**Abstract**

Tunable filters enable dynamic spectrum access for the wireless systems, and the tunable bandpass filters with constant bandwidth (BW) are most favorable for practical applications. This chapter investigates the synthesis and realization techniques for the tunable filters using the coupling matrix with variable entries synthesizes the tunable filter and guides the filter design. The synthesis method and the matrix extraction procedures for the constant-bandwidth bandpass filter are included, and the typical numerical examples are given. This chapter also discusses the relationship between the theoretical matrix and the physical circuits, and then a planar tunable filter design is presented to verify this relationship. Furthermore, the general approach to designing the constant-bandwidth filters using the element variable coupling matrix is concluded. The planar circuit, as well as the 3D structure realizations, are offered to practically demonstrate the synthesis design approach.

**Keywords:** tunable filter, constant bandwidth, constant shape, synthesis of tunable filter, element variable coupling matrix
