A simple, low‐cost conductance bridge circuit, which provides high‐resolution measurements ofdI/dVandd2I/dV2for a voltage‐biased load, is presented. A resolution indI/dVfor a 90‐&OHgr; tunnel junction of several parts in 105has been measured using a 35‐&mgr;V‐rms modulation level and a 1‐s postdetection time constant (Bn=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 &OHgr;. A detailed discussion of Johnson‐Nyquist, tunnel junction, and amplifier noise is presented.