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This paper introduces a Transimpedance Amplifier (TIA) design capable of producing an incremental input resistance in the ohmic range, for input signals in the microampere range, such as are encountered in the design of instrumentation for electrochemical ampero-metric sensors, optical-sensing and current-mode circuits. This low input-resistance is achieved using an input stage incorporating negative feedback. In a Cadence simulation of an exemplary design using a 180nm CMOS process and operating with ±1.8V supply rails, the input resistance is 1.05ohms and the power dissipation is 93.6µW. The bandwidth, for a gain of 100dBohm, exceeded 9MHz. For a 1µA, 1MHz sinusoidal input signal the Total Harmonic Distortion, with this gain, is less than 1%. The input referred noise current with zero photodiode capacitance is 2.09pA/√Hz and with a photodiode capacitance of 2pF is 8.52pA/√Hz. Graphical data is presented to show the effect of a photodiode capacitance varying from 0.5pF to 2pF, when the TIA is used in optical sensing. In summary, the required very low input resistance, at a low input current level (µA) is achieved and furthermore a Table is included comparing the characteristics and a widely used Figure of Merit (FOM) for the proposed TIA and similar published low-power TIAs. It is apparent from the Table that the FOM of the proposed TIA is better than the FOMs of the other TIAs mentioned.