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The black-box model of a microstrip transmission line is worked out. The input free variables taken are the substrate thickness, H, the conductor strip width, W, and the conductor thickness, T, as the geometric dimensions of the system, as well as the normalized frequency, fH, (GHz mm), and the dielectric constants, εx, εy; the functions of characteristic impedance, Z0, and effective dielectric constant, εeff, are the results at the output of the black-box. A simple neural network with a single hidden layer is employed for the evaluation inside the black-box, which is activated by a sigmoid function and trained by the Levenberg-Marquard algorithm. Approximate analytic solutions, with empirical adjustment of their numerical constants to achieve the desired accuracy, are utilized to obtain the training and test data. Commonly used materials, such as alumina, PTFE/microfiber glass, gallium arsenide, and RT/Duroid 6006 are applied to the neural network and their Z0 and εeff are obtained as functions of H, W/H, T, fH, εx and εy. This neural network model can be used for the analysis and the synthesis of microstrip circuits, including monolithic microwave integrated circuits.