Literature Survey

For the recent developments in dual-band filter design, there are three major techniques. The first one is to connect two individual filters with common input/output feeding networks. However, this technique will face the large size and large insertion loss due to the usage of the large number of resonators. Moreover, directly connection of two single-band filter will degrade the filter response and rough tuning is required. The second technology is to cascade a wideband filter with a bandstop filter. Such kind of dual-band filters has very narrow separation between two adjacent passbands, and it also occupies large area of the wireless communication system. The third technology is to use the multi-mode resonators to design the dual-band filters. Due to the multi-mode property, the small size and low insertion loss can be achieved. Stepped-impedance resonator (SIR), stub-loaded resonator, and those resonators with degenerate modes belong to the third category. For this category, the drawbacks of the dual-band filters composites with the dual-mode resonators are individually controlling of each passband and introducing finite transmission zeros. To overcome these problems, many researcher keeps in studying and providing novel schematics. Here a brief survey of recent three years (2009-2011) is introduced.

To obtain both dual-band characteristic and the size reduction, many novel dual-band schematics are proposed. Dual-mode ring resonators [1]-[2], stub-loaded resonators [3]-[9], SIR [10]-[22], signal-interference structures [23]-[25] and composite right\left handed (CRLH) resonators [26]-[29] are used to develop the dual-band filter based on their

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intrinsic dual-band characteristics. Within these designs, to separately control each passband, stub-loaded can used to change response of one passband and keep the response within another passband unchanged [3]-[9]. To obtain the miniaturized dual-band filters, SIR is the suitable candidate in those dual-mode resonators. But the intrinsic SIR has the limitation in controllability in each passband and lacks an efficient way to introducing the finite transmission zeros. In [10]-[13], [18], [22], they provide efficient way to control the passband separately. To introduce the finite transmission zeros, source-load coupling is used in [10], [16], [18]. Moreover, for the wide-bandwidth application, the modifications have been developed in [17], [19]. And the further size reduction techniques have been be extended in [16], [17]. The techniques in [23]-[25] provide the transversal topology to create the dual-band characteristic. And the closed form is provided in [24]. CRLH in [26]-[29] are provide to those applications which require both the highly suppressed response of higher harmonic and the miniaturize size.

Besides, many novel configuration for dual-band filters are proposed [30]-[51]. In these designs, quarter-wavelength resonators [31], [39] are proposed for size reduction. and some analytical analysis [42], [49], [50] are applied to some interesting configurations.

Resonators with slot are used to separate two degenerate modes [30], [37], and high Q resonators are considered for the low insertion loss in filter designs [36], [46]. For some specific responses, the suitable coupling schemes are considered [31], [35], [40], [41], [43], [44], [45], [51].

Some dual-band filters need specific purpose, such as controllable dual-band characteristic [29], [52]-[58], balun filter [59], balanced filter [60]-[65], ultra-wideband (UWB) application [7], [66]-[68], and low insertion loss (i.e., high Q) applications [69]-[72]. Pin diodes [52], [53] or varactor-diode capacitors [54], [57], [58] are used to control if the filter operates at single-band or dual-band operation. Moreover, the bias voltage can be used to achieve the wide stopband [57]. For balanced filter, the common

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mode suppression is a major problem and is eliminated using the proposed techniques in [62]-[65]. To cover a wide-passband bandwidth, the techniques in [7], [66]-[68] have provided some solutions. For the low insertion loss applications, substrate integrated waveguide (SIW) resonator has a high quality factor [69]-[72]. To design such kind of dual-band filter efficiently, the analytical synthesis is provide [71] and the corresponding coupling matrix is used in helping the design [72].

In order to further reduce the circuit size, the multi-layer structure using low-temperature co-fired ceramic substrate (LTCC) [7], [29],[66], [72]-[76] and single ring structure are proposed [77]-[81].

To relate the requested dual-band characteristic to the real-world design, coupling matrix has the advantage in the hardware implementation. The real-world designs based on corresponding coupling matrix are more easily to be developed under the specific coupling configuration [82]-[89]. Moreover, due to the exact synthesis for the transversal coupling matrix based on the specifications, the transversal topology has been studied in the real-world dual-band filter design [87], [89].

After the brief review, the most efficient way to design the dual-band filter is to obtain the corresponding coupling matrix first, and then relate the coupling coefficient with the practical design parameters under the required coupling scheme. Hence the efficient dual-band coupling matrix synthesis is required. Recent developments in coupling matrix synthesis for single-band filter design are very attractive. Analytical methods for the single-band filter synthesis [90]-[93] are proposed to generate a transversal coupling matrix. For other specific coupling schemes, the coupling matrices are obtained using matrix rotation or optimization [94], [95]. To design dual-band or multi-band filters, many methods were proposed. Frequency transformation [96]-[98] was proposed to generate the response function analytically for dual-band filters. It was developed with governing equations of single-band filters. It was unrealizable, however, for multi-band filters.

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Another method was based on parallel-coupled line model [99]; this was used to generate the dual-band performances. This method was limited for dual-band filters, though, and could not be used for multiband filters.

To obtain the multi-band performance, an equivalent lumped-element network [100]-[102] was introduced. This network simplified the design procedure for dual-band or multi-band filters via the iterative procedure. The problems, however, such as the need for optimization for roots finding [100], [102] or inability to achieve equal-ripple [101], [102], occurred while applying those equivalent networks.

In filter design, the coupling matrix technique is well-known with the advantage of the hardware implementation. To take advantage of coupling matrices for dual-band or multi-band filters, optimization methods [103], [104] were proposed to generate the coupling matrix numerically, via proper cost functions. Fully analytical coupling matrix synthesis for dual-band or multi-band filters, however, has not been proposed yet. In this dissertation, the novel multi-band coupling matrix synthesis will be proposed in Chapter 2.

For the aspect of the dual-band filter design, the corresponding polynomials of the reflection and transfer functions are firstly modified into the dual-band characteristics, and the dual-band coupling matrix is then synthesized based on those modified polynomials [97], [105]. Considering the implementation of the dual-band filter, some coupling schemes, for examples, cul-de-sac [98], inline topology [97], and extended box topology [100], are generated via a series of similarity transformations [98], [106]. Some of those topologies, however, are difficult to be realized in microstrip circuit form. Considering the dual-band microstrip filter, dual-mode [107] and frequency-separated coupling scheme [108] are proposed to realize the dual-band characteristics. The phenomenon in placing transmission zeros related to corresponding coupling topologies, however, is not clear yet such that the mechanism in transmission zeros generation of the dual-band filter is still unobservable under proper coupling schemes. In the Chapter 3 of this dissertation, the

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dual-path coupling scheme will be discussed for its ability in microstrip implementation.

For the purpose of size reduction, the two-mode dual-band filters have been an attractive solution for dual-band applications. Moreover, two-mode resonators also have the advantage of intrinsic dual-band characteristic and separated design parameters of each passband [109]-[121]. To develop a two-mode dual-band resonator, different approaches are provided. A resonator with perturbations is widely used to excite the two-mode property of the resonator, and the dual-band filter is designed by carefully combining two such two-mode resonators. For examples, a waveguide filter [109] and dual-band filters using ring resonators [110]-[114] are constructed by two resonators operated at two frequencies. To achieve specifications of each passband, the perturbations are added and tuned. An alternative two-mode resonator is the stub-loaded open-loop resonator [115]-[117]. The stub is used to excite another mode of the resonator. Recently, two-mode dual-band filters constructed by a single resonator are provided for further size reduction [77], [118]-[121]. These two-mode dual-band filters have small size, and they have tuning stubs or patches for tuning performances of each passband and transmission zeros.

However, there is still lack of analytical approach in two-mode dual-band filter design yet.

E-shaped resonator is validated in two-mode single-band filter design [122]-[124] and it is a good candidate in dual-band filter design [125]. The even- and odd-mode analysis of the E-shaped resonator is proposed in [122] and corresponding coupling scheme is proposed in [124]. The analytical approach for two-mode dual-band filter synthesis using E-shaped resonators is proposed in Chapter 4 for the closely adjacent passbands.

For the aspect of tri-band and quad-band filter design, the compact size is still a key issue in microwave application. Lots of dual-mode resonators have been proposed for multi-band filter design [126]-[131]. Those filter designs, however, have no analytical procedure and the designer needs more efforts to obtain the multi-band performance. In this dissertation, the semi-analytical procedure is proposed in Chapter 5.

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