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Necessary and sufficient conditions are derived for a function to be the driving-point impedance of a physically realizable network consisting (essentially) of lumped resistors and lossless transmission lines. The circuits so developed are thoroughly practical for pure reactances and in many other special cases, but, in general, ideal transformers are sometimes required. A rigorous correspondence between lumped-constant circuits and line-resistor circuits is established. This correspondence immediately extends the usefulness of a wealth of theorems and techniques.