A circuit for measuring variations in the capacitance of a variable capacr forming part of a sensor includes an oscillator which generates an alternating signal which is supplied to two branches of a detection bridge. The first branch includes the variable capacitor connected in series with a variable capacitance diode. The second branch includes a capacitor connected in series with a variable capacitance diode. A differential stage has each of its in puts connected to the common point of a respective one of the branches. Synchronous demodulation means connected to the oscillator, are connected to the output of the differential stage for delivering a DC unbalance voltage Ve which is injected by a feedback line to the common point of the first branch, thereby continuously balancing the detection bridge.