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An efficient tuning method for narrowband superconducting filters with interdigital capacitor resonators in the time domain
Physica C 499 (2014) 57–62
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
An efficient tuning method for narrowband superconducting filters with interdigital capacitor resonators in the time domain X.K. Song a, X.P. Zhang a, B.S. Cao a,⇑, B. Wei a, L.M. Gong b, Y.D. Chen c, T.N. Zheng a, X.B. Guo a, G.Y. Zhang c, X. Zhan a a b c
State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China Sci. & Technol. on Space Microwave Lab., CAST (Xi’an), Xi’an 710100, China Superconductor Technology Co. Ltd., Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 21 September 2013 Received in revised form 25 December 2013 Accepted 23 January 2014 Available online 1 February 2014 Keywords: Superconducting filter Interdigital-capacitor resonator Time domain Tuning
a b s t r a c t This article proposes an effective tuning method based on the time domain for improving the performance of high-temperature superconducting (HTS) bandpass filters with interdigital capacitor resonators (ICRs). Analysis of the causes of HTS filter performance deterioration reveal that such deterioration is primarily caused by the resonant frequency deviation of the resonator of the HTS filter; this deviation results from fabrication errors and from the non-uniformity of the thickness and dielectric constant of the substrate. The sensitivity of the filter, which arises from the non-uniformity of the substrate thickness and dielectric constant, is related to the type of the resonator and the group delay characteristic of the filter. A 0.4% fractional bandwidth HTS filter with ICRs at the UHF band is fabricated and tuned using mechanical rods in the time domain. By applying this method, the resonant frequency deviation of each resonator and the coupling coefficient between resonators can be measured and tuned individually. The insertion loss of the HTS filter is improved from 1.06 dB to 0.43 dB, whereas the return loss is improved from 9.57 dB to 15.1 dB. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction High-temperature superconducting (HTS) microwave filters designed for mobile communication systems are characterized by having low insertion loss, high selectivity, and high band edge steepness [1–4]. Filters with interdigital capacitor resonators (ICRs) have been recently developed to realize a wide stopband performance with compact structures [4–6]. The first spurious frequency of ICRs is usually located at approximately 3f0 [2], and the fundamental frequency can be reduced by increasing the selfcapacitance [4–6]. Thus, ICRs are suitable for designing wide stopband filters at a low frequency. HTS filters with ICRs demonstrate both high in-band and wide stopband performance [4]. However, the non-uniformity of the substrate materials, along with fabrication errors, degrades the filter performance. Numerous tuning methods have been proposed for improving HTS filter performance [7–14]. Most of these studies have focused either on tuning the center frequency (CF) and the bandwidth or on improving the in-band performance of the filter [7–11]. Although ⇑ Corresponding author. Tel./fax: +86 10 6279 2473. E-mail address: [email protected] (B.S. Cao). http://dx.doi.org/10.1016/j.physc.2014.01.009 0921-4534/Ó 2014 Elsevier B.V. All rights reserved.
dielectric plate method can effectively adjust the CF of HTS filters [7], waveguides and electric pads have also been used in tuning the CF and the bandwidth [8,9]. Ohshima et al. constructed a trimming library by using a dielectric plate and trimming rods to improve HTS filter performance [10]. Mechanical rods, which have great flexibility and excellent tuning effect, are often used to tune HTS filters [11–13]. However, few studies have analyzed the inconsistency between the initial measured in-band performance of the HTS filter and the simulated results. The majority of reports have used tuning methods based on the frequency domain, which is a trial-and-error process. Few papers have discussed the effect of the resonant frequency deviations of the resonators and the tuning effects of mechanical rods in the time domain. This paper describes in detail a mechanical tuning method based on the time domain for coupled resonator filters, such as filters with lumped LC resonators, coaxial line resonators, cavity resonators, or microwave waveguide resonators. The tuning effects of the dielectric and metallic rods are calculated and analyzed. The proposed method is more effective and less complex than tuning in the frequency domain. In the time domain, the resonant frequency of each resonator and the coupling coefficients between resonators can be distinguished accurately and adjusted individually. In fact,
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X.K. Song et al. / Physica C 499 (2014) 57–62
the tuning mechanism is resonant frequency tuning and coupling coefficients tuning so that this method could be widely used no matter what response type of the coupled resonator filters, which include Chebyshev response, quasi-elliptic response and, Butterworth response and so on. In addition, this study analyzes the resonant frequency deviation of the resonator, which is primarily caused by the non-uniformity of the substrate thickness and dielectric constant. The deterioration of the filter in-band performance caused by the resonant frequency deviation is discussed. The sensitivity of the filter performance is related to the type of the resonator and the group delay characteristic of the filter. Basing on the group delay performance, we can predict the level of consistency between filter design and fabrication. Tuning refers to the effective correction of the resonant frequency deviation. A 0.4% fractional bandwidth HTS filter with the ICRs is tuned to demonstrate the effectiveness of the proposed method, and the in-band performance of this filter is significantly improved after such fine-tuning.
2. Sensitivity analysis of the filter performance with nonuniform substrate 2.1. Resonant frequency deviation of different types of resonators The resonant frequency of a resonator can change after fabrication because of fabrication errors and the non-uniformity of the substrate thickness and dielectric constant [11,13]. Three types of resonators, namely, interdigital capacitor, twin spiral, and meander line types, are selected to show the sensitivity of the filter to resonant frequency deviation. The resonators are simulated using Sonnet electromagnetic software to illustrate different resonant frequency deviations. The original resonant frequencies of the three resonators are all 500 MHz, the dielectric constant of the substrate is 9.73, and the substrate thickness is 0.51 mm. The structure layouts of the three types of resonators are shown in Fig. 1. The simulation results of the resonant frequency deviation are shown in
Table 1 Simulated resonant frequency deviation of the resonator with the variations of the substrate dielectric constant. Dielectric constant (e)
9.7
9.71
9.72
Deviation of the resonant frequency (MHz) Interdigital capacitor 0.7 0.46 0.22 Twin spiral 0.74 0.48 0.24 Meander line 0.75 0.5 0.25
9.73
9.74
9.75
9.76
0 0 0
0.24 0.24 0.25
0.48 0.48 0.5
0.7 0.72 0.75
Tables 1 and 2, which illustrate that variations in substrate thickness and dielectric constant can cause resonant frequency deviation of the resonators. Results show that the change in resonant frequency deviation ranges from 0.22 MHz to 0.75 MHz and from 0.14 MHz to 10.6 MHz when De = ±0.01, ±0.02, ±0.03 and Dd = ±0.01, ±0.02, ±0.03, respectively. Among the three types of resonators, ICR has the least sensitivity to resonant frequency deviation because of the changes in substrate thickness and dielectric constant. This finding indicates that substrate uniformity and the type of the resonator are important factors that affect the resonant frequency deviation of the resonator. 2.2. Degradation of in-band filter performance with different resonant frequency deviations The resonant frequency deviation of the resonator has a significant effect on the performance of narrowband HTS filters, particularly on the in-band performance. A six-pole Chebyshev prototype filter (CF: 500 MHz; bandwidth: 2 MHz; pass-band ripple: 0.01 dB; and return loss: 26 dB) is designed to illustrate this effect. Table 3 shows that when the resonant frequency deviation of the first resonator is changed from ±0.2 MHz to ±2 MHz, the corresponding in-band return loss changes from 14 dB to 2 dB, as shown in Fig. 2. The curves of a–f in Fig. 2(A) denote the deterioration of S11 when the resonant frequency of the first resonator
Fig. 1. The structures and sizes of three resonators: interdigital capacitor, twin spiral and meander line.
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X.K. Song et al. / Physica C 499 (2014) 57–62 Table 2 Simulated resonant frequency deviation of the resonator with the variations of the substrate thickness. Substrate thickness (d/mm)
0.48
Deviation of the resonant frequency (MHz) Interdigital capacitor 0.46 Twin spiral 4.7 Meander line 10.6
0.49
0.5
0.51
0.52
0.53
0.54
0.3 3.1 7
0.14 1.5 3.6
0 0 0
0.16 1.5 3.4
0.32 3 6.6
0.46 4.45 10
Table 3 The S11 when the resonant frequency of the first resonator changes. Curve
a
b
c
d
e
f
Deviation of the resonant frequency (MHz) S11 (dB)
±2.0
±1.0
±0.6
±0.4
±0.2
0
4
8
11
14
18
26
begins to decrease, whereas the curves of a–f in Fig. 2(B) denote the deterioration of S11 when the resonant frequency of the first resonator begins to increase. The curves of a–f in Fig. 2(A) and (B) correspond to the deviation of the resonant frequency a–f listed in Table 3, which shows that the in-band return loss worsens as the resonant frequency deviation increases. However, this simulation considered the deviation of one resonator only. However, all the resonant frequencies of the resonators of the filter change at different levels because of fabrication errors and the non-uniformity of the substrate and dielectric constant. Thus, an effective tuning method should be applied to adjust the resonant frequency deviation. 2.3. Degradation of the in-band filter performance at different bandwidths According to [15,16], the degradation of the in-band filter performance caused by substrate non-uniformity and fabrication errors can be obtained by the group delay of the filter s(x), which can be expressed as follows:
DjS11jmax 6 s ð xÞ DM 11 where D|S11| denotes the degradation of S11, and DM11 denotes the variation in the coupling matrix term M11 caused by substrate non-uniformity and fabrication errors. We suppose that the fabrication errors are the same for the three bandwidth filters. Thus, the sensitivity of the in-band performance is directly revealed from the group delay s(x) of the inline Chebyshev filter. With the use of ICRs, three six-pole Chebyshev prototype filters of different bandwidths are designed to analyze the sensitivity of
the filter performance to degradation. The CFs of the three filters are all 500 MHz, and the bandwidths are 2, 12, and 25 MHz. The simulation results show that the in-band ripples are below 0.01 dB and the return losses are below 26 dB. The group delay curves of the three filters are shown in Fig. 3(a)–(c). The 2 MHz bandwidth filter has a maximum group delay value of 605 ns in-band, whereas the group delay of the 25 MHz bandwidth filter is 48 ns. Thus, the in-band performance of the 25 MHz bandwidth filter has the least sensitivity among the three filters. The in-band performance of the filters is shown in Table 4. We suppose that the resonant frequency of the second resonator Df2 has shifted by 0.2, 0.4, 0.7, and 1 MHz, whereas the resonant frequencies of the other resonators remain unchanged at 500 MHz. The simulation result shows that the performance of the 2 MHz bandwidth filter exhibits the worst deterioration. The performance of the 12 MHz bandwidth filter, which has a return loss of over 14.4 dB in the passband even when Df2 shifts by 1.0 MHz, is suitable for engineering application. As the bandwidth increases to 25 MHz, the filter shows the least sensitivity to the degradation of the filter performance; this finding is consistent with the conclusion presented above. These results indicate that the narrow band filter requires tuning.
3. Tuning in the time domain 3.1. Tuning preparations Dielectric and metallic tuning rods are often used to adjust the resonant frequency deviation of a resonator [11–13]. In an electrical field concentrated area, a dielectric rod is equivalent to a capacitance combined with a resonator to decrease the resonant frequency. In a magnetic field concentrated area, a metallic rod is equivalent to an inductance combined with a resonator to increase the resonant frequency [12,13]. A sapphire electric rod and a copper metallic rod are respectively placed above the electrical field concentrated area and magnetic field concentrated area to simulate the tuning effects of the two rods. The distance S between the rod bottom and the resonator is changed from 0 mm to 1 mm to simulate the tuning effect. As shown in Fig. 4, the tuning effect becomes more obvious as the distance becomes closer to the
Fig. 2. The deterioration of S11 (A) when the resonant frequency of the first resonator decreases (B) when the resonant frequency of the first resonator increases, the curves of a–f are corresponding to the a–f in Table 3.
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Fig. 3. The curves of group delay of the three filters, of which the center frequency is 500 MHz and the bandwidths are (a) 2 MHz, (b) 12 MHz and (c) 25 MHz.
Table 4 The degradation of S11 when the resonant frequency of the second resonator of three filters with different bandwidths changes. Bandwidth (MHz)
2 12 25
S11 (dB)
Df2 = 0 MHz
Df2 = 0.2 MHz
Df2 = 0.4 MHz
Df2 = 0.7 MHz
Df2 = 1.0 MHz
26.0 26.0 26.0
12.7 20.8 26.0
8.1 20.8 20.8
5.7 17.7 20.8
3.7 14.4 18.6
Fig. 4. The tuning effects of the metallic rod and dielectric rod for a single resonator.
resonator surface. In the simulation, the resonant frequency of a single resonator can be increased by 5.54 MHz by using a metallic rod and be decreased by 6.43 MHz by using a dielectric rod. A six-pole narrowband HTS filter with ICRs is designed and fabricated at the UHF band with a CF of 500 MHz and a bandwidth of 2 MHz. The filter structure is symmetrical and compact. Moreover, the filter has weak couplings and a high Q value. The current density distribution of the filter circuit is simulated using Sonnet electromagnetic software (Fig. 5). At the fundamental resonant frequencies, the dark area represents the low current density, whereas the bright area represents the high current density. The electrical field is concentrated at both ends of the ICRs, whereas the magnetic field is concentrated at the resonator central area. The untuned filter is first measured by using an Agilent 8720ES vector network analyzer in a cryocooler at 70 K. Prior to tuning, the resonant frequency of each resonator is measured in the time domain. The results are listed in Table 5. The largest deviation occurs in the fifth resonator (1.96 MHz), indicating that the fifth resonant frequency is 1.96 MHz lower than 500 MHz. The cmeasured results imply that the substrate variations and the fabricated errors may have a half-and-half contribution to the resonant frequency deviation. This finding can help in deciding whether metallic rods or dielectric rods should be set up above each resonator depending on whether resonant frequency deviation is low or high. The measurement result is consistent with the simulation results in Tables 1 and 2.
Fig. 5. The simulated current density distribution of the six-pole narrowband HTS filter with ICRs and tuning rod positions diagram (dashed and solid circles represent metallic rods and dielectric rods respectively).
Table 5 The resonant frequency deviations of the six resonators toward 500 MHz. Resonator no.
1
2
3
4
5
6
Resonant frequency deviation (MHz)
0.30
0.22
0.03
1.66
1.96
1.10
As shown in Fig. 5, three metallic rods and three dielectric rods are set up on the basis of the diagram of the current density and resonant frequency deviation of each resonator. The metallic rods are placed above the first, third, and fifth resonators so that the resonant frequencies of the three resonators can be increased. The dielectric rods are then set up above the second, fourth, and sixth resonators to decrease their resonant frequencies. 3.2. Tuning The S-parameter response curves prior to tuning in the frequency domain are shown in Fig. 6(a). The return and insertion loss of the untuned filter is 9.57 and 1.06 dB, respectively. The following steps are performed in the network analyzer to measure the response in the time domain: CF is set to 500 MHz, which is the CF of the filter; and the span is set to 10 MHz, which is approximately five times that of the bandwidth. The return loss curve S11 is transformed into the time domain, which is obtained by a
X.K. Song et al. / Physica C 499 (2014) 57–62
61
Fig. 6. (a) The simulated and untuned S21 and S11 response curves (b) the simulated and untuned transformed S11 response curves in the time domain.
discrete inverse Fourier transform [11,14]. The start and stop time depend on the filter sections and the expected bandwidth of the filter. The start time is t0 = (2/pBW) = 326 ns, whereas the stop time is ts = (2N + 1/pBW) = 2122 ns. The N in the formula is the number of filter sections so that this transform method could be used for high-order filters. The number of the distinctive dips of the transformed S11 in the time domain is N between t0 to ts. The response curve prior to tuning in the time domain is shown in Fig. 6(b), which shows that the filter is mistuned because the six dips are not minimized. Two steps are adopted to tune the six-pole narrowband HTS filter and improve its performance. The first step is to adjust the resonant frequency of each resonator, and the second step is to tune the coupling coefficients between the resonators. In the first step, tuning is sequentially conducted from the first resonator (marked 1) to the sixth resonator (marked 6) to minimize the resonator dips, as shown in Fig. 7(b) and (d). Fig. 7(c) shows the response curve after the resonators are tuned. Comparison of Fig. 7(b) and (d) reveal the last two resonators have coupled to each other strongly because the resonator dips cannot be minimized. The distances between the resonators are sufficiently small that the coupling coefficients are inevitably affected when the individual resonant frequency of the resonator is tuned. The peak heights in the transform response show the coupling coefficients. If the height is higher than the designed one, then
the coupling coefficient increases. If the height is lower than the designed one, the coupling coefficient decreases. Compared with the simulation, the peak height has a big gap, indicating a coupling mismatched. The in-band performance is not in the optimal state; thus, the coupling coefficients between the resonators should be considered and readjusted. When adjusting the coupling coefficients, the peaks in the time domain and the return loss curve in frequency domain should be observed and analyzed. The aim is to tune the peak height to obtain the proper coupling coefficients, consequently optimizing the return and insertion losses. The coupling coefficients M45 and M56 are adjusted on the basis of the tuning the resonant frequency of each resonator. After tuning, the coupling coefficient M45 increases by 7.5% and the coupling coefficient M56 decreases by 2.4%, as shown in Fig. 8(a). The six distinctive dips of the transformed S11 in the time domain in Fig. 8(a) are characteristic dips that occur when the resonators are exactly tuned. The corresponding performance in the frequency domain is shown in Fig. 8(b). As shown in Fig. 9(b), there is a deviation between the simulated and final tuned transformed S11 in the time domain because the final tuned coupling coefficient M12 is smaller so that less energy are coupled to the next resonator due to more energy reflection. The corresponding final tuned results of the HTS filter in the frequency domain are shown in Fig. 9(a). The return loss exceeds 15.1 dB, whereas the insertion loss is below 0.43 dB.
Fig. 7. (a and b) The curves of simulation and after tuning three resonators in the frequency domain and time domain, (c and d) the curves of simulation and after tuning six resonators in the frequency domain and time domain.
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X.K. Song et al. / Physica C 499 (2014) 57–62
Fig. 8. (a) The transformed S11 response curves: the dash line represents the response curve after tuning the resonant frequency of each resonator, and the solid line represents the response curve after tuning coupling coefficients M45 and M56 in the time domain (b) the tuned and unturned S21 and S11 response curves.
Fig. 9. (a) The simulated and final tuned S21 and S11 response curves (b) the simulated and final tuned transformed S11 response curves in the time domain.
4. Conclusion
References
This paper proposes an effective tuning method based on the time domain. In this method, the resonant frequency of each resonator and the coupling coefficients between resonators can be distinguished accurately and adjusted individually, so that this method could be used for coupled resonator filters. The sensitivity of the filter performance can be directly evaluated from the filter group delay. Fabrication errors and the non-uniformity of the dielectric constant and thickness of the substrate induce resonator frequency deviation from the design, further degrading the filter performance. A six-pole HTS filter with ICRs, with a CF of 500 MHz and a bandwidth of 2 MHz, is fabricated and tuned to demonstrate the effectiveness of the proposed method. After tuning, the return loss has increased from 9.57 dB to 15.1 dB, whereas the insertion loss has decreased from 1.06 dB to 0.43 dB.
[1] J.-S. Hong, E.P. McErlean, B. Karyamapudi, IEEE Proc. Microw. Antenn. Propag. 151 (2004) 491. [2] G.Y. Zhang, M.J. Lancaster, F. Huang, IEEE Trans. Microw. Theory Technol. 54 (2006) 559. [3] Q.R. Li, X.B. Guo, X.P. Zhang, B. Wei, W. Chen, Y. Zhang, C. Feng, Z.J. Yin, S.C. Jin, B.S. Cao, Physica C 483 (2012) 5. [4] L.M. Gong, B. Wei, B.S. Cao, S.W. Dong, Y.Z. Dong, H.X. Yu, L. Jun, Microw. Opt. Technol. Lett. 55 (2013) 443. [5] C.-W. Tang, W.-T. Liu, IEEE Trans. Microw. Wireless Compon. Lett. 18 (2008) 767. [6] J.W. Zhu, Z.H. Feng, IEEE Trans. Microw. Wireless Compon. Lett. 16 (2006) 672. [7] M. Ohsaka, S. Takeuchi, S. Ono, J.H. Lee, A. Saito, A. Akasegawa, K. Yamanaka, K. Kurihara, S. Ohshima, Physica C 468 (2008) 1966. [8] N. Sekiya, Y. Nakagawa, A. Saito, S. Ohshima, Physica C 469 (2009) 1653. [9] H. Harada, N. Sekiya, S. Kakio, S. Ohshima, Physica C 471 (2011) 1224. [10] S. Ohshima, M. Ohsaka, J.H. Lee, S. Takeuchi, H. Kinouchi, S. Ono, Y. Takano, T. Nakamura, M. Yokoo, A. Saito, IEEE Trans. Appl. Supercond. 19 (2009) 903. [11] H.L. Peng, X.B. Guo, X.P. Zhang, B. Wei, B.S. Cao, S.C. Jin, X.X. Lu, IEEE Trans. Appl. Supercond. 19 (2009) 3683. [12] H.L. Peng, X.P. Zhang, X.B. Guo, L.J. Mu, B. Wei, B.X. Gao, B.S. Cao, Microw. Opt. Technol. Lett. 49 (2007) 1565. [13] F. Aita, N. Sekiya, S. Ono, A. Saito, S. Hirano, S. Ohshima, IEICE Trans. Electron. E89–C (2006) 119. [14] J. Dunsmore, IEEE MTT-S Int. Microw. Symp. Dig. 3 (1999) 1351. [15] M. Martinez-Mendoza, C. Ernst, J.A. Lorente, A. Alvarez-Melcon, F. Seyfert, IEEE Trans. Microw. Theory Technol. 60 (2012) 2131. [16] M. Martinez-Mendoza, F. Seyfert, C. Ernst, A. Alvarez-Melcon, IEEE Trans. Microw. Theory Technol. 60 (2012) 3369.
Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants 61127001 and 60901002.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
An efficient tuning method for narrowband superconducting filters with interdigital capacitor resonators in the time domain X.K. Song a, X.P. Zhang a, B.S. Cao a,⇑, B. Wei a, L.M. Gong b, Y.D. Chen c, T.N. Zheng a, X.B. Guo a, G.Y. Zhang c, X. Zhan a a b c
State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China Sci. & Technol. on Space Microwave Lab., CAST (Xi’an), Xi’an 710100, China Superconductor Technology Co. Ltd., Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 21 September 2013 Received in revised form 25 December 2013 Accepted 23 January 2014 Available online 1 February 2014 Keywords: Superconducting filter Interdigital-capacitor resonator Time domain Tuning
a b s t r a c t This article proposes an effective tuning method based on the time domain for improving the performance of high-temperature superconducting (HTS) bandpass filters with interdigital capacitor resonators (ICRs). Analysis of the causes of HTS filter performance deterioration reveal that such deterioration is primarily caused by the resonant frequency deviation of the resonator of the HTS filter; this deviation results from fabrication errors and from the non-uniformity of the thickness and dielectric constant of the substrate. The sensitivity of the filter, which arises from the non-uniformity of the substrate thickness and dielectric constant, is related to the type of the resonator and the group delay characteristic of the filter. A 0.4% fractional bandwidth HTS filter with ICRs at the UHF band is fabricated and tuned using mechanical rods in the time domain. By applying this method, the resonant frequency deviation of each resonator and the coupling coefficient between resonators can be measured and tuned individually. The insertion loss of the HTS filter is improved from 1.06 dB to 0.43 dB, whereas the return loss is improved from 9.57 dB to 15.1 dB. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction High-temperature superconducting (HTS) microwave filters designed for mobile communication systems are characterized by having low insertion loss, high selectivity, and high band edge steepness [1–4]. Filters with interdigital capacitor resonators (ICRs) have been recently developed to realize a wide stopband performance with compact structures [4–6]. The first spurious frequency of ICRs is usually located at approximately 3f0 [2], and the fundamental frequency can be reduced by increasing the selfcapacitance [4–6]. Thus, ICRs are suitable for designing wide stopband filters at a low frequency. HTS filters with ICRs demonstrate both high in-band and wide stopband performance [4]. However, the non-uniformity of the substrate materials, along with fabrication errors, degrades the filter performance. Numerous tuning methods have been proposed for improving HTS filter performance [7–14]. Most of these studies have focused either on tuning the center frequency (CF) and the bandwidth or on improving the in-band performance of the filter [7–11]. Although ⇑ Corresponding author. Tel./fax: +86 10 6279 2473. E-mail address: [email protected] (B.S. Cao). http://dx.doi.org/10.1016/j.physc.2014.01.009 0921-4534/Ó 2014 Elsevier B.V. All rights reserved.
dielectric plate method can effectively adjust the CF of HTS filters [7], waveguides and electric pads have also been used in tuning the CF and the bandwidth [8,9]. Ohshima et al. constructed a trimming library by using a dielectric plate and trimming rods to improve HTS filter performance [10]. Mechanical rods, which have great flexibility and excellent tuning effect, are often used to tune HTS filters [11–13]. However, few studies have analyzed the inconsistency between the initial measured in-band performance of the HTS filter and the simulated results. The majority of reports have used tuning methods based on the frequency domain, which is a trial-and-error process. Few papers have discussed the effect of the resonant frequency deviations of the resonators and the tuning effects of mechanical rods in the time domain. This paper describes in detail a mechanical tuning method based on the time domain for coupled resonator filters, such as filters with lumped LC resonators, coaxial line resonators, cavity resonators, or microwave waveguide resonators. The tuning effects of the dielectric and metallic rods are calculated and analyzed. The proposed method is more effective and less complex than tuning in the frequency domain. In the time domain, the resonant frequency of each resonator and the coupling coefficients between resonators can be distinguished accurately and adjusted individually. In fact,
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X.K. Song et al. / Physica C 499 (2014) 57–62
the tuning mechanism is resonant frequency tuning and coupling coefficients tuning so that this method could be widely used no matter what response type of the coupled resonator filters, which include Chebyshev response, quasi-elliptic response and, Butterworth response and so on. In addition, this study analyzes the resonant frequency deviation of the resonator, which is primarily caused by the non-uniformity of the substrate thickness and dielectric constant. The deterioration of the filter in-band performance caused by the resonant frequency deviation is discussed. The sensitivity of the filter performance is related to the type of the resonator and the group delay characteristic of the filter. Basing on the group delay performance, we can predict the level of consistency between filter design and fabrication. Tuning refers to the effective correction of the resonant frequency deviation. A 0.4% fractional bandwidth HTS filter with the ICRs is tuned to demonstrate the effectiveness of the proposed method, and the in-band performance of this filter is significantly improved after such fine-tuning.
2. Sensitivity analysis of the filter performance with nonuniform substrate 2.1. Resonant frequency deviation of different types of resonators The resonant frequency of a resonator can change after fabrication because of fabrication errors and the non-uniformity of the substrate thickness and dielectric constant [11,13]. Three types of resonators, namely, interdigital capacitor, twin spiral, and meander line types, are selected to show the sensitivity of the filter to resonant frequency deviation. The resonators are simulated using Sonnet electromagnetic software to illustrate different resonant frequency deviations. The original resonant frequencies of the three resonators are all 500 MHz, the dielectric constant of the substrate is 9.73, and the substrate thickness is 0.51 mm. The structure layouts of the three types of resonators are shown in Fig. 1. The simulation results of the resonant frequency deviation are shown in
Table 1 Simulated resonant frequency deviation of the resonator with the variations of the substrate dielectric constant. Dielectric constant (e)
9.7
9.71
9.72
Deviation of the resonant frequency (MHz) Interdigital capacitor 0.7 0.46 0.22 Twin spiral 0.74 0.48 0.24 Meander line 0.75 0.5 0.25
9.73
9.74
9.75
9.76
0 0 0
0.24 0.24 0.25
0.48 0.48 0.5
0.7 0.72 0.75
Tables 1 and 2, which illustrate that variations in substrate thickness and dielectric constant can cause resonant frequency deviation of the resonators. Results show that the change in resonant frequency deviation ranges from 0.22 MHz to 0.75 MHz and from 0.14 MHz to 10.6 MHz when De = ±0.01, ±0.02, ±0.03 and Dd = ±0.01, ±0.02, ±0.03, respectively. Among the three types of resonators, ICR has the least sensitivity to resonant frequency deviation because of the changes in substrate thickness and dielectric constant. This finding indicates that substrate uniformity and the type of the resonator are important factors that affect the resonant frequency deviation of the resonator. 2.2. Degradation of in-band filter performance with different resonant frequency deviations The resonant frequency deviation of the resonator has a significant effect on the performance of narrowband HTS filters, particularly on the in-band performance. A six-pole Chebyshev prototype filter (CF: 500 MHz; bandwidth: 2 MHz; pass-band ripple: 0.01 dB; and return loss: 26 dB) is designed to illustrate this effect. Table 3 shows that when the resonant frequency deviation of the first resonator is changed from ±0.2 MHz to ±2 MHz, the corresponding in-band return loss changes from 14 dB to 2 dB, as shown in Fig. 2. The curves of a–f in Fig. 2(A) denote the deterioration of S11 when the resonant frequency of the first resonator
Fig. 1. The structures and sizes of three resonators: interdigital capacitor, twin spiral and meander line.
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X.K. Song et al. / Physica C 499 (2014) 57–62 Table 2 Simulated resonant frequency deviation of the resonator with the variations of the substrate thickness. Substrate thickness (d/mm)
0.48
Deviation of the resonant frequency (MHz) Interdigital capacitor 0.46 Twin spiral 4.7 Meander line 10.6
0.49
0.5
0.51
0.52
0.53
0.54
0.3 3.1 7
0.14 1.5 3.6
0 0 0
0.16 1.5 3.4
0.32 3 6.6
0.46 4.45 10
Table 3 The S11 when the resonant frequency of the first resonator changes. Curve
a
b
c
d
e
f
Deviation of the resonant frequency (MHz) S11 (dB)
±2.0
±1.0
±0.6
±0.4
±0.2
0
4
8
11
14
18
26
begins to decrease, whereas the curves of a–f in Fig. 2(B) denote the deterioration of S11 when the resonant frequency of the first resonator begins to increase. The curves of a–f in Fig. 2(A) and (B) correspond to the deviation of the resonant frequency a–f listed in Table 3, which shows that the in-band return loss worsens as the resonant frequency deviation increases. However, this simulation considered the deviation of one resonator only. However, all the resonant frequencies of the resonators of the filter change at different levels because of fabrication errors and the non-uniformity of the substrate and dielectric constant. Thus, an effective tuning method should be applied to adjust the resonant frequency deviation. 2.3. Degradation of the in-band filter performance at different bandwidths According to [15,16], the degradation of the in-band filter performance caused by substrate non-uniformity and fabrication errors can be obtained by the group delay of the filter s(x), which can be expressed as follows:
DjS11jmax 6 s ð xÞ DM 11 where D|S11| denotes the degradation of S11, and DM11 denotes the variation in the coupling matrix term M11 caused by substrate non-uniformity and fabrication errors. We suppose that the fabrication errors are the same for the three bandwidth filters. Thus, the sensitivity of the in-band performance is directly revealed from the group delay s(x) of the inline Chebyshev filter. With the use of ICRs, three six-pole Chebyshev prototype filters of different bandwidths are designed to analyze the sensitivity of
the filter performance to degradation. The CFs of the three filters are all 500 MHz, and the bandwidths are 2, 12, and 25 MHz. The simulation results show that the in-band ripples are below 0.01 dB and the return losses are below 26 dB. The group delay curves of the three filters are shown in Fig. 3(a)–(c). The 2 MHz bandwidth filter has a maximum group delay value of 605 ns in-band, whereas the group delay of the 25 MHz bandwidth filter is 48 ns. Thus, the in-band performance of the 25 MHz bandwidth filter has the least sensitivity among the three filters. The in-band performance of the filters is shown in Table 4. We suppose that the resonant frequency of the second resonator Df2 has shifted by 0.2, 0.4, 0.7, and 1 MHz, whereas the resonant frequencies of the other resonators remain unchanged at 500 MHz. The simulation result shows that the performance of the 2 MHz bandwidth filter exhibits the worst deterioration. The performance of the 12 MHz bandwidth filter, which has a return loss of over 14.4 dB in the passband even when Df2 shifts by 1.0 MHz, is suitable for engineering application. As the bandwidth increases to 25 MHz, the filter shows the least sensitivity to the degradation of the filter performance; this finding is consistent with the conclusion presented above. These results indicate that the narrow band filter requires tuning.
3. Tuning in the time domain 3.1. Tuning preparations Dielectric and metallic tuning rods are often used to adjust the resonant frequency deviation of a resonator [11–13]. In an electrical field concentrated area, a dielectric rod is equivalent to a capacitance combined with a resonator to decrease the resonant frequency. In a magnetic field concentrated area, a metallic rod is equivalent to an inductance combined with a resonator to increase the resonant frequency [12,13]. A sapphire electric rod and a copper metallic rod are respectively placed above the electrical field concentrated area and magnetic field concentrated area to simulate the tuning effects of the two rods. The distance S between the rod bottom and the resonator is changed from 0 mm to 1 mm to simulate the tuning effect. As shown in Fig. 4, the tuning effect becomes more obvious as the distance becomes closer to the
Fig. 2. The deterioration of S11 (A) when the resonant frequency of the first resonator decreases (B) when the resonant frequency of the first resonator increases, the curves of a–f are corresponding to the a–f in Table 3.
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Fig. 3. The curves of group delay of the three filters, of which the center frequency is 500 MHz and the bandwidths are (a) 2 MHz, (b) 12 MHz and (c) 25 MHz.
Table 4 The degradation of S11 when the resonant frequency of the second resonator of three filters with different bandwidths changes. Bandwidth (MHz)
2 12 25
S11 (dB)
Df2 = 0 MHz
Df2 = 0.2 MHz
Df2 = 0.4 MHz
Df2 = 0.7 MHz
Df2 = 1.0 MHz
26.0 26.0 26.0
12.7 20.8 26.0
8.1 20.8 20.8
5.7 17.7 20.8
3.7 14.4 18.6
Fig. 4. The tuning effects of the metallic rod and dielectric rod for a single resonator.
resonator surface. In the simulation, the resonant frequency of a single resonator can be increased by 5.54 MHz by using a metallic rod and be decreased by 6.43 MHz by using a dielectric rod. A six-pole narrowband HTS filter with ICRs is designed and fabricated at the UHF band with a CF of 500 MHz and a bandwidth of 2 MHz. The filter structure is symmetrical and compact. Moreover, the filter has weak couplings and a high Q value. The current density distribution of the filter circuit is simulated using Sonnet electromagnetic software (Fig. 5). At the fundamental resonant frequencies, the dark area represents the low current density, whereas the bright area represents the high current density. The electrical field is concentrated at both ends of the ICRs, whereas the magnetic field is concentrated at the resonator central area. The untuned filter is first measured by using an Agilent 8720ES vector network analyzer in a cryocooler at 70 K. Prior to tuning, the resonant frequency of each resonator is measured in the time domain. The results are listed in Table 5. The largest deviation occurs in the fifth resonator (1.96 MHz), indicating that the fifth resonant frequency is 1.96 MHz lower than 500 MHz. The cmeasured results imply that the substrate variations and the fabricated errors may have a half-and-half contribution to the resonant frequency deviation. This finding can help in deciding whether metallic rods or dielectric rods should be set up above each resonator depending on whether resonant frequency deviation is low or high. The measurement result is consistent with the simulation results in Tables 1 and 2.
Fig. 5. The simulated current density distribution of the six-pole narrowband HTS filter with ICRs and tuning rod positions diagram (dashed and solid circles represent metallic rods and dielectric rods respectively).
Table 5 The resonant frequency deviations of the six resonators toward 500 MHz. Resonator no.
1
2
3
4
5
6
Resonant frequency deviation (MHz)
0.30
0.22
0.03
1.66
1.96
1.10
As shown in Fig. 5, three metallic rods and three dielectric rods are set up on the basis of the diagram of the current density and resonant frequency deviation of each resonator. The metallic rods are placed above the first, third, and fifth resonators so that the resonant frequencies of the three resonators can be increased. The dielectric rods are then set up above the second, fourth, and sixth resonators to decrease their resonant frequencies. 3.2. Tuning The S-parameter response curves prior to tuning in the frequency domain are shown in Fig. 6(a). The return and insertion loss of the untuned filter is 9.57 and 1.06 dB, respectively. The following steps are performed in the network analyzer to measure the response in the time domain: CF is set to 500 MHz, which is the CF of the filter; and the span is set to 10 MHz, which is approximately five times that of the bandwidth. The return loss curve S11 is transformed into the time domain, which is obtained by a
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Fig. 6. (a) The simulated and untuned S21 and S11 response curves (b) the simulated and untuned transformed S11 response curves in the time domain.
discrete inverse Fourier transform [11,14]. The start and stop time depend on the filter sections and the expected bandwidth of the filter. The start time is t0 = (2/pBW) = 326 ns, whereas the stop time is ts = (2N + 1/pBW) = 2122 ns. The N in the formula is the number of filter sections so that this transform method could be used for high-order filters. The number of the distinctive dips of the transformed S11 in the time domain is N between t0 to ts. The response curve prior to tuning in the time domain is shown in Fig. 6(b), which shows that the filter is mistuned because the six dips are not minimized. Two steps are adopted to tune the six-pole narrowband HTS filter and improve its performance. The first step is to adjust the resonant frequency of each resonator, and the second step is to tune the coupling coefficients between the resonators. In the first step, tuning is sequentially conducted from the first resonator (marked 1) to the sixth resonator (marked 6) to minimize the resonator dips, as shown in Fig. 7(b) and (d). Fig. 7(c) shows the response curve after the resonators are tuned. Comparison of Fig. 7(b) and (d) reveal the last two resonators have coupled to each other strongly because the resonator dips cannot be minimized. The distances between the resonators are sufficiently small that the coupling coefficients are inevitably affected when the individual resonant frequency of the resonator is tuned. The peak heights in the transform response show the coupling coefficients. If the height is higher than the designed one, then
the coupling coefficient increases. If the height is lower than the designed one, the coupling coefficient decreases. Compared with the simulation, the peak height has a big gap, indicating a coupling mismatched. The in-band performance is not in the optimal state; thus, the coupling coefficients between the resonators should be considered and readjusted. When adjusting the coupling coefficients, the peaks in the time domain and the return loss curve in frequency domain should be observed and analyzed. The aim is to tune the peak height to obtain the proper coupling coefficients, consequently optimizing the return and insertion losses. The coupling coefficients M45 and M56 are adjusted on the basis of the tuning the resonant frequency of each resonator. After tuning, the coupling coefficient M45 increases by 7.5% and the coupling coefficient M56 decreases by 2.4%, as shown in Fig. 8(a). The six distinctive dips of the transformed S11 in the time domain in Fig. 8(a) are characteristic dips that occur when the resonators are exactly tuned. The corresponding performance in the frequency domain is shown in Fig. 8(b). As shown in Fig. 9(b), there is a deviation between the simulated and final tuned transformed S11 in the time domain because the final tuned coupling coefficient M12 is smaller so that less energy are coupled to the next resonator due to more energy reflection. The corresponding final tuned results of the HTS filter in the frequency domain are shown in Fig. 9(a). The return loss exceeds 15.1 dB, whereas the insertion loss is below 0.43 dB.
Fig. 7. (a and b) The curves of simulation and after tuning three resonators in the frequency domain and time domain, (c and d) the curves of simulation and after tuning six resonators in the frequency domain and time domain.
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Fig. 8. (a) The transformed S11 response curves: the dash line represents the response curve after tuning the resonant frequency of each resonator, and the solid line represents the response curve after tuning coupling coefficients M45 and M56 in the time domain (b) the tuned and unturned S21 and S11 response curves.
Fig. 9. (a) The simulated and final tuned S21 and S11 response curves (b) the simulated and final tuned transformed S11 response curves in the time domain.
4. Conclusion
References
This paper proposes an effective tuning method based on the time domain. In this method, the resonant frequency of each resonator and the coupling coefficients between resonators can be distinguished accurately and adjusted individually, so that this method could be used for coupled resonator filters. The sensitivity of the filter performance can be directly evaluated from the filter group delay. Fabrication errors and the non-uniformity of the dielectric constant and thickness of the substrate induce resonator frequency deviation from the design, further degrading the filter performance. A six-pole HTS filter with ICRs, with a CF of 500 MHz and a bandwidth of 2 MHz, is fabricated and tuned to demonstrate the effectiveness of the proposed method. After tuning, the return loss has increased from 9.57 dB to 15.1 dB, whereas the insertion loss has decreased from 1.06 dB to 0.43 dB.
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Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants 61127001 and 60901002.