A frequency tuning circuit includes a connection for coupling to a signal tap of an element which has a resonant frequency. The tuning circuit contains a controllable-capacitance capacitance array for tuning of a signal frequency of the element. The capacitance array has a multiplicity of capacitances which can be connected to a control connection via a signal. In this case, the capacitance array is coupled to the connection. A control input is used to supply a digital control word. Furthermore, the tuning circuit contains a sigma-delta modulator whose input side is coupled to the control input and whose output side is coupled to the control connection of the capacitance array. This makes it possible to produce a tuning word by means of which the effective resolution of the capacitance array can be increased.