In this thesis, the correlation of microstrip and its underneath defected ground structure (DGS) is studied so as to offer a simple DGS element design. Toward this goal, three novel DGS elements are proposed and their applications for the microstrip bandpass filter design are also investigated. The first element is T-shaped DGS offering bandgap at some frequency which can be easily tuned by the DGS geometry. This DGS element can be applied on to tapped-line of the conventional microstrip bandpass filter to achieve spurious response suppression. An interdigital bandpass filter example was then designed at 900 MHz and the T-shaped DGs was incorporated with input/output tapped-lines. It was found that the wide stopband with overall good 30 dB attenuation was realized. The second element is about projective DGS using l-shaped pattern. By this design, the microstrip resonator's 2nd harmonic can be critically tuned whilst the fundamental resonance is kept. To demonstrate this projective DGS usefulness, a dual-band bandpass filter was presented. Its fundamental passband was designed at 1.44 GHz by the l-shaped resonator whilst the second passband at 2.35 GHz was implemented by the resonator's harmonic relocation controlled by the etched l-shaped pattern, The third element is also a projective DGS employing H-shaped DGS and H-shaped resonator. The proposed projective H-shaped DGS resonator not only exhibits size reduction for the circuits but also possesses spurious free response till three times of its fundamental resonance.