Application of the bilinear transformation to broad-band microwave amplifier design

A microwave amplifier will give maximum gain when it is fed from a signal source which presents an impedance to the amplifier which is, in general, different from the characteristic impedance of the feeder. A similar situation arises at the output. Further, if noise figure is to be minimized, input and output impedances are required which again are not the characteristic impedances of the input or output lines nor are they the same impedances required to maximize the gain. It is well known that reflection coefficients along a lossless transmission line system are related by bilinear transformations. In such transformations, circles transform into other circles or (exceptionally) into straight lines. Therefore it is to be expected that the unknown loci will be another family of circles