A pulsed quantum-cascade distributed-feedback laser, temperature tunable from -41°\text{C} to +31.6°\text{C} , and a resonant differential photoacoustic detector are used to measure trace-gas concentrations to as low as 66 parts per {10}^9 by volume \left(\text{ppbv}\right) ammonia at a low laser power of \text{2 \hspace{0.17em}}\mathrm{mW} . Good agreement between the experimental spectrum and the simulated HITRAN spectrum of {\mathrm{NH}}_3 is found in the spectral range between 1046 and \text{1052 \hspace{0.17em}}{\text{cm}}^{-1} . A detection limit of 30\text{\hspace{0.17em} ppbv} ammonia at a signal-to-noise ratio of 1 was obtained with the quantum-cascade laser (QCL) photoacoustic (PA) setup. Concentration changes of \sim 50\text{\hspace{0.17em} ppbv} were detectable with this compact and versatile QCL-based PA detection system. The performance of the PA detector, characterized by the product of the incident laser power and the minimum detectable absorption coefficient, was 4.7\times {10}^{-9}\text{\hspace{0.17em} W \hspace{0.17em}}{\text{cm}}^{-1} .