Chapter 4 Two-mode Dual-band Filter Design Using E-shaped Resonators
4.4 Examples for Practical Filter Implementation
4.4.2 Example 2: Sixth-order Two-mode Dual-band Bandpass Filter
To validate the ability of the proposed method for high order two-mode dual-band filter, here a sixth-order two-mode dual-band filter is used. The performance of the sixth-order two-mode dual-band bandpass filter is also determined by the analytical coupling matrix synthesis procedure in Chapter 2. The relative error can be obtained by the lines with square symbol in Figure 4-11. In this example, we choose Δodd/Δeven = 1.3 and fo
= 0.79fe, so that the relative error is within 0% ~ -7%. Here we choose fo = 1.79 GHz and fe
= 2.265 GHz. The settings for the synthesis procedure are as follows: The first passband central frequency is firstly shifted from 0 to -0.738 rad/s and the multi-band lowpass domain bandwidth is 0.515 rad/s in the lowpass domain. Similarly, the second passband central frequency is shifted from 0 to 0.797 rad/s and the multi-band lowpass domain bandwidth is 0.396 rad/s in the lowpass domain. Both filters are the third-order filters with return loss of 15 dB. After parallel addition of two filtering functions, the lowpass domain response of the dual-band filter is shown in Figure 4-26 and the coupling scheme is shown in Figure 4-9 (c). The corresponding coupling matrix is listed in Table 4.6. The six-pole dual-band filter is then transformed to the bandpass domain with the central frequency of 2GHz and bandwidth of 30%.
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Figure 4-26 The lowpass response and the coupling scheme for example 2.
Table 4.6 The Coupling Matrix for Dual-band Filter in Example 2
Before applying the proposed method to analyze the sixth-order two-mode dual-band filter, the circuit layout used in this example is circuit A in Figure 4-27. First phase is to determine the values of J inverter. The coupling path of odd-mode analysis is S-1o-2o-3o-L of the coupling scheme in Figure 4-9 (c). The initial E1, E3, and E4 are 60o, and E2 and E5
are 30o. Hence the values of J inverters can be calculated by (3-6), (3-7), and (4-1) with MS,1o, M1o
,2o, M2o
,3o, and M3o
,L, and the calculated Zoe and Zoo are listed in Table 4.7. After determining the Zoe and Zoo, the second phase is to do the even-mode analysis. The central
LOWPASS PROTOTYPE FREQUENCY (rad/sec)
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frequencies of these two passbands are 1.79 and 2.265 GHz, such that the ZS,6 is 15 Ω, E6
is 53.5750o based on MS,1e, ZS,7 is 29.3353 Ω, E7 is 59.3250o based on M2e
,3e, and ZS,8 is 15 Ω, E8 is 53.5750o based on M3e
,L by (4-3) and (4-4). The performance can be improved due to the asynchronously tuned property. By slightly tuning the lengths, E1 is 59o, E2 is 31o, E3
is 58.5o, E4 is 61.5o, E5 is 30.5o, E6 is 53.5o, E7 is 71o, and E8 is 52.5o. The response of the synthesized circuit is illustrated in Figure 4-28. As we mention previously, the circuit A and circuit B in Figure 4-15 will have 180 degree out-of-phase. To validate the separation enhancement, the performances of circuit A and B in Figure 4-27 are analyzing without changing values of design parameters and they are presented in Figure 4-29. The S11 are similar, but the rejection between two passbands is better in the circuit A than that in the circuit B.
Figure 4-27 The circuit schematic of two-mode dual-band filter in example 2.
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Table 4.7 The Calculated Impedances for the Odd-mode Analysis in Example 2.
MS,1o M1o
,2o M2o
,3o M3o
,L
J 0.0066 0.0011 0.0021 0.0066
Zoe 77.1181 56.7306 56.8866 77.1181
Zoo 37.7917 44.4001 44.6139 37.7917
Figure 4-28 The performance of the synthesized circuit in example 2.
Figure 4-29 The performance of circuit A and circuit B in example 2.
For the microstrip implementation, the final layout is shown in Figure 4-30 and the Frequency (GHz)
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circuit photograph is shown in Figure 4-31 with dimensions listed in Table 4.8. The measured and simulated results are shown in Figure 4-32.
Figure 4-30 The layout of the two-mode dual-band filter in example 2.
Figure 4-31 The circuit photograph of the two-mode dual-band filter in example 2.
Table 4.8 The Dimensions in Figure 4-31 (Unit: mm)
WS W1 W2 W3 W4 W5 W6 W7
0.575 0.200 0.575 0.575 0.550 0.575 0.2 3.375
W8 W9 LS L1 L2 L3 L4 L5
1.700 4.225 2.500 11.000 8.475 6.650 7.950 6.650
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L6 L7 L8 L9 L10 L11 S1 S3
9.250 7.600 9.550 6.500 6.675 7.950 0.200 1.000
S4 S6
0.500 0.200
Figure 4-32 Measured and simulated performances and group delay of the two-mode dual-band filter in example 2.
4.5 Conclusion
The novel analytical approach has been presented to design two-mode dual-band filters. Two examples with different filter orders have been implemented to show the feasibility of the method. By using these configurations and requested coupling matrices, even- and odd-mode analysis of E-shaped resonators have been used to determine the circuit parameters. Back-to-back E-shaped resonators have been analyzed to show the out-of-phase property by coupling at the specific edge. This out-of-phase property is used to enhance the filter selectivity. The transmission zeros are implemented to achieve the sharp rollpff. With the coupling-matrix-based synthesis of two-mode dual-band filter
Frequency (GHz)
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design, the compact size, flexible responses, good performances and quick design procedure are achieved.
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Chapter 5
Two-mode Tri-band and Quad-band Filter Design with Close Adjacent Passbands Using E-shaped Resonators
5.1 Introduction
Dual-path topology has been validated for the convenient coupling scheme for dual-band filter design in the microstrip implementation. Based on the idea, that is one path governs one passband, the tri-path and quad-path topologies here are proposed for the tri-band and quad-band filters design. The filter consisted of the parallel-coupled lines discussed in Chapter 3 will be limited in tri-band and quad-band filter design by its spatial limitation, that is, the coupling between adjacent paths will ruin the filter performance due to the close distance. Moreover, the size of such kind of filters is large.
The two-mode E-shpaed resonator proposed in Chapter 4 has been proposed to used in dual-band filter design with small size and is valid in microstrip implementation.
Furthermore, the dual-band coupling scheme has been demonstrated the validation in illustrating the coupling effects in this two-mode dual-band filter. Due to these properties, in this chapter the E-shaped resonators are proposed to be applied in tri-band and quad-band filter design using the tri-path and quad-path topologies.
Based on the analysis in Chapter 4, the design parameters can be extracted analytically. Moreover, by grouping two adjacent passbands, the tri-band and quad-band performances are then divided into two groups in each design. In each group, the filter with dual-band performance can be synthesized analytically using E-shaped resonator. Finally, to combine these two synthesized filter, double diplexing configuration is used with some
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fine tunes, and then the tri-band and quad-band filter can be obtained.
5.2 Double Diplexing Configuration
The double diplexing configuration for dual-band filter design is shown in Figure 3-15. To apply the configuration for the tri-band and quad-band filter, Figure 5-1 shows the schematic. The design equation will be modified as follows:
[ ]
( )[ ]
( )3 4
1 2
1 ,
2 ,
Im 0,
Im 0.
f f f f f f
Y Y
∈
∈
=
= (5-1)
The above equation needs to be satisfied within an interval of frequencies, such that the configuration has bandwidth limitation in each path. Hence the passbands in each path should be close enough to each other. Moreover, in order to cover the dual-band bandwidth in each path, three transmission lines with characteristic impedance ZA, ZB, and ZC and electrical length θA, θB, and θC are used as variables to meet the specifications.
Figure 5-1 Double diplexing configuration for tri-band and quad-band filter design.
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5.3 Tri-band and Quad-band Filter Synthesis
To take the quad-band filter as example, the quad-band coupling matrix is firstly synthesized. Next, grouping it as two dual-band filters from the frequency domains and synthesize each dual-band filter with the filter topology shown in Figure 5-2. Finally, the double-diplexing configuration is applied to connect two dual-band filters to form the quad-band filter. For the tri-band filter, substitute one of the dual-band filters to be a single-band filter by changing E-shape two-mode resonators to hair-pin single-mode resonators. For the practical implementation, a 0.635-mm-thich Rogers RT/Duroid 6010 substrate, with a relative dielectric constant 10.2 and a loss tangent of 0.0021.
Figure 5-2. Proposed unit cell for the two-mode dual-band filter.
5.3.1 Example 1: Tri-band Filter
In the tri-band filter design, the tri-band coupling matrix is synthesized using the IN
OUT ZS,4 ZS,5
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proposed multi-band coupling matrix synthesis. The settings are shown in Table 5.1, and coupling matrix is shown in Table 5.2 with corresponding coupling scheme shown in Figure 5-3. For the bandpass filter design, the central frequency is 1.92 GHz and fractional bandwidth is 56.2%, the performance of the coupling matrix is shown in Figure 5-4.
Table 5.1 Setting of Tri-band Coupling Matrix Synthesis Passband fc
(rad/s) δ RL
(dB)
Circuit Performances
fc (GHz) RL (dB) Bandwidth
-0.825 0.35 15 1.523 16 9.77%
0 0.3 15 1.935 19.5 9.11%
0.825 0.35 15 2.417 16 9.81%
Table 5.2 Coupling Matrix of the Tri-band Filter
Figure 5-3 The coupling scheme of the tri-band filter in example 1.
S 1 2 3 4 5 6 L
S 0.0 0.4430 0.0 0.3796 0.0 0.4435 0.0 0.0 1 0.4430 0.8807 0.2211 0.0 0.0 0.0 0.0 0.0 2 0.0 0.2211 0.8807 0.0 0.0 0.0 0.0 -0.4430
3 0.3796 0.0 0.0 0.0 0.1866 0.0 0.0 0.0
4 0.0 0.0 0.0 0.1866 0.0 0.0 0.0 0.3796
5 0.4435 0.0 0.0 0.0 0.0 -0.8806 0.2215 0.0 6 0.0 0.0 0.0 0.0 0.0 0.2115 -0.8806 -0.4435 L 0.0 0.0 -0.4430 0.0 0.3796 0.0 -0.4435 0.0
S L
1 2
5
Source/Load Resonator
3 4
6
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Figure 5-4 Performances of the coupling matrix and synthesized circuit in example 1.
The central frequencies of three passbands are 1.533, 1.92, and 2.417 GHz, and their return losses are 15.01, 19.33 and 15 dB, with individual bandwidth 9.21%, 8.37% and 9.63%. To implement this filter, the two-mode dual-band filter is used to govern the first two passbands (i.e., the resonators numbered #1, #2, #3, and #4) and a single bandpass filter (i.e., resonators numbered #5 and #6) is used to govern the third passband. The synthesized variables are listed in Table 5.3 and Table 5.4. To connect these two filters, the double-diplexing configuration is design at 1.92 GHz with ZA, ZB, and ZC are 39 Ω, 41 Ω, and 72 Ω, and EA, EB, and EC are 96o, 96o, and 136o. The synthesized filter performance is also shown in Figure 5-4.
Table 5.3 Synthesized Zoe and Zoo Based on Coupling Matrix in Table 5.2
MS,1 M1,2 M2,L MS,5 M5,6 M6,L
Zoe (Ω) 88.95 63.16 88.95 88.95 63.16 88.95
Zoo (Ω) 36.79 40.56 36.79 36.79 40.56 36.79
Frequency (GHz)
1.0 1.5 2.0 2.5 3.0
|S11|,|S21| (dB) -50 -40 -30 -20 -10 0
Coupling Matrix Circuit
S L
1 2
5 Source/Load Resonator
3 4
6
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Table 5.4 Synthesized Electrical Lengths and Stub Impedances Based on Coupling Matrix in Table 5.2
Passband #1 & #2 fo = 1.533 GHz, fe = 1.92 GHz
Design Variable ZS,4 (Ω) ZS,5 (Ω) E1 E2 E3 E4 E5
Synthesized 12.877 12.877 60o 60o 30o 47.09o 47.09o
Fine tuned 13 13 58o 58o 33o 47o 47o
Passband # 3 fo = 2.417 GHz
Design Variable E1 E2 E3
Synthesized 60o 60o 30o Fine tuned 60o 60o 28o
For microstrip implementation, the layout is shown in Figure 5-5 with dimensions listed in Table 5.5, and the circuit photograph is shown in Figure 5-6. Figure 5-7 shows the simulated and measured results.
Figure 5-5 The layout of the tri-band filter.
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Table 5.5 Dimensions of the Tri-band Filter (Unit: mm)
WS LS Wfeed Lfeed Wu LU1 L6_2 LU2
Figure 5-6 The circuit photograph of the tri-band filter in example 1.
Figure 5-7 The simulated and measured results of the tri-band filter.
Frequency (GHz)
119
5.3.2 Example 2: Quad-band Filter
In the quad-band filter design, the quad-band coupling matrix synthesized using the proposed method in Chapter 2. The settings are shown in Table 5.6, and corresponding coupling matrix is shown in Table 5.7 with corresponding coupling matrix shown in Figure 5-8. The synthesized values of M4,L, ML,4, M8,L, and ML,8, are all positive based on the settings in Table 5.6. In order to generate two transmission zeros between passband #1 and
#2 and passband #3 and #4, these four components of the coupling matrix should be set to be negative, as shown in Table 5.7.
Table 5.6 Setting of Quad-band Coupling Matrix Synthesis.
Passband fc
(rad/s) δ Circuit Performances
fc (GHz) RL (dB) Bandwidth
-0.8990 0.2 1.286 14.86 6.97%
-0.2929 0.1 1.663 20.47 4.27%
0.2929 0.17 2.176 16.97 6.49%
0.8990 0.12 2.809 15.88 5.02%
*# of poles = 2, # of zeros = 0 & RL = 13 dB in each passband
Table 5.7 Coupling Matrix of the Quad-band Filter in Example 2.
S 1 2 3 4 5 6 7 8 L
S 0.0 0.3143 0.0 0.2700 0.0 0.3056 0.0 0.2791 0.0 0.0
1 0.3143 0.9240 0.1142 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 0.0 0.1142 0.9240 0.0 0.0 0.0 0.0 0.0 0.0 0.3143
3 0.2700 0.0 0.0 0.2975 0.0853 0.0 0.0 0.0 0.0 0.0
4 0.0 0.0 0.0 0.0853 0.2975 0.0 0.0 0.0 0.0 -0.2700
5 0.3056 0.0 0.0 0.0 0.0 -0.3208 0.1106 0.0 0.0 0.0
6 0.0 0.0 0.0 0.0 0.0 0.1106 -0.3208 0.0 0.0 0.3056
7 0.2791 0.0 0.0 0.0 0.0 0.0 0.0 -0.9411 0.0881 0.0
8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0881 -0.9411 -0.2791
L 0.0 0.0 0.3143 0.0 -0.2700 0.0 0.3056 0.0 -0.2791 0.0
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Figure 5-8. The coupling scheme for the quad-band filter in example 2.
For the bandpass filter design, the central frequency is 1.9 GHz and fractional bandwidth is 87.4%, the performance is shown in Figure 5-9, and the synthesized central frequencies, return loss and fractional bandwidth are shown in Table 5.6. To implement this filter, one two-mode dual-band filter is used to govern the first two passbands, while the other one is used to govern the third and fourth passbands. The synthesized variables are listed in Table 5.8 and Table 5.9. To connect these two filters, the double-diplexing configuration is designed at 2 GHz with ZA, ZB, and ZC are 43 Ω, 54 Ω, and 52 Ω, and EA, EB, and EC are 99o, 40o, and 125o. The circuit performance is shown in Figure 5-9.
Figure 5-9 Performances of the coupling matrix and synthesized circuit.
S L
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Table 5.8 Synthesized Zoe and Zoo Based on Coupling Matrix in Table 5.7.
MS,1 M1,2 M2,L MS,5 M5,6 M6,L
Zoe (Ω) 81.74 60.47 81.74 80.53 60.10 80.53
Zoo (Ω) 37.20 42.02 37.20 37.33 42.25 37.33
Table 5.9 Synthesized Electrical Lengths and Stub Impedances Based on Coupling Matrix in Table 5.7
Passband #1 & #2 fo = 1.286 GHz, fe = 1.663 GHz
Design Variable ZS,4 (Ω) ZS,5 (Ω) E1 E2 E3 E4 E5
Synthesized 20.78 20.78 60o 60o 30o 59.17o 59.17o
Fine tuned 17 17 62o 62o 30o 51o 51o
Passband # 3 fo = 2.176 GHz, fe = 2.809 GHz
Design Variable ZS,4 (Ω) ZS,5 (Ω) E1 E2 E3 E4 E5
Synthesized 10.94 10.94 60o 60o 30o 41.70o 41.70o
Fine tuned 12 12 60o 60o 28o 49o 49o
Figure 5-10 The layout of the quad-band filter
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For the microstrip implementation, the layout is shown in Figure 5-10 with dimensions listed in Table 5.10. The circuit photograph is shown in Figure 5-11, and the simulated and measured results are shown in Figure 5-12
Table 5.10 Dimensions of the Quad-band Filter (Unit: mm)
WS LS Wfeed Lfeed Wu LU1 W1Z LU2
0.58 5.00 0.93 16.13 0.28 10.55 5.50 14.03
LU3 LU4 WD LD1 LD2 L1Z LD3 W1
4.68 19.88 0.70 7.40 3.75 5.18 3.75 0.45
S1 L1_1 L1_2 WZ W2Z W2 S2 L2
0.20 8.10 7.68 0.58 2.43 0.43 0.68 2.50
W3 S3 L3_1 L3_2 L2Z W4 S4 L4_1
0.45 0.20 8.38 7.60 10.40 0.38 0.23 15.03
L4_2 W5 S5 L5 W6 S6 L6_1 L6_2
13.15 0.73 0.70 7.03 0.38 0.23 14.98 13.18
Figure 5-11 The circuit photograph of the quad-band filter in example2.
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Figure 5-12 The simulated and measured results of the quad-band filter.
5.4 Conclusion
A coupled-matrix based semi-analytic procedure, i.e., analytic synthesis for the two-mode dual-band filters and then connecting them together by the double-diplexing configuration with slight tuning, for tri-band and quad-band filter design has been provided.
For tri-band and quad-band filter, two examples with tri-band and quad-band filters are shown to validate the procedure and the measured results show the good agreement with the simulated performances. The proposed procedure in tri-band and quad-band filter design has shown the properties of good performance, semi-analytic synthesized method and quick design procedure.
Frequency (GHz)
1.2 1.6 2.0 2.4 2.8 3.2
|S11|,|S21| (dB) -60 -50 -40 -30 -20 -10 0
Measurement Simulation
Frequency (GHz) 1.0 1.5 2.0 2.5 3.0
Group Delay (ns)
0 2 4 6
1.0 1.5 2.0 2.5 3.0 -6
-4 -2 0
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Chapter 6
Conclusion and Future Work
6.1 Conclusion
This dissertation describes a design flow for the dual-band, tri-band and quad-band filter. Based on the specifications, the corresponding coupling matrix of the requested filter is synthesized. For the aspect of the filter realization, the multi-path coupling scheme is analyzed and validated for its convenient in multi-band filter design. The analytical filter synthesis procedures, which are based on parallel-coupled line or two-mode E-shaped resonator, are then applied to extract the design parameters based on the corresponding coupling matrix with the multi-path topology. The measured results show the well agreement with the simulated responses.
In chapter 2, a novel multi-band coupling matrix synthesis for multi-band filter design is developed. Based on the well-known single-band coupling matrix synthesis, the extracted polynomials are then shifted to the specific central frequencies and shrank to the specific bandwidths. After parallel addition, the multi-band filtering function and corresponding polynomials can be obtained. Moreover, the prescribed transmission zeros can be placed to the specific locations once the transmission zeros in each passband are assigned carefully.
In chapter 3, the single-path and dual-path coupling schemes for the dual-band filter design are analyzed. The dual-path coupling scheme has been validated to be convenient in dual-band filter design, Cross-coupling paths are designed in each passband in order to generate the specific transmission zeros. Tri-section coupling topology is used to generate
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one transmission zero above or below the corresponding central frequency in one passband, while the quadruplet coupling scheme is used to generate two transmission zeros above and below the corresponding central frequency. Moreover, the dual-path coupling topology provides an intrinsic transmission zero, which can improve the isolation between adjacent passbands.
The dual-band filters with two-mode E-shaped resonators are analyzed and designed based on the dual-path coupling schemes. The detail derivations of the analytical synthesized procedure are described in chapter4. The 180-degree out-of-phase property also shows its advantage in the isolation improvement between two adjacent passbands.
The limitation in back-to-back E-shaped resonators has also been discussed and find out the feasible design based on the specific coupling scheme.
In the chapter 5, the tri-band and quad-band filter designs are realized based on the E-shaped resonator and double-diplexing configuration. By grouping the tri-band or quad-band into two categories, one is a dual-band characteristic, and the other is a single-band characteristic for the tri-band filter design or a dual-band characteristic for the quad-band filter design. And then, the double diplexing configuration is used to connect the two filters in these two categories.
6.2 Future Work
In this dissertation, the double-diplexing configuration is widely used, but there is no analytical approach to determine the design parameters. Such an approach can be studied in the future to make the whole design more efficient. Moreover, based on the synthesized multi-band coupling matrix, some specific coupling scheme can be studied for its property in transmission zeros generation for the multi-band filter design. Moreover, some specific
126
two-mode resonators can be analyzed based on the coupling matrix and provide a systematic guide line in multi-band filter design. To use the diagnosis technique [143] to fine-tuning the EM performance of dual-band and multi-band filter, a automatic tuning can be achieved via Matlab-EM co-simulation.
To make the multi-band design flow more easy and convenient, a user-interface can be developed in Matlab. Users can enter the specifications, such as number of passband, filter order, return loss, and transmission zeros in each passband, and then they can describe the user-specific coupling scheme, and then the corresponding coupling matrix will be extracted. Moreover, while choose the prescribed layout, the initial design parameters can be obtained and then be optimized by the Matlab-EM co-simulation solver.
Thus, if we can complete all above steps, the requested layout will then be generated automatically. It will provide filter designers a fast and efficient design procedure.
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References
[1] J. W. Baik, L, Zhu, Y. S. Kim, “Dual-mode dual-band bandpass filter using balun structure for single substrate configuration,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 11, pp. 613-615, Nov. 2010.
[2] E. E. Djoumessi and K. Wu, “Multilayer dual-mode dual-bandpass filter,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 1, pp. 21-23, Jan. 2009.
[3] F. C. Chen and Q. X. Chu, “Novel multistub loaded resonator and its application to high-order dual-band filters,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 6, pp.
1551–1556, Dec. 2010.
[4] X. H. Wu, Q. X. Chi, and L. Fan, “Compact dual-band bandpass filter with controllable bandwidths,” in International Conference on Microwave and Millimeter Wave Technology, Chengdu, China, May 2010, pp. 1305–1307.
[5] S. Lee and Y. Lee, “A uniform coupled-line dual-band filter with different bandwidths,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 10, pp. 545-547, Oct.
2010.
[6] S. Lee and Y. Lee, “A planar dual-band filter based on reduced-length parallel coupled lines,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 1, pp. 16-18, Jan.
2010.
[7] C. X. Zhou, Y. X. Guo, S. L. Yan, and Z. L. Wang, “Dual-band UWB filter with LTCC technology,” Electron. Lett., vol. 47, no. 22, pp. 1230-1232, Oct. 2011.
[8] X. Y. Zhang, C. H. Chan, Q. Xue, and B. J. Hu, “Dual-band bandpass filter with controllable bandwidths using two coupling paths,” IEEE Microw. Wireless Compon.
Lett., vol. 20, no. 11, pp. 616-618, Nov. 2010.
[9] L. Wang, C. Zhao, C. Li, and X. Lin, “Dual-band bandpass filter using stub loaded resonators with multiple transmission zeros,” in 9th International Symposium on Antennas Propagation and EM Theory, Guangzhou, China, Nov. 2010, pp.
1208–1211.
[10] H. W. Deng, Y. J. Zhao, X. S. Zhang, W. Chen, and J. K. Wang, “Compact and high selectivity dual-band dual-mode microstrip BPF with single stepped-impedance resonator,” Electron. Lett., vol. 47, no. 5, pp. 326-327, Mar. 2011.
[11] H. W. Deng, Y. J. Zhao, L. Zhang, X. S. Zhang, and W. Zhao, “Dual-band BPF with DSIR and TSIR,” Electron. Lett., vol. 46, no. 17, pp. 1205-1206, Aug. 2010.
[12] W. S. Chang and C. Y. Chang, “Analytical design of microstrip short-circuit terminated stepped-impedance resonator dual-band filters,” IEEE Trans. Microw.
Theory Tech., vol. 59, no. 7, pp. 1730–1739, Jul. 2011.
[13] Z. Yang, L. Zhang, Z. Ma, and X. Yang, “A compact microstrip dual-mode dual-band
128
filter with source-load coupling,” in China-Japan Joint Microwave Conference, Hangzhou, China, Apr. 2011, pp. 1–4.
[14] W. P. Liu and Y. W. Tung, “Dual-band stepped-impedance resonant filter with dual-band admittance inverter,” in International Conference on Microwave and Millimeter Wave Technology, Chengdu, China, May 2010, pp. 1409–1493.
[15] M. L. Chuang, M. T. Wu, and S. M. Tsai, “Dual-band filter design using L-shaped stepped impedance resonators,” IET Microw. Antenna. P., vol. 4, no. 7, pp. 855–862, Jul. 2010.
[16] C. H. Tseng and H. Y. Shao, “Design of dual-band net-type bandpass filter,” in IEEE
[16] C. H. Tseng and H. Y. Shao, “Design of dual-band net-type bandpass filter,” in IEEE