Chapter 5 Two-mode Tri-band and Quad-band Filter Design with Close Adjacent
5.3 Tri-band and Quad-band Filter Synthesis
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
125
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.
127
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