166CHAPTER 7. MIXED-FREQUENCY AC SIGNALS7.3Other waveshapesAs strange as it may seem, any repeating, non-sinusoidal waveform is actually equivalent to a seriesof sinusoidal waveforms of diﬀerent amplitudes and frequencies added together. Square waves are avery common and well-understood case, but not the only one.Electronic power control devices such as transistors and silicon-controlled rectiﬁers (SCRs) oftenproduce voltage and current waveforms that are essentially chopped-up versions of the otherwise“clean” (pure) sine-wave AC from the power supply. These devices have the ability to suddenlychange their resistance with the application of a control signal voltage or current, thus “turning on”or “turning oﬀ” almost instantaneously, producing current waveforms bearing little resemblance tothe source voltage waveform powering the circuit. These current waveforms then produce changes inthe voltage waveform to other circuit components, due to voltage drops created by the non-sinusoidalcurrent through circuit impedances.Circuit components that distort the normal sine-wave shape of AC voltage or current are callednonlinear. Nonlinear components such as SCRs ﬁnd popular use in power electronics due to theirability to regulate large amounts of electrical power without dissipating much heat. While this is anadvantage from the perspective of energy eﬃciency, the waveshape distortions they introduce cancause problems.These non-sinusoidal waveforms, regardless of their actual shape, are equivalent to a series ofsinusoidal waveforms of higher (harmonic) frequencies. If not taken into consideration by the circuitdesigner, these harmonic waveforms created by electronic switching components may cause erraticcircuit behavior. It is becoming increasingly common in the electric power industry to observeoverheating of transformers and motors due to distortions in the sine-wave shape of the AC powerline voltage stemming from “switching” loads such as computers and high-eﬃciency lights. This isno theoretical exercise: it is very real and potentially very troublesome.In this section, I will investigate a few of the more common waveshapes and show their harmoniccomponents by way of Fourier analysis using SPICE.One very common way harmonics are generated in an AC power system is when AC is converted,or “rectiﬁed” into DC. This is generally done with components called diodes, which only allow thepassage of current in one direction. The simplest type of AC/DC rectiﬁcation is half-wave, where asingle diode blocks half of the AC current (over time) from passing through the load. (Figure 176,7.16)Oddly enough, the conventional diode schematic symbol is drawn such that electrons ﬂow againstthe direction of the symbol’s arrowhead:halfwave rectifierv1 1 0 sin(0 15 60 0 0)rload 2 0 10kd1 1 2 mod1.model mod1 d.tran .5m 17m.plot tran v(1,0) v(2,0).four 60 v(1,0) v(2,0).endhalfwave rectifierFirst, we’ll see how SPICE analyzes the source waveform, a pure sine wave voltage: (Figure 177,7.18)