Graphical Analysis of Transformed Feedback Bilinear Expressions Applied to Differential Active Phase Shifters Design

Graphical analysis has become a powerful tool to design advanced high frequency circuits. By mapping complex expressions on a smith chart, complex functions can visually be designed. This paper presents a graphical method applied to active high frequency phase shifters design. By mapping bilinear expressions resulting from an active device with a serial or parallel feedback, active phase shifters can be designed. For the method proposed, first the expressions for the bilinear transformed component are obtained from original active device S parameters, then, a computer program performs the mapping process and plots constant amplitude and phase circles on a smith chart representing the feedback component. Finally by selecting the adequate circles the differential phase shifter can be designed.