cmos small signal model rout
Small signal analysis ,as its name implies, is used for input signals of very small amplitudes .It is based mainly on dividing voltages and currents into bias voltages and currents and small signal ones .Then, equations of transistors are linearized (expanding the equations into polynomials and considering only the first order terms and neglecting higher powers) thus the linearized model is achieved (the one containing the voltage controlled current source gm*vgs) .For this solution to be valid ,higher power terms should be very small considered to the linear term, else non linearity occurs and harmonics of the signal may get significant .
Large signal solution is used for signals of large amplitude specially when it causes your transistor to go from certain mode of operation to another (e.g: saturation to triode or cutoff) .A very famous case is calculating the slew rate of an amplifier .
For more details ,you can refer to "design of analog CMOS integrated circuits "by Razavi, chapters 9(p326) and 13 .