4.1 General Concepts

Before the 1970s, engineers used mathematical analysis of rather simple problems and experimental experience as guides to design. The enormous growth of computer power since that time has added a third stage to the processes of research, development, and design, numerical simulation. Now the basic sequence of any of these processes is (1) analysis of relatively simple models, (2) numerical solution of the equations describing the full complexity of the target device or system, and (3) experimental verification. This statement assumes that we know the equations needed; if we don t, the problem is science, not engineering.

In stage (1), the models are approximate but the analytical solutions are exact. In stage (2), the models are as exact as we know them, and the numerical solutions are approximate. For example, if we want to design an audio amplifier to meet some requirements, and we choose to use a bipolar transistor of appropriate ratings, we can analytically evaluate a proposed design by modeling the transistor as a dependent current source between base and collector terminals and a resistor between the base and emitter terminals. The transistor s current gain will be assumed constant, and we may include or ignore internal capacitances. After writing and solving the frequency-domain circuit equations and choosing component values on this basis, we can go to the next stage. The next stage will use a very complex model of the transistor, which includes its internal capacitances, several more resistors and diodes, and parameters that depend on...