7 Advanced Circuit Analysis Techniques

Chapter Outline

Chapter 7 Review

(Figure 7.0.1)   \begin{gather*}.\end{gather*}

Figure 7.0.1 A resistive circuit (a) drawn as it might appear in the real world, and (b) redrawn for the purpose of analysis via Kirchhoff’s rules. (credit: original content contributed by Seth Dueck of University of Saskatchewan to Introduction to Electricity, Magnetism, and Circuits)

In the last chapter, you learned the basic rules that enable you to analyse any circuit: at any junction, the sum of incoming currents equals the sum of outgoing currents; and, the potential difference around a closed loop is zero. However, applying these rules can be cumbersome. Consider Figure 7.0.1(a), which shows a circuit with two voltage sources and five resistors, drawn as you might find it in the physical world. To apply Kirchhoffs rules, e.g. for the purpose of determining the power dissipated by one of the resistors, one should first redraw the equivalent circuit in Figure 7.0.1(b). As circuits become more complex, the task of redrawing circuits becomes more challenging, as does the task of finding and solving all the simultaneous equations found through application of Kirchhoff’s rules.

While Kirchhoff’s rules will enable you to solve any circuit, the method you learned in Kirchhoff’s Rules is often not the most practical or the most efficient. At times, you may not be up to the challenge of redrawing an abstract circuit to better show which components are in series and which are in parallel, or perhaps you’d just rather not bother dealing with all the equations that come from applying Kirchhoff’s junction rule. In this case, you could solve the circuit in Figure 7.0.1(a) by direct application of the Mesh Analysis technique. But this solution requires solving four simultaneous equations for the four loops in the circuit, and you may not have a computer handy, and may not be inclined to solve the linear system by hand. In this case, you could choose to redraw the circuit as in Figure 7.0.1(b) and solve it using the Superposition Theorem. Perhaps your concern isn’t so much how to solve the system, but that you have a load resistor that needs to change on a regular basis and you’d rather not re-solve the whole circuit every time. In this case, Thévenin’s Theorem provides a solution from which you can always quickly determine the current through the new load resistor.

There are many reasons why you might decide to use one circuit analysis technique instead of another. Ultimately, the choice depends on which technique is most practical and provides the most efficient solution given the circumstances. For this reason, the advanced circuit analysis techniques you learn in this chapter will be powerful tools to draw on in a variety of situations.