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Work of R. M. Fano on the theoretical limitations of broad-band impedance-matching is utilized to give a straightforward procedure for synthesis of optimum, lossless, Tchebycheff, wide-band impedance-matching networks for various classes of loads. The loads which are treated consist of an inductance, capacitance, and a resistance (all of arbitrary size) connected in series, parallel, or any of a variety of series-parallel combinations. Procedures are described and examples are presented for low-pass, high-pass, and band-pass matching network design for use with specified loads so as to meet prescribed bandwidth and reflection coefficient magnitude specifications (i.e., any specifications that are physically realizable). The design procedure is simplified by the use of tabulated reflection coefficient polynomials, each of which is a function of frequency and a design parameter. The application of this procedure to Tchebycheff filter and vacuum-tube amplifier, interstage design, is also discussed.