Power analysis for IoT devices is strongly required to reduce power consumption and realize secure communications. In this paper, we propose a scalable and small-sized power analyzer with signal-averaging noise reduction for low-power IoT devices. The proposed power analyzer reduces a wide frequency range of noises by using a signal averaging method and is implemented on just a 2cmx3cm board, which is the smallest size among the other existing power analyzers for IoT devices. It further has the following advantages: (a) It has a two-level amplifier that amplifies current signals adaptively depending on their magnitude. Hence maximum readable current can be increased with keeping minimum readable current small enough. (b) If long-time analysis is required, it can be partitioned into several analysis segments. The proposed power analyzer can measure currents and voltages of each analysis segment by using a small amount of data memories. After that, by combining these analysis segments using a timer module, we can obtain long-time analysis results. We have analyzed power and energy consumption of encryption processes of AES block cipher on the IoT device and demonstrated that the proposed power analyzer has only 1.8% measurement error compared with a high-precision oscilloscope.