In this paper, we report on an approach for shaping the spectra of THz pulse generation in photoconductive antennas (PCAs) by frequency-dependent impedance modulation. We introduce a theoretical model describing the THz pulse generation in PCAs and accounting for impedances of the photoconductor and of the antenna. In order to showcase an impact of frequency-dependent impedance modulation on the spectra of THz pulse generation, we applied this model to simulating broadband PCAs with log-spiral topology. Finally, we fabricated two different log-spiral PCAs and characterized them experimentally using the THz pulsed spectroscopy. The observed results demonstrate excellent agreement between the theoretical model and experiment, justifying a potential of shaping the spectra of THz pulse generation in PCA by modulation of frequency-dependent impedances. This approach makes possible optimizing the PCA performance and thus accommodating the needs of THz pulsed spectroscopy and imaging in fundamental and applied branches of THz science and technologies.