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This article proposes a general circuit model for a thin wire antenna and a generalized approach to design an $N$ th-order parallel coupled wire antenna with its companion circuit model. Frequency-variant $K$ -inverters are involved in the new equivalent circuit to describe the frequency-variant radiation effect of the antenna. The design procedure starts with an initial prototype developed from a synthesized arrow coupling matrix, and then, its companion circuit is constructed accordingly. All the circuit parameters associated with the prototype can be extracted from EM models using space mapping technology. Iterative tuning is employed in the EM and circuit model, such that the final response satisfies the given specifications. An analytic method based on the circuit model is proposed to predict the radiation performance of the antenna. It is the first time ever that this type of filtering antenna has been designed and predicted quantitatively by using its circuit model, and the tuning of the antenna structure can also be guided by its circuit model. The proposed method offers a deterministic way for optimally designing an arbitrary-order filtering wire antenna with proper frequency characteristics.