A simple, low-cost conductance bridge circuit, which provides high-resolution measurements of dI/dV and d2I/dV2 for a voltage-biased load, is presented. A resolution in dI/dV for a 90-Ω tunnel junction of several parts in 105 has been measured using a 35-μV-rms modulation level and a 1-s postdetection time constant (B n = 0.25 Hz). The output impedance of the voltage source and the error in the conductance measurement are discussed. The output impedance of the circuit with an AD119 operational amplifier is 0.02 Ω. A detailed discussion of Johnson-Nyquist, tunnel junction, and amplifier noise is presented.