This study reports a systematic synthesis process to design higher-order defected ground structures (DGS)-based lowpass filters (LPF) with Chebyshev and Butterworth responses on any useful substrate in the range εr=2.2-12.9, h=0.6-2 mm. The existing circuit models are re-examined and closed-form expressions are presented to compute the area of the DGS slot-heads for the given inductance. The present design method improves the design of the existing DGS-based LPF reported by several investigators - both in terms of the electrical performances and reduction in length up to 57.8%. The improvement in sharpness of the transition is up to 16 dB/GHz. The improvement in the 20 dB rejection bandwidth is up to 4.5 GHz. The group delay response of Butterworth LPF is better than that of Chebyshev LPF. However, length of Chebyshev LPF is small when compared with that of Butterworth LPF. The study also presents the design results of the ultra-wideband DGS-type LPF - at the cut-off frequencies of 5, 7.5 and 12 GHz.