Keyword spotting (KWS) systems must always be on to capture spoken keywords; thus, low power is critical for edge KWS hardware to achieve long battery life. A typical KWS system consists of a front-end feature extractor and a back-end classifier. This paper proposes an area-efficient ultra-low-power serial digital infinite impulse response (IIR) filter-based feature extractor, which is optimized with a low-cost computing structure and mixed-precision selection methods. Evaluated under 65nm process technology, this proposed feature extractor has an area of 0.02mm^2 and achieves a power consumption of 3.3uW @ 1.2V and 830nW @ 0.6V when supporting up to 10 keywords. This work can achieve ultra-low power consumption compared to state-of-the-art works while maintaining higher accuracy.