Clarification of the complex chemical processes governing polarized wide-range air-to-fuel-ratio sensors should enable one to determine characteristics of the system geometry and physical properties necessary for successful sensor operation. To develop a mathematical description of these sensors, we have combined well-established theories for electron, electron-hole, and oxygen-vacancy transport within yttria-stabilized zirconia with transport equations that apply to gaseous diffusion within the dense, porous layer that covers the solid electrolyte. Along the interface between the solid electrolyte and the porous layer, a thin platinum electrode catalyzes various chemical reactions and an electrochemical charge-transfer reaction. The model equations have been simplified using an asymptotic analysis which is Valid over a broad range of conditions of practical interest; in particular, it is valid for all simulations presented in this work. Model calculations are shown to compare well with experimental data, and acceptable ranges for the four dimensionless groups that dictate sensor performance are considered.