The focus of this thesis is the investigation of thin-film transistors (TFTs) based on amorphous oxide semiconductors (AOSs) in two circuit applications. To date, circuits implemented with AOS-based TFTs have been primarily enhancement-enhancement inverters, ring oscillators based on these inverters operating at peak frequencies up to ~400 kHz, and two-transistor one-capacitor pixel driving circuits for use with organic light-emitting diodes (OLEDS). The first application investigated herein is AC/DC rectification using two circuit configurations based on staggered bottom-gate TFTs employing indium gallium oxide (IGO) as the active channel layer; a traditional full bridge rectifier with diode-tied transistors and a cross-tied full-wave rectifier are demonstrated, which is analogous to what has been reported previously using p-type organic TFTs. Both circuit configurations are found to operate successfully up to at least 20 MHz; this is believed to be the highest reported operating frequency to date for circuits based on amorphous oxide semiconductors. Output voltages at one megahertz are 9 V and ~10.5 V, respectively, when driven with a differential 7.07 Vrms sine wave. This performance is superior to that of previously reported organic-based rectifiers. The second AOS-based TFT circuit application investigated is an enhancement-depletion (E-D) inverter based on heterogeneous channel materials. Simulation results using models based on a depletion-mode indium zinc oxide (IZO) TFT and an enhancement-mode IGO TFT result in a gain of ~15. Gains of other oxide-based inverters have been limited to less than 2; the large gain of the E-D inverter makes it well suited for digital logic applications. Deposition parameters for the IGO and IZO active layers are optimized to match the models used in simulation by fabricating TFTs on thermally oxidized silicon and patterned via shadow masks. Integrated IGO-based TFTs exhibit a similar turn-on voltage and decreased mobility compared to the shadow masked TFTs. However, the integrated IZO-based TFTs fabricated to date are found to be conductive and exhibit no gate modulation. Due to the conductive nature of the load, the fabricated E-D inverter shows no significant output voltage variation. This discrepancy in performance between the integrated and shadow-masked IZO devices is attributed to processing complications. / Graduation date: 2009