Impedance Analysis

Overview

For analyzing the frequency response of circuits with various components, it is convenient to think of a generalized form of resistance, or opposition to current flow, known as impedance ($ Z $). Clearly, we know that a resistor's resistance to current flow is known by its resistance. Although capacitors and inductors don't technically have a "resistance" value, they do resist current flow in their own ways and we can call those their respective impedances. Thus, Ohm's law applies not only to resistances, but to impedances as well: $ V = I Z $, where $ V $ is the voltage drop across the components of interest, $ I $ is the current, and $ Z $ is the impedance of those components.

The table below indicates the impedance values for different circuit elements. Here, $ j $ is the imaginary number and $ \omega $ is frequency in units of radians. Recall that $ \omega = 2 \pi f $, where $ f $ is frequency in units of Hz.