Introductory Electrical Engineering With Math Explained in Accessible Language

17Impedance and Phase: Circuit Analysis

17.1 Introduction

In this chapter, we will examine impedance, admittance, and their relations with resistance and reactance, important themes of electrical engineering.

We will use complex numbers extensively. For anyone not familiarized with the concepts behind complex numbers, we advise to read Appendix D, before starting this chapter.

17.2 This Is Just a Phase

In previous chapters, we have examined capacitors and inductors and how these components respond when they are subjected to DC and AC.

Capacitance and inductance are not just properties of capacitors and inductors. In real life, all components, even resistors, have a little bit of both. In most cases these are spurious undesired properties of materials and construction methods.

Simple wires, for example, placed side by side, show capacitance and inductance properties that, in some cases, can prevent more sensitive circuits from working.

We have also examined how alternating current creates reactance in capacitors and inductors and how this reactance creates phase shifts between current and voltage and between input and output signals.

At the end, we have seen two kinds of resistances in a circuit: pure resistance that does not alter the phase of signals and reactance that alters the phase of signals.

Impedance is the sum of both, resistance, and reactance.

17.3 Impedance

Reactance and resistance cannot be added together directly because they are different entities.

To make ...