A compact model of amorphous indium gallium zinc oxide thin-film transistors, suitable for CAD simulators, is proposed. The model is simple, symmetric, and accurately accounts for the subthreshold, linear, and saturation regimes via a unique formulation. It accounts for both trapped and free charges by means of multiple-trapping-and-release and percolation in the conduction band. Aim of the paper is to work out the analytic expression of the current and of the terminal charges, along with the surface potential and the electric field as a function of position in the channel. The availability of the surface potential and of the electric field is the key to model advanced physical effects as, for example, the carrier injection from the electrodes into the channel.