Comparative Analysis of two Methods for High-Resolution Differential Conductance Measurement*

We compare two methods of differential conductance measurement. The first is a traditional method in which current and voltage data is acquired via four-wire measurement, then averaged and differentiated numerically. The second method calculates $dI/dV$ in real time by superimposing a small DC signal $dI$ on the input step function, alternating between addition and subtraction of the signal with each step, then averaging the small signal voltage response over three steps to obtain $dV$. This requires two instruments: a DC current source and a high-resolution voltmeter. Keithley Instruments has commercially promoted the Keithley 622x current source and 2182A nanovoltmeter as means to achieve this measurement; we therefore refer to it as the Keithley method. We compare the two methods by performing high-resolution measurements of the energy gap of MgB$_{2}$ thin film Josephson junctions. We show that the Keithley method has advantages of cleaner data, easier implementation, and overall faster data collection, but may lack the traditional method's high resolution.