This invention uses the structures of the finite-sized conductor-backed coplanar waveguides for designing broadband switchable and tunable signal filters. The design methods construct a plurality of configurations, which including waveguides, via holes, metallic posts, and conductor planes in the structures, for selecting, coupling, converting, and dissipating of the signals with specific electromagnetic modes and frequencies propagating through the structures. The dominant electromagnetic modes of the signals include Coplanar Waveguide Modes and Microstrip-Like Modes. The design methods thereby produce a plurality of filter types, such as bandstop filters, bandpass filters, multiband filters, etc. The design methods can apply to the structures with single and multi-layer dielectric and metallic materials, such as Integrated Circuits, Thin-film transistor Circuits, Low Temperature/High Temperature Co-fired Ceramics (LTCC/HTCC), PCB, and others. In addition, the design methods add switches to perform electrically controllable functions including frequency band selection and filter type selection. The design methods can also perform impedance matching of broadband signals by electrically tuning the values of inductance and capacitance in conjunction with the structures.