The hardware Trojan (HT) has become a major threat for the integrated circuit (IC) industry and supply chain, and has motivated numerous developments of Trojan detection schemes. Although the side-channel method is the most promising one, nearly all of the side-channel methods require fabricated golden chips, which are very difficult to obtain in reality. In this paper, we propose a novel strategy for HT detection using electromagnetic side-channel-based spectrum modeling and analyzing. We utilize the design data at early stage of the IC lifecycle, and the generated spectrum can serve as the golden reference, and thus we do not need the fabricated golden chips anymore. Another very important feature is that our method is immune to the process variation theoretically. Experimental results on selected Advanced Encryption Standard benchmark circuits on FPGA show that our proposed method can effectively detect Trojans even with very small traces.