We designed and fabricated a semiconductor optical amplifier-integrated dual-mode laser (SOA-DML) as a compact and widely tunable continuous-wave terahertz (CW THz) beat source, and a pin-photodiode (pin-PD) integrated with a log-periodic planar antenna as a CW THz emitter. The SOA-DML chip consists of two distributed feedback lasers, a phase section for a tunable beat source, an amplifier, and a tapered spot-size converter for high output power and fiber-coupling efficiency. The SOA-DML module exhibits an output power of more than 15 dBm and clear four-wave mixing throughout the entire tuning range. Using integrated micro-heaters, we were able to tune the optical beat frequency from 380 GHz to 1,120 GHz. In addition, the effect of benzocyclobutene polymer in the antenna design of a pin-PD was considered. Furthermore, a dual active photodiode (PD) for high output power was designed, resulting in a 1.7-fold increase in efficiency compared with a single active PD at 220 GHz. Finally, herein we successfully show the feasibility of the CW THz system by demonstrating THz frequency-domain spectroscopy of an ${\alpha}$-lactose pellet using the modularized SOA-DML and a PD emitter.