- Email: [email protected]
K inverters
Int. J. Electron. Commun. (AEÜ) 70 (2016) 1028–1033
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular Paper
Design of a high-selectivity quad-band bandpass filter based on k/4 resonators with alternative J/K inverters Jing Ai a, Yong-Hong Zhang a, Kai-Da Xu b,c,⇑, Dao-Tong Li a, Qing-Huo Liu d a
EHF Key Lab of Science, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China Institute of Electromagnetics and Acoustics & Department of Electronic Science, Xiamen University, Xiamen 361005, China c Shenzhen Research Institute of Xiamen University, Shenzhen 518057, China d Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA b
a r t i c l e
i n f o
Article history: Received 13 October 2015 Accepted 28 April 2016
Keywords: Alternative J/K inverters High selectivity Quad-band bandpass filter Quarter-wavelength resonator Synthesis design
a b s t r a c t Based on k/4 resonators, the synthesis design method for a miniaturized high-selectivity microstrip quadband bandpass filter (BPF) with alternative J/K inverters has been presented. Two dual-band k/4 stepped impedance resonators (SIRs) are employed to generate the 1st and 4th passbands, while the 2nd and 3rd passbands are achieved by utilizing four coupled k/4 uniform impedance resonators (UIRs). Moreover, the alternative J/K inverters form is proposed to create an additional cross coupling, resulting in one pair of transmission zeros (TZs) at each side of all the four passbands. To verify the validity of the proposed method, a quad-band BPF centered at 1.9, 4.1, 4.6 and 6.1 GHz with respectively fractional bandwidths of 13.7%, 5.1%, 5.9% and 7.6% has been designed and fabricated, whose measured results show consistent match with the simulated ones. Ó 2016 Elsevier GmbH. All rights reserved.
1. Introduction With the advent of modern multi-service system, it is necessary to provide stable transceiver to establish the requirement of wireless communication condition. As one of the critical building block in the multi-band transceiver, the quad-band BPFs have garnered a great deal of attention and a variety of methods have been proposed [1–5]. In [1], the stub-loaded resonators (SLRs), which can be analyzed by the odd- and even-mode technique, were used to realize a quad-band filter with three finite TZs, including the one produced by the resonator itself. In [2], the authors proposed a quad-band microstrip BPF with two sets of the asymmetric SIRs, whose TZs were generated by the mixed electric and magnetic coupling. Negative refractive-index transmission-line (NRI-TL) metamaterials were also employed to construct a quad-band BPF [3]. However, it suffers from a large area and its out-of-band rejection characteristic is not good enough. In [4], an improved CPW-fed configuration with dual mode double-square-ring resonators was also used in quad-band filter, where the TZs can be realized by tuning the slits in the branch of the twin-T CPW. Recently the multimode resonator is utilize to develop quad-band BPF, which can
reduce circuit size and fabrication complexity. A multi-stubloaded resonator was employed to produce the 1st, 2nd and 4th passband frequencies, while a short-end stub-loaded resonator was used to yield the 3rd passband, and six finite TZs were generated in order to increase the roll-off skirts of the passbands [5]. It is well known that finite TZs are of considerable importance in the filter design, which can improve out-of-band rejection performance and achieve sharp roll off skirts. To increase the number of finite TZs, a promising quad-band BPF based on k/4 resonators with alternative J/K inverters demonstrated in Fig. 1 is presented in this paper. Especially, at least one TZ has been excited in proximity of both lower and upper sides of each passband. These paired TZs are primarily introduced by the opposite polarity between the mainline and cross couplings. Compared with the filters in [1–5], the proposed work features compact size, high selectivity and controllable center frequencies and bandwidths for each passband. To verify the proposed method, a quad-band BPF with eight finite TZs is designed and fabricated. The measured results show good agreement with the predicted frequency performance.
2. Synthesis design of quad-band bandpass filter ⇑ Corresponding author at: Institute of Electromagnetics and Acoustics & Department of Electronic Science, Xiamen University, Xiamen 361005, China. E-mail address: [email protected] (K.-D. Xu). http://dx.doi.org/10.1016/j.aeue.2016.04.019 1434-8411/Ó 2016 Elsevier GmbH. All rights reserved.
The coupling topology of the proposed BPF based on k/4 resonator in the alternative J–K–J form is shown in Fig. 1(a), where the J inverters are generated by the parallel coupled microstrip
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To clarify the proposed quad-band BPF design, its design procedure is summarized as follows: Step 1: According to the required frequencies and bandwidths of the 1st and 4th passbands, we can get the reactance slope ratio of the k/4 SIRs by extracting the broadband dispersive K value of the common grounded metallic via from the full-wave simulated S parameters. Step 2: The preliminary dimensions of an uncoupled SIR are achieved by the synthesis approach of the dual-band microstrip BPF with k/4 SIRs, and the required J and K inverter values can be obtained by appropriately designing the physical dimensions. Step 3: When two of the uncoupled k/4 SIRs are inductively coupled together, an average-weighted length is needed to subtract from the normal uncoupled one to alleviate the length mismatch of the two passbands. Then, the U-shaped feed lines are utilized to offer appropriate Qe at the 4th passband by altering the length LU. Step 4: The lower path cell is formed by a split-type dual-band BPF, which could be illustrated by fully canonical split-type coupling topology. The center frequency of virtual wide passband qffiffiffiffiffiffiffiffiffiffiffiffiffiffi II III equals to f 0 f 0 , which is primarily determined by the lengths L5 and L6. Step 5: The bandwidths of the 2nd and 3rd passbands and the location of the four TZs (TZ5–TZ8) can be synthesized based on 4th-order split-type coupling matrix. Step 6: Note that the center frequencies and bandwidths will be slightly shifted when combining the upper and lower paths together. Therefore, a fine tuning is needed to get a better quadband response. Fig. 1. (a) Coupling topology for the proposed quad-band BPF. (b) k/4 SIR for the 1st and 4th passbands. (c) k/4 UIR for the 2nd and 3rd passbands.
2.1. Upper path cell: 1st and 4th passbands The 1st and 4th passbands are composed of a 2nd-order ChebyI
lines and the K inverters are implemented with the metallic vias. In the upper path, two same k/4 SIRs shown in Fig. 1(b) with inductively coupled by a hole via are introduced to form the 1st and 4th passbands, while in the lower path, four k/4 UIRs shown in Fig. 1(c) are connected and coupled to independently produce the split-type of the 2nd and 3rd passbands which are among the 1st and 4th passbands. Then, parallel-path transmission is utilized to combine the above upper and lower path cells into a quad-band BPF. The structure of the proposed BPF is demonstrated in Fig. 2. Benefiting from the parallel-path transmission coupling scheme, the upper path cell consisting of the 1st and 4th passbands and lower path cell comprising of the 2nd and 3rd passbands can be designed and adjusted independently.
IV
shev dual-band BPF centered at f 0 = 1.9 GHz and f 0 = 6.1 GHz with 20 dB in-band return loss, and the fractional bandwidths of FBWI = 13.7% and FBWIV = 7.6%, respectively. Based on the classical filter synthesis method, the inter resonator coupling K12 can be obtained as
FBWx K 12 ¼ pffiffiffiffiffiffiffiffiffiffi g1 g2
ð1Þ
where x is the resonator’s reactance slope, and g1, g2 are the normalized elements in the lowpass filter prototype. Herein, the upper path of the quad-band BPF can be considered as two k/4 SIRs coupled together with a common grounded metallic via which is implemented to serve as the dual-band K inverters. The broadband
25
30
20
25 20
15
15 10
10
5 0
Fig. 2. Structure of the proposed quad-band BPF.
5 0
1
2
3
4
5
6
7
8
0
Fig. 3. Extracted K12 and associated electrical length for the 1st/4th passbands as a function of frequency.
J. Ai et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 1028–1033
Frequency Ratio f0
/ f0
1030
dimension of the k/4 SIR, it is possible not only to possess two resonant frequencies with desired ratio, but also to achieve the reactance slopes, thereby influencing the inter resonator coupling and obtaining a dual-band response simultaneously. The reactance slope xin of the k/4 SIR is derived as
6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
xin ¼
f dX 2 df f ¼f I ;f IV 0
ð3Þ
0
Z a ha sec2 ha þ Rz hb sec2 ha sec2 hb þ R2z ha sec2 ha tan2 hb ¼ 2 ðRz tan hb þ tan ha Þ2
where Rz is the impedance ratio of the k/4 SIR, which is defined as Rz ¼ Z a =Z b , ha and hb are the electrical lengths with the frequency I
Fig. 4. Frequency ratio parameters.
IV I f 0 =f 0
f 0 . Therefore, the preliminary dimensions of an uncoupled SIR in Fig. 1(b) can be determined as: Wa = 0.3 mm, La = 3.5 mm, Wb = 1 mm, Lb = 10.8 mm. Two associated electrical lengths at the central frequencies of 1.9 GHz and 6.1 GHz are respectively 7.6°and 21.7°, which are equal to physical lengths of 1.34 mm and 1.19 mm, respectively. To alleviate the length mismatch of the two passbands, an average-weighted length of 1.22 mm is subtracted from La in the uncoupled k/4 SIR when two of them are inductively coupled together.
versus length ratio and impedance ratio as
dispersive K value and its associated electrical length can be extracted or de-embedded from the full-wave simulated S parameters as shown in Fig. 3. Since the K12 is utilized by a metallic via, its coupling strength increases monotonically with the frequency, K I12 = 5.4 and K IV 12 = 15.6 at the frequency of 1.9 and 6.1 GHz, respectively, and the required x reactance slope ratio of the k/4 SIRs can be derived as
xIV FBW I K IV 13:7% 15:6 12 ¼ 5:21 ¼ ¼ I 7:6% 5:4 x FBW IV K I12
IV
ð2Þ
With the center frequency ratio of 3.21 (6.1/1.9) and the reactance slope ratio of 5.21, the dimension of k/4 SIR can be rigorously derived to meet the specified K12 couplings at the 1st and 4th passbands based on the synthesis approach for the dual-band microstrip BPF with k/4 SIRs [6]. By appropriately determining the
6.5
fTP4
5
Frequency (GHz)
Frequency (GHz)
7 6 fTP3 fTP2 2 fTP1 1
7
8
9 10 L2 (mm)
11
12
fTP4
6.0 fTP3
5.5 fTP2 2.0 1.5
fTP1 0.15 0.20 0.25 0.30 0.35 0.40 0.45 L1 / (L1+L2)
(a)
(b)
160
0.20
120
0.16 0.12
80
M
Qe
I
Fig. 4 shows the relationship between the frequency ratio f 0 =f 0 and the impedance ratio Rz ¼ Z a =Z b , the length ratio ha =ðha þ hb Þ. Note that the frequency ratio can vary from 2.12 to 6.46 theoretically (i.e. when ha =ðha þ hb Þ ¼ 0:5, 0.4 < Rz < 5). It can be seen that the 1st and 4th passbands can be designed with wide band spacing by controlling the impedance ratio and length ratio of the k/4 SIRs. Because of the wide stopband spacing between these two passbands, it creates the condition that we can embed a dual-band filtering cell centered at different frequencies into the wide spacing thereby forming a quad-band BPF finally. Fig. 5(a) and (b) plot the extracted resonant frequencies of the k/4 SIR with varied L2 and L1/(L1 + L2), respectively. It can be seen
Qe Qe
40
0.08 0.04
0
0.0
0.5
1.0 1.5 LU (mm)
(c)
2.0
2.5
0.8
1.2
1.6 L3 (mm)
2.0
2.4
(d)
Fig. 5. Extracted resonant frequencies with varied (a) L2 and (b) L1/(L1 + L2); (c) extracted Qe with varied LU; and (d) extracted M with varied L3 in the upper path BPF cell.
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that when L1/(L1 + L2) is changed, fTP3 and fTP4 can be adjusted greatly while fTP1 and fTP2 vary slightly. Thus, the frequencies of the 1st and 4th passbands can be controlled individually. For the bandwidths, they depend on the external quality factors Qe and coupling coefficients M. Fig. 5(c) and (d) show the variation of extracted Qe and M against different values of LU and L3, respectively. When the height of the U-folded shape LU is changed, the external coupling factor Q Ie for the 1st passband almost keeps the same, while the external coupling factor Q IV e for the 4th passband varies obviously. While for the coupling coefficients, M I and M IV are relevant with varying L3 as demonstrated in Fig. 5(d). Therefore, a non-uniform feed line with U-folded shape can be utilized to offer the external couplings at the 4th passband [7]. Furthermore, a small open-end coupled line section with length of 0.8 mm and coupling space of 0.2 mm is utilized to enhance the source-load cross coupling and introduce one pair of TZs at each side of all the four passbands.
Fig. 7. EM simulated isolated response of |S21| for the upper and lower paths filter, as well as the whole response of quad-band BPF.
2.2. Lower path cell: 2nd and 3rd passbands As shown in Fig. 2, four UIRs in the lower path with the width of 0.4 mm are utilized to design the 2nd and 3rd passbands. The synthesis design method for dual-band microwave filters with required passbands and attenuation at stopbands directly using frequency transformation was proposed in [8], which could be illustrated by fully canonical coupling matrix shown in Fig. 6(a) with four TZs at X = 3.75, 0.02, 0.47, 3.35, possessing 20 dB return losses for both passbands. The center frequency of virtual II
(b)
(c)
(d)
III 1=2
wide passband equals to ðf 0 f 0 Þ = 4.33 GHz, and fractional bandwidth FBW = 20%. By adjusting the inter coupling strength between the k/4 resonators, a pair of finite TZs initially located at the outside of the 4th-order quadruplet filter are shifted into the center of the single passband, therefore the quadruplet BPF can be modified into a split-type dual-band BPF. Furthermore, Fig. 6 (b) and (c) plot the variation of Q e and M against different values of G2 and S2. As G2 increases from 0.2 mm to 0.6 mm, the variation Q ΙΙΙ e
QIIe
(a)
III
is very apparent but is relatively weak, and M can be of separately modified by tuning S2, thus the bandwidth of 2nd and 3rd passbands can be controlled individually.
I
II
III
IV
Fig. 8. Surface current distribution at (a) f 0 , (b) f 0 , (c) f 0 and (d) f 0 .
0
3 4 5 6 L
0.9561 0 0 0 0.1067
3 0.9561
4 0
5 0
6 0
0.2269 -0.9014 0 -1.1350 -0.9014 -0.2549 0.0057 0 0 0.0057 -0.2549 -0.9014 -1.1350 0 -0.9014 0.2269 0 0 0 0.9561
L 0.1067
-10
|S21| & |S11| (dB)
S
S 0
0 0 0 0.9561 0
(a)
Qe
M
Qe
-40 -50 -60
Simulation Measurement
2
3
4
5
6
7
Frequency (GHz)
0.12
Qe
-30
1
0.16
80
-20
-70
120
|S11|
|S21|
Fig. 9. Photograph, simulated and measured results of the quad-band BPF.
0.08
40
0.04 0
0.2
0.3
0.4 0.5 G2 (mm)
(b)
0.6
0.0
0.2
0.4 0.6 S2 (mm)
0.8
1.0
(c)
Fig. 6. (a) Coupling matrix, (b) extracted Qe with varied G2, (c) extracted M with varied S2 in the lower path BPF cell.
As shown in Fig. 2, the parallel coupled microstrip lines with length of L9 and gap of G2 are employed to form the JS3, JL6 inverters. The metallic vias with the diameter of 0.6 mm are used to implement the K34, K56 inverters. The J45 inverter is generated by the two anti-parallel coupled k/4 UIRs with length of 1.0 mm, and the cross coupling K36 inverter is implemented by the inductive coupling between two closely arranged grounded-end of k/4 UIRs.
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Table 1 Comparison with reported quad-band BPFs. References
Passbands (GHz)
IL (insertion loss) (dB)
Fractional bandwidth (%)
Number of TZs
Circuit size (mm mm) (k0 k0)
[1]
1.5/2.5/ 3.6/4.6 2.4/3.5/ 5.2/6.8 0.87/1.06/ 1.78/2 0.95/1.26/ 1.89/2.29 1.8/2.45/ 3.5/5.5
1.98/1.74/ 3.58/3.4 0.5/1.3/ 1.3/1 0.94/1.1/ 0.73/1.8 2.18/2.09/ 1.40/0.93 1.5/1.7/ 2.3/1.8
5.5%/12%/ 11%/4.3% 6.4%/9.4%/ 3.8%/4.9% 2.8%/2.8%/ 3.9%/6.5% 6.7%/5.1%/ 12%/15.3% 6.7%/4.1%/ 2.9%/14.8%
3
32 32 0.16k0 0.16k0 22 22 0.20k0 0.20k0 55 21 0.16k0 0.07k0 55 55 0.17k0 0.17k0 19.8 15.8 0.12k0 0.10k0
1.9/4.1/ 4.6/6.1
0.97/1.28/ 1.78/2.16
13.7%/5%/ 5.9%/7.6%
[2] [3] [4] [5] This paper
Based on the analysis in [6], the physical dimensions of all the J and K inverters and their associated electrical lengths can be analytically derived, then the compensating transmission line segments can be inserted between the alternative J and K inverters to construct the whole effective k/4 resonators. In addition, the four UIRs are embedded inside of the U-folded coupled feed lines to realize miniaturization. 2.3. Analysis on the parallel-path transmission and transmission zeros The proposed quad-band filter can be achieved readily by appropriately combining two dual-band cells based on parallelpath transmission. As shown in Fig. 7, the isolated responses of the upper path and lower path cells are presented separately. The design of the lower path cell comprising of the 2nd and 3rd passbands is independent of the upper path cell. This is because that the two inductively coupled k/4 SIRs just perform loading effect on the lower path circuit, so as that on the upper path cell. Fig. 8 shows the current distribution of quad-band BPF at four I
II
III
IV
resonant modes f 0 , f 0 , f 0 and f 0 . It can be seen that the surface currents are very strong on the two inductively coupled k/4 SIRs I
IV
when the resonators resonate at f 0 and f 0 . While the surface curII
rents are very strong on the four k/4 UIRs when they resonate at f 0 III f0 .
4 4 6 6 8
16 10 0.11k0 0.07k0
The overall physical circuit size of the quad-band BPF excluding the feeding ports is 16 mm 10 mm, or equivalent to 0.11 k0 0.07 k0 , where k0 is the free space wavelength at 1.9 GHz. The simulation and measurement are accomplished using HFSS and vector network analyzer, respectively. The photograph, simulated and measured S-parameters of the quad-band BPF over the frequency range from 1 to 7.5 GHz are plotted in Fig. 9. The minimum measured insertion losses, including the losses from two SMA connectors, are found to be 0.9, 1.2, 1.7 and 2.1 dB within the four passbands, while the return losses are above 17.1, 11.2, 10.1 and 23.5 dB, respectively. The band-to-band isolations are achieved to be 31.8, 23.1 and 25.8 dB. As expected in theory, four pairs of finite TZs at 1.48 and 2.49 GHz, 3.26 and 4.32 GHz, 4.42 and 5.32 GHz, 5.66 and 6.54 GHz are demonstrated, resulting in high selectivity. The emergence of these TZs located at each side of the four passbands introduces highly sharpened roll-off skirts for all the passbands. Slight deviation is observed, which could be attributed to fabrication tolerance in the implementation. Table 1 compares the performance of the proposed quad-band BPF with some other reported works, which shows that the presented study has realized miniaturization and improved selectivity, and the frequency locations and bandwidths of all of the passbands in this quad-band BPF can be flexibly controlled.
and These results validate the above analysis. One critical factor in the design of multi-band filter is to consider the TZs between two adjunct passbands to enhance the isolation degree. Some discussion in this aspect is given below. The dual-band BPF cell in the upper path can produce 4 TZs (TZ1– TZ4), which are introduced by the out-of-phase cancelation due to capacitive source-load cross coupling. The lower path together with the source-load cross coupling can implement 4 additional TZs (TZ5–TZ8), where TZ5 and TZ8 are primarily introduced by the opposite polarity between the mainline and cross couplings as discussed in [9]. While TZ6 and TZ7 are produced by strong inter-resonator couplings. Since the cross coupling K36 is out-ofphase with the mainline K34–J45–K56, and it is much stronger than the relatively weak coupling J45, it brings a pair of finite TZs to split the virtual wide passband, resulting in the achievement of creating a closely proximate dual passband.
In this paper, the synthesis design method of a miniaturized high-selectively quad-band BPF comprising of two distinct dualband BPF cells based on k/4 resonators with alternative J/K inverters is proposed. The k/4 SIRs are utilized to produce the 1st and 4th passbands with wide band spacing, while the four k/4 UIRs are connected and coupled to independently form the 2nd and 3rd passbands with close band proximity setting between the 1st and 4th passbands. Benefiting from the parallel-path transmission, the two different types of dual-band cell are constructed into a quadband BPF with controllable center frequencies and bandwidths for each passband. Finally, the proposed quad-band BPF is fabricated and the measured results provide good verification on the predicted frequency responses.
3. Measured results
Acknowledgments
According to the above discussion, the proposed quad-band filter is fabricated on the substrate of Rogers TMM10 with a relative dielectric constant of 9.2, substrate thickness of 1 mm and copper thickness of 0.017 mm, and loss tangent of 0.0022. The dimensions are determined as follows (all in mm): G1 = 0.5, G2 = 0.3, L1 = 4, L2 = 10.1, L3 = 1.3, L4 = 8.4, L5 = 7, L6 = 7.05, L7 = 1, L8 = 2.2, L9 = 4.8, LU = 1.6, W1 = W4 = W5 = 0.4, W2 = 0.8, W3 = 1, S1 = 0.3, S2 = 2.7.
This work is partially supported by the National Key Scientific Instrument and Equipment Development Projects (Grant No. 2013YQ200503), Natural Science Foundation of Fujian Province of China (No. 2016J05164), Natural Science Foundation of Guangdong Province of China (No. 2016A030310375), and the Fundamental Research Funds for the Central Universities (No. 20720160094).
4. Conclusion
J. Ai et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 1028–1033
References [1] Wu J-Y, Tu W-H. Design of quad-band bandpass filter with multiple transmission zeros. IET Electron Lett Apr. 2011;47(8):554–6. [2] Wu H-W, Yang R-Y. A new quad-band bandpass filter using asymmetric stepped impedance resonators. IEEE Microw Wireless Compon Lett Apr. 2011;21 (4):203–5. [3] Studniberg M, Eleftheriades GV. A quad-band bandpass filter using negativerefractive-index transmission-line (NRI-TL) metamaterials,. In: Proc. IEEE Antennas Propag. Soc. Int. Symp.. p. 4961–4. [4] Liu J-C, Wang J-W, Zeng B-H, Chang D-C. CPW-fed dual-mode double-squarering resonators for quad-band filters. IEEE Microw Wireless Compon Lett Mar. 2010;20(3):142–4.
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[5] Zhang Y, Gao L, Zhang XY. Compact quad-band bandpass filter for DCS/WLAN/ WiMAX/5G Wi-Fi application. IEEE Microw Wireless Compon Lett Oct. 2015;25 (10):645–7. [6] Zhang S-B, Zhu L. Synthesis design of dual-band bandpass filters with k/4 steppedimpedance resonators. IEEE Trans Microw Theory Tech 2013;61(5):1812–9. [7] Xu J, Wu W, Miao C. Compact and sharp skirts microstrip dual-mode dual-band bandpass filter using a single quadruple-mode resonator. IEEE Trans Microw Theory Tech Mar. 2013;61(3):1104–13. [8] Lee J, Sarabandi K. A synthesis method for dual-passband microwave filters. IEEE Trans Microw Theory Techn Jun. 2007;55(6):1163–70. [9] Hong J-S, Lancaster M. Design of highly selective microstrip bandpass filters with a single pair of attenuation poles at finite frequencies. IEEE Trans Microw Theory Tech Jul. 2000;48(7):1098–107.
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Regular Paper
Design of a high-selectivity quad-band bandpass filter based on k/4 resonators with alternative J/K inverters Jing Ai a, Yong-Hong Zhang a, Kai-Da Xu b,c,⇑, Dao-Tong Li a, Qing-Huo Liu d a
EHF Key Lab of Science, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China Institute of Electromagnetics and Acoustics & Department of Electronic Science, Xiamen University, Xiamen 361005, China c Shenzhen Research Institute of Xiamen University, Shenzhen 518057, China d Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA b
a r t i c l e
i n f o
Article history: Received 13 October 2015 Accepted 28 April 2016
Keywords: Alternative J/K inverters High selectivity Quad-band bandpass filter Quarter-wavelength resonator Synthesis design
a b s t r a c t Based on k/4 resonators, the synthesis design method for a miniaturized high-selectivity microstrip quadband bandpass filter (BPF) with alternative J/K inverters has been presented. Two dual-band k/4 stepped impedance resonators (SIRs) are employed to generate the 1st and 4th passbands, while the 2nd and 3rd passbands are achieved by utilizing four coupled k/4 uniform impedance resonators (UIRs). Moreover, the alternative J/K inverters form is proposed to create an additional cross coupling, resulting in one pair of transmission zeros (TZs) at each side of all the four passbands. To verify the validity of the proposed method, a quad-band BPF centered at 1.9, 4.1, 4.6 and 6.1 GHz with respectively fractional bandwidths of 13.7%, 5.1%, 5.9% and 7.6% has been designed and fabricated, whose measured results show consistent match with the simulated ones. Ó 2016 Elsevier GmbH. All rights reserved.
1. Introduction With the advent of modern multi-service system, it is necessary to provide stable transceiver to establish the requirement of wireless communication condition. As one of the critical building block in the multi-band transceiver, the quad-band BPFs have garnered a great deal of attention and a variety of methods have been proposed [1–5]. In [1], the stub-loaded resonators (SLRs), which can be analyzed by the odd- and even-mode technique, were used to realize a quad-band filter with three finite TZs, including the one produced by the resonator itself. In [2], the authors proposed a quad-band microstrip BPF with two sets of the asymmetric SIRs, whose TZs were generated by the mixed electric and magnetic coupling. Negative refractive-index transmission-line (NRI-TL) metamaterials were also employed to construct a quad-band BPF [3]. However, it suffers from a large area and its out-of-band rejection characteristic is not good enough. In [4], an improved CPW-fed configuration with dual mode double-square-ring resonators was also used in quad-band filter, where the TZs can be realized by tuning the slits in the branch of the twin-T CPW. Recently the multimode resonator is utilize to develop quad-band BPF, which can
reduce circuit size and fabrication complexity. A multi-stubloaded resonator was employed to produce the 1st, 2nd and 4th passband frequencies, while a short-end stub-loaded resonator was used to yield the 3rd passband, and six finite TZs were generated in order to increase the roll-off skirts of the passbands [5]. It is well known that finite TZs are of considerable importance in the filter design, which can improve out-of-band rejection performance and achieve sharp roll off skirts. To increase the number of finite TZs, a promising quad-band BPF based on k/4 resonators with alternative J/K inverters demonstrated in Fig. 1 is presented in this paper. Especially, at least one TZ has been excited in proximity of both lower and upper sides of each passband. These paired TZs are primarily introduced by the opposite polarity between the mainline and cross couplings. Compared with the filters in [1–5], the proposed work features compact size, high selectivity and controllable center frequencies and bandwidths for each passband. To verify the proposed method, a quad-band BPF with eight finite TZs is designed and fabricated. The measured results show good agreement with the predicted frequency performance.
2. Synthesis design of quad-band bandpass filter ⇑ Corresponding author at: Institute of Electromagnetics and Acoustics & Department of Electronic Science, Xiamen University, Xiamen 361005, China. E-mail address: [email protected] (K.-D. Xu). http://dx.doi.org/10.1016/j.aeue.2016.04.019 1434-8411/Ó 2016 Elsevier GmbH. All rights reserved.
The coupling topology of the proposed BPF based on k/4 resonator in the alternative J–K–J form is shown in Fig. 1(a), where the J inverters are generated by the parallel coupled microstrip
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To clarify the proposed quad-band BPF design, its design procedure is summarized as follows: Step 1: According to the required frequencies and bandwidths of the 1st and 4th passbands, we can get the reactance slope ratio of the k/4 SIRs by extracting the broadband dispersive K value of the common grounded metallic via from the full-wave simulated S parameters. Step 2: The preliminary dimensions of an uncoupled SIR are achieved by the synthesis approach of the dual-band microstrip BPF with k/4 SIRs, and the required J and K inverter values can be obtained by appropriately designing the physical dimensions. Step 3: When two of the uncoupled k/4 SIRs are inductively coupled together, an average-weighted length is needed to subtract from the normal uncoupled one to alleviate the length mismatch of the two passbands. Then, the U-shaped feed lines are utilized to offer appropriate Qe at the 4th passband by altering the length LU. Step 4: The lower path cell is formed by a split-type dual-band BPF, which could be illustrated by fully canonical split-type coupling topology. The center frequency of virtual wide passband qffiffiffiffiffiffiffiffiffiffiffiffiffiffi II III equals to f 0 f 0 , which is primarily determined by the lengths L5 and L6. Step 5: The bandwidths of the 2nd and 3rd passbands and the location of the four TZs (TZ5–TZ8) can be synthesized based on 4th-order split-type coupling matrix. Step 6: Note that the center frequencies and bandwidths will be slightly shifted when combining the upper and lower paths together. Therefore, a fine tuning is needed to get a better quadband response. Fig. 1. (a) Coupling topology for the proposed quad-band BPF. (b) k/4 SIR for the 1st and 4th passbands. (c) k/4 UIR for the 2nd and 3rd passbands.
2.1. Upper path cell: 1st and 4th passbands The 1st and 4th passbands are composed of a 2nd-order ChebyI
lines and the K inverters are implemented with the metallic vias. In the upper path, two same k/4 SIRs shown in Fig. 1(b) with inductively coupled by a hole via are introduced to form the 1st and 4th passbands, while in the lower path, four k/4 UIRs shown in Fig. 1(c) are connected and coupled to independently produce the split-type of the 2nd and 3rd passbands which are among the 1st and 4th passbands. Then, parallel-path transmission is utilized to combine the above upper and lower path cells into a quad-band BPF. The structure of the proposed BPF is demonstrated in Fig. 2. Benefiting from the parallel-path transmission coupling scheme, the upper path cell consisting of the 1st and 4th passbands and lower path cell comprising of the 2nd and 3rd passbands can be designed and adjusted independently.
IV
shev dual-band BPF centered at f 0 = 1.9 GHz and f 0 = 6.1 GHz with 20 dB in-band return loss, and the fractional bandwidths of FBWI = 13.7% and FBWIV = 7.6%, respectively. Based on the classical filter synthesis method, the inter resonator coupling K12 can be obtained as
FBWx K 12 ¼ pffiffiffiffiffiffiffiffiffiffi g1 g2
ð1Þ
where x is the resonator’s reactance slope, and g1, g2 are the normalized elements in the lowpass filter prototype. Herein, the upper path of the quad-band BPF can be considered as two k/4 SIRs coupled together with a common grounded metallic via which is implemented to serve as the dual-band K inverters. The broadband
25
30
20
25 20
15
15 10
10
5 0
Fig. 2. Structure of the proposed quad-band BPF.
5 0
1
2
3
4
5
6
7
8
0
Fig. 3. Extracted K12 and associated electrical length for the 1st/4th passbands as a function of frequency.
J. Ai et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 1028–1033
Frequency Ratio f0
/ f0
1030
dimension of the k/4 SIR, it is possible not only to possess two resonant frequencies with desired ratio, but also to achieve the reactance slopes, thereby influencing the inter resonator coupling and obtaining a dual-band response simultaneously. The reactance slope xin of the k/4 SIR is derived as
6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
xin ¼
f dX 2 df f ¼f I ;f IV 0
ð3Þ
0
Z a ha sec2 ha þ Rz hb sec2 ha sec2 hb þ R2z ha sec2 ha tan2 hb ¼ 2 ðRz tan hb þ tan ha Þ2
where Rz is the impedance ratio of the k/4 SIR, which is defined as Rz ¼ Z a =Z b , ha and hb are the electrical lengths with the frequency I
Fig. 4. Frequency ratio parameters.
IV I f 0 =f 0
f 0 . Therefore, the preliminary dimensions of an uncoupled SIR in Fig. 1(b) can be determined as: Wa = 0.3 mm, La = 3.5 mm, Wb = 1 mm, Lb = 10.8 mm. Two associated electrical lengths at the central frequencies of 1.9 GHz and 6.1 GHz are respectively 7.6°and 21.7°, which are equal to physical lengths of 1.34 mm and 1.19 mm, respectively. To alleviate the length mismatch of the two passbands, an average-weighted length of 1.22 mm is subtracted from La in the uncoupled k/4 SIR when two of them are inductively coupled together.
versus length ratio and impedance ratio as
dispersive K value and its associated electrical length can be extracted or de-embedded from the full-wave simulated S parameters as shown in Fig. 3. Since the K12 is utilized by a metallic via, its coupling strength increases monotonically with the frequency, K I12 = 5.4 and K IV 12 = 15.6 at the frequency of 1.9 and 6.1 GHz, respectively, and the required x reactance slope ratio of the k/4 SIRs can be derived as
xIV FBW I K IV 13:7% 15:6 12 ¼ 5:21 ¼ ¼ I 7:6% 5:4 x FBW IV K I12
IV
ð2Þ
With the center frequency ratio of 3.21 (6.1/1.9) and the reactance slope ratio of 5.21, the dimension of k/4 SIR can be rigorously derived to meet the specified K12 couplings at the 1st and 4th passbands based on the synthesis approach for the dual-band microstrip BPF with k/4 SIRs [6]. By appropriately determining the
6.5
fTP4
5
Frequency (GHz)
Frequency (GHz)
7 6 fTP3 fTP2 2 fTP1 1
7
8
9 10 L2 (mm)
11
12
fTP4
6.0 fTP3
5.5 fTP2 2.0 1.5
fTP1 0.15 0.20 0.25 0.30 0.35 0.40 0.45 L1 / (L1+L2)
(a)
(b)
160
0.20
120
0.16 0.12
80
M
Qe
I
Fig. 4 shows the relationship between the frequency ratio f 0 =f 0 and the impedance ratio Rz ¼ Z a =Z b , the length ratio ha =ðha þ hb Þ. Note that the frequency ratio can vary from 2.12 to 6.46 theoretically (i.e. when ha =ðha þ hb Þ ¼ 0:5, 0.4 < Rz < 5). It can be seen that the 1st and 4th passbands can be designed with wide band spacing by controlling the impedance ratio and length ratio of the k/4 SIRs. Because of the wide stopband spacing between these two passbands, it creates the condition that we can embed a dual-band filtering cell centered at different frequencies into the wide spacing thereby forming a quad-band BPF finally. Fig. 5(a) and (b) plot the extracted resonant frequencies of the k/4 SIR with varied L2 and L1/(L1 + L2), respectively. It can be seen
Qe Qe
40
0.08 0.04
0
0.0
0.5
1.0 1.5 LU (mm)
(c)
2.0
2.5
0.8
1.2
1.6 L3 (mm)
2.0
2.4
(d)
Fig. 5. Extracted resonant frequencies with varied (a) L2 and (b) L1/(L1 + L2); (c) extracted Qe with varied LU; and (d) extracted M with varied L3 in the upper path BPF cell.
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that when L1/(L1 + L2) is changed, fTP3 and fTP4 can be adjusted greatly while fTP1 and fTP2 vary slightly. Thus, the frequencies of the 1st and 4th passbands can be controlled individually. For the bandwidths, they depend on the external quality factors Qe and coupling coefficients M. Fig. 5(c) and (d) show the variation of extracted Qe and M against different values of LU and L3, respectively. When the height of the U-folded shape LU is changed, the external coupling factor Q Ie for the 1st passband almost keeps the same, while the external coupling factor Q IV e for the 4th passband varies obviously. While for the coupling coefficients, M I and M IV are relevant with varying L3 as demonstrated in Fig. 5(d). Therefore, a non-uniform feed line with U-folded shape can be utilized to offer the external couplings at the 4th passband [7]. Furthermore, a small open-end coupled line section with length of 0.8 mm and coupling space of 0.2 mm is utilized to enhance the source-load cross coupling and introduce one pair of TZs at each side of all the four passbands.
Fig. 7. EM simulated isolated response of |S21| for the upper and lower paths filter, as well as the whole response of quad-band BPF.
2.2. Lower path cell: 2nd and 3rd passbands As shown in Fig. 2, four UIRs in the lower path with the width of 0.4 mm are utilized to design the 2nd and 3rd passbands. The synthesis design method for dual-band microwave filters with required passbands and attenuation at stopbands directly using frequency transformation was proposed in [8], which could be illustrated by fully canonical coupling matrix shown in Fig. 6(a) with four TZs at X = 3.75, 0.02, 0.47, 3.35, possessing 20 dB return losses for both passbands. The center frequency of virtual II
(b)
(c)
(d)
III 1=2
wide passband equals to ðf 0 f 0 Þ = 4.33 GHz, and fractional bandwidth FBW = 20%. By adjusting the inter coupling strength between the k/4 resonators, a pair of finite TZs initially located at the outside of the 4th-order quadruplet filter are shifted into the center of the single passband, therefore the quadruplet BPF can be modified into a split-type dual-band BPF. Furthermore, Fig. 6 (b) and (c) plot the variation of Q e and M against different values of G2 and S2. As G2 increases from 0.2 mm to 0.6 mm, the variation Q ΙΙΙ e
QIIe
(a)
III
is very apparent but is relatively weak, and M can be of separately modified by tuning S2, thus the bandwidth of 2nd and 3rd passbands can be controlled individually.
I
II
III
IV
Fig. 8. Surface current distribution at (a) f 0 , (b) f 0 , (c) f 0 and (d) f 0 .
0
3 4 5 6 L
0.9561 0 0 0 0.1067
3 0.9561
4 0
5 0
6 0
0.2269 -0.9014 0 -1.1350 -0.9014 -0.2549 0.0057 0 0 0.0057 -0.2549 -0.9014 -1.1350 0 -0.9014 0.2269 0 0 0 0.9561
L 0.1067
-10
|S21| & |S11| (dB)
S
S 0
0 0 0 0.9561 0
(a)
Qe
M
Qe
-40 -50 -60
Simulation Measurement
2
3
4
5
6
7
Frequency (GHz)
0.12
Qe
-30
1
0.16
80
-20
-70
120
|S11|
|S21|
Fig. 9. Photograph, simulated and measured results of the quad-band BPF.
0.08
40
0.04 0
0.2
0.3
0.4 0.5 G2 (mm)
(b)
0.6
0.0
0.2
0.4 0.6 S2 (mm)
0.8
1.0
(c)
Fig. 6. (a) Coupling matrix, (b) extracted Qe with varied G2, (c) extracted M with varied S2 in the lower path BPF cell.
As shown in Fig. 2, the parallel coupled microstrip lines with length of L9 and gap of G2 are employed to form the JS3, JL6 inverters. The metallic vias with the diameter of 0.6 mm are used to implement the K34, K56 inverters. The J45 inverter is generated by the two anti-parallel coupled k/4 UIRs with length of 1.0 mm, and the cross coupling K36 inverter is implemented by the inductive coupling between two closely arranged grounded-end of k/4 UIRs.
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Table 1 Comparison with reported quad-band BPFs. References
Passbands (GHz)
IL (insertion loss) (dB)
Fractional bandwidth (%)
Number of TZs
Circuit size (mm mm) (k0 k0)
[1]
1.5/2.5/ 3.6/4.6 2.4/3.5/ 5.2/6.8 0.87/1.06/ 1.78/2 0.95/1.26/ 1.89/2.29 1.8/2.45/ 3.5/5.5
1.98/1.74/ 3.58/3.4 0.5/1.3/ 1.3/1 0.94/1.1/ 0.73/1.8 2.18/2.09/ 1.40/0.93 1.5/1.7/ 2.3/1.8
5.5%/12%/ 11%/4.3% 6.4%/9.4%/ 3.8%/4.9% 2.8%/2.8%/ 3.9%/6.5% 6.7%/5.1%/ 12%/15.3% 6.7%/4.1%/ 2.9%/14.8%
3
32 32 0.16k0 0.16k0 22 22 0.20k0 0.20k0 55 21 0.16k0 0.07k0 55 55 0.17k0 0.17k0 19.8 15.8 0.12k0 0.10k0
1.9/4.1/ 4.6/6.1
0.97/1.28/ 1.78/2.16
13.7%/5%/ 5.9%/7.6%
[2] [3] [4] [5] This paper
Based on the analysis in [6], the physical dimensions of all the J and K inverters and their associated electrical lengths can be analytically derived, then the compensating transmission line segments can be inserted between the alternative J and K inverters to construct the whole effective k/4 resonators. In addition, the four UIRs are embedded inside of the U-folded coupled feed lines to realize miniaturization. 2.3. Analysis on the parallel-path transmission and transmission zeros The proposed quad-band filter can be achieved readily by appropriately combining two dual-band cells based on parallelpath transmission. As shown in Fig. 7, the isolated responses of the upper path and lower path cells are presented separately. The design of the lower path cell comprising of the 2nd and 3rd passbands is independent of the upper path cell. This is because that the two inductively coupled k/4 SIRs just perform loading effect on the lower path circuit, so as that on the upper path cell. Fig. 8 shows the current distribution of quad-band BPF at four I
II
III
IV
resonant modes f 0 , f 0 , f 0 and f 0 . It can be seen that the surface currents are very strong on the two inductively coupled k/4 SIRs I
IV
when the resonators resonate at f 0 and f 0 . While the surface curII
rents are very strong on the four k/4 UIRs when they resonate at f 0 III f0 .
4 4 6 6 8
16 10 0.11k0 0.07k0
The overall physical circuit size of the quad-band BPF excluding the feeding ports is 16 mm 10 mm, or equivalent to 0.11 k0 0.07 k0 , where k0 is the free space wavelength at 1.9 GHz. The simulation and measurement are accomplished using HFSS and vector network analyzer, respectively. The photograph, simulated and measured S-parameters of the quad-band BPF over the frequency range from 1 to 7.5 GHz are plotted in Fig. 9. The minimum measured insertion losses, including the losses from two SMA connectors, are found to be 0.9, 1.2, 1.7 and 2.1 dB within the four passbands, while the return losses are above 17.1, 11.2, 10.1 and 23.5 dB, respectively. The band-to-band isolations are achieved to be 31.8, 23.1 and 25.8 dB. As expected in theory, four pairs of finite TZs at 1.48 and 2.49 GHz, 3.26 and 4.32 GHz, 4.42 and 5.32 GHz, 5.66 and 6.54 GHz are demonstrated, resulting in high selectivity. The emergence of these TZs located at each side of the four passbands introduces highly sharpened roll-off skirts for all the passbands. Slight deviation is observed, which could be attributed to fabrication tolerance in the implementation. Table 1 compares the performance of the proposed quad-band BPF with some other reported works, which shows that the presented study has realized miniaturization and improved selectivity, and the frequency locations and bandwidths of all of the passbands in this quad-band BPF can be flexibly controlled.
and These results validate the above analysis. One critical factor in the design of multi-band filter is to consider the TZs between two adjunct passbands to enhance the isolation degree. Some discussion in this aspect is given below. The dual-band BPF cell in the upper path can produce 4 TZs (TZ1– TZ4), which are introduced by the out-of-phase cancelation due to capacitive source-load cross coupling. The lower path together with the source-load cross coupling can implement 4 additional TZs (TZ5–TZ8), where TZ5 and TZ8 are primarily introduced by the opposite polarity between the mainline and cross couplings as discussed in [9]. While TZ6 and TZ7 are produced by strong inter-resonator couplings. Since the cross coupling K36 is out-ofphase with the mainline K34–J45–K56, and it is much stronger than the relatively weak coupling J45, it brings a pair of finite TZs to split the virtual wide passband, resulting in the achievement of creating a closely proximate dual passband.
In this paper, the synthesis design method of a miniaturized high-selectively quad-band BPF comprising of two distinct dualband BPF cells based on k/4 resonators with alternative J/K inverters is proposed. The k/4 SIRs are utilized to produce the 1st and 4th passbands with wide band spacing, while the four k/4 UIRs are connected and coupled to independently form the 2nd and 3rd passbands with close band proximity setting between the 1st and 4th passbands. Benefiting from the parallel-path transmission, the two different types of dual-band cell are constructed into a quadband BPF with controllable center frequencies and bandwidths for each passband. Finally, the proposed quad-band BPF is fabricated and the measured results provide good verification on the predicted frequency responses.
3. Measured results
Acknowledgments
According to the above discussion, the proposed quad-band filter is fabricated on the substrate of Rogers TMM10 with a relative dielectric constant of 9.2, substrate thickness of 1 mm and copper thickness of 0.017 mm, and loss tangent of 0.0022. The dimensions are determined as follows (all in mm): G1 = 0.5, G2 = 0.3, L1 = 4, L2 = 10.1, L3 = 1.3, L4 = 8.4, L5 = 7, L6 = 7.05, L7 = 1, L8 = 2.2, L9 = 4.8, LU = 1.6, W1 = W4 = W5 = 0.4, W2 = 0.8, W3 = 1, S1 = 0.3, S2 = 2.7.
This work is partially supported by the National Key Scientific Instrument and Equipment Development Projects (Grant No. 2013YQ200503), Natural Science Foundation of Fujian Province of China (No. 2016J05164), Natural Science Foundation of Guangdong Province of China (No. 2016A030310375), and the Fundamental Research Funds for the Central Universities (No. 20720160094).
4. Conclusion
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