Design formulae for microwave amplifiers employing conditionally-stable transistors

Abstract

When designing microwave amplifiers, it is the task to select values of the source (input generator) and load reflection coefficients for the transistor, to achieve certain amplifier performance requirements and ensure stability. For unconditionally stable transistors, simultaneous conjugate matching can be achieved using \vell-known design formulae. Under this condition, the gain is maximised, and the input and output ports are matched. On the other hand when the transistor is conditionally stable, source and load reflection coefficients are selected using graphical design methods, involving gain and stability circles. To eliminate the reliance on graphical techniques, this paper shows the derivation of explicit design formulae that ensure maximum gain for a minimum specified safety margin, with one port matched. In this work, the safety margin is the distance between the chosen source or load reflection coefficient and its respective stability circle. In a production environment, where the circuit and transistor parameters are subject to random variations, the safety margin therefore makes allowance for such variations. This paper shows that the design problem for conditionally stable transistors can be reduced from the selection of values for two complex variables (port terminations) to the selection of the value for just one scalar variable.