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A novel approach with a new configuration is introduced to design an ultra-wideband (UWB) band-pass filter (BPF) that demonstrates double/single notch-bands using micro-strip transmission lines without using any via-hole. The proposed approach is established using two parallel stepped-impedance resonators (SIR) that provide two paths with different electrical lengths. The mechanism of realising notch-bands within the pass-band of the UWB BPF is developed based on the waves' cancellation theory. To realise single or double notch-bands (DNBs) within the pass-band of a UWB BPF, the conventional tri-section stepped-impedance resonator (TSSIR) is adopted and its fundamental and first spurious resonance frequencies are chosen either to be suppressed or supported. New parallel dual-section T-shaped and TSSIRs are proposed, optimised and fabricated to provide single and DNBss, respectively. The proposed concept avoids using via holes, which is conventionally used in notch filters. In addition, a size reduction of about 75% is reported in comparison with the conventional BPF with a single notch-band accompanied by two transmission zeroes at the lower and upper stop-bands. Moreover, our proposed DNBs BPF demonstrates a comparable performance while being smaller in size (up to a 12.6% size reduction) to that of the latest UWB BPF design that used complicated and expensive multilayer liquid crystal polymer (LCP) technology.