Volume 3 Issue 8 - March 21, 2008
Synthesis of Microwave Planar Dual-Band Filters
Chih-Ming Tsai* and Hong-Ming Lee

Institute of Computer and Communication Engineering
Email: tsaic@mail.ncku.edu.tw

IEEE Transactions on Microwave Theory and Techniques, vol. 53, no. 11, pp. 3429-3439, Nov. 2005.
IEEE Transactions on Microwave Theory and Techniques, vol. 55, no. 5, pp. 1002-1009, May 2007.

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In recent years, the fast growing cellular phones and wireless local area network (WLAN) provide the convenient and ubiquitous wireless communications, and the dual-band systems could help to enhance the reliability. For example, a dual-band cellular phone could automatically select the most unobstructed channel between those at 900 MHz and 1800 MHz under the GSM system. There are also two channels at 2.4 GHz and 5.8 GHz for WLAN under the IEEE 802.11 standards. Therefore, dual-band filters become key components in the front end of these portable devices. The simplest way to construct a dual-band filter is combining two single-band filters at different passband frequencies. They have, however, the double size and cost of a single-band filter. Therefore, it is attractive to design a single filter structure with dual-band properties. For the widely-used microwave planar filters, such as stripline and microstrip filters, the passband responses would appear periodically due to the transmission-line structures. By properly adjusting these passband responses, dual-band filters might be achievable.
Fig 1. a: traditional half-wavelength uniform-impedance resonator; b and c: step-impedance resonators.

Many researches have been reported on developing the dual-band filters using stepped-impedance resonators. The half-wavelength stepped-impedance resonators are as shown in Fig. 1. In traditional uniform-impedance resonator designs, the second resonant frequency is fixed at twice the fundamental frequency. On the other hand, for stepped-impedance resonators, their resonant frequencies are tunable by properly adjusting the impedances and lengths of the transmission lines. Most of the researches focused on the design of two passbands with required central frequencies, but very little have been done about the control of bandwidth for each band. In order to fully control the two passband frequencies and bandwidths, new dual-band filter structures are proposed in this study. Given the specifications in the two passbands, the filters can be rigorously designed, using distributed network synthesis techniques.
Fig 2. Generalized filter structure.

The generalized filter structure is shown in Fig. 2, which includes resonator Y and inverter J. In the classical filter synthesis method, the resonators are characterized by the resonant frequencies and slope parameters, and the inverters are then calculated based on the specifications. Therefore, for a resonator to have the correct resonant frequencies and slope parameters at two passbands, at least four variables are needed. Three types of dual-band filter structures are proposed in this study, as shown in Fig. 3, and they are called type-I, type-II, and type-III filters, respectively. These filter structures include the dual-band resonators (the transmission-line sections in Fig. 3) and dual-band inverters (J and K in Fig. 3). The resonators are composed of two open stubs in parallel for type-I filters, two open stubs in series for type-II filters, and open and short stubs in parallel for type-III filters. Their characteristic impedances and lengths could be designed to achieve the required dual-band parameters. It should be noted that the proposed structures of dual-band filters are similar to those of traditional single-band filters, and no additional elements are needed. Since classical synthesis rules are employed, they can be designed in a more rigorous procedure.
Fig 4. Dual-band inverter structures: (a) type-I inverter and (b)(c) stepped-impedance coupled-line structures for type-II and type-III filters.
Fig 3. Dual-band filter structures: (a) type-I, (b) type-II, and (c) type-III filters.

The dual-band inverter design is also an important topic in this study. It was found that the dual-band inverters are crucial and have great impacts on the bandwidth performance and the realization of a dual-band filter. A simple quarter-wavelength transmission line is usually used as an inverter; however, it is only suitable for single-band filter designs. In order for the inverters to meet the dual-band requirements, their structures might be more complicated than those of single-band inverters. Furthermore, the compatibility with the adjacent resonators should also be taken into account. Three types of dual-band inverters are proposed as shown in Fig. 4, which are applied to type-I to type-III filters, respectively. Type-I inverter is a transmission line with two additional open stubs attached to its ends, and type-II and type-III inverters are implemented with stepped-impedance coupled-line structures. Similar to the design method of dual-band resonators, the characteristic impedances and lengths of the transmission-line sections in these inverters are designed to have the required dual-band properties. The lengths of the open stubs in type-I inverters are close to those of the adjacent resonators, and thus they can be easily merged together. The stepped-impedance coupled lines consist of the required dual-band inverters and open (in series)/short (in parallel) stubs for adjacent resonators, and are suitable for type-II and type-III dual-band filter applications.

Fig. 5. Typical transmission response of type-I filters.
For the performance comparison between these three types of dual-band filters, it was found that type-I and type-II filters have the limitation of passband frequency ratio. Fig. 5 shows the typical transmission response of type-I filters, it is apparent that the two passbands are separated by three transmission zeros, at the frequencies of fz1, fz2, and fz3, where fz3 = 3 fz1. Therefore, the passband frequency ratio of type-I filters has an upper limit of three. Also, type-II filters have the same limitation. It is observed that type-I filters have low-pass and high-pass responses, and they will be close to the passbands if the passband frequency ratio is increased. This might lead to a reduced stopband rejection. Type-II filters are free of such a problem, however, it was found that they have an upper limit of bandwidth ratio. For the type-II filter designs with passband frequency ratio close to three, the upper limit of passband bandwidth ratio will be close to one. Therefore, dual-band filter designs with these two filter types should be carefully inspected if the specifications are within the limits. Type-III filters overcome the drawbacks of type-I and type-II filters, and can achieve relatively large passband frequency ratios (in theory infinite). Moreover, type-III filters have more freedom of bandwidth ratio than type-II filters. The total circuit size is also reduced, and is about two-thirds of those of type-I and type-II filters for the same specifications.

Fig. 7. Comparisons between the simulation and measured responses for (a) type-I, (b) type-II, and (c) type-III filters.
Fig. 6. Physical structures of the realized (a) type-I, (b) type-II, and (c) type-III filters.

The physical structures of the realized type-I to type-III filters are shown in Fig. 6, all of them were designed as third-order Chebyshev filters. Type-I filter was realized with a microstrip-line structure, and type-II filter was fabricated on multilayer printed circuit boards as a strip-line filter. Type-III filter was implemented in a low-temperature co-fired ceramic structure. For their specifications, type-I filter has the central frequencies of the two passbands at 1 GHz and 1.5 GHz, and both the corresponding bandwidths are 10%; type-II filter has the two passbands at 2.45 GHz and 5.25 GHz, and the corresponding bandwidths are 5% and 4.5%, respectively; type-III filters also has the two passbands at 2.45 GHz and 5.25 GHz, and both the corresponding bandwidths are 4%. The simulation and measured responses of these three types of filters are shown in Fig. 7, and it is obvious that the measured results are well with the predictions.

Three new types of dual-band filter structures are introduced in this study. The dual-band resonators and inverters can be rigorously designed based on the classical filter synthesis theory. It was found that type-I and type-II filters have the limitations of passband frequency ratios and bandwidth ratios, and type-III filters have overcome these drawbacks. Furthermore, type-III filters have reduced circuit size, which is about two-thirds of those of type-I and type-II filters. Finally, the measured results of three dual-band filter designs have successfully validated the theoretical study.
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