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This paper introduces an equivalent circuit model to estimate the resonant frequency and reflection phase of Jerusalem cross-based artificial magnetic conductor (JC-AMC) structures for waves normally incident on the structure. The JC-AMC structure is composed of an array of Jerusalem cross-shaped frequency selective surfaces (JC-FSSs) printed on a metal-backed dielectric slab without vias. This approach is based on the coupled microstrip lines and transmission line theories. Analytical expressions for the resonant frequency and reflection phase resulting from our model are thoroughly verified by full-wave simulations for different samples reported in the open literature. A comprehensive parametric study of the design parameters of JC-AMC structure and the influence of these parameters on the reflection phase properties are presented. This model can easily be extended to complex-shaped AMCs.