Impedance Matching (Correspondence)

Matching an impedance to a transmission line by the use of a cascaded section of line is a well-known process. However, the range of terminating impedance that can be matched by this method, I believe, is not so well-known. Consider a lossless line of characteristic impedance R/sub0/ to which is to be matched an arbitrary impedance /bar Z/ = R + jX by means of another lossless line of lentgh d and characteristic impedance R₁ cascaded between the first line and the load as shown schematically in Fig. 1. The problem is to determine for what range of values of /bar Z/ a match can be thus obtained for any values of R₁, and d.