We present a new analytical model for the current-voltage characteristics of polycrystalline-silicon thin-film transistors (poly-Si TFTs). We use an "effective medium" approach which treats a polycrystalline film with grain boundaries as a uniform effective medium with an effective mobility and density of states in the energy gap. The current-voltage characteristics and their derivatives with respect to terminal voltages are continuous for both the below and above threshold regimes. A new interpretation of the saturation voltage allows us to accurately describe the finite output conductance in saturation, and we also realistically describe the "kink" effect. Our model has only five parameters which are easily extractable from experimental data: ideality factor (eta), low-field mobility (mu-0), threshold voltage (V(T)), output conductance parameter (GAMMA), and kink parameter (V0). We calculate the current-voltage characteristics of n- and p-channel poly-Si TFTs with 5, 6, 10, 15, and 30-mu-m gate lengths and 50-mu-m gate width and obtain a good agreement between calculation and experiment. Our analytical model is suitable for automatic parameter extraction and has been used for computer aided design.