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A complete lumped component model representing the wideband impedance of water-cooled multi-layered core-less solenoid coils is presented and analytical and numerical calculation methods for model elements are reviewed and extended. The model includes stray capacitances, mutual inductances and frequency-dependent resistive losses. Contrary to previous treatments of this topic, the model is not simplified further and is evaluated in its complete form, allowing accurate prediction of the coil impedance beyond the first resonant frequency. This aspect is especially important if the coil is part of a passive filter circuit, where higher resonances limit the filter bandwidth. Also, a liquid coolant is included in the calculations.Additionally, figures of merit for the evaluation of field homogeneity inside the coil are given.The model is applied to a MPI drive coil and is compared to measured data. It shows good agreement up to 4 MHz, including the second series resonance of the coil. Additionally, the influence of water-cooling on the coil impedance is investigated. Comparison of model results to measured data shows additional losses.Int. J. Mag. Part. Imag. 4(1), 2018, Article ID: 1804001, DOI: 10.18416/IJMPI.2018.1804001