bands filters[17,18] or construct wide stopband filters.[19–21] Compared with conventional symmetric SIRs, ASIRs can control spurious modes as symmetric SIRs while occupying smaller circuit sizes.

On the other hand, because of characteristics of low insertion loss, high out-of-band rejection, and high selectivity,[22,23] high-temperature superconducting (HTS) filters have been widely used to fabricate high-performance radio-frequency front end or microwave devices,[24–27] including wide stopband filters.[6,7,10,19]

In this work, a novel self-embedding ASIR (SE-ASIR) with miniaturized size and controllable spurious harmonics is proposed. The topology of the SE-ASIR is derived from conventional ASIR. The SE-ASIR has an advantage of miniaturized size over conventional ASIR with one discontinuity, but can push its spurious harmonics higher than it. The construction process of the SE-ASIR is described in detail, through two topology transformations. Furthermore, an equivalent model of the SE-ASIR is proposed. Finally, for demonstration, a small HTS filter is designed and fabricated using the SE-ASIR. The measurements of the filter agree well with simulations, and exhibit good spurious suppression performance in terms of both wide stopband and high rejection level.

2. Resonator design
2.1. Structure and resonant characteristics of SE-ASIR

The structure of the proposed SE-ASIR is shown in Fig. 1. It is composed of three segments with different impedances: a low-impedance rectangle patch (segment A), a high-impedance spiral line (segment B) and a hollow patch (segment C). By embedding the large segment A in the hollow segment C, the circuit size of SE-ASIR is much smaller than a conventional SIR.

Fig. 1. (color online) Structure of SE-ASIR.

Meanwhile, the spurious suppression performance of SE-ASIR is better than that of conventional ASIR with one discontinuity. figure 2 shows that the spurious resonance frequencies of SE-ASIR can be manipulated by changing the width and length of segment A. The larger the parameters and , the higher the is. And when increases to 3 mm, i.e., , the can be increased to be higher than 3.8, which is much larger than the ratio of conventional ASIR with two step discontinuities. According to the analyses in Refs. [19] and [20], even when the impedance ratio of a conventional ASIR with one discontinuity is as high as 10, the maximum ratio is still smaller than 3.0.

Fig. 2. Plots of simulated versus length of SE-ASIRs for different values of line width with and .
2.2. Construction process of SE-ASIR

The topology of SE-ASIR is derived from conventional ASIR with two discontinuities. The resonant properties of SE-ASIR can be analyzed by using the equivalent model, which is an ASIR as shown in Fig. 3. However, this equivalent model is not very intuitive. Thus, in this subsection, two topology transformations (shown in Fig. 4) and the corresponding conditions are discussed in detail, to describe the construction process of the equivalent model. And figure 4 shows that the circuit size of Topology I is about 60% of that of Topology III.

Fig. 3. Equivalent model of SE-ASIR.
Fig. 4. (color online) (a) Topology I, topology of SE-ASIRs, (b) Topology II, topology of hollow ASIRs, and (c) Topology III, topology of folded ASIRs.

Topology I is the original topology of SE-ASIR. It can be divided into two parts: the interior, which is printed in blue, and the exterior, which is printed in black as shown in Fig. 4(a). Topology II is constructed by taking the inner part of Topology I out and tapping this part on the outside edge of the exterior as shown in Fig. 4(b).

Resonant characteristics of Topology I and Topology II are equal, on condition that the inner blue part and the black exterior part of Topology I are far apart. This conclusion is verified by the EM simulations shown in Fig. 5. Actually, it is seen that when the gap distance d between the inner part and exterior part is 0.48 mm, the maximum deviations of f0 and between Topology I and Topology II are only 0.9% and 1.4%, respectively. And when gap distance d decreases to 0.04 mm, the maximum deviations of f0 and between the two topologies increase to 5.5% and 8.1%, respectively. Besides, it is worthy to mention that when d decreases from 0.48 mm to 0.04 mm, f0 of SE-ASIR topology decreases and of SE-AISR increases, thereby increasing , as shown in Fig. 5. Nevertheless, the gap distance d is still set to be 0.48 mm in this work, to ensure that Topology I and Topology II exhibit equally resonant patterns.

Fig. 5. (color online) Deviations of resonant frequencies between Topology I and Topology II at (a) fundamental frequency f0 and (b) the first spurious frequency .

The above effect of gap distance d on resonant frequency is caused by the self-capacitance between the interior and exterior of SE-ASIR. The current and charge distributions of SE-ASIR at f0 and are plotted in Fig. 6. Like traditional half-wavelength straight resonators, unlike and like charges concentrate at the two ends of SE-ASIR at f0 and , respectively. In Topology I, the two ends of ASIR are very close, especially when the gap distance d is small. In such a situation, the unlike charges on the two ends of SE-ASIR will enlarge the self-capacitance of the area surrounded by the dash line in Fig. 5(c). At , the like charges will diminish the elf-capacitance. According to the expression , the larger self-capacitance C at f0 will reduce the fundamental frequency, and the smaller self-capacitance C at will diminish the spurious frequency. Therefore, as illustrated in Fig. 5, the resonant frequencies of Topology I and Topology II have the following relationships:

Fig. 6. (color online) Current and charge distributions of (a) a straight-line resonator at f0, (b) a straight-line resonator at , (c) SE-ASIR at f0, and (d) SE-ASIR at .

The topology transformation from Topology II to Topology III is also studied. The two topologies have similar resonant patterns. Topology III is a folded conventional ASIR, which is constructed through replacing the hollow segment C of Topology II by a solid one as shown in Fig. 4(c). As a result of skin effect, almost no current is present in the central area of the large microstrip patch segment C of Topology III. Thus, the absence of the central area will not change the basic resonant pattern of the large microstrip patch of Topology III. EM simulations support this conclusion. As shown in Fig. 7, the resonant frequencies curves of Topology II with different values of border width have the same trend as those of Topology III. When the border width increases to 2.4 mm, the resonant frequencies of Topology II and Topology III are almost the same.

Fig. 7. (color online) Deviations of resonant frequencies between Topology II and Topology III at (a) fundamental frequency f0 and (b) the first spurious frequency .
2.3. Equivalent model of SE-ASIR

Through the above discussion, it is known that an SE-ASIR can be equivalent to the ASIR model in Fig. 3. Considering the deviation between Topology II and Topology III, the hollow segment C of SE-ASIR is equivalent to a microstrip line with characteristic impedance . is larger than , which is the characteristic impedance of a solid patch with the same size as the hollow segment C.

On the basis of the model, the resonant frequencies f0 and of SE-AISR can be obtained from the transmission line theory.[28] The input admittance of the proposed SE-ASIR is derived as

in which
Under the resonant condition , the resonant frequencies of the SE-ASIR can then be calculated by employing a simple root-searching program. For example, in this work, dielectric constant , , , and , the resonant frequency ratio against under different values of are calculated and plotted in Fig. 8. Notably, when , the ratio increases with a growing , which accords with the plots in Fig. 2. And when u = 0, which means that the ASIR is reduced to a conventional ASIR with two step discontinuities, and the is smaller than 3. The extreme of the SE-ASIR occurs at . In addition, figure 8 shows that a smaller corresponds to a higher ratio.

Fig. 8. (color online) Ratios of versus u of SE-ASIR for different values of .

Our objective is to obtain a large ratio of and a small circuit size. Figure 8 shows that when , the increases with growing and . However, the increases in and will also increase the whole size of SE-ASIR. Taken together, in this work, parameter u is approximately 0.3, and parameter is approximately 0.1 . The of the designed SE-ASIR is 3.8, which indicates that real is about 0.2 , according to Fig. 8.

2.4. Coupling properties of SE-ASIR

There are three kinds of resonator coupling patterns for SE-ASIR as shown in Fig. 9. Because their different inner parts are embedded in the same hollow large patch of SE-ASIR and will not influence the adjacent coupling, and their coupling coefficients are similar. This coupling property is convenient for filter design.

Fig. 9. (color online) Three kinds of coupling patterns of SE-ASIR at 1112 MHz.
3. Filter design, fabrication, and measurements

For demonstration, a four-pole Chebyshev bandpass filter is designed using the proposed SE-ASIRs. The center frequency and bandwidth of the filter are chosen as 1112 MHz and 10 MHz, respectively. On the basis of these settings, the resonator parameters of the proposed filter are determined, which are , , , , , , d = 0.48, and (all in unit mm) as shown in Fig. 1. The and are the width and whole length of the segment B of SE-ASIR, respectively. The coupling coefficients and external quality factor of the filter are obtained by using the standard design procedure in Ref. [28], which are, , , and . Then, the other physical parameters of the filter are determined as follows: , , , , , , w2 = 0.24, , , , and (all in unit mm) as shown in the following Fig. 10.

Fig. 10. Layout of SE-ASIR filter.

The filter is fabricated on a double-sided YBCO film with a relative dielectric constant of 9.74 and a thickness of 0.50 mm, deposited on an MgO substrate. The filter size is 31 mm × 13 mm or , where is the guided wavelength at 1112 MHz. A photograph of the fabricated HTS filter is shown in Fig. 11.

Fig. 11. (color online) Photograph of fabricated filter with top cover removed.

The fabricated HTS filter is cooled to 60 K and measured using an Agilent E5072A network analyzer with an input power of 0 dBm. The measurement agrees well with the simulation. As shown in Fig. 12, the filter is centered at 1112 MHz with a 3-dB fractional bandwidth of 10 MHz. The maximum insertion loss is 0.12 dB and the return loss is better than 20 dB. As shown in Fig. 13, the stopband rejection of the filter is better than 60 dB up to 4088 MHz, which is approximately 3.7 times the fundamental frequency. The performance of the fabricated filter is summarized and compared with those of other SIR filters as shown in Table 1. The filter in this work exhibits wide stopband, high rejection level and small circuit size simultaneously.

Fig. 12. (color online) Simulated and measured narrow-band responses of the proposed HTS filter.
Fig. 13. (color online) Simulated and measured wide-band responses of the proposed HTS filter.
Table 1.

HTS wide stopband filter comparisons.

.
4. Conclusions

In this article, we present a novel self-embedding SIR structure. This resonator structure can shift the spurious harmonics to higher than 3.7 times the fundamental frequency while occupying a miniaturized circuit size. For demonstration, an HTS bandpass filter with wide stopband, high rejection level and small size is designed and fabricated using the proposed SIRs. The measurement agrees well with the simulation.

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