In a simplified analysis of thyristor amplifiers in closed-loop control systems, the amplifier is represented at all frequencies by its d.c. gain, and the effect of the output ripple voltage is neglected. This approach is inadequate for wide-bandwidth systems, and fails to predict the occurrence of ripple instability. A more accurate analysis is made in the paper, taking into account the sampling action of the amplifier in the presence of alternating component voltages in the loop. Ripple instability is characterised by the generation of continuous oscillations at a subharmonic of the balanced-amplifier ripple frequency, and manifests itself in the amplifier as a periodic variation in the firing pattern. The behaviour of an m-phase amplifier in an otherwise linear system of any order is investigated, and an exact analysis is given for subharmortic oscillations of order ½. At the ½-order, and other, subharmonic frequencies, describing functions are derived, and the amplifier response is seen to differ markedly from the simple assumption of constant gain at all frequencies. The describing-function technique is extended to evaluate phase margins which must be satisfied at the various subharmonic frequencies to prevent ripple instability, thus allowing a straightforward design technique based on conventional frequency-response methods. The results of the analysis are compared with experimental results from regulated power-supply systems, and good agreement is reached.