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The paper describes the design of a fail-safe sensor used for the detection of the speed of a moving railway vehicle. The sensor is required for use in automatically controlled trains that run at one of a number of predetermined speeds, selected with reference to safety criteria, and governed by conditions ahead of the train. The device uses an axle-coupled permanent-magnet a.c. generator that, at the predetermined speed, saturates a transformer with low-frequency current, choking the passage of an audio-frequency signal from a constant-voltage source, and hence cutting off the output. Positive feedback is employed to sharpen the cut-off slope. A computer model based on a sinusoidal analytical method, superimposing the low and audio-frequency signals, predicts the possibility of in stability and hysteresis occuring in the output characteristic under certain conditions. Computed and test results are found to be in good agreement, and a series of circuit-design criteria are derived.