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A simple and accurate five-terminal switched transformer average model is proposed and its generalized equations are derived. The proposed model is capable of both time domain and ac analysis of dc-dc, ac-dc, and is especially suitable for single-stage power factor correction (PFC) converters. Unlike other models presented in literature, the proposed switching cell includes the transformer leakage inductance, an intermediate bus input, and still addresses both continuous and discontinuous conduction modes. The model was applied to two topologies, the bi-flyback and the flyboost parallel/series forward converters. The time domain results show great accuracy when compared with the slower and time consuming switching simulation. The ac analysis is also predicted with greater accuracy exposing the dynamics of such converters, a task that was not as easily addressed before when the unique characteristics of single-stage are considered. The frequency domain analysis was also verified with experimental results for the bi-flyback converter. The model is very relevant to isolated flyback converters including the PFC examples provided, which are not as easily or as accurately modeled by other approaches.Index Terms-Average modeling, modeling and simulation of power factor correction (PFC) converters.

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Background To explore the feasibility of corrected slack angle acquired from two-dimensional shear wave elastography (2D-SWE) for quantitating the spasticity of medial gastrocnemius (MG) in stroke patients. Methods Consecutive stroke patients with spastic MG and matched healthy controls were recruited. Intra- and interobserver reliability of 2D-SWE measurement were evaluated, and the correlation between corrected slack angle and modified Ashworth scale (MAS) score was examined. The corrected slack angle before and after botulinum toxin A (BoNT-A) injection was compared and its diagnostic performance in classifying the severity of spasticity were assessed with receiver operating characteristic (ROC) curve analysis. Results The intra- (0.791 95% CI 0.432–0.932) and interobserver (0.751 95% CI 0.382–0.916) reliability of slack angle acquired with 2D-SWE were good. Significant correlation was found between corrected slack angle and MAS score (R = − 0.849, p < 0.001). The corrected slack angle increased after BoNT-A injection. The cutoff value of MAS ≥ 3 had the highest sensitivity (100%) and specificity (93.33%). The positive predictive value (PPV) for classification of MAS ≥ 1+ and the negative predictive value (NPV) for classification of MAS ≥ 3 were greater than 90%. Conclusion 2D-SWE was a reliable method to quantitate the post-stroke spasticity. The corrected slack angle had advantage in classifying the severity of spasticity, especially in early identification of mild spasticity and confirmation of severe spasticity.