Stability Analysis of Digital Microwave Power Amplifiers

This paper presents a stability analysis of microwave power amplifiers (PAs) driven by binary pulse trains, as in the case of class-S PAs. First, using a simplified digital PA test bench in class-D configuration, different qualitative behaviors are obtained when varying the pulsewidth, including subharmonic and incommensurable oscillations. The mechanisms affecting the stability properties are studied with a harmonic balance-based formulation, by means of pole-zero identification and bifurcation detection. A sufficiently high number of harmonic components must be considered, together with the Krylov decomposition for an efficient computation of the inverse of the Jacobian matrix. It is demonstrated that, when varying the pulsewidth, the distinct pairs of complex-conjugate poles may shift to the right-hand side of the complex plane and, therefore, lead to different kinds of unstable behavior. This phenomenon is related to the dependence of the critical poles on the average value of the input signal. Boundaries of the various types of unstable behavior are traced in the plane defined by the pulse repetition rate and pulsewidth, using bifurcation detection techniques. All the predicted phenomena have been confirmed experimentally. In a second step, the algorithms derived from the simple class-D circuit are transferred to study the stability of a more complex tri-band class-S amplifier. It has been analyzed versus the input bitrate, obtaining a fully stable behavior that has been validated experimentally.