We report a portable broadband photoacoustic spectroscopic system for trace gas detection using distributed feedback quantum cascade laser arrays. By sequentially firing 128 lasers, our system acquires a photoacoustic spectrum covering 565cm-1 (935-1500cm-1) with a normalized-noise-equivalent-absorption coefficient of 2.5×10-9cm-1WHz-1/2. The firing sequence that determines when and which laser to activate is programmable, which enables frequency-multiplexing excitation. For demonstration, 12 lasers are modulated simultaneously at distinct frequencies, and a photoacoustic spectrum is acquired within 13 ms. The compactness (28cm×17cm×13cm, 3.5 kg) and low power consumption enable convenient installation for on-site monitoring.