A new quasi-analytical synthesis method is presented for designing spiral defected microstrip structures (DMS). A comprehensive analysis based on circuit models, mathematical relations, and extensive simulations is used to achieve an exact, straightforward, and tunable wide-range frequency design process. The design process benefits of some novel formulas derived based on the overall form of resonance frequency functions and the study of extensive simulations. We used the Levenberg Marquardt Iteration (LMI) algorithm for the derivation of closed-form formulas. The resonance frequency of a spiral DMS called notch frequency can be independently tuned in a large frequency span by employing the proposed method. The designed spiral DMSs and the new synthesis method can be applied to applications such as filters, antennas, amplifiers, and multipliers. The proposed spiral DMS design/synthesis method and the derived closed-form formulas are verified and validated by simulations and fabrication of six filters with different geometries and specifications. A comparison of the simulation and measurement results of the fabricated filters proves the accuracy and validity of the proposed design method and formulas where the relative effort is less than 0.38%. The return loss and group delay of the filters are less than 0.48 dB and 0.5 ns, respectively.

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