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A wide stopband band-pass HTS filter with staggered resonators
Physica C 495 (2013) 79–83
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Physica C journal homepage: www.elsevier.com/locate/physc
A wide stopband band-pass HTS filter with staggered resonators Jingchen Wang, Bin Wei ⇑, Bisong Cao, Xubo Guo, Xiaoping Zhang, Xiaoke Song State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 11 July 2013 Accepted 23 August 2013 Available online 5 September 2013 Keywords: Band-pass filter High temperature superconducting (HTS) Harmonic suppressed Staggered resonators Wide stopband
a b s t r a c t This letter presents a novel high-temperature superconducting (HTS) band-pass filter with a very wide stopband using the method of staggered resonant modes, that is, dissimilar resonators with the same fundamental frequency but different harmonic frequencies. A new type of resonator that is suitable for this method is proposed. The design rules and design process of this method are analyzed in detail. A six-pole HTS band-pass filter centered at 500 MHz with a 2 MHz bandwidth is successfully designed and fabricated. Measured out-of-band rejection is better than 60 dB and can reach up to 13 GHz, which is about 26 times the fundamental frequency. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction High-temperature superconducting (HTS) filter has many advantages over conventional filter, such as low insertion loss, steep skirt, and high out-of-band rejection. Thus, it has been widely developed for modern RF receiver front-end [1,2]. However, there are always unwanted spurious bands for microstrip filter, which degrades the out-of-band performance of the filter. Many approaches have been proposed to solve this problem. Fractal configurations are used for the equalization of phase velocities of even and odd modes of the filter to suppress the second harmonic frequency [3]. Stepped impedance resonators (SIRs) can theoretically push spurious bands up to significantly higher frequencies [4,5]. Quasi-lumped element resonators, which are composed of an interdigital capacitor in parallel with a double-spiral inductor, are useful in extending the stopband [6]. A quarter wavelength shorted to the ground has its first spurious band at three times the fundamental frequency [7]. Utilizing transmission zeros is also a popular approach to suppress spurious bands [8,9]. In [10– 12], a wide stopband is achieved by employing the method of staggered resonant modes, that is, designing a filter using dissimilar resonators with the same fundamental frequency but different harmonic frequencies. However, the first spurious bands of the reported filters are no more than four times the fundamental frequency (f0), or the out-of-band rejection is no better than 30 dB. In this paper, the method of staggered resonant modes is further developed. The design rules and design process of this method are analyzed and summarized in detail for the first time.
⇑ Corresponding author. Tel./fax: +86 10 6279 2473. E-mail address: [email protected] (B. Wei). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.08.008
Furthermore, a new type of resonator composed of vertical interdigital fingers and a meander line that is suitable for this method is introduced. In addition, a meander line resonator that has capacitive coupling with feed line is proposed for the first and last poles of the filter. Thereafter, a 500 MHz six-pole HTS band-pass filter with a very wide stopband is designed and fabricated. The measured out-of-band rejection is better than 60 dB, and the first spurious band locates at approximately 13 GHz, which reaches as high as 26f0.
2. Filter design 2.1. Topology of resonator The common topology of resonator for the method of staggered resonant modes is the SIR structure [10–12]. However, the impedance ratio of SIR should be very large to obtain a series of resonators with large scattered harmonic frequencies. It will result in a very large size of the resonator, especially for a filter with fundamental frequency below 1 GHz, which will go against the compactness of the filter. A new resonator composed of vertical interdigital fingers and a meander line is proposed to address this issue, as shown in Fig. 1. When the resonator resonates, most charges concentrate on the interdigital fingers, and most of the current concentrates on the meander line. Therefore, the self-capacitance C is primarily determined by the interdigital finger part, and the self-inductance L is mainly determined p byffiffiffiffiffiffithe meander line part. According to the expression f ¼ 1=2p LC ; the change in C and L lead to a change in the resonant behavior of the resonator. Three size parameters of the resonator can be tuned to change C and L, as illustrated in
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Fig. 1. Topology of the proposed resonator. L and S represent the height and width of the meander line part, N represents the number of interdigital fingers. The line width of interdigital fingers and meander line is 0.08 mm. The distance between fingers is 0.08 mm.
Fig. 1. By adjusting these parameters, resonators with the same fundamental frequency but different harmonic frequencies can be easily designed without deteriorating the filter size. Fig. 2 shows the resonant performance of two resonator samples in a wide frequency range. The two resonators have a similar size but different size parameters, and their resonant modes significantly differ from one another.
them will resonate simultaneously for every fAi. Thus, considering symmetry, six possible resonant cases exist for each fAi, as shown in Fig. 3. The third step is to determine the position of resonators in group B. To suppress spurious bands at each fAi to lower than 50 dB, several requirements of the external Q factor (Qex) at fAi should be satisfied. Notably, spurious bands will not appear at frequencies other than fAi because group A does not resonate at these frequencies, and Qex significantly deviates from the desirable value. Fig. 4 shows the simulated performance of the spurious band at fAi with different Qex for every case in Fig. 3. Given the judgment standard that the spurious band should be suppressed to lower than 50 dB, the requirements of Qex are derived and shown in Table 1 based on Fig. 4. Thus, the arrangement of the position of resonators in group B should guarantee that for every fAi, only cases (a), (d), and (f) will emerge regardless of Qex at fAi, or cases (c) and (e) will emerge under the condition that Qex at fAi is greater than 10,000. Case (b) should be avoided because S(21) is always larger than 50 dB in this case. If the arrangement in the third step cannot be satisfied, the design process should either return to the first step to redesign the first and last resonators to provide an appropriate Qex to meet the requirements in Table 1, or return to the second step to redesign the resonators in group B to meet the arrangement in the third step. 2.3. Design of first and last resonators
2.2. Method of staggered resonant modes For a multi-pole filter, all resonators can be divided into two groups: group A includes the first and last resonators, and group B includes the other resonators. Our design goal of the method of staggered resonant modes is to suppress the simulated intensity of each spurious band to below 50 dB. The intensity will be further lower in measurement because the perfect conductor is used in simulation and is, in fact, lossy. The first step in the design process is the design of the first and last resonators (group A) of the filter, which will be discussed in Section 2.3. Suppose that these resonators have already been designed. Their fundamental frequency is f0, and harmonic frequencies are fAi (i = 1, 2, 3, . . .). The second step is to design a series of resonators by changing the three parameters in Fig. 1 to form the n 2 resonators in group B. The fundamental frequency of each resonator is designed as f0. The n 2 resonators should guarantee that no more than two of
According to the discussion in Section 2.2, a type of resonator with Qex larger than 10,000 is desirable, so that cases (c) and (e) can be satisfied more easily. A meander line resonator, which has capacitive coupling with feed lines, is proposed, as shown in Fig. 5a. The resonant performance of such resonator is shown in Fig. 6 (the simulated topology is illustrated in Fig. 5b) Apart from the first few peaks, all resonant peaks below 9 GHz are very sharp, and the corresponding Qex is greater than 10,000. Therefore, the requirements of Qex for cases (c) and (e) can be satisfied for each fAi, thus facilitating the design process. When frequency is larger than 9 GHz, the resonant peaks are very flat, and the value of Qex is approximately 100. Thus, the arrangement of resonators in group B should obey cases (a), (d) and (f), and avoid cases (b), (c), and (e). In fact, the number of resonant peaks above 9 GHz is limited, which will not add to the complexity of the design process. Fig. 7 illustrates the reason behind the change in resonant behavior above 9 GHz. The resonator behaves as a meander line
Fig. 2. Two samples of the proposed resonator topology and their resonant performances in a wide frequency range.
Fig. 3. Six possible resonant cases for resonators in group B for each fAi. Six boxes denote six resonators of the filter. The box containing fAi means that this resonator resonates at frequency fAi. The crossed box means that this resonator does not resonate at frequency fAi.
J. Wang et al. / Physica C 495 (2013) 79–83
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Fig. 4. Simulated performance of the spurious band at fAi with different Qex for every case in Fig. 3. The performance is based on the coupling coefficients of objective filter (500 MHz, 0.4%): M12 M23 M34 M45 M56 4 103, M13 M24 M35 M46 1 104, M14 M25 M36 1 105, M15 M26 5 106, and M16 is about 3 107 or even smaller.
Table 1 Rules of method of staggered resonant modes. Case
Rules
(a) (b) (c) (d) (e) (f)
Any value of Qex is allowed Avoid, S(21) is always greater than 50 dB Qex > 10,000 Any value of Qex is allowed Qex > 10,000 Any value of Qex is allowed
below 9 GHz. Fig. 7(1)–(3) represents the current distribution of the first three harmonic frequencies of the resonator. When frequency is greater than 9 GHz, the resonant mode behavior changes to multi-coupled parallel lines. The transition frequency is the fundamental frequency of a single microstrip line with length L. Fig. 7(4)–(6) represents the current distribution of the first three harmonic frequencies of the resonator in this resonant mode. 2.4. Filter design A six-pole HTS band-pass filter centered at 500 MHz with a 1 dB bandwidth of 2 MHz is designed using the method of staggered resonant modes. The resonator proposed in Fig. 5 is used to make
the first and last poles. The resonator topology in Fig. 1 is used as the basis for the middle four resonators. The size parameters of these resonators are determined based on their harmonic frequencies, which should agree with the given rules of the method of staggered resonant modes. The size parameters of the middle four resonators are as follows: L1 = 2.06 mm, S1 = 5.44 mm, and N1 = 19; L2 = 2.18 mm, S2 = 5.44 mm, and N2 = 18; L3 = 2.46 mm, S3 = 5.44 mm, and N3 = 16; and L4 = 2.24 mm, S4 = 5.92 mm, and N4 = 16. Table 2 shows the first seven resonant frequencies of the middle four resonators. Full-wave electromagnetic simulator Sonnet is used to determine the geometrical configuration of the filter, as shown in Fig. 8. The filter size is 40 mm 11 mm, which is approximately 0.17 k0 0.05 k0, where k0 is the guided wavelength of the 50 X line on the substrate at the center frequency. The simulated result is shown in Fig. 9. To obtain a precise simulated result, the frequency step used in the simulation is 0.01 MHz, which is approximately 0.002% of the fundamental frequency. The out-of-band S(21) is suppressed to a level lower than 60 dB up to 13 GHz. S(21) then approaches zero at about 14 GHz, which is where the resonant mode frequency of the box is located. This frequency can be calculated from the following expression (by ignoring the influence of substrate, which is a minor correction of the box resonant frequency):
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Fig. 5. (a) Proposed topology for the first and last poles, where L = 5.88 mm, the number of turns of meander line is 66, the line width and distance between lines are 0.08 mm; (b) topology to simulate this resonator’s resonant performance in Fig. 6 and current distribution in Fig. 7.
1 f ¼ pffiffiffiffiffiffiffiffiffiffi 2 l0 e0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ L21 L22
ð1Þ
where L1 and L2 denote the length of the two longest sides of the box. For the fabricated filter, L1 = 40 mm, L2 = 11 mm, and the calculated box resonant frequency is 14.1 GHz, which agrees well with the simulation. 3. Fabrication and measurement
Fig. 6. Resonant performance of the first and last resonators in Fig. 5.
The layout of the filter is patterned onto a double-sided YBCO thin film with thickness of 600 nm using photolithography and iron beam etching. The thin film is mounted on an MgO substrate with a dielectric constant of 9.70. The manufactured HTS filter circuit is then packaged into a metal shield box. Fig. 10 shows an image of the filter. The filter is tested in a vacuum Dewar and is cooled down to 72 K by a Stirling cooler. The microwave performance of the filter
Fig. 7. Current distributions of the first and last resonators for six different frequencies in Fig. 6.
Table 2 First seven resonant modes for middle four resonators.
fs0 fs1 fs2 fs3 fs4 fs5 fs6
Resonator II (MHz)
Resonator III (MHz)
Resonator IV (MHz)
Resonator V (MHz)
500.0 2505.3 2609.2 3443.0 4001.5 4196.4 4625.3
500.0 2423.9 2691.8 3511.3 3924.9 4233.3 4735.6
500.0 2253.7 2841.6 3488.6 3809.5 4435.6 4953.1
500.0 2294.6 2736.9 3414.0 3687.1 4159.6 4689.2
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Fig. 8. Layout of the six-pole HTS band-pass filter (the first and last resonators are not to scale; each actually has 66 vertical lines).
and the frequency step is 0.01 MHz. Fig. 11 shows the measured results. The fabricated filter is centered at 500 MHz with a 1 dB bandwidth of 2 MHz. The maximum insertion loss is 0.32 dB, and the return loss is better than 20 dB. The out-of-band rejection is higher than 60 dB and reaches up to 13 GHz. 4. Conclusions
Fig. 9. Simulated result of the filter.
In this paper, a six-pole 500 MHz band-pass HTS filter with a bandwidth of 2 MHz and a very wide stopband is designed and fabricated using the method of staggered resonant modes. A novel resonator composed of vertical interdigital fingers and meander line as well as a meander line resonator that has capacitive coupling with feed lines for Qex are proposed. Detailed rules for the method of staggered resonant modes are analyzed and summarized. The measured out-of-band rejection of the filter is better than 60 dB and reaches up to approximately 13 GHz, or 26 f0. Acknowledgement This work was supported by the National Science Foundation of China under Grants 60901002 and 61127001. References
Fig. 10. Image of the fabricated filter.
Fig. 11. Measured result of the filter.
is measured using an Agilent N5230C network analyzer. To measure the performance of the filter as precisely as possible, the intermediate frequency bandwidth in measurement is chosen as 1 kHz,
[1] R.W. Simon, R.B. Hammond, S.J. Berkowitz, B.A. Willemsen, Superconducting microwave filter systems for cellular telephone base stations, Proceedings of the IEEE 92 (2004) 1585–1596. [2] Yongbo Biana, Jin Guo, Changzheng Gao, Chunguang Li, Hong Li, Jia Wang, Bin Cui, Xiaofeng He, Chao Li, Na Li, Guoqiang Li, Qiang Zhang, Xueqiang Zhang, Jibao Meng, Yusheng He, A miniaturized HTS microwave receiver front-end subsystem for radar and communication applications, Physica C: Superconductivity 470 (2010) 617–621. [3] T. Lopetegi, M.A.G. Laso, F. Falcone, F. Martin, J. Bonache, J. Garcia, L. PerezCuevas, M. Sorolla, M. Guglielmi, Microstrip ‘‘wiggly-line’’ bandpass filters with multispurious rejection, Microwave and Wireless Components Letters, IEEE 14 (2004) 531–533. [4] Q.R. Li, X.B. Guo, X.P. Zhang, B. Wei, W. Chen, Y. Zhang, C. Feng, Z.J. Ying, S.C. Jin, B.S. Cao, Design of a narrowband HTS filter at 7.4 GHz with improved upperstopband performance, Physica C: Superconductivity 483 (2012) 5–7. [5] C.H. Kim, K. Chang, Wide-stopband bandpass filters using asymmetric stepped-impedance resonators, Microwave and Wireless Components Letters, IEEE 23 (2013) 69–71. [6] Z. Jiafeng, M.J. Lancaster, H. Frederick, N. Roddis, D. Glynn, HTS narrow band filters at UHF band for radio astronomy applications, Applied Superconductivity, IEEE Transactions 15 (2005) 1004–1007. [7] Z. Guoyong, M.J. Lancaster, H. Frederick, A high-temperature superconducting bandpass filter with microstrip quarter-wavelength spiral resonators, IEEE Transactions on Microwave Theory and Techniques 54 (2006). [8] J.T. Kuo, E. Shih, Microstrip stepped impedance resonator bandpass filter with an extended optimal rejection bandwidth, Microwave Theory and Techniques, IEEE Transactions 51 (2003) 1554–1559. [9] W. Xiao-Hu, C. Qing-Xin, T. Xu-Kun, O. Xiao, Quintuple-mode UWB bandpass filter with sharp roll-off and super-wide upper stopband, Microwave and Wireless Components Letters, IEEE 21 (2011) 661–663. [10] C. Chi-Feng, H. Ting-Yi, W. Ruey-Beei, Design of microstrip bandpass filters with multiorder spurious-mode suppression, Microwave Theory and Techniques, IEEE Transactions 53 (2005) 3788–3793. [11] L. Shih-Cheng, D. Pu-Hua, L. Yo-Shen, W. Chi-Hsueh, C. Chun Hsiung, Widestopband microstrip bandpass filters using dissimilar quarter-wavelength stepped-impedance resonators, Microwave Theory and Techniques, IEEE Transactions 54 (2006) 1011–1018. [12] L. Shih-Cheng, J. Tai-Lang, Microstrip bandpass filters with various resonators using connected- and edge-coupling mechanisms and their applications to dual-band filters and diplexers, Microwave Theory and Techniques, IEEE Transactions 60 (2011) 975–988.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
A wide stopband band-pass HTS filter with staggered resonators Jingchen Wang, Bin Wei ⇑, Bisong Cao, Xubo Guo, Xiaoping Zhang, Xiaoke Song State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 11 July 2013 Accepted 23 August 2013 Available online 5 September 2013 Keywords: Band-pass filter High temperature superconducting (HTS) Harmonic suppressed Staggered resonators Wide stopband
a b s t r a c t This letter presents a novel high-temperature superconducting (HTS) band-pass filter with a very wide stopband using the method of staggered resonant modes, that is, dissimilar resonators with the same fundamental frequency but different harmonic frequencies. A new type of resonator that is suitable for this method is proposed. The design rules and design process of this method are analyzed in detail. A six-pole HTS band-pass filter centered at 500 MHz with a 2 MHz bandwidth is successfully designed and fabricated. Measured out-of-band rejection is better than 60 dB and can reach up to 13 GHz, which is about 26 times the fundamental frequency. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction High-temperature superconducting (HTS) filter has many advantages over conventional filter, such as low insertion loss, steep skirt, and high out-of-band rejection. Thus, it has been widely developed for modern RF receiver front-end [1,2]. However, there are always unwanted spurious bands for microstrip filter, which degrades the out-of-band performance of the filter. Many approaches have been proposed to solve this problem. Fractal configurations are used for the equalization of phase velocities of even and odd modes of the filter to suppress the second harmonic frequency [3]. Stepped impedance resonators (SIRs) can theoretically push spurious bands up to significantly higher frequencies [4,5]. Quasi-lumped element resonators, which are composed of an interdigital capacitor in parallel with a double-spiral inductor, are useful in extending the stopband [6]. A quarter wavelength shorted to the ground has its first spurious band at three times the fundamental frequency [7]. Utilizing transmission zeros is also a popular approach to suppress spurious bands [8,9]. In [10– 12], a wide stopband is achieved by employing the method of staggered resonant modes, that is, designing a filter using dissimilar resonators with the same fundamental frequency but different harmonic frequencies. However, the first spurious bands of the reported filters are no more than four times the fundamental frequency (f0), or the out-of-band rejection is no better than 30 dB. In this paper, the method of staggered resonant modes is further developed. The design rules and design process of this method are analyzed and summarized in detail for the first time.
⇑ Corresponding author. Tel./fax: +86 10 6279 2473. E-mail address: [email protected] (B. Wei). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.08.008
Furthermore, a new type of resonator composed of vertical interdigital fingers and a meander line that is suitable for this method is introduced. In addition, a meander line resonator that has capacitive coupling with feed line is proposed for the first and last poles of the filter. Thereafter, a 500 MHz six-pole HTS band-pass filter with a very wide stopband is designed and fabricated. The measured out-of-band rejection is better than 60 dB, and the first spurious band locates at approximately 13 GHz, which reaches as high as 26f0.
2. Filter design 2.1. Topology of resonator The common topology of resonator for the method of staggered resonant modes is the SIR structure [10–12]. However, the impedance ratio of SIR should be very large to obtain a series of resonators with large scattered harmonic frequencies. It will result in a very large size of the resonator, especially for a filter with fundamental frequency below 1 GHz, which will go against the compactness of the filter. A new resonator composed of vertical interdigital fingers and a meander line is proposed to address this issue, as shown in Fig. 1. When the resonator resonates, most charges concentrate on the interdigital fingers, and most of the current concentrates on the meander line. Therefore, the self-capacitance C is primarily determined by the interdigital finger part, and the self-inductance L is mainly determined p byffiffiffiffiffiffithe meander line part. According to the expression f ¼ 1=2p LC ; the change in C and L lead to a change in the resonant behavior of the resonator. Three size parameters of the resonator can be tuned to change C and L, as illustrated in
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Fig. 1. Topology of the proposed resonator. L and S represent the height and width of the meander line part, N represents the number of interdigital fingers. The line width of interdigital fingers and meander line is 0.08 mm. The distance between fingers is 0.08 mm.
Fig. 1. By adjusting these parameters, resonators with the same fundamental frequency but different harmonic frequencies can be easily designed without deteriorating the filter size. Fig. 2 shows the resonant performance of two resonator samples in a wide frequency range. The two resonators have a similar size but different size parameters, and their resonant modes significantly differ from one another.
them will resonate simultaneously for every fAi. Thus, considering symmetry, six possible resonant cases exist for each fAi, as shown in Fig. 3. The third step is to determine the position of resonators in group B. To suppress spurious bands at each fAi to lower than 50 dB, several requirements of the external Q factor (Qex) at fAi should be satisfied. Notably, spurious bands will not appear at frequencies other than fAi because group A does not resonate at these frequencies, and Qex significantly deviates from the desirable value. Fig. 4 shows the simulated performance of the spurious band at fAi with different Qex for every case in Fig. 3. Given the judgment standard that the spurious band should be suppressed to lower than 50 dB, the requirements of Qex are derived and shown in Table 1 based on Fig. 4. Thus, the arrangement of the position of resonators in group B should guarantee that for every fAi, only cases (a), (d), and (f) will emerge regardless of Qex at fAi, or cases (c) and (e) will emerge under the condition that Qex at fAi is greater than 10,000. Case (b) should be avoided because S(21) is always larger than 50 dB in this case. If the arrangement in the third step cannot be satisfied, the design process should either return to the first step to redesign the first and last resonators to provide an appropriate Qex to meet the requirements in Table 1, or return to the second step to redesign the resonators in group B to meet the arrangement in the third step. 2.3. Design of first and last resonators
2.2. Method of staggered resonant modes For a multi-pole filter, all resonators can be divided into two groups: group A includes the first and last resonators, and group B includes the other resonators. Our design goal of the method of staggered resonant modes is to suppress the simulated intensity of each spurious band to below 50 dB. The intensity will be further lower in measurement because the perfect conductor is used in simulation and is, in fact, lossy. The first step in the design process is the design of the first and last resonators (group A) of the filter, which will be discussed in Section 2.3. Suppose that these resonators have already been designed. Their fundamental frequency is f0, and harmonic frequencies are fAi (i = 1, 2, 3, . . .). The second step is to design a series of resonators by changing the three parameters in Fig. 1 to form the n 2 resonators in group B. The fundamental frequency of each resonator is designed as f0. The n 2 resonators should guarantee that no more than two of
According to the discussion in Section 2.2, a type of resonator with Qex larger than 10,000 is desirable, so that cases (c) and (e) can be satisfied more easily. A meander line resonator, which has capacitive coupling with feed lines, is proposed, as shown in Fig. 5a. The resonant performance of such resonator is shown in Fig. 6 (the simulated topology is illustrated in Fig. 5b) Apart from the first few peaks, all resonant peaks below 9 GHz are very sharp, and the corresponding Qex is greater than 10,000. Therefore, the requirements of Qex for cases (c) and (e) can be satisfied for each fAi, thus facilitating the design process. When frequency is larger than 9 GHz, the resonant peaks are very flat, and the value of Qex is approximately 100. Thus, the arrangement of resonators in group B should obey cases (a), (d) and (f), and avoid cases (b), (c), and (e). In fact, the number of resonant peaks above 9 GHz is limited, which will not add to the complexity of the design process. Fig. 7 illustrates the reason behind the change in resonant behavior above 9 GHz. The resonator behaves as a meander line
Fig. 2. Two samples of the proposed resonator topology and their resonant performances in a wide frequency range.
Fig. 3. Six possible resonant cases for resonators in group B for each fAi. Six boxes denote six resonators of the filter. The box containing fAi means that this resonator resonates at frequency fAi. The crossed box means that this resonator does not resonate at frequency fAi.
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Fig. 4. Simulated performance of the spurious band at fAi with different Qex for every case in Fig. 3. The performance is based on the coupling coefficients of objective filter (500 MHz, 0.4%): M12 M23 M34 M45 M56 4 103, M13 M24 M35 M46 1 104, M14 M25 M36 1 105, M15 M26 5 106, and M16 is about 3 107 or even smaller.
Table 1 Rules of method of staggered resonant modes. Case
Rules
(a) (b) (c) (d) (e) (f)
Any value of Qex is allowed Avoid, S(21) is always greater than 50 dB Qex > 10,000 Any value of Qex is allowed Qex > 10,000 Any value of Qex is allowed
below 9 GHz. Fig. 7(1)–(3) represents the current distribution of the first three harmonic frequencies of the resonator. When frequency is greater than 9 GHz, the resonant mode behavior changes to multi-coupled parallel lines. The transition frequency is the fundamental frequency of a single microstrip line with length L. Fig. 7(4)–(6) represents the current distribution of the first three harmonic frequencies of the resonator in this resonant mode. 2.4. Filter design A six-pole HTS band-pass filter centered at 500 MHz with a 1 dB bandwidth of 2 MHz is designed using the method of staggered resonant modes. The resonator proposed in Fig. 5 is used to make
the first and last poles. The resonator topology in Fig. 1 is used as the basis for the middle four resonators. The size parameters of these resonators are determined based on their harmonic frequencies, which should agree with the given rules of the method of staggered resonant modes. The size parameters of the middle four resonators are as follows: L1 = 2.06 mm, S1 = 5.44 mm, and N1 = 19; L2 = 2.18 mm, S2 = 5.44 mm, and N2 = 18; L3 = 2.46 mm, S3 = 5.44 mm, and N3 = 16; and L4 = 2.24 mm, S4 = 5.92 mm, and N4 = 16. Table 2 shows the first seven resonant frequencies of the middle four resonators. Full-wave electromagnetic simulator Sonnet is used to determine the geometrical configuration of the filter, as shown in Fig. 8. The filter size is 40 mm 11 mm, which is approximately 0.17 k0 0.05 k0, where k0 is the guided wavelength of the 50 X line on the substrate at the center frequency. The simulated result is shown in Fig. 9. To obtain a precise simulated result, the frequency step used in the simulation is 0.01 MHz, which is approximately 0.002% of the fundamental frequency. The out-of-band S(21) is suppressed to a level lower than 60 dB up to 13 GHz. S(21) then approaches zero at about 14 GHz, which is where the resonant mode frequency of the box is located. This frequency can be calculated from the following expression (by ignoring the influence of substrate, which is a minor correction of the box resonant frequency):
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Fig. 5. (a) Proposed topology for the first and last poles, where L = 5.88 mm, the number of turns of meander line is 66, the line width and distance between lines are 0.08 mm; (b) topology to simulate this resonator’s resonant performance in Fig. 6 and current distribution in Fig. 7.
1 f ¼ pffiffiffiffiffiffiffiffiffiffi 2 l0 e0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ L21 L22
ð1Þ
where L1 and L2 denote the length of the two longest sides of the box. For the fabricated filter, L1 = 40 mm, L2 = 11 mm, and the calculated box resonant frequency is 14.1 GHz, which agrees well with the simulation. 3. Fabrication and measurement
Fig. 6. Resonant performance of the first and last resonators in Fig. 5.
The layout of the filter is patterned onto a double-sided YBCO thin film with thickness of 600 nm using photolithography and iron beam etching. The thin film is mounted on an MgO substrate with a dielectric constant of 9.70. The manufactured HTS filter circuit is then packaged into a metal shield box. Fig. 10 shows an image of the filter. The filter is tested in a vacuum Dewar and is cooled down to 72 K by a Stirling cooler. The microwave performance of the filter
Fig. 7. Current distributions of the first and last resonators for six different frequencies in Fig. 6.
Table 2 First seven resonant modes for middle four resonators.
fs0 fs1 fs2 fs3 fs4 fs5 fs6
Resonator II (MHz)
Resonator III (MHz)
Resonator IV (MHz)
Resonator V (MHz)
500.0 2505.3 2609.2 3443.0 4001.5 4196.4 4625.3
500.0 2423.9 2691.8 3511.3 3924.9 4233.3 4735.6
500.0 2253.7 2841.6 3488.6 3809.5 4435.6 4953.1
500.0 2294.6 2736.9 3414.0 3687.1 4159.6 4689.2
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83
Fig. 8. Layout of the six-pole HTS band-pass filter (the first and last resonators are not to scale; each actually has 66 vertical lines).
and the frequency step is 0.01 MHz. Fig. 11 shows the measured results. The fabricated filter is centered at 500 MHz with a 1 dB bandwidth of 2 MHz. The maximum insertion loss is 0.32 dB, and the return loss is better than 20 dB. The out-of-band rejection is higher than 60 dB and reaches up to 13 GHz. 4. Conclusions
Fig. 9. Simulated result of the filter.
In this paper, a six-pole 500 MHz band-pass HTS filter with a bandwidth of 2 MHz and a very wide stopband is designed and fabricated using the method of staggered resonant modes. A novel resonator composed of vertical interdigital fingers and meander line as well as a meander line resonator that has capacitive coupling with feed lines for Qex are proposed. Detailed rules for the method of staggered resonant modes are analyzed and summarized. The measured out-of-band rejection of the filter is better than 60 dB and reaches up to approximately 13 GHz, or 26 f0. Acknowledgement This work was supported by the National Science Foundation of China under Grants 60901002 and 61127001. References
Fig. 10. Image of the fabricated filter.
Fig. 11. Measured result of the filter.
is measured using an Agilent N5230C network analyzer. To measure the performance of the filter as precisely as possible, the intermediate frequency bandwidth in measurement is chosen as 1 kHz,
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