A new simple unified analytical compact model for the amorphous InGaZnO Thin Film Transistors is proposed based on an analytical drain current model that uses a Gaussian distribution of subgap states, which is approximated by two exponential distributions. The model is continuous on all regions of operation, accurate also for the first derivatives of the transfer and output characteristics. A simple model is also proposed for the mobility to simulate the super-linear behavior of the drain current for low drain voltages. The model is verified for experimental data in all regions of operation and also for the transconductance and drain conductance of the transistors.