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Circuit (Network) analysis is the process of finding the voltages across, and the currents through, every component in the network. Consider using in conjunction with tags for the particular analysis technique(s) in question: "nodal-analysis", "mesh-analysis", "superposition", etc.
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How are MOSFET gate capacitances (Cgs, Cgd) calculated?
The factor of 2/3 comes from looking at the spatially-resolved gradual-channel model. There (at VDsat) the inversion-layer density varies as the square-root of the distance measured from the drain. …