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A novel compact microstrip bandpass/Bandstop filters realized by combining new Multilayer Method with electrically coupled microstrip U-shaped DGS resonators, is proposed. The proposed filters have low insertion loss and are compact in size due to the slow-wave effect. They also have sharp transition regions due to the presence of two- transmission zeros on both sides of their passband. The measured center frequency, bandwidth and insertion loss are 3.4 GHz, 40%, and 0.5 dB respectively. The simulated and measured results show good agreement and validate the proposed approach.