7.5.CIRCUIT EFFECTS183are rarely seen in those applications. This is good to know if you’re a power system designer andare planning ahead for harmonic reduction: you only have to concern yourself with mitigating theodd harmonic frequencies, even harmonics being practically nonexistent. Also, if you happen tomeasure even harmonics in an AC circuit with a spectrum analyzer or frequency meter, you knowthat something in that circuit must be unsymmetrically distorting the sine-wave voltage or current,and that clue may be helpful in locating the source of a problem (look for components or conditionsmore likely to distort one half-cycle of the AC waveform more than the other).Now that we have this rule to guide our interpretation of nonsinusoidal waveforms, it makesmore sense that a waveform like that produced by a rectiﬁer circuit should contain such strong evenharmonics, there being no symmetry at all above and below center.• REVIEW:• Waveforms that are symmetrical above and below their horizontal centerlines contain no even-numbered harmonics.• The amount of DC “bias” voltage present (a waveform’s “DC component”) has no impact onthat wave’s harmonic frequency content.7.5Circuit eﬀectsThe principle of non-sinusoidal, repeating waveforms being equivalent to a series of sine waves atdiﬀerent frequencies is a fundamental property of waves in general and it has great practical importin the study of AC circuits. It means that any time we have a waveform that isn’t perfectly sine-wave-shaped, the circuit in question will react as though it’s having an array of diﬀerent frequencyvoltages imposed on it at once.When an AC circuit is subjected to a source voltage consisting of a mixture of frequencies, thecomponents in that circuit respond to each constituent frequency in a diﬀerent way. Any reactivecomponent such as a capacitor or an inductor will simultaneously present a unique amount ofimpedance to each and every frequency present in a circuit. Thankfully, the analysis of such circuitsis made relatively easy by applying the Superposition Theorem, regarding the multiple-frequencysource as a set of single-frequency voltage sources connected in series, and analyzing the circuit forone source at a time, summing the results at the end to determine the aggregate total:60 Hz90 Hz5 V5 VR2.2 kΩC1 µFFigure 7.41: Circuit driven by a combination of frequencies: 60 Hz and 90 Hz.Analyzing circuit for 60 Hz source alone: