Microwave Filters for Communication Systems: Fundamentals, Design and Applications

CHAPTER 2

FUNDAMENTALS OF CIRCUIT THEORY APPROXIMATION

Engineering problems represent exercises in approximation. The same can be said when we analyze any physical phenomena. At the most fundamental level, quantum mechanics can describe the properties of matter only in terms of probabilities. The point being made here is that with any engineering problem, there is always a tradeoff lurking somewhere, whether explicit or implicit. With that understanding, we can always optimize the parameters that are available within the constraints of a given system. The principles that unify communication theory and circuit theory approximations are explained in this chapter, which highlights the essential assumptions and the success of the frequency analysis approach that we take for granted in analyzing electrical networks.

2.1 LINEAR SYSTEMS

In nature, most systems, if not all, are nonlinear. Such systems are highly complex and not amenable to any general solution. Each problem and boundary condition requires an individual solution. However, most engineering problems can be approximated by linear systems over a limited range; herein lies our first assumption. It implies that we must ensure that all equipment used in the communication system satisfy the assumption of linearity over the operating range. Analysis of linear systems is well developed and covered in many textbooks [1].

Figure 2.1 ...