Abstract: In the post-Moore era, traditional solid-state electronic devices face the challenge of reaching physical limits due to size reduction. In contrast, nanoscale vacuum channel transistors （NVCTs）, which operate based on a mechanism fundamentally different from that of solid-state devices, have emerged as one of the most promising electronic devices for the next generation. Their low power consumption and high reliability have attracted significant attention from researchers. However, NVCTs with a single cathode structure typically demonstrate low operating currents, and extending them into an array structure has been identified as an effective method for enhancing the operating current. Based on a back-gate transistor structure, a back-gate nanoscale vacuum channel transistor array is proposed in this study, and its electrical characteristics are systematically investigated through parametric optimization. The systematic investigation focuses on three critical design parameters governing device performance: Firstly, emission tip spacing within cathode arrays is optimized to minimize the electric field shielding effect. Secondly, gate dielectric layer thickness is correlated with electrostatic control performance, revealing thickness-dependent performance tradeoffs. Thirdly, the effect of High-k dielectric materials applied to our proposed NVCT on its electrical characteristics. These parametric studies establish quantitative relationships between structural configurations and device functionality. Furthermore, this study proposes two high-frequency small-signal equivalent circuit models based on nanoscale vacuum channel transistor arrays: the common-cathode high-frequency small-signal equivalent circuit and the common-gate high-frequency small-signal equivalent circuit. The simulation results of these two equivalent circuit models show that the common gate high-frequency small-signal equivalent circuit model is able to regulate the output current more significantly and efficiently than the common cathode high-frequency small-signal equivalent circuit model under the same DC bias conditions. These findings offer new insights and guidance for the application of nanoscale vacuum channel transistors in next-generation electronics requiring ultra-low power consumption and radiation-hardened reliability.