We can divide analysis of diode and transistor into Small signal analysis and Large signal analysis.
Large signal analysis
While doing a large signal analysis, a large dc voltage is applied and find out the behavior of diode or transistor towards this signal(find an operating point of these components). The voltage applied are of the order of few volts to few tens of volts. Here we use current and voltage equations such as
to find bias points. This analysis is applicable to any value of current and voltage applied to the devices.
Small signal analysis
Small signal analysis approximate nonlinear behavior of electronic components with linear equations. This approximation is taken across the bias point.