Chapter | 1 Circuit Analysis 35 This is a shorthand formula, but understanding the distribution of harmonics is much easier if we express them in the following form: square wave ~ 1ðf Þ 1 1 ð3f Þ 1 1 ð5f Þ 1 1 ð7f Þ 1 1 ð9f Þ 1 . . . 3 5 7 9 We can now see that the harmonics die away very gradually and that a 1 kHz square wave has significant harmonics well beyond 20 kHz. What is not explicitly stated by these formulae is that the relative phase of these components is critical. The square wave thus tests not only amplitude response, but also phase response. Square Waves and Transients We briefly mentioned earlier that the square wave contained a transient com- ponent. One way of viewing a square wave is to treat it as a DC level whose polarity is inverted at regular intervals. At the instant of inversion, the volt- age has to change instantaneously from its negative level to its positive level, or vice versa. The abrupt change at the leading edge of the square wave is the transient, and because it occurs so quickly, it must contain a high propor- tion of high frequency components. Although we already knew that the square wave contained these high frequencies, it is only at the leading edge