Introduction to sensitivity analysis approaches
In this chapter, we give an initial introduction to adjoint techniques. We first review the classical approaches for derivative estimation and illustrate their computational cost. Approaches such as forward finite differences (FFD), backward finite differences (BFD), and central finite differences (CFD) are addressed. These approaches are utilized in later chapters as a reference to compare the estimated adjoint sensitivities against. We then present an adjoint sensitivity formulation that is suitable for analyzing electric circuits. The adjoint SA of electrical circuits and conductor transmission lines was addressed by several researchers. This analysis serves as a smooth introduction to the basic concepts involved in adjoint analysis of high-frequency structures. The same theorem is extended to high-frequency electromagnetic simulations as will be illustrated in the following chapters. We illustrate the theory presented in this chapter with circuit examples.