This article presents a wide bandwidth transimpedance amplifier based on the series of an integrator and a differentiator stage, having an additional feedback loop to discharge the standing current from the device under test (DUT) to ensure an unlimited measuring time opportunity when compared to switched discharge configurations while maintaining a large signal amplification over the full bandwidth. The amplifier shows a flat response from 0.6 Hz to 1.4 MHz, the capability to operate with leakage currents from the DUT as high as tens of nanoamperes, and rail-to-rail dynamic range for sinusoidal current signals independent of the DUT leakage current. Also available is a monitor output of the stationary current to track experimental slow drifts. The circuit is ideal for noise spectral and impedance measurements of nanodevices and biomolecules when in the presence of a physiological medium and in all cases where high sensitivity current measurements are requested such as in scanning probe microscopy systems.