**1. Introduction**

The tunable filter is generally employed as a switched filter bank with a substantially reduced size. It self-adaptive selects the frequency spectrum and filters out undesired signals to meet the need for tunability/reconfiguration in wireless systems. As exemplified in **Figure 1**, the core part of a typical mobile transceiver module is realized by a transceiver IC with many blocks of filters (or multiplexers), switch matrices, power amplifiers, and two antennas. The filters andswitch matrices constitute the unintegrable switched filter banks that are used to select the signal dynamically. It is predictable that if the compact and high-performance tunable filters replace the bulky filter banks, this part of the circuit will consist of only a transceiver IC, two tunable filters, a wideband power amplifier, and two antennas (right side of **Figure 1**). Nowadays, with a more complex wireless electromagnetic environment, the frequency spectrum is more crowded, and thus it is even more significant to facilitate efficient utilization of the available frequency spectrum. The tunable filter, which plays a crucial role in utilizing the frequency spectrum, has become the hotspot not only in the research area but also for industrial applications.

The filter with tunability and without too much Q degradation known as the high-Q tunable filter has been widely used in the industry. Magnetically tunable filters or yttrium iron garnet (YIG) filter, which provides the tunable band with the high Q factor and multi-octave tuning range, is the essential part in front-ends of the microwave test and

**Figure 1.** *Tunable filters replace switched filter banks with a substantially reduced size [1].*

measurement instruments [2, 3]. This type of filter can be tunable by magnetically adjusting the ferrimagnetic resonance of the crystal YIG spheres, thus resulting in the filter frequency adjustment. The mechanically tunable filter is another type of high-Q filter that can provide the high-Q tunable passband with a relatively compact size (compared with the YIG filter). This type of filter's frequency or response shape is reconfigured by changing the physical dimensions of the filter structures or disturbing the electromagnetic field in the resonators. The mechanically tunable filter has been commonly employed for tunable wireless infrastructure equipment or reconfigurable communication satellite operators to extend their service life and functionality [4–6]. A great deal of high-Q mechanically tunable filters, including coaxial, waveguide, or dielectric resonator structures, have been exploited. For example, mechanically adjusting the end-loading capacitors (or equivalent capacitors) of each coaxial resonator, the coaxial filter can be tunable with a wide tuning range [7–10]. The reconfigurability of the waveguide filter is enabled by reshaping the cavity dimension of the resonator or moving the perturbations inserted in the waveguide cavities [11–15]. For the dielectric resonator filter, moving the movable disks above the dielectric resonators can tune their resonant frequencies resulting in filter passband tunability [16–18].

The ever-increasing demand for the miniaturized and highly integrated wireless system requires the future tunable filter with a more compact size and fully electrical control. The giant tuning mechanisms inevitably make YIG filters and mechanically tunable filters oversize. With this regard, the electrically tunable filter with the semiconductor tuning element has been drawing a lot of attention and getting extensively exploited because of its very compact size, fast tuning speed, and straightforward control mechanism, even though the semiconductor tuning element loaded on the resonator will dramatically deteriorate the filter Q factor. Planar tunable filter is a popular research topic because of its easy integration with semiconductor tuning elements. For example, the planar λ/4, λ/2, and multimode resonators loaded by tunable varactors or PIN diodes or both are employed to construct the tunable filters with frequency and bandwidth (BW) control [19–23]. In addition, emerging tuning semiconductor devices such as Radio Frequency Microelectromechanical Systems (RF-MEMS) and ferroelectric devices are also used as the variable capacitor in the planar tunable filters to alleviate the Q factor deterioration [20, 24–26]. Aside from the planar filter, the high-Q tunable three-dimensional (3D) filter with tuning semiconductor elements is also a research hotspot because of its low loss, good power handling, and high selectivity. For example, coaxial filters or quasi-coaxial

#### *Tunable Filter DOI: http://dx.doi.org/10.5772/intechopen.104391*

filters [7, 27–31], dielectric resonator filters [32, 33], and waveguide filters [34] are loaded by the various variable capacitors or switchable devices, thus constructing the tunable/ reconfigurable 3D high-Q filters.

Among a large variety of tunable filters, the bandpass filter with the tunable center frequency (CF) is attractive for its widespread application. It is preferable to use the minimum number of tuning elements to control the frequency of the bandpass filter and realize the constant absolute bandwidth (BW). This realization will minimize the Q fact degradation introduced by the loaded tuning elements and maintain the filter response shape as the frequency is tuned. It is also the simplest tunable filter with the most straightforward control mechanism. Therefore, the tunable filter with constant bandwidth has been one of the emerging trends in filter design. For example, the planar filters [35–37], waveguide filters [15], coaxial filters [7], etc., have been all investigated to approach the constant-BW tunable filters.

In general, since the tunable filters have not large-scale replaced the filter banks, the research and development of the tunable filter is still indispensable, especially for the frequency tunable bandpass filter with constant bandwidth. This chapter will mainly deal with the tunable bandpass filter and offer the general synthesis-based approach. The synthesis method, tuning behavior, and physical realization techniques are included and discussed. The synthesis is based on the coupling matrix where the elements are variable, and the coupling matrix with the variable elements can represent the tunable filter response as well as the tuning behavior. The direct relationship between the matrix and the filter realization will be established, and thus various physical structures can be employed to realize the tunable filter accordingly. Furthermore, the constant-BW tunable filter will also be investigated, and the synthesis with its design approach will be included. A planar and a 3D tunable filter design examples will be offered to realize the theory.
