The double matching problem: Analytic and real frequency solutions

A new and simplified analytic solution is given for the double matching problem. That problem requires the matching of a complex generator impedance to a complex load over a frequency band. The analytic solution is fundamental to understanding theoretical gain-bandwidth performance of systems but introduces severe difficulties when employed in design practice. Following the analytic presentation a CAD technique [the Real Frequency method] which bypasses the analytic theory and its difficulties of implementation is discussed. Various examples comparing the Real Frequency method to the analytic procedure are examined, It is shown that for double matching problems (as for single matching problems) the analytic method generally yields suboptimal performance characteristics. Thus just as in single matching problems, the Real Frequency method for double matching compared to the analytic procedure gives superior equalizer performance, simpler equalizer structures, and also is applicable to problems where the analytic method is virtually impossible to implement. As a final example the Real Frequency method is applied to the design of a two-stage microwave FET amplifier including input, output, and interstage equalizers.