A sample and hold amplifier includes an input node for receiving an input current signal, a non-linear sampling capacitor circuit having an input coupled to the input node, an operational amplifier having a negative input coupled to an output of the non-linear sampling capacitor circuit, a positive input coupled to ground, and an output for providing a sample and hold voltage signal, and a linear capacitor coupled between the negative input and the output of the operational amplifier. The non-linear sampling capacitor includes a non-linear capacitor coupled between an intermediate node and ground, a first switch coupled between the input and the intermediate node configured to switch according to a first phase signal, and a second switch coupled between the output and the intermediate node configured to switch according to a second phase signal.