A Space-Limited Construction for the Smith Chart

Smith chart conversion of complex numbers from rectangular form to polar form, and vice versa, often involves the construction of one or more constant magnitude circular arcs. If the magnitude is being sought, it is frequently necessary to resort to graphical interpolation between the arcs. In any event, should the magnitude, given or desired, be between approximately one-fourth and four, the centers of the constant magnitude arcs inconveniently lie off the conventional Smith chart. This paper presents geometric methods with brief proofs for keeping all magnitude constructions on the commercial chart and for increasing the accuracy of results by referring interpolations to the accurately printed scalings on the horizontal axis.