A mathematical method is proposed to calculate the field distribution theoretically of folded half mode substrate integrated waveguide(FHMSIW) for the first time. The phase constant is also given using an improved multi-line method, verifying its equivalence with conventional waveguide and substrate integrated waveguides. The FHMSIW transmission line properties of resonance effect, quasi-rotational symmetry of two PCB layers and high-pass feature are proposed. An FHMSIW equalizer loaded equivalent HMSIW resonant cavities, and an FHMSIW bandpass filter loaded folded quarter-wave FHMSIW resonators are designed. The two components share the same structure with a little difference. The model analysis, simulated results and measured results are all provided. The FHMSIW equalizer is achieved without increasing extra excitation structures. The measured results show a good performance and are in agreement with the simulated results. Compared with the other planar circuits, these structures have superiorities of small size, simple structure, low loss and high Q, suitable for the miniaturization development, and are easily integrated with other circuits.