As presented in the previous chapter, series-parallel analysis broadened our ability to analyze circuits beyond simple series and parallel networks, and leveraged the laws and techniques learned in earlier chapters. In this chapter we shall examine a number of theorems and techniques to help us analyze yet more complex circuits and address specialized applications. Specifically, we will address a method of analyzing circuits that contain multiple current and/or voltage sources that are connected in a non-trivial fashion (i.e., not just series voltage sources or parallel current sources). It is called the superposition theorem and can be applied to any circuit or parameter that meets certain requirements, including circuits that have both current sources and voltage sources together.

We shall also examine several ways of simplifying circuits or making functional equivalents for them. These are more tools to aid in the process of circuit simplification and analysis. The first item in this category is to make more accurate models of our idealized constant voltage and current sources. Once this is completed, it will be possible to convert from one type of source to another, such as creating a current source that is the functional equivalent of a voltage source. By this we mean that if we swap one for the other in any circuit, the remainder of the circuit will behave identically, producing the same component voltage drops and branch currents. This technique is useful in a number of ways, not the least of which is that it can help reduce more complex circuits to ease analysis.

The concept of equivalence can be extended beyond just a single source to an entire network. For this we will explore Thévenin's and Norton's theorems. Using these theorems, entire circuits utilizing dozens of components can be modeled as a single source with an associated resistance. When coupled with the maximum power transfer theorem, these theorems will allow us to determine component values that produce the maximum amount of load power.

Finally, we will examine how to find equivalent circuits for certain resistor arrangements that use three connecting points, in other words, resistor arrangements shaped like the letter Y or like a triangle. These are known as delta and Y configurations. These configurations are difficult to address with basic seriesparallel simplification techniques but the conversion equivalences will help solve that issue.