A circuit controls a dynamic time constant to remove DC offset from a received optical data signal. The circuit has a first capacitor coupled between a first terminal and a second terminal. A first resistance network is coupled between the second terminal and a reference voltage. A control circuit has a first output coupled to a control input of the first resistance network. The control circuit monotonically increases an effective resistance of the first resistance network to increase the dynamic time constant. The first resistance network has a resistor coupled to the second terminal, and a transistor with a first conduction terminal coupled to the resistor, a second conduction terminal coupled to the reference voltage, and a control terminal coupled to the first output of the control circuit. The first capacitor has a variable capacitance. The monotonic increase in the dynamic time constant can be linear or non-linear.