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

4.2 Analytical Solutions

• Node method and its foundational Kirchhoff’s voltage and current laws are derived from Maxwell’s Equations with no assumptions about linearity.
• The superposition method, the Thévenin method, and the Norton method however do require a linearity assumption

4.1 Introduction to Nonlinear Elements

• Diode is a nonlinear device

• An analytical expression of diode

3.6 The Norton Equivalent Network

The Norton equivalent circuit for any linear network at a given pair of terminals consists of a current source iN in parallel with a resistor RN. The current iN and resistance RN can be obtained as follows:

1. iN can be found by applying a short at the designated terminal pair on the original network and calculating or measuring the current through the short circuit.

2. RN can be found in the same manner as RTH, that is, by calculating or measuring the resistance of the open-circuit network seen from the designated terminal pair with all independent sources internal to the network set to zero; that is, with voltage sources replaced with short circuits, and current sources replaced with open circuits.