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This paper introduces a simple algebraic limiting loop proximity ((L2P)) model to describe magnetic hysteresis. With only four parameters, it has low computational cost and reduced mathematical complexity, thus permitting a fast numerical implementation and simple parameter estimation procedure. The paper presents simulation results and discusses the model performance in terms of its capacity to represent common nonlinearities of the magnetic hysteresis phenomenon. The model avoids the heavy computational burden that results when magnetic hysteresis is included in computer-aided tools for electromagnetic devices and circuit analysis - for example, when hysteresis is combined with the finite-element method. The model also avoids the need to use repeated numerical approximation steps to adjust traditional models to experimental data.