5.0 The Digital Abstraction

• Value discretization forms the basis of the digital abstraction
• Although the digital approach seems wasteful of signal dynamic range, it has a significant advantage over analog transmission in the presence of noise

4.5 Incremental Analysis

• Process of linearizing device models over a very narrow operating range is called incremental analysis
• Systematic procedure for finding incremental voltages and currents for a circuit with a nonlinear device characterized by the v-i relation iD = f(vD) :

4.4 Piecewise Linear Analysis

• Piecewise linear analysis represents the nonlinear v-i characteristics of each nonlinear element by a succession of straight-line segments, then make calculations within eachstraight-line segment using the linear analysis tools already developed

4.3 Graphical Analysis

• There are many nonlinear circuits that cannot be solved analytically. Usually we must resort to trial-and-error solutions on a computer. Such solutions provide answers, but usually give little insight about circuit performance and design. Graphical solutions, on the other hand, provide insight at the expense of accuracy

• For circuits with two nonlinear elements, the method is less useful, as it involves sketching one nonlinear characteristic on another. Nonetheless, crude sketches can still provide much insight
• Assuming E = 3 V, R = 500 ohm