The system exploits a previuosly-developed high- resistivity-silicon detector with internal amplification capability based on the bipolar-transistor (BJT) effect and readout electronics based on commercial IC's. We present a simple, low-cost, and low-power alpha-particle detection system for environmental radioactivity monitoring. The analysis is useful in choosing suitable pixel size for future pixelated detectors. The contribution of electronic noise to energy resolution for 400 $\mu$m pixel size and 1 $\sigma$ threshold is 45 keV FWHM, which is comparable to the energy resolution causing by energy fluctuation in ionization process inside TPC ($\sim$20keV). After introducing an empirical expression, it can be shown that this variation is due to a combination effect of pixel size and threshold on pixel. A non-monotonic trend is observed for energy resolution varies with pixel size for small pixel size region. Using Great4-based simulation, we figure out to what extent it worsens the energy resolution. Although smaller pixel can generally achieve higher spatial resolution, electronic noise might come into play in worsening the energy resolution. In this paper, we study how pixel size influences energy resolution for a pixelated detector - a proposed high sensitivity, low cost, and real time radon monitor based on Topmetal-$^-$ TPC.
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