An equivalent circuit model for single negative metamaterial (MTM) transmission line based on microstrip complementary electric inductive-capacitive resonator (CELC) is proposed for the first time. The verified circuit model gives strong support to the interpretation of all exhibited electromagnetic (EM) phenomena. The nonpure magnetic and electric resonances have been demonstrated by constitutive EM parameters. Based on the conclusions that have drawn, a more compact sub-wavelength particle based on Hilbert-shaped CELC (H-CELC) is proposed. The design procedures of the H-CELC-loaded MTM cell are derived based on the circuit model. For application, a bandstop filter covering one of the ISM bands 5.2 GHz by cascading two H-CELC cells is designed, fabricated and measured. Consistent results between simulation and measurement have confirmed the design. The established theory based on the proposed circuit model is of reference value for the design of novel bandstop devices.
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