This paper presents a broadband terahertz (THz) high-temperature superconducting (HTS) mixer based on a log-periodic antenna-coupled YBa2Cu3O7-x (YBCO) step-edge Josephson junction. The THz thin-film antenna, as well as the microwave coupling circuits, have been carefully designed to optimize the power transmission from and into the junction while realizing good isolation between the DC bias, local-oscillator (LO) and intermediate-frequency (IF) ports. This mixer device has been fabricated, packaged and characterized to demonstrate a frequency down-conversion capability with a view to potential application in THz wireless communication systems.