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For low power CMOS analog design the requirements of modeling MOS devices are both very demanding and stringent. For low power, the devices operate at low voltage and low current. The operating regions of the devices pertain to strong, moderate and weak inversion modes with its characteristics device physics and model parameters. From simulation viewpoint the major concern of model development has been the continuity of current and model parameters in the transition region of these modes of operation. For a compact model for analog design these issues have to be addressed along with the effects of scaling down to submicron level. The tutorial discusses briefly the following: criteria for compact MOSFET model with reference to low power analog design; review of two and three terminal MOS capacitor (definition of strong, moderate and weak inversion, threshold voltage, capacitance-voltage characteristics); long channel MOSFET's static characteristics and Memelink-Wallinga graphical model; EKV (Enz-Krummenacher-Vittoz) MOST model for static drain current in weak, moderate and strong inversion; quasi-static small signal model of long channel MOST as a function of inversion level; nonquasi static high frequency small signal model for MOST; ACM (advanced single piece compact MOSFET model); noise model for MOSFET in different inversion regions; modification of long channel analytical MOSFET model due to scaling; quantum effect; and a brief review of SPICE model parameters as a benchmark.